Max Planck Institute · integration. The mission of the Max Planck Institute for Dynamics and Self-Organization (MPIDS) is the investigation of the physics of such phenomena. Founded

and Self-Organizationfor Dynamics

Max Planck Institute

Research Report 2006

© Max Planck Institute for Dynamics and Self-Organization, Göttingen (www.ds.mpg.de). 2006

Editing: Dr. Kerstin MölterCAD-Drawings: Udo SchminkePhotos: Kai Bröking, Irene Böttcher-Gajewski, Will Brunner, Ragnar Fleischmann,

Peter Goldmann, Anna Levina, David Vincent, Stephan WeissDesign/Layout: dauer design, GöttingenPrinted by: Goltze Druck, Göttingen

DIRECTORS

Prof. Dr. Eberhard Bodenschatz (Managing Director)

Prof. Dr. Theo Geisel

Prof. Dr. Stephan Herminghaus

SCIENTIFIC ADVISORY BOARD

Prof. Dr. William Bialek, Princeton University, USA

Prof. Dr. David K. Campbell, Boston University, USA

Prof. Dr. Jerry P. Gollub, Haverford College, USA

Prof. Dr. Pierre C. Hohenberg, New York University, USA

Prof. Dr. Alexei R. Khokhlov, Moscow State University, Russia

Prof. Dr. Tim Salditt, Georg August University Göttingen, Germany

Prof. Dr. Boris I. Shraiman, University of California at Santa Barbara, USA

Prof. Dr. Uzy Smilansky, Weizmann Institute of Science, Israel

Prof. Dr. Sandra M. Troian, Princeton University, USA

Max Planck Institute for Dynamics and Self-Organization

Research Report 2006

1. Introduction 4

2. Departments2.1 Nonlinear Dynamics2.1.1 Overview 62.1.2 People 72.1.3 Projects

2.1.3.1 Pattern Formation and Self-Organization in the Visual Cortex 102.1.3.2 Self-Organized Criticality in the

Activity Dynamics of Neural Networks 132.1.3.3 Dynamics of Anomalous Action Potential

Initiation in Cortical Neurons 152.1.3.4 Nonlinear Dynamics of Networks:

Spatio-Temporal Patterns in Neural Activity 172.1.3.5 Quantum Graphs: Network Models for Quantum Chaos 202.1.3.6 Random Matrix Theory and its Limitations 222.1.3.7 From Ballistic to Ohmic Transport

in Semi-Conductor Nanostructures 252.1.3.8 What are the Quantum Signatures of

Typical Chaotic Dynamics 282.1.3.9 Topological Superdiffusion – A New Theory for

Lévy Flights in Inhomogeneous Environments 312.1.3.10 Human Travel and the Spread of Modern Epidemics 34

2.2 Dynamics of Complex Fluids2.2.1 Overview 392.2.2 People 402.2.3 Projects

2.2.3.1 Wet Granular Matter and Irreversibilit 422.2.3.2 Statics and Dynamics of Wet Random Assemblies 442.2.3.3 Wetting of Topographic Substrates 462.2.3.4 Discrete Microfluidics 492.2.3.5 Wetting and Structure Formation at Soft Matter Interfaces 522.2.3.6 Membrane Assembly for Nanoscience 542.2.3.7 Spectroscopy of Aqueous Surfaces 562.2.3.8 Biological Matter in Microfluidic Environment 582.2.3.9 Locomotion in Biology at Low Reynolds Number 612.2.3.10 Colloids In and Out of Equilibrum 63

2.3 Fluid Dynamics, Pattern Formation and Nanobiocomplexity2.3.1 Overview 672.3.2 People 682.3.3 Projects

2.3.3.1 Particle Tracking Measurements in Intense Turbulence 702.3.3.2 Development of Fluid Dynamics Measurement Techniques 722.3.3.3 The Göttinger Turbulence Tunnel 752.3.3.4 Polymer Solutions and Viscoelastic Flows 772.3.3.5 Experiments on Thermal Convection 792.3.3.6 Wax Modeling of Plate Tectonics 812.3.3.7 Nonlinear Dynamics and Arrhytmia of the Heart 842.3.3.8 Chemotaxis and Cell Migration 872.3.3.9 The Cell Culture Laboratory –

Myocardial Tissue Engineering 91

2.4 Associated Scientists2.4.1 People 922.4.2 Projects

2.4.2.1 Elementary Gas-Phase Reactions 932.4.2.2 Mathematical Physics 95

2.5 Publications2.5.1 Nonlinear Dynamics (1996–2006) 982.5.2 Dynamics of Complex Fluids (2003–2006) 1092.5.3 Fluid Dynamics, Pattern Formation and Nanobiocomplexity (2003–2006) 1122.5.4 Associated Scientists (2003–2006) 114

3. Services and Infrastructure3.1 Design and Engineering 1183.2 Computing Facilities and IT Service 1203.3 Facility Management 1203.4 Administration 1213.5 Library 1213.6 Outreach Activities 122

4 | MPI for Dynamics and Self-Organization

Introduction

The self-organization of systems far fromequilibrium plays a key role in many fields ofinterest. Be it the pattern formation of adewetting liquid film, the complex signalingof neurons in the brain, or even the collectivedynamics of eddies in a thunderstorm cloud;a large number of intimately coupled entitiesoften conspire to generate unanticipatedstructure and dynamics at higher levels ofintegration. The mission of the Max PlanckInstitute for Dynamics and Self-Organization(MPIDS) is the investigation of the physics ofsuch phenomena. Founded in 2003 as thesuccessor of the 80 year old Max Planck Insti-tute for Fluid Dynamics, it combines expertisefrom fluid dynamics, soft condensed matterphysics, and nonlinear dynamics. Presently,the institute has three departments, whichtackle various aspects of non-equilibriumcomplex systems.

Considerable attention is devoted to patternformation phenomena in media as differentas convection in fluids, the visual cortex ofthe brain, plate tectonics of Earth, or thesignaling of cell colonies. While the micro-scopic properties of the systems are quite dis-parate, certain aspects of the emerging struc-tures are often strikingly similar. Finding thegeneral principles underlying the communal-ity of the non-linear processes is at the centerof this research.

The realm of life and biology intensivelyexploits such mechanisms. As a further com-plication, however, life is strongly influencedby discrete events (gene expression, muta-tions, etc.), has active components (molecu-

lar motors, transport, etc.), and operates in astochastic or disordered environment. In ad-dition, many biological processes evolve atthe micron scale or below, where the molecu-lar properties become important. The fluiddynamics of these systems is strongly influ-enced by large macromolecules or other self-assembling, often dynamical structures andcomponents. Due to the small size, someaspects of the comparably simple continuousdescriptions may break down, and molecularscale properties must be considered.

Our current research includes the applicationof concepts from self-organization to medi-cine (cellular signaling, neural brain dynam-ics, cardiac fibrillation, spread of epidemics),which necessitates a sometimes stronglyinterdisciplinary approach. The research pro-grams of the departments are set up incollaboration with the Bernstein Center forComputational Neuroscience, the Inter-national Collaboration for TurbulenceResearch, and the faculties of Physics andMedicine at the University of Göttingen.

For the time being the institute is present attwo separate locations. The departments ofTheo Geisel and Stephan Herminghaus are lo-cated at the original campus of the MPI forFluid Dynamics close to downtown Göttin-gen. The department of Eberhard Boden-schatz is accommodated at the Max PlanckInstitute for Biophysical Chemisty, adjacentto which the first part of our new building hasalready been completed. This includes the ex-perimental hall, which will accommodate theturbulence wind tunnel and other fluid dy-

1. Introduction

5MPI for Dynamics and Self-Organization |

namics experiments, a computational facility,and the clean room. The latter will be instru-mental for many of the micro-fluidic andnano-scale experiments, which are plannedin the near future. The second (main) part ofthe building will provide space for all depart-ments including services, and is scheduledfor completion in 2009. It will reunite the in-

stitute in stimulating neighborhood to theMax-Planck Institute for Biophysical Chem-istry and the Campus of the University.

The following pages give an introduction tothe current research projects and the infra-structure of the institute.

Prof. Eberhard BodenschatzProf. Theo GeiselProf. Stephan Herminghaus

Göttingen, May 2006

How do the myriads of neurons in our braincooperate when we perceive an object or per-form a task? How does the dynamics of net-works in general depend on their topology?What are the dynamical properties of quantummechanical networks and how can they be de-scribed semiclassically? How does the inter-play of quantum mechanics and disordershape the branching flows of the two-dimen-sional electron gas? Are there statistical princi-ples underlying human travel and can they beused to forecast the geographical spread of epi-demics?Several of these questions, which among oth-ers, motivate our research address the complexdynamics of spatially extended or multicom-ponent nonlinear systems, which still reservemany surprises. For instance, in networks ofspiking neurons we found unstable attractors,a phenomenon which would neither havebeen guessed nor understood without mathe-matical modelling and which many physicistsconsider an oxymoron. Under external stimu-lation the network can rapidly switch betweenthese unstable attractors. They may play afunctional role in the central nervous systemby providing it with a high degree of flexibilityto respond to frequently changing tasks.This example illustrates the need and role ofmathematical analysis for the understandingof many complex systems which nature pres-ents us in physics and biology. The conceptsand methods developed in nonlinear dynamics

and chaotic systems in recent times can nowhelp us clarify the dynamics and function ofspatially extended and multicomponent natu-ral systems. On the other hand rigorous mathe-matical analysis of the dynamics of such sys-tems often cannot rely on mainstream recipes,but poses new and substantial challenges. Inparticular, neural systems exhibit several fea-tures that make them elude standard mathe-matical treatment. These features include net-work communication at discrete times onlyand not continuously as in most cases in phy-sics, significant interaction delays, which makethe systems formally infinite-dimensional, andcomplex connectivities, which give rise to anovel multi-operator problem. For the latter,e.g., we devised new methods based on graphtheory to obtain rigorous analytic results.Graph theory is also applied in our work onquantum chaos, the same is true for randommatrix theory, which we applied to the stabil-ity matrices of synchronized firing patterns ofdisordered neural networks. Neuronal spiketrains may be considered as stochastic pointprocesses and so may energy levels of quan-tum chaotic systems. This enumeration showsto which extent cross-fertilization among ourvarious areas of research is possible. In fact, ithas often been essential for our progress. Thescientists of this department feel that thebreadth of existing research activities and theopportunity of intense scientific exchange arekey prerequisites for the success of our work.


Nonlinear Dynamics

Nonlinear Dynamics2.1

2. Departments

2.1.1 Overview

Theo Geisel

People

2.1.2 People

People

Prof. Dr. Theo Geiselstudied Physics at the Universities of Frankfurt

and Regensburg, where he received his Ph.D. in

1975. He worked as a Postdoc at the MPI for

Solid State Research in Stuttgart and at the Xerox

Palo Alto Research Center before becoming a

Heisenberg fellow in 1983. He was Professor of

Theoretical Physics at the Universities of

Würzburg (1988-1989) and

Frankfurt (1989-1996), where he also acted as a

chairperson of the Sonderforschungsbereich

Nichtlineare Dynamik. In 1996 he became

director at the MPI for Fluid Dynamics (now MPI

for Dynamics and Self-Organization). He also

teaches as a full professor in the Faculty of

Physics of the University of Göttingen and heads

its Bernstein Center for Computational

Neuroscience Göttingen.

Dr. Dirk Brockmannis postdoctoral researcher in the Department ofNonlinear Dynamics. He studied theoreticalphysics and mathematics at Duke University,Durham N.C. and the Georg-August Universityin Göttingen. Before he joined the group of Theo Geisel,where he received his doctorate in 2003, heworked in the group of Annette Zippelius at the

Institute for Theoretical Physics at the Universityof Göttingen.

They are also important for establishing andsustaining a culture of analytic rigor in theoret-ical work close to biological experiments. Quite generally, theoretical studies of complexsystems are most fruitful scientifically whenanalytical approaches to mathematically tract-able and often abstract models are pursued inclose conjunction with computational model-ing and advanced quantitative analyses ofexperimental data. The department thus natu-rally has a strong background in computa-tional physics and operates considerable com-puter resources. Research for which this isessential besides the network-dynamics men-tioned above includes studies of pattern forma-tion in the developing brain, of the dynamicsof spreading epidemics, and of transport inmesoscopic systems.When this department was created by the MaxPlanck Society in 1996, the focus of the insti-tute was on mesoscopic systems. With the

opening of two new experimental departmentsin our institute this focus has changed; we areshifting our accents and tackling new subjectsin the interest of a coherent research program.Besides, this department has initiated andhosts the federally (BMBF) funded BernsteinCenter for Computational Neuroscience Göt-tingen, in which it cooperates with advancedexperimental neuroscience labs in Göttingen.Our group is closely connected with the Fac-ulty of Physics, it is financed to a large part bythe Max Planck Society and to a smaller partby the University of Göttingen through its Insti-tute for Nonlinear Dynamics. On the followingpages we are describing some of our recentand ongoing research projects. As this depart-ment began its work already in 1996, an ac-count of past research activities may be foundin the publication list (2.5.1), which extends tothe period from its creation in the year 1996 tothe year 2006.


People


Nonlinear Dynamics

Dr. J. Michael Herrmann

studied mathematical physics and computer

science and has defended a doctoral thesis on ar-

tificial neural networks at Leipzig University. He

did postdoctoral research at NORDITA

(Copenhagen), RIKEN (Wako) and the Max-

Planck-Institut für Strömungsforschung

(Göttingen). Presently, he is Assistant Professor

at the Institute of Nonlinear Dynamics of the

University of Göttingen and adjunct scientist at

the Max Planck Institute for Dynamics and Self-

Organization. Besides he is a member of the

Center of Informatics at the University of

Göttingen as well as a principal investigator at

the Bernstein Center for Computational

Neuroscience Göttingen.

Dr. Lars Hufnagel received his diploma in mathematics from the

University of Hagen. He studied physics at the

Philipps-University in Marburg and conducted

his diploma thesis at the Fritz-Haber-Institute of

the Max-Planck Society in Berlin. In 1999 he

joined the Max-Planck Institute for Dynamics

and Self-Organization in Göttingen and received

his doctorate in theoretical physics from the

Georg-August University in Göttingen. Since

2004 he has worked as a post-doctoral fellow at

the Kavli-Institute for Theoretical Physics at the

University of California at Santa Barbara.

Dr. Ragnar Fleischmann studied physics at the Johann-Wolfgang-Goethe

University in Frankfurt am Main and received his

PhD in 1997. His thesis was awarded the

Otto-Hahn-Medal of the Max-Planck-Society.

From 1997 to 1999 he was Postdoc in the group

of Theo Geisel at the Max-Planck-Institut für

Strömungsforschung and from 1999 to 2000 in

the group of Eric Heller at Harvard University.

Since 2000 he has worked as a scientific staff

member in the Department for Nonlinear

Dynamics and as deputy institute manager of

the Max-Planck-Institute for Dynamics and Self-

Organization.

Dr. Denny Fliegnerstudied physics at the University of Heidelberg

and received his doctoral degree in theoretical

particle physics in 1997. From 1997 to 2000 he

was a Postdoc at Karlsruhe University working on

parallel computer algebra and symbolic

manipulation in high energy physics. He joined

the group of Theo Geisel at the Max-Planck-

Institut für Strömungsforschung as an IT

coordinator in 2000. In 2003 he became head of

the IT service group of the Max-Planck-Institute

for Dynamics and Self-Organization.

People

Dr. Tsampikos Kottos received his PhD in theoretical solid-state physics

from the University of Crete in 1997. In 1997 he

received a US European Office of Air Force

Research and Development Fellowship. In the

same year, he received the Feinberg Fellowship

and joined the Quantum Chaos group of U.

Smilansky at the Weizmann Institute of Science,

Israel. In 1999 he moved to Germany as a

postdoctoral research fellow in the group of T.

Geisel at the Max Planck Institute for Dynamics

and Self-Organization in Göttingen. In 2005 he

has become an Assistant Professor at Wesleyan

University, USA and continues working with the

Department of Nonlinear Dynamics as an

adjunct scientist.

PD Dr. Holger Schanz studied physics at the Technical University of

Dresden and graduated in 1992. He worked

towards his PhD in the groups of Werner Ebeling

(Humboldt University Berlin) and Uzy Smilansky

(The Weizmann Institute of Science, Rehovot,

Israel) and received his doctorate from the

Humboldt University in 1996. After two years as

a Postdoc at the Max Planck Institute for Physics

of Complex Systems in Dresden, he joined the

group of Theo Geisel at the Max-Planck-Institut

für Strömungsforschung in Göttingen. Currently

he is Assistant Professor at the Institute of

Nonlinear Dynamics of the University of

Göttingen, and adjunct scientist at the Max

Planck Institute for Dynamics and Self-

Organization.

Dr. Marc Timme

studied physics at the University of Würzburg,

Germany, at the State University of New York at

Stony Brook, USA, and at the University of

Göttingen, Germany. He received an MA in

physics in 1998 (Stony Brook) and a doctorate in

theoretical physics in 2002 (Göttingen). After

working as a postdoctoral researcher at the Max


Organization, Göttingen, from 2003 to 2005, he

is currently a research scholar at the Center of

Applied Mathematics, Cornell University. He is

also a founding member of and a principal

investigator at the Bernstein Center for

Computational Neuroscience, Göttingen.

Dr. Fred Wolf

studied physics and neuroscience at the J.W.Goethe

University in Frankfurt, where he received his

doctorate in theoretical physics in 1999. After

postdoctoral research at the MPI für

Strömungsforschung (Göttingen) and the

Interdisciplinary Center for Neural Computation of

the Hebrew University of Jerusalem (Israel), he

became a research associate at the MPI für

Strömungsforschung in 2001. Since 2001 he has

participated in various research programs of the

Kavli Institute for Theoretical Physics (Santa

Barbara, USA). In 2004 he became head of the

research group of Theoretical Neurophysics at the

MPI for Dynamics and Self-Organization. He is a

faculty member of the International Max Planck

Research School Neurosciences and of the Center

for Systems Neuroscience at Göttingen University.


People

The ontogenetic development of the cere-bral cortex of the brain is a process of aston-ishing complexity. In every cubic millimeterof cortical tissue about a million of neuronsmust be wired appropriately for their respec-tive functions such as the analysis of sensoryinputs, the storage of skills and memory, orfor motor control. In the brain of an adultmammal, each neuron receives input viaabout 10000 synapses from neighboring andremote neurons. At the outset of brain devel-opment, however, the cortical network isformed only rudimentarily: For instance inthe cat’s visual cortex at the day of birth,most neurons have just finished the migrationfrom their birth zone lining the cerebral ven-tricle to the cortical plate. The number ofsynapses in the tissue is then only 10% and atthe time of eye-opening, about two weekslater, only 25% of its adult value. In the fol-lowing 2-3 months the cortical circuitry issubstantially expanded and reworked and theindividual neurons acquire their final speci-ficities in the processing of visual informa-tion. Many lines of evidence suggest that dur-ing this period the brain in a very fundamen-tal sense ›learns to see‹ [1,2].

Viewed from a dynamical systems perspec-tive, the activity-dependent remodeling of thecortical network during development is aprocess of dynamical pattern formation.Spontaneous symmetry breaking in the devel-opmental dynamics of the cortical networkunderlies the initial emergence of cortical se-lectivities such as orientation preference [3].After symmetry breaking, ongoing improve-ment may result in the convergence of thecortical architecture to a stable stationarystate constituting an attractor of the visualsystem’s learning dynamics. Because the de-velopment of the visual cortical architectureis in many respects reminiscent of dynamical


Nonlinear Dynamics

Figure 1: (a) Essentially complex planforms (ECPs).

Preferred stimulus orientations are color coded (seebars in (b)). Diagrams show positions of active mode

wave vectors. For n = 3, 5, and 15, there are 2, 4, and612 different ECPs respectively. (b) Orientation

preference map in cat area 17 (data: S. Löwel, Univ. ofJena, Germany). Arrows pinwheel centers. Scale bar 1

mm. (c) Pinwheel densities (dots) of ECPs for n = 3 -17. Bar: band of pinwheel densities in the large n

limit. Experimentally observed pinwheel densitiesrange between 2 and 3.5.

2.1.3.1 Pattern Formation and Self-Organization in the Visual Cortex

Fred WolfDominik Heide, Min Huang, Matthias Kaschube, Wolfgang Keil, Lars Reichl, Michael Schnabel

D. Coppola (Ashland, USA), H. Dinse (Bochum), S. Löwel (Jena), L. White (Durham, USA),

2.1.3 Projects

pattern formation in physical systems farfrom equilibrium, it is natural to ask whetherthis process might be modeled by dynamicalequations for macroscopic order parametersas often proved successful and instructive insimpler pattern formation problems.

Symmetries in visual cortical developmentAs a paradigmatic model system our studiesare focusing on the development and the spa-tial structure of the pattern of contour detect-ing neurons in the visual cortex called the ori-entation preference map (OPM, see Figure1b). Functional brain imaging has revealedthat the spatial structure of OPMs is aperiodicbut roughly repetitive with a characteristicwavelength in the millimeter range (see e.g.[4]) and that OPMs contain numerous singu-lar points called pinwheel centers (seeFig. 1b).In previous work, Wolf and Geisel demon-strated that basic symmetry assumptions im-ply a universal minimal initial density of pin-wheel defects [3]. They also found, however,

that the defects generated initially are typi-cally unstable and are decaying by pairwiseannihilation in various models of visual corti-cal development. To solve the problem of pin-wheel stability, subsequent studies haveraised the hypothesis, that a reduced symme-try of the dynamics of visual cortical patternformation may underlie the formation of sta-ble pinwheel patterns [5,6]. In the proposedmodels of reduced symmetry, however, pin-wheels generally crystallize in periodic spa-tial patterns that are clearly distinct from thepatterns observed experimentally. In recent work, we have therefore investi-gated conditions for the emergence of spa-tially nonperiodic OPMs theoretically. To thisend, Wolf introduced an analytically tractableclass of model equations [7], which wasshown to possess solutions that qualitativelyand quantitatively resemble the experimen-tally observed patterns. Its construction isbased on the requirement that the visual cor-tex must develop detectors for contours of allorientations. Assuming a supercritical bifur-cation of the pattern this turned out to beguaranteed near criticality by a novel permu-tation symmetry. This symmetry in additionimplies the existence of a large number of dy-namically degenerate solutions that are quali-tatively very similar to OPMs in the visualcortex (Fig. 1a). Further analysis revealedthat, judged by their pinwheel densities,these patterns even quantitatively resemblethe experimentally observed OPMs (seeFig. 1c). The stability boundaries of varioussolutions were calculated in a generalizedSwift-Hohenberg model incorporating long-range interactions, a key feature of visual cor-tical processing. Generically, long-range inter-actions were found to be essential for the sta-bility of realistic solutions. Their existenceand stability, however, turned out to be ratherinsensitive to full or reduced symmetries ofthe developmental dynamics [8].

Quantification of cortical column layoutBecause these and related results indicatethat the apparently complicated layout of vi-sual cortical maps can be quantitatively ex-

Figure 2: Phase diagram of the Swift-Hohenberg model introduced in [7] nearcriticality. The graph shows the regions of the parameter space in which n-ECPs haveminimal energy (n=1-25, n>25 dots). x-axis: interaction range in non dimensionalunits. y-axis: coupling constant. Inset: stability region of n-ECPs in the large n limit.


Projects


Nonlinear Dynamics

plained by relatively simple model equations,substantial effort is dedicated to developingmethods for the precise quantification of lay-out parameters from experimentally obtainedbrain imaging data. The layout of functionalcortical maps exhibits a high degree of in-terindividual variability that may account forindividual differences in sensory and cogni-tive abilities. By quantitatively assessing theinterindividual variability of OPMs in the pri-mary visual cortex using a newly developedwavelet based analysis method, we demon-strated that column sizes and shapes as wellas a measure of the homogeneity of columnsizes across the visual cortex are significantlyclustered in genetically related animals and inthe two hemispheres of individual brains[4,9]. Taking the developmental timetable ofcolumn formation into account, these obser-vations indicate that essential control param-eters of the dynamics of visual cortical pat-tern formation are tightly controlled geneti-cally. More recently, application of these methodsled to the first demonstration of a dynamicalrearrangement of cortical orientation columns

during visual development. In a study com-paring the layout of orientation columns intwo different visual cortical areas in kittensand cats we found that maps in the two areasexhibit matched column sizes at retinotopi-cally corresponding positions in adult cats. Inaddition the data revealed that in kittens ofvarious ages, column sizes progressively be-came better matched in the two areas over thecourse of visual cortical development [10].Based on these methodological advances, wealso started to characterize the statistics ofpinwheel defects in collaboration with Len E.White (Duke University). Here it turned outthat virtually all basic statistics of pinwheelsin orientation maps are universal in a widerange of animals [11]. These findings are verysurprising are beginning to shed a completelynew light on the formation of corticalcolumns. Current model studies are address-ing the conditions under which dynamicalpattern formation can account qualitativelyand quantitatively for the observed universalstatistics.

[1] M.C. Crair, Curr. Opin. Neurobiol. 9(1999) 88.[2] L.C. Katz and J.C. Crowley, Nat. Rev.Neurosci. 3 (2002) 34.[3] F. Wolf and T. Geisel, Nature 395(1998) 73.[4] M. Kaschube et al., J. Neurosci. 22(2002) 7206.[5] H.Y. Lee, M. Yahyanejad and M.Kardar,Proc. Natl. Acad. Sci. 100 (2003) 16036.

[6] P.J. Thomas and J.D. Cowan. Phys. Rev.Lett. 92 (2004) 188101.[7] F. Wolf, Phys. Rev. Lett. 95 (2005)208701.[8] M. Schnabel et al., (in prep.).[9] M. Kaschube et al., Eur. J. Neurosci. 22(2003) 7206.[10] M. Kaschube et al., (in prep.). [11] M. Kaschube et al., (in prep.).

2.1.3.2 Self-Organized Criticality in the Activity Dynamics of Neural Networks

J. Michael HerrmannAnna Levina

U. Ernst (Bremen), M. Denker (Göttingen), K. Pawelzik (Bremen)

The Gutenberg-Richter law describes the re-lation between strengths and frequencies ofearthquakes and thus an aspect of the com-plex processes in the upper terrestric crust. Itprovides a precision which challenges thetheoretical approaches to the statistics ofevents in other domains of the physics ofcomplex systems including applications to fi-nance as well as social and ecological sys-tems. A neural system shares the characteris-tics of such systems in the sense that the ex-tent of neural activities may span the fullrange from the level of single neural firing tothe length scale of the whole nervous system.Most interesting are the cases where theevents can be triggered by arbitrarily smalldriving forces or even by noise and spread inthe system in an avalanche-like fashion. The hallmark of criticality are power laws ofthe distribution of event sizes which indicatethat large events occur much less frequently,but still sufficiently often in order to have anon-ignorable effect to the evolution of thesystem. In self-organized criticality the intrin-sic dynamic of the system is such that the sys-

tem evolves into a state which is barely stable[1]. Small disturbances of the system willthen lead to responses on all time and lengthscales and there is no need to fine-tune anyparameters.At least for a decade, theoretical neurophysicshas aimed at describing the dynamics of theactivity in the brain by models which showthe effect of self-organized criticality [2],while at the same time maintaining a level ofbiological realism that supports the explana-tory power of the approach.

The prediction of criticality in neuralsystems

Already for a globally coupled network ofrather simple model neurons there are param-eter values which give rise to a power-lawdistribution of the responses to a weak exter-nal stimulation. In Ref. [7] we have provideda finite-size analysis in order to able to com-pare the theoretical results directly to the thenumerically obtained response distributions.The exact analytical treatment in that study,however, required a rather abstract neural

Figure 1:Probability distributions of avalanche sizes. With

increasing maximal efficiency level we observe differentregimes (a) in the subcritical, (b) the critical, α =0.53 ,

and (c) supra-critical regime, α =0.74.Here the curves are temporal averages over 106

avalanches in a network of 100 neurons.


Projects

model. The more astonishing was the factthat about one year later an in-vitro experi-ments revealed (and acknowledged) a quali-tatively identical picture for the local fieldspotential in rat cortex [4] and in a number ofother cases in the following years.The model lacked, however, the aspect of self-organization towards the critical case, but re-quired rather a precise parameter tuning,while the real neurons returned to the power-law activity distribution even after strongchanges in the biochemical milieu. A furtherelaboration in our modelling project demon-strated however that by an increase in biolog-ical detail the network easily achieved the re-quired self-organizational capabilities. By theintroduction of a realistic neurotransmitterdynamics [8] at the synapses the network ex-hibited a phase transition towards criticalityand a very large range of the maximal synap-tic efficiency where a nearly critical behav-iour is present.

Towards a biological modelThe biological function of self-organized criti-cality is much less understood than the physi-cal mechanisms behind this phenomenon.Surely a stereotyped response to externalstimuli would be less advantageous than aflexible reaction which may amplify barelynoticeable events in the environment basedon information which has been accumulatedin the internal state of the brain. In additionsuch systems are expected to provide optimalcapabilities for control and sequential infor-mation processing. A more simple explana-tion results from an effectiveness constraint.If the system adjusts its parameters such thateach spike causes one of the target neurons tobecome consequently active and, on theother hand, the total activity is to remainbounded and stationary, then it can be provenwithin the framework of branching theorythat the resulting activity distribution is in-deed critical. Moreover from this a learningrule can be derived which controls the systemtowards criticality and which resembles bio-logical learning rules [5].


Nonlinear Dynamics

[1] P. Bak, C. Tang, and K. Wiesenfeld,Phys. Rev. Lett. 59 (1987) 381.[2] A. Herz and J. J. Hopfield, Phys. Rev.Lett. 75 (1995) 1222.[3] Z. Olami, H. J. Feder and K.Christensen (1992). Phys. Rev. Lett. 68(1992)1244.[4] J. Beggs and D. Plenz, J Neurosci. 23(2003) 11167.[5] A. Levina, U. Ernst, and J. M.Herrmann, Proceedings of ComputationalNeuroscience, Edinburgh (2006).[6] A. Levina, J. M. Herrmann, and T.Geisel, Advances in Neural InformationProcessing Systems (2005).[7] C. W. Eurich, J. M. Herrmann, and U.Ernst, Phys. Rev. E 66 (2002). [8] M. Tsodyks, K. Pawelzik and H.Markram, Neural Computation 10 (1998)821.

Figure 2: The best matching power-law exponent of the numericallyobtained event size distribution. The red line represents the realistic model[6,8], while the green one stands fo the abstract model [7]. Maximalsynaptic efficiency α varies from 0.3 to 1.0 with step 0.001. The curves aretemporal averages over 107 avalanches with N=200.

Nerve cells communicate with each other bysending out and receiving electrical impulses,called action potentials (APs). For a while ithas become clear that the majority of thesesignals remain unanswered in the mam-malian brain. Every second, a typical cell ofthe cerebral cortex receives thousands of sig-nals from other nerve cells. In that same sec-ond, however, the cell only rarely decides –often not more than a dozen times – to sendout an impulse itself. Since the result of virtually all computationaloperations performed at the level of individ-ual nerve cells are coded into sequences of ac-tion potentials, understanding the machinerythat performs this encoding is of prime im-portance for deciphering the operation of cor-tical networks. To theoretically clarify howdynamical features of neuronal action poten-tial generators shape the encoding propertiesof cortical neurons we are using concepts andmethods from bifurcation theory and fromthe theory of stochastic processes. Quantify-ing key parameters of action potential initia-tion in cortical neurons in the living brain incollaboration with experimental neurophysi-

ologists, we recently discovered evidence fora cooperative activation of neuronal sodiumchannels. This non-canonical type of actionpotential initiation probably qualitatively ex-pands the bandwidth of neuronal action po-tential encoding.

Dynamic response theory of fluctuationdriven neurons

In the cerebral cortex, due to its columnar or-ganization, large numbers of neurons are in-volved in any individual processing task. It istherefore important to understand how theproperties of coding at the level of neuronalpopulations are determined by the dynamicsof single neuron AP generation. To answerthis question we studied how the dynamics ofAP generation determines the speed withwhich an ensemble of neurons can representtransient stochastic input signals. Using ageneralization of the θ -neuron, the normalform of the dynamics of Type-I excitablemembranes, we calculated the transmissionfunctions for small modulations of the meancurrent and noise amplitude. Because of its qualitative dependence onmodeling details previous theoretical studiesfocused mainly on the high frequency limit ofthese transmission functions [1-3]. Using anovel sparse matrix representation of theFokker Planck equation to calculate the fulltransmission function we found that in thephysiologically important regime up to 1 kHzthe typical response speed is, however, inde-pendent of the high-frequency limit and is setby the rapidness of the AP onset [4] (seeFig. 1). In this regime modulations of thenoise amplitude can be transmitted faithfullyup to much higher frequencies than modula-tions in the mean input current, explainingrecent experimental observations by Silber-berg et al. [5].

Figure 1: Effect of increasing the AP onset rapidness. With increasing onset rapidness,the transmission function shifts to larger values irrespective of the stationary firingrate. For the case of an instantaneous AP onset dynamics (fixed threshold), thetransfer function remains finite in the high frequency limit. Curves are labelled fordifferent stationary firing rates (modified from [4]).

2.1.3.3 Dynamics of Action Potential Initiation in Cortical Neurons

Fred WolfMin Huang, Björn Naundorf, Andreas Neef

M. Volgushev (Bochum), M. Gutnick (Jerusalem, Israel)


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Nonlinear Dynamics

The cooperative sodium channel activationhypothesis

As these results predict that apparently minormodifications of the AP generation mecha-nism can qualitatively change the nature ofneuronal encoding an accurate quantitativedescription of the AP initiation dynamics op-erating in the intact brain became a focus ofour research. In collaboration with Neuro-physiologist Maxim Volgushev (Bochum Uni-versity) we thus performed a quantitativeanalysis of the dynamics of action potentialinitiation in all major physiological classes ofcortical neurons as observed in vivo and inbrain slices. Unexpectedly, this study showedthat key features of the initiation dynamics ofcortical neuron action potentials – their veryrapid initiation and the large variability of on-set potentials – are outside the range of be-haviors that can be modeled in the frameworkof the classical Hodgkin–Huxley theory [6]. To explore the possible origin of ›anomalous‹action potential initiation dynamics we devel-oped a new model based on the hypothesis ofa cooperative activation of sodium channels.In this model, the gating of individual sodium

channels follows a scheme introduced byAldrich, Corey, and Stevens [7]. It incorpo-rates state-dependent inactivation from theopen state and voltage-dependent inactiva-tion from closed states. The key feature of ourmodel is a coupling between neighboringchannels: the opening of a channel shifts theactivation curve of each channel to which it iscoupled towards more hyperpolarized values,thus increasing its probability of opening.This model is able to reproduce the key fea-tures of cortical action potential initiation(Fig. 2). With strongly cooperative activation,voltage-dependent inactivation from closedstates, and slow deinactivation (recoveryfrom inactivation) of sodium channels, thesimulated action potentials show both a largeonset rapidness and large variability in onsetpotentials (Fig. 2a). Turning off the interchan-nel coupling made the onset dynamics muchshallower, while leaving onset variability un-affected (Fig. 2b). Hodgkin–Huxley-type dy-namics of action potential onset was recov-ered when inactivation and de-inactivationwere set to be fast and voltage-independent(Fig. 2c). Figure 2 also shows results of a first

Figure 2: Cooperative activation of voltage-gated sodiumchannels can account for dynamics of AP initiation in corticalneurons. (a) Waveform (top) and phase plot (bottom) of APselicited by fluctuating inputs in a conductance-based modelincorporating cooperative activation of Na+ channels andclosed-state inactivation. Both the AP onset potentialvariability and rapidness are comparable to in vivorecordings. (b) Same model, but without inter-channelcoupling, and (c) with Hodgkin-Huxley-like channelactivation. (d-g) Reducing the effective density of availableNa+ channels by TTX application reversibly reduces the APamplitude and onset rapidness in cortical neurons in vitro. APwaveforms (d) and phase plots of their initial parts (e). Timecourse of the AP onset rapidness (f) in a cortical neuronbefore, during and after the TTX application. (g) Reversiblereduction of the AP onset rapidness by TTX in 6 neurons(error bars: s.e.m, modified from [6]) .

[1] B. Lindner, L. Schimansky-Geier, Phys.Rev. Letters 86 (2001) 2934.[2] N. Brunel et al., Phys. Rev. Lett. 86(2001) 2186.[3] N. Fourcaud-Trocme et al., J. Neurosci.23 (2003) 11628.[4] B. Naundorf, T. Geisel, and F. Wolf, J.Comput. Neurosci. 18 (2005) 297.[5] G. Silberberg et al., J. Neurophysiol. 91(2004) 704.[6] B. Naundorf, F. Wolf, and M.Volgushev, Nature 440 (2006) 1060.[7] R.W. Aldrich, D.P. Corey, and C.F.Stevens, Nature 306 (1983) 436.

2.1.3.4 Nonlinear Dynamics of Networks: Spatio-Temporal Patterns in Neural Activity

Marc TimmeMichael Denker, Markus Diesmann, Fred Wolf, Alexander Zumdieck

P. Ashwin (Exeter, UK)

New challenges for theorySynchronization and precise spatio-tempo-ral dynamics are ubiquitous in nature. Pat-terns of neural spikes that are precisely timedand spatially distributed constitute importantexamples: they have been observed experi-mentally in different neuronal systems [1,2]and are discussed as key features of neuralcomputation. Their dynamical origin, how-ever, is unknown. One possible explanationfor their occurrence is the existence of feed-forward structures with excitatory coupling,so called synfire chains [3,4] which are em-bedded in otherwise random networks. Suchstochastic models can explain the recurrenceof coordinated spikes but do not account forthe specific relative spike times of individualneurons.As an alternative approach, we investigatehow and under which conditions determinis-tic recurrent neural networks may exhibit pat-

terns of spikes that are precisely coordinatedin time. Exact investigations of models for bi-ological neural networks, however, requirenew mathematical tools for multi-dimen-sional systems, because neural systems ex-hibit several features that make them eludestandard mathematical analysis. These fea-tures include e.g. network communication atdiscrete times only instead of continuously,as is the case in most systems of physics; sig-nificant delays in the interactions, which for-mally make the systems studied infinite-di-mensional; complicated network connectivitywhere mean-field analyses fail; and strongheterogeneities, which require tools beyondthose applicable to the homogeneous orclose-to-homogeneous systems studied so far.

Time delays and unstable attractors As a starting point towards addressing thesechallenges we investigated a very simple and

experimental test of the cooperative model.Assuming that channel interactions are dis-tance-dependent in neuronal membranes, ourmodel predicts that reducing the effectivedensity of channels should weaken coopera-tivity, reduce the action potential onset rapid-ness and eventually lead to Hodgkin–Huxleytype onset dynamics. We tested this predic-tion in vitro, recording action potentials whilereducing the density of available sodiumchannels by the application of tetrodotoxin(TTX). As expected, TTX application led to adecrease in action potential amplitude(Fig. 2d). More importantly, it also led to asubstantial reduction in the onset rapidnessof action potentials (Fig. 2d, e) in all testedcortical neurons (Fig. 2g), as predicted by our

model. Current and planned studies are fo-cusing on theoretically deriving critical pre-dictions of the cooperative channel activationhypothesis to guide the next generation ofneurophysiological experiments.


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Nonlinear Dynamics

homogeneous neural network model, yet in-cluding interaction delays. We found the firstexample of a dynamical system that naturallyexhibits unstable attractors, periodic orbitsthat are (Milnor) attracting and yet unstable[5]. They occur robustly in model neural net-works which possess high symmetry and im-ply that the typical dynamics in such net-works often is perpetual switching (Fig. 1)among states (periodic orbits) [6]. Given thatthe delayed interactions make this system for-mally infinite-dimensional, this problem alsorequired mathematically rigorous analysis[7]. In systems similar to but less symmetricthan the above we found that unstable attrac-tors still exist, and moreover that they are theprobable cause of another new phenomenon:long chaotic transients induced by dilution ofthe network connectivity [8]. This impliesthat in these neural networks, the transientphase and not the attractor dominate the dy-namics. These studies also demonstrate animportant fact commonly neglected in theo-retical neuroscience: certain neural networksmay not need to converge to stable state at-tractors in order to perform a computation,but computation might as well be performedin a transient phase, where it could be, more-over, much more flexible and more efficient.Therefore, in certain biological neural sys-tems information processing might as well bebased on unstable states [9].

Networks of complicated connectivity: Coexistence of states and their stability

problem It was widely believed that cortical networkswith complicated (sparse random) connectiv-ity necessarily also show complicated dynam-ics. In the same network, however, there cancoexist a very different dynamical state [10],which despite irregular network connectivitydisplays very regular dynamics. For the caseof completely regular (synchronous) dynam-ics we developed the first exact stabilitytheory for networks of complex connectivi-ties, where a novel multi-operator problememerges that cannot be solved by standardmethods. Developing new methods, partially

based on graph theoretical arguments, wecould solve this multi-operator problem ana-lytically for any given network.

Strongly heterogeneous networks: Do they still admit precise timing?

As mentioned above, it is still an open ques-tion how spikes can be coordinated preciselyin time into patterns that emerge in the dy-namics of neural networks. The insights ob-tained in the above studies and the new meth-ods that were stimulated have enabled us toaddress this question even for non-homoge-neous systems: (i) We developed a method topredict short spike sequences from knowingthe topology of the network and its inhomo-geneous parameters [11]. The inverse prob-lem was also solved: we designed networkswhich exhibit a prescribed spike sequence(Fig. 2). (ii) Recently we discovered a connec-tivity-induced speed limit to coordinatingspike times in neural networks [12]. As ex-pected, the speed of coordinating spike times– in the simplest case the speed of synchro-nization – increases with increasing couplingstrengths. Surprisingly, however, these sys-tems could not synchronize faster than atsome speed limit (Fig.. 3). We used RandomMatrix Theory to derive an analytical predic-tion for the speed of the asymptotic networkdynamics, explaining both the speed and itslimit [13]. (iii) Very recently, we demon-strated that patterns of precisely timed spikesoccur even in strongly heterogeneous net-works with distributed delays and compli-cated connectivity [14]. In combination with many interesting studies

Figure 1: Perpetual switching in asystem with unstableattractors. The figure showsthe dynamics of the relativephases of N=100 neuronswhich are globally coupledin a homogenous networkwith time-delayedexcitatory coupling. Onefinds a repetitive decay andregrouping of synchronizedgroups of neurons.

of other research groups from all over theworld these recent findings just constitute afew islands of knowledge contributing to atheory for the precise dynamics of spikingneural networks. For neural network dynam-ics it will be exciting to see the next steps to-wards uncovering the secrets that natureposes – and to further understand the distrib-uted spatio-temporal code of the brain. Moregenerally, interest in the dynamics of net-works is currently growing and rapidlyspreading into many fields of science. Theseactivities are linked through their commonmathematical foundations, which to a largeextent are still to be developed. Non-standardfeatures such as delays, complicated networkconnectivity, and heterogeneities will play amajor role in many of the future investiga-tions of network dynamics.

[1] M. Abeles et al., J. Neurophysiol. 70 (1993)1629.[2] Y. Ikegaya et al., Science 304 (2004) 559.[3] M. Diesmann, M.O. Gewaltig and A. Aertsen,Nature 402 (1999) 529.[4] Y. Aviel et al., Neural Comput. 15 (2003) 1321.[5] M. Timme, F. Wolf, and T. Geisel, Phys. Rev.Lett. 89 (2002) 154105.[6] M. Timme, F. Wolf, and T. Geisel, Chaos 13(2003) 377.[7] P. Ashwin and M. Timme, Nonlinearity 18(2005) 2035.[8] A. Zumdieck et al., Phys. Rev. Lett. 93 (2004)244103.[9] P. Ashwin and M. Timme, Nature 436 (2005)36.[10] M. Timme, F. Wolf and T. Geisel,Phys.Rev.Lett. 89 (2002) 258701.[11] M. Denker et al., Phys.Rev.Lett. 92 (2004)074103.[12] M. Timme, F. Wolf, and T. Geisel,Phys.Rev.Lett. 92 (2004) 074101.[13] M. Timme, F. Wolf, and T. Geisel, Chaos 16(2006) 015108.[14] R.-M. Memmesheimer and M. Timme,http://arXiv.org: q-bio.NC/0601003 (2006).

Figure 2:Designing inhomogeneous

networks such that theyexhibit prescribed patterns

of spikes. One pattern ofprecisely timed spikes

(center, grey) is prescribed;the task is to design

networks that generate thispattern. The two statisticallydistinct networks shown on

the left and on the rightboth exhibit such patterns

(shown in black in thecenter panel). The networkshave been calculated using

a linear approximation innetwork space. The

thickness of eachconnection indicates its

strength of coupling.

Figure 3: Speed limits to network synchronization. (a,b) The location of eigenvalues (black dots) in the complex plane of stability matricesof two networks agrees well with the prediction by Random Matrix Theory (circle). The rightmost point on the circle is an estimate for thesecond largest eigenvalue, determining the asymptotic speed of network synchronization. (c) Asymptotic synchronization time versuscoupling strength (theory: solid line; numerical simulations: circles). The asymptote (dashed line) indicates a minimum characteristicsynchronization time and thus a speed limit.

c


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In quantum chaos one tries to understandthe implications of a chaotic classical limit fora quantum system. Despite the large varietyof such systems, they have a number of uni-versal physical properties in common. For ex-ample, a statistical analysis of the energy lev-els invariably shows striking similarities withthe ›energies‹ obtained from the diagonaliza-tion of random matrices. For the Sinai billiard(left column of Fig. 1) this has been knownfor more than 20 years. Nevertheless, until re-cently no satisfactory explanation for this ob-servation could be given. In the semiclassicalapproach to this problem the quantum den-sity of states is expressed as a sum over classi-cal periodic orbits by Gutzwiller’s trace for-mula. One can then describe fluctuations inquantum spectra on the basis of informationabout the classical dynamics (sum rules andaction correlations of periodic orbits). Quantum graphs are minimal models whichretain the trace formula and relevant proper-ties of the contributing periodic orbits (Fig. 1,right). By contrast, other important featuresof classical chaos such as the deterministicnature of the dynamics and the generic coex-istence of regular and chaotic trajectories areignored by these models. In this way onegains numerical and analytical simplicity andcan attack problems which are otherwisehard to solve. For example, the mentionedcorrelations between periodic orbits reduce tothe simple fact, that on a graph different cy-cles can share the same length (Fig. 2) [1]. Inthe trace formula it is then necessary to sumthe contributions from all these orbits coher-ently including all phases. We have devel-oped methods to solve this combinatorialproblem exactly for some simple networks [3]and approximately in a more general situa-tion [5].For the construction of a quantum graph oneconsiders a network of B bonds which repre-


Nonlinear Dynamics

2.1.3.5 Quantum Graphs: Network Models for Quantum ChaosHolger Schanz, Tsampikos KottosMarten Kopp, Mathias Puhlmann

G. Berkolaiko (Texas, USA), U. Smilansky (Rehovot, Israel)

Figure 1: Comparison between the Sinai billiard (left) and a quantumgraph (right). In a chaotic classical system all periodic orbits areunstable and small deviations in the initial conditions are amplifiedexponentially (a). The classical analogue of a quantum graph is arandom walk on a network. Also in this case the probability to followa given cycle decreases exponentially with the number of steps taken(b). Both models have stationary states with a discrete spectrum ofallowed energies. For the Sinai billiard one finds these states bysolving the Helmholtz equation in two dimensions (c). For thequantum graph diagonalization of a finite unitary matrix suffices.The resulting probability amplitudes to occupy a given bond areshown with a grey scale (d). The statistical properties of thequantum spectra are similar in both systems and follow closely theprediction of random-matrix theory (blue). This is shown in (e,f) forthe spectral form factor (Fourier transform of the two-pointcorrelation function).

sent the possible quantum states. Transitionscan occur only between bonds which are con-nected at a vertex. The amplitudes of all pos-sible transitions are collected in a B-dimen-sional matrix U which represents the time-evolution operator of the network. Theclassical version of the model is obtainedwhen the elements of U are replaced by theirmodulus squared and interpreted as transi-tion probabilities of a random walk. A statisti-cal analysis of the spectrum of U yields resultswhich are very similar to those found inchaotic systems if the underlying network iswell connected and if there is some random-ness in the phases of the transition ampli-tudes [1].With a suitable choice for the transition am-plitudes and the topology of the network theconstruction of a quantum graph is easilyadapted to various physical situations. Wehave investigated the spectra and eigenfunc-

tions of isolated chaotic systems [1,5,6], thescattering properties of networks with at-tached leads [2,4,7,8] and also extended sys-tems with disorder [3]. The questions ad-dressed in these publications were quite di-verse and included for example thesemiclassical foundation of the universality inquantized chaotic systems [5], the quantummanifestation of substructures in the classicalphase space [4] or the electronic transportthrough chaotic quantum dots [7]. Here wewill discuss only one example in some detail,namely the phenomenon of ›scarring‹ in thewave functions of chaotic systems [6]. Fig. 1d shows one selected stationary state ofa fully connected graph with 20 vertices (eachpair of vertices is connected by one bond). Al-though there are some quantum fluctuations,the state essentially covers the whole net-work. However, this is not typical. Mosteigenstates of the network live on a small

Figure 2: One can rearrange the itinerary of a periodic orbit ona network such that the new orbit passes through thesame set of bonds in a different order. In the exampleshown here there are exactly six possibilities. In thetrace formula the contributions from all these orbitsmust be added coherently when the spectral formfactor or other quantum correlation functions arecalculated [3,5,7,8].

Figure 3: Most stationary states of a quantumgraph occupy only a small fraction of the network.The majority of states are similar to the exampleshown in (a). Eigenstates which are restricted to aperiodic orbit are called scars (b). The enhancedlocalization in (a) is due to the orbits shown in (c).These orbits are short and relatively stable.However, strong scarring is observed exclusively onthe orbits shown in (d) although they are veryunstable. Relevant is here that to each vertex alongthe orbit at least two scarred bonds are connectedunless the vertex has degree one. Note that the v-shaped orbit falls into the first or the secondgroup according to the topology of the network(fully connected vs. star graph).


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fraction of the 380 available bonds and looksimilar to Fig. 3a. Sometimes one even ob-serves states which are almost completely re-stricted to a triangle or some other short peri-odic orbit on the network. This phenomenonis not an artifact of quantum graphs. It hadbeen observed before in many other chaoticquantum systems and is called scarring ofwave functions by periodic orbits. The en-hanced localization of eigenstates can also beseen in experiments. For example, scarringleads to strong fluctuations of the conduc-tance of semiconductor quantum dots as afunction of energy. The conventional theoryof scarring predicts enhanced localization onshort and relatively stable periodic orbits.However, this theory applies only to an aver-age over a large number of states with similarenergy while the properties of individualstates remain unknown. Quantum graphs areno exception in this respect. The increased lo-calization observed in the majority of statescan be explained quantitatively by the influ-ence of period-two orbits which bounce backand forth between two vertices. Therefore itwas surprising that the states with thestrongest localization correspond to triangu-

lar orbits while there are almost no stateswhich are localized on a single bond. Wehave analyzed this behavior in detail andfound a topological criterion for strong scar-ring in individual states which does not in-volve the stability exponent of the orbit(Fig. 3c-d). In this way we have demonstratedthat enhanced average localization due toshort orbits and strong scarring are two com-pletely unrelated phenomena. Moreover, ourtheory allows to predict the energy and the lo-cation of strong scars in individual eigen-states of quantum graphs.


Nonlinear Dynamics

[1] T. Kottos and U. Smilansky, Phys. Rev.Lett. 79 (1997) 4794.[2] T. Kottos and U. Smilansky, Phys. Rev.Lett. 85 (2000) 968.[3] H. Schanz and U. Smilansky, Phys. Rev.Lett. 84 (2000) 1427.[4] L. Hufnagel, R. Ketzmerick and M.Weiss, Europhys. Lett. 54 (2001) 703.[5] G. Berkolaiko, H. Schanz ,and R. S.Whitney, Phys. Rev. Lett. 88 (2002) 104101.[6] H. Schanz and T. Kottos, Phys. Rev.Lett. 90 (2003) 234101.[7] H. Schanz, M. Puhlmann, and T.Geisel, Phys. Rev. Lett. 91 (2003) 134101.[8] M. Puhlmann et al., Europhys. Lett. 69(2005) 313.

2.1.3.6 Random Matrix Theory and its LimitationsTsampikos Kottos, Holger Schanz

Moritz Hiller, Antonio Méndez-Bermúdez, Alexander Ossipov, Matthias WeissD. Cohen (Beer-Sheva, Israel), F. M. Izrailev (Puebla, Mexico), U. Smilansky (Rehovot, Israel)

Random matrix theory (RMT) has become amajor theoretical tool in so-called quantumchaos studies. In fact RMT has been appliedfruitfully to other areas of physics rangingfrom solid-state to nuclear atomic and molec-ular physics [1] to neural networks [2]. Thestudy of RMT models has been initiated byWigner and it has almost become a dogmathat this theory captures the universal proper-ties of systems with underlying classicalchaotic dynamics. However, the applicabilityof RMT is limited. What are these limitationsand can we go beyond them? An answer to

this question is essential for any meaningfulapplication of RMT regarding real physicalsystems such as driven quantum dots ormesoscopic open devices. Also, it should beremembered that RMT is commonly regardedas a reference case for comparison wheneveran actual physical system is considered. The past quantum chaos literature wasstrongly focused on understanding the inter-play between universal (RMT-like) and non-universal (semiclassical) features as far asspectral properties are concerned. However,the study of spectral statistics is just the lower

level in the hierarchy of challenges to under-stand quantum systems. The two other levelsare: studies of the shape of the eigenstates,and studies of the generated dynamics. Thelatter two aspects had been barely treatedprior to our studies.Recognizing this need, we have undertakenthe task of investigating the validity of RMT inquantum dynamics studies. In this respect, avariety of dynamical scenarios has been in-vestigated: wavepacket dynamics (see Fig. 1)[3,4], persistent driving [5], quantum dissipa-tion due to interaction with chaos [6], andtime reversal (fidelity) schemes [7]. In allthese cases we have found that, depending onthe driving strength, quantized chaotic sys-tems have an adiabatic, a perturbative, and anon-perturbative regime. The distinction be-tween these three regimes is associated withthe existence of two energy scales: the meanlevel spacing ∆~ hd , and the bandwidth∆b~h/τ where τ is the classical correlationtime that characterizes the chaotic dynamicsand d is the dimension of the limit. In theh →0 limit∆<< ∆b. In the quantum chaos lit-erature, ∆b is known as the non-universal en-ergy scale while in the context of ballisticquantum dots this energy scale is known asthe Thouless energy.We investigated the effects of ∆b in the frameof quantum dynamics. We have found thatwhile the dynamics in the former two regimesshows universal features which can be de-scribed by RMT models, the latter regime isnon-universal and reflects the underlyingsemiclassical dynamics (see Fig. 1). Further-more, for RMT models (suitable to describedisordered systems or many body interacting

fermions) we have found a ›strong‹ non-lin-earity in the response, due to a quantal non-perturbative effect [3,5]. Having establishedthe limitations of RMT modeling our currentefforts are threefold: (a) to create non-pertur-bative theories that go beyond RMT consider-ations (main emphasis to the problem ofquantum dissipation) (b) to extend our dy-namics studies for systems with classicalphase space where chaotic and integrablecomponents co-exist and (c) to investigatequantum dynamics of interacting (Bose)many body systems. At the same time we have made importantprogress in understanding the applicability ofRMT to describe the statistical properties ofscattering in complex systems. Particular at-tention was given to the time dependent as-pects of scattering (like current relaxation –see Fig. 2 –and delay times) and to the statisti-cal properties of resonance widths. Our aimwas to go beyond the universal RMT predic-tions [8,9] by taking into account specificproperties of the system like localization [10],diffusion [11], fractality of the spectrum [12],or geometry of the sample [10]. This researchis relevant not only for understanding elec-tron transport in mesoscopic disorderedsolids but also to other areas such as quan-tum optics, microwave transport through ran-dom media, and atomic physics. As an exam-ple we refer to the ›random laser technology‹which relies heavily on the properties of shortresonances which determine the behavior oflasing thresholds.Having acquired knowledge of the statisticalproperties of resonances and delay times forvarious cases, we have recently analyzed the

Figure 1: A diagram that illustrates the various time scales in

›wavepacket dynamics‹[3,4], depending on the

strength of the perturbationε . Here, ε c is the

perturbation needed to mixtwo nearby levels (hence

related with ∆) while ε prt isthe perturbation needed to

mix levels within thebandwidth ∆b . The diagram

on the left refers to an RMTmodel, while that on the

right is for a quantizedsystem that has a classical

limit. The two cases differ inthe non-perturbative regime

(large ε): In the case of aquantized model we have a

genuine ballistic behaviorwhich reflects detailed

Quantum ClassicalCorrespondence, while in

the RMT case we have adiffusive stage. In the latter

case the times scale tsdn marksthe crossover from reversible

to non-reversible diffusion.


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properties of random systems that exhibit aMetal-Insulator Transition (MIT) [10,13,14].We showed that at the MIT both distributionsare scale invariant, independent of the micro-scopic details of the random potential, andthe number of channels. Theoretical consid-erations suggest the existence of a scaling the-ory for finite samples, and numerical calcula-tions confirm this hypothesis [10,13].

Based on this, we gave a new criterion for thedetermination and analysis of the MIT(see

Fig. 3) [10,13]. Recently, we have initiated anew research line [15], by studying the decayof the survival probability of a Bose-Einsteincondensate which is periodically driven witha standing wave of laser light and coupled toa continuum. This study was performed inthe frame of the nonlinear Gross-Pitaevskii

Figure 2: The ratio between quantum and classical survival probability has been computed for aballistic quantum graph with L=10 attached decay channels and G=500(+), 750(x), 1000(£ ),2000(o) internal states. It is shown as a function of the scaled time τ=t/G. Quantum corrections arevisible as deviations of the data from the horizontal line. For small τ they follow (a) P(τ)=[1+(L/2)τ 2 ]Pcl(τ) in the case with time-reversal symmetry and (b) P(τ)=[1+(L2/24)τ4 ] Pcl(τ) without aspredicted by RMT. These semiclassical predictions account for the interference within the pairs ofclassical trajectories shown schematically in the insets. The two trajectories forming a pair are identicalalong the segments a,b,... but differ in the crossing regions (solid vs. dashed arrows) [9].


Nonlinear Dynamics

Figure 3: Integrated resonance width distribution P int(Γ 0)≡ ∫ Γ0

∞P(Γ)dΓ, (here Γ 0 ~r,wherer is the

mean level spacing) as a function of the disorder strength V for different system sizes L provides ameans to determine the critical point Vcwhere we have a MIT (vertical line at Vc=16.5). (b) The one-parameter scaling of P int(Γ 0) =f(L/ξ ( V ) is confirmed for various system sizes L and disorderstrengths V (ξ (V) is the localization length)) using a box distribution for the on-site potential of a 3DAnderson model.

[1] H.-J. Stöckmann, Quantum Chaos: anIntroduction, Cambridge 1998[2] M. Timme, T. Geisel, and F. Wolf, Chaos 16 (2006)015108.[3] M. Hiller et al., Annals of Physics 321 (2006) 1025.[4] D. Cohen, F. Izrailev, and T. Kottos, Phys. Rev.Lett. 84 (2000) 2052.[5] D. Cohen and T. Kottos, Phys. Rev. Lett. 85(2000) 4839.[6] D. Cohen and T. Kottos, Phys. Rev. E 69 (2004)055201 (R).[7] M. Hiller et al., Phys. Rev. Lett. 92 (2004) 010402.[8] T. Kottos and U. Smilansky , Phys. Rev. Lett. 85

(2000) 968.[9] M. Puhlmann et al., Europhys. Lett. 69 (2005) 313.[10] T. Kottos, J. Phys. A: Math. Gen. 38 (2005) 10761.[11] A. Ossipov, T. Kottos, and T. Geisel, Europhys.Lett. 62 (2003) 719.[12] F. Steinbach et al., Phys. Rev. Lett. 85(2000) 4426.[13] T. Kottos and M. Weiss, Phys. Rev. Lett. 89(2002) 056401.[14] Y. V. Fyodorov and A. Ossipov, Phys. Rev. Lett. 92 (2004) 084103.[15] T. Kottos and M. Weiss, Phys. Rev. Lett. 93(2004) 190604.

(GP) equation describing the mean-field dy-namics of the open condensate. We havefound that the survival probability decays asP(t)~1/tα with the power α being a scalingfunction of the ratio of the interactionstrength between Bose particles and the local-ization properties of the corresponding linearsystem. Our next steps involve a full quantummechanical study of such systems. We plan to

operate in the regime where the Bose-Hub-bard Hamiltonian is applicable. In this re-spect, the study of small open quantum lat-tices (dimer or trimer) promises new excitingopportunities. These studies will be compli-mented with scattering analysis from non-lin-ear quantum graphs where we will investi-gate the effect of non-linearity to chaotic scat-tering.

2.1.3.7 From Ballistic to Ohmic Transport in Semiconductor Nanostructures

Ragnar Fleischmann, Holger SchanzKai Bröking, Jackob Metzger, Marc-Felix Otto, Manamohan Prusty

E. J. Heller (Harvard, USA), R. Ketzmerick (Dresden)

According to Ohm’s law, the resistance of awire is proportional to its length. This is astraightforward consequence of the diffusivemotion of electrons in the disordered poten-tial of a normal material. Today, unlike thetime when Ohm arrived at his fundamentalobservation, conductors can be tailor-madewith almost complete control over the micro-scopic structure. In semiconductors the resid-ual impurities can be so weak that the aver-age free electron path between two scatteringevents can exceed the typical system size onthe nanometer scale. Then the motion of elec-trons is ballistic rather than diffusive andOhm’s law does not apply. For example, con-duction measurements with almost perfect

semiconductor nanowires showed a resist-ance which was independent of the wirelength.Clearly it is a relevant question how the tran-sition from ballistic to diffusive electron dy-namics takes place and what replaces Ohm’slaw in such an intermediate situation. We arestudying this question in various contexts andgive only two examples here. First we showhow the electron dynamics departs from apurely ballistic motion under the influence ofthe residual disorder which is present in a realtwo-dimensional electron gas (2DEG) at theinterface between two semiconductors. Al-though the disorder is very weak it turns outto have a very strong effect on the distribution


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of electrons inside the sample. In the secondexample we manipulate the electron dynam-ics such that it is ballistic or diffusive depend-ing on the transport direction. We shall seehow the resistance of such an unusual wireinterpolates between the two extremes whichare present simultaneously.

Influence of weak disorder: Branching of theelectron flow

It has been known for a long time that impu-rity scattering in the high mobility two-dimensional electron-gas (2DEG) in semicon-ductor systems at low temperatures isdominated by small-angle scattering. Theconsequences of the small-angle scattering onlength-scales short compared to the meanfree path (MFP), however, come as a greatsurprise: instead of a fanning-out of the cur-rent paths it leads to a pronounced branchingof the electron flow. In an experiment performed in the Westerveltgroup at Harvard using scanning gate mi-croscopy the current density exiting from aquantum point contact (QPC) into the 2DEG

of a GaAs/AlGaAs heterostructure could beobserved [1]. To theoretically validate the un-expected outcome of the experiment (Fig. 1B)as a consequence of impurity scattering it wasnecessary for us to model the disorder poten-tial in the 2DEG in some detail [S. Shaw, R.Fleischmann, E. Heller in 1]. The disorder ismainly due to spatial fluctuations in thecharge density of the donor-layer in the mod-ulation-doped heterostructure. The resultingdisorder potentials (Fig.1A) turn out to have avariance on the order of a few percent of theFermi-energy of the electrons (red plane inFig. 1A) and to be smooth on length scaleslarger than the Fermi-wavelength of the elec-trons. Numerical simulations in these modelpotentials corroborate the experimental find-ings and show that the branching effect is ba-sically a classical effect (Fig. 2). It is impor-tant to notice, that the formation of branchesis not at all similar to the flow of rivers in val-leys. In Fig. 2a the shadow of the classical cur-rent density cast over the disorder potentialclearly shows that the branches do not flow

along valleys but rather run equally over val-leys and hills. This effect can not only befound in semiconductors, however, but is avery general phenomenon. Similar findingsthat have been described for the sound propa-gation in the ocean [2] on length-scales a tril-lion (1012) times larger can be attributed to thesame effect. In general, every two dimen-sional Hamiltonian system with weak corre-lated disorder should show the branching ofthe flow, even though the disorder potential issmall compared to the kinetic energy andthus only allows for small changes in the ve-locities. But what is the mechanism behindthe branching of the flow? While a satisfyingquantitative analytical theory is still lackingand is the aim of ongoing work, we alreadycan well demonstrate the origin of thebranching numerically [3]. It is caused by the

Figure 1: Model potential (A) of the experimental setup (sketched in the inset) thatwas used to image the current density emitting from a quantum point contact. Thetip of a scanning probe microscope was used as a point scatterer. In first order itinduces a change in the conductance proportional to the current density at theposition of the tip. By scanning the tip over the sample and recording theconductance differences a map of the current density (B) could thus be measured.Here the gate voltage defining the QPC is adjusted so that only the first mode ispropagating through it. The mean free path in the 2DEG is approximately 7 µm; theexperiment was performed at temperatures of 1.7 K.


Nonlinear Dynamics

formation of caustics and the fact that in twodimensions caustics in general appear in pairsas illustrated in Fig.3.

Competition of diffusive and ballistictransport

Figure 4 shows a model in which the electrondynamics is ballistic or diffusive dependingon the transport direction. Under the in-fluence of a transverse magnetic field an elec-tron moves on a circular arc until it isreflected from one of the boundaries of thequasi one-dimensional wire. Due to the spe-cific geometry there are regular and chaotic

trajectories. Some electrons simply skip alongthe straight boundary of the wire from right toleft (green). The chaotic trajectories collidewith the obstacles at the lower wall and fre-quently change their transport direction(red). In the limit where the size of the obsta-cles and their distance shrink to zero, the dy-namics corresponds to biased diffusion withdrift velocity v and diffusion constant D. Wehave shown in a more general context thatthe chaotic drift exactly compensates for theregular (skipping) transport [4]. In the pres-ent case the relevant parameters are thelength scale L=D/v and the relative weight cof the chaotic orbits in phase space. Both canbe changed by tuning the magnetic field. Forthe resistance of a wire with length l wefound the formula R(l)=(1–c exp[–l/L]) /(1–c)up to a constant prefactor and confirmed thisnumerically for a wide parameter range [5].This expression interpolates in a non-trivialway between Ohm's law R(l)~ l for c→1 andthe ballistic case R(l)= const for c→0. Thecharacteristic length scale L is a new featureand a qualitative difference to the two limit-ing cases. We continue to study models of thistype because the intrinsic direction depend-ence of transport is an unusual and poten-tially useful effect. Currently we are inter-ested in time-resolved transport propertiesand quantum effects.

Figure 3: The time evolution of the initial manifold of a point source with cosine characteristic at fixed timeintervals (turquoise and violet lines). The shadings represent the current density. The inset on the rightshows a cut through the density (solid line) compared to the density in an idealized clean system (dottedline) and demonstrates that the branching is not necessarily a small effect and the rise in the density in theregion between two sibling caustics due to the folding of the manifold.

Figure 2:Numerical simulations of

the current density emittedby the first mode of a

quantum point contact:(a) False colour map of the

used potentialovershadowed by the

classical current density. (b)Classical current density. (c)

Quantum mechanicalscattering wave function.


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Typical Hamiltonian systems are neither in-tegrable nor ergodic [1,2,3] but have a mixedphase space, where regular and chaotic re-gions coexist. Fig. 1b shows a phase spaceportrait of a typical mixed phase space of thewell known kicked rotor, which is a paradigmfor a generic Hamiltonian system. The regularregions are organized in a hierarchical wayand chaotic dynamics is clearly distinct fromthe dynamics of fully chaotic systems. In par-ticular, chaotic trajectories are trapped in thevicinity of the hierarchy of regular islands.The most prominent quantity reflecting this,is the probability P(t) to be trapped longerthan a time t, which decays as

P(t) ~ t -γ ,

in contrast to the typically exponential decayin fully chaotic systems. While the power-lawdecay is universal, the exponent γ is systemand parameter dependent [4,5]. The origin of

the algebraic decay is an infinite hierarchy ofpartial transport barriers [1,3], e.g., Cantori,surrounding the regular islands. Transportacross each of these barriers is described by aturnstile, whose area is the flux exchangedbetween neighboring regions [14]. The fluxesdeep in the hierarchy become arbitrarilysmall.For mixed systems two types of eigenfunc-tions are well studied: There are ›regular‹states living on KAM-tori of the regular is-lands and there are ›chaotic‹ states extendingacross most of the chaotic region as first de-scribed by Percival [6]. In addition, we wereable to identify and quantify a third type ofeigenstates (see Fig.2). They directly reflectthe hierarchical structure of the mixed phasespace and are thus called hierarchical states[7]. These states are supported by the chaoticregion but predominantly live in the vicinityof the regular islands with only a small contri-bution in the main part of the chaotic sea.


Nonlinear Dynamics

[1] M. A. Topinka et al., Nature 410(2001) 183.[2] Michael A. Wolfson and StevenTomsovic, J. Acoust. Soc. Am. 109 (2001)2693.

[3] R. Fleischmann et al., in preparation(2006).[4] H. Schanz et al., Phys. Rev. Lett. 87(2001) 070601.[5] M. Prusty and H. Schanz, Phys. Rev.Lett. 96 (2006) 130601.

Figure 4: Electrons move under the influence of a perpendicular magnetic field in a structure which isdesigned to allow for the simultaneous presence of ballistic and diffusive transport. The characteristicfeature is that backscattering of electrons occurs only at one of the two boundaries of the channel. A periodicarrangement of large semicircular obstacles is shown here for clarity, but it could be replaced, e.g., by aboundary with a rough surface [5].

Lars HufnagelMatthias Weiss

R. Ketzmerick (Dresden)

2.1.3.8 What are the Quantum Signatures of Typical Chaotic Dynamics?

They are separated from the main chaotic seaby the partial transport barriers of the classi-cal phase space.The occurrence of the hierarchical states canbe understood as follows: While the classicalfluxes become arbitrarily small, quantum me-chanics can mimic fluxes φ > h only [8]. Thisleads to the concept of the flux barrier, whichis defined to be the partial transport barrier inphase space with flux φ ≈ h. This flux barrierdivides the chaotic component of the phasespace into two parts: Regions connected byfluxes φ >h are strongly coupled and thus ap-pear quantum mechanically as one part. Theysupport the chaotic eigenstates. Regions con-nected by fluxes φ < h couple only weakly toone another and support the hierarchicalstates. Thus the fraction of hierarchical statesscales as

ƒhier ~ h 1-1/γ,

where the classical exponent determines thescaling. Not only has the existence of the fluxbarrier important consequences for eigenstates and eigenfunctions, it also limits quan-tum-classical correspondence and underlies anew type of conductance fluctuations, whichwas observed recently.One of the central phenomena in mesoscopic

physics are conductance fluctuations [9].They occur as a function of an external pa-rameter, e.g., magnetic field or energy, whenthe phase coherence length exceeds the sam-ple size. They can be measured, e.g., in semi-conductor nanostructures at sub-Kelvin tem-peratures. For typical billiards, which exhibita mixed phase space, the power-law decay ofEq.(1) led together with semiclassical argu-ments to the prediction of FCF [10]. They arecharacterized by a fractal dimensionD=2–γ/2,γ<2, of the conductance curve g(E).A new type of conductance fluctuations hasbeen observed for the cosine billiard with amixed phase space [11]. In contrast to the pre-viously found FCF, the conductance as afunction of energy shows a smoothly varyingbackground with many isolated resonances. We have shown that both types are quantumsignatures of the classical mixed phase spaceand in general appear simultaneously, but ondifferent energy scales [12]. Furthermore, iso-lated resonances are caused by regions be-hind the flux barrier and are therefore scatter-ing signatures of the hierarchical states. Foropen quantum systems the flux barrier intro-duces an important new time scalet*=Ωn*+1/Φn*,n*+1. (Fig. 3) Beyond this time,regions behind the flux barrier are importantand quantum dynamics differs from classicaldynamics. Therefore the semiclassical deriva-tion of FCF is only valid for energy scales∆E>∆E*≡ h/t*.We were able to calculate the scaling of thisenergy and the corresponding time scale,which nicely agrees with numerical simula-tions [12,13]. The coexistence of FCF and iso-lated resonances is illustrated in Fig. 4.Although generic Hamiltonian systems pos-sess a mixed phase space, classical propertiesof mixed systems and their quantum mechan-ical signatures are still only partly under-stood. In particular, we have shown recentlythat, for transporting islands, even the dis-tinctions in regular and chaotic eigenstatesfails [14].

Figure 1: Phase space portraits of (a) mostly regular, (b) mixed, and (c) fullychaotic dynamics. The successive magnifications in (d) and (e) illustrate thehierarchical nature of mixed phase spaces.


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Nonlinear Dynamics

Figure 3: Sketch of the hierarchical phasespace structure in the vicinity of aregular island. A linear infinitechain of phase space regions withvolume Ωn+1 are separated bypartial transport barriers. The fluxΦn,n+1 between two neighboringregions is given by the area of theturnstile. The quantum fluxbarrier at n*divides the hierarchyinto two regions.

Figure 2 : Phase space representation of aregular, hierarchical, and chaoticeigenfunction. Solid lines indicateKAM tori of the classical phasespace.

Figure 4: Dimensionless conductance as afunction of energy showing thecoexistence of fractal fluctuationson large energy scales (a) andisolated resonances on smallscales (b).

[1] R. S. MacKay, J. D. Meiss, and I. C.Percival, Physica D 55 (1984) 13.[2] J. D. Meiss, Rev. Mod. Phys. 64 (1992)795.[3] L. Markus and K. R. Meyer, in Memoirsof the American Mathematical Society 114(American Mathematical Society,Providence, RI, 1974)[4] M. Weiss, L. Hufnagel, and R.Ketzmerick, Phys. Rev. E 67 (2003) 046209.[5] M. Weiss, L. Hufnagel, and R.Ketzmerick, Phys. Rev. Lett. 89 (2002)239401.[5] C. Percival, J. Phys. B: Atom. Molec.Phys 6 (1973) L229.[7] R. Ketzmerick et al., Phys. Rev. Lett. 85(2000) 1214.

[8] O. Bohigas, S. Tomsovic, and D. Ullmo,Phys. Rep. 223 (1993) 45.[9] S. Datta, Electronic transport in meso-scopic systems (Cambridge University Press1995).[10] R. Ketzmerick, Phys. Rev. B 54 (1996)10841.[11] B. Huckestein, R. Ketzmerick, and C.Lewenkopf, Phys. Rev. Lett. 84 (2000)5504.[12] R. Ketzmerick, L. Hufnagel, and M.Weiss, Adv. Sol. St. Phys. 41 (2001) 473.[13] L. Hufnagel, R. Ketzmerick, and M.Weiss, Europhys. Lett. 54 (2001) 703.[14] L. Hufnagel et al., Phys. Rev. Lett. 89(2002) 154101.

Diffusion processes are ubiquitous innature. A freely diffusive particle is character-ized by a relationship between the typical dis-tance |x(t) | it traveled and the time t thatelapsed, i.e. |x(t) |~ t 1/2. However, a variety ofinteresting physical systems violate this scal-ing behavior. For example, the distance of asuperdiffusive particle from its starting pointtypically scales with time according to

|x(t) |~ t 1/ß

with ß<2. Superdiffusion has been observedin a number of systems ranging from earlydiscoveries in intermittent chaotic sys-tems[1], fluid particles in fully developedturbulence[2], and human eye movements[3]and most recently discovered, the geographicmovement of bank notes[4]. Among the mostsuccessful theoretical concepts that havebeen applied to superdiffusive phenomenaare random walks known as Lévy flights[5]

(see Fig.1). In contrast to ordinary randomwalks, the spatial displacements ∆x of a Lévyflight lack a well-defined variance, due to aheavy tail in the single step probability den-sity, i.e.

with an exponent ß<2 which is usually re-ferred to as the Lévy index. Lévy flights havepaved the way towards a description of su-perdiffusive phenomena in terms of fractionalFokker-Planck equations (FFPE). Since manyof the aforementioned systems evolve in in-homogeneous environments, it is crucial tounderstand the influence of external poten-tials on the dynamics. While in ordinary dif-fusive systems an external force is easily in-corporated into the dynamics by a drift termin the corresponding Fokker-Planck equation(FPE), the matter is subtler in superdiffusivesystems due to the nonlocal properties of thefractional operators involved. Depending onthe underlying physical model, different typesof FFPEs are appropriate[6], therefore the adhoc introduction of fractional operators maylead to severe problems. In cases where the external inhomogeneitycan be represented by an additive force, con-siderable progress has been made in a gener-alized Langevin approach, which led to anFFPE in which deterministic and stochasticmotion, segregate into independent compo-nents. This approach, however, is suited onlyfor systems in which such a segregation canbe justified on physical grounds. For somereason though, it has been considered as thecanonic theory for Lévy flights in external po-tentials.One feature of generalized Langevin dynam-ics is its validity only for systems far fromthermodynamic equilibrium. It fails in thelarge class of systems, which obey Gibbs-Boltzmann thermodynamics, e.g., where su-perdiffusion is caused by the complex topol-ogy on which the process evolves.A good example is diffusion along rapidly fol-ding heteropolymers[7] as depicted in Figure 2. A particle is attached to a het-eropolymer and performs a random walkalong the chain. The chain is flexible and rap-

p(∆x)~ ––––––1

|∆x| 1+ß

2.1.3.9 Topological Superdiffusion – A New Theory for Lévy Flightsin Inhomogeneous Environments

Dirk Brockmann

Figure 1:Ordinary random walks and

Lévy flights. A) The twodimensional trajectory of an

ordinary random walkresembles Brownian motion.

B) The trajectory of a Lévyflight with Lévy index ß=1.0.C) The distance |xn| from the

origin of an ordinary randomwalk (blue) and a Lévy flight

(red) as a function of thenumber of steps . The

diffusive scaling |xn|~ N1/2

isdepicted by the blue dashed

line, the superdiffusivescaling

|xn|~ N1/ß

with ß=1.0 by thered dashed line.


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idly changes its conformational state. Theheterogeneity of the chain is modeled by a po-tential V which defined along the chemicalcoordinate of the chain and which specifiesthe probability of the particle being attachedto a site. In a thermally equilibrated systemthis probability is proportional to the Boltz-mann factor e –V/KBT. If the polymer is flexibleand rapidly folding the attached particle canperform intersegment transfer by virtue ofsegments which are close in Euclidean spacebut far apart along the chemical coordinate.The probability of observing a jump of lengthl in chemical coordinates depends on the fold-ing dynamics of the polymer and generallydecreases according to a powerlaw with dis-tance. Effectively, the particle performs aLévy flight along the chain in a heteroge-neous environment imposed by the potential.However, superdiffusion is not caused bylarge fluctuations in stochastic forces but israther a consequence of the topology of thesystem, the system is topologically superdif-fusive.We were able to show that systems of thistype can be described by a novel type of FFPE

of the form

∂t p = e–ßV/2∆µ /2e ßV/2p–peßV/2∆µ /2e –ßV/2

where ß is the inverse temperature, µ theLévy index, ∆µ /2 the fractional generalizationof the Laplacian and p=p(x,t) the probabilityof finding the particle at a position x at time t.In8 we investigated the impact of external po-

tentials on this class of systems. Based on theparadigmatic case of a randomly hopping par-ticle on a folded copolymer, we discovered anumber of bizarre phenomena, which emergewhen Lévy flights evolve in periodic and ran-dom potentials and showed that externalpotentials have profound effect on thesuperdiffusive transport. This is in sharp con-trast to generalized Langevin dynamics,which displays trivial asymptotic behavior inthese systems, a possible reason why Lévyflights in such potentials have attracted littleattention in the past. We demonstrated thateven strongly superdiffusive Lévy flights arehighly susceptible to periodic potentials, ascan be seen in the complexity of the eigen-value band structure (Fig. 3). The range of applications of this type of dy-namics is wide. For instance the trajectoriesof human saccadic eye movements can be ac-

Figure 2: Topological superdiffusion A) A particle(green) performs a random walk on a polymer chain.Along the chemical coordinate x a potential is defined.B) The polymer is flexible and rapidly changes is 3-Dconformation. C) Segments which are far apart alongthe chemical coordinate of the chain can come closeand the hopping particle can perform intersegmenttransfer. D) effectively the random walk takes place ona complex network topology induced by the locationsat which intersegment tranfer can occur.


Nonlinear Dynamics

Figure 3: Eigenvalue bands fortopologically superdiffusiveprocesses in a smoothed boxperiodic potential.κ n (ε) = Ε n (ε) 1 / µ denote thegeneralzed chrystal momentumas a function of the inversetemperature ε = ß / 2 .Superdiffusive processes exhibita rich behavior as opposed to thelimiting case of ordinarydiffusion, i.e. µ = 2 .

[1] T. Geisel, J. Nierwetberg, and A. Zacherl,Physical Review Letters 54 (1985) 616.[2] A. La Porta et al., Nature 409 (2001) 1017.[3] D. Brockmann and T. Geisel, Neurocomputing 32(2000) 643.[4] D. Brockmann, L. Hufnagel, and T. Geisel,Nature 439 (2006) 462.[4] Lévy flights and related Topics in Physics (eds.

Shlesinger, M. F., Zaslavsky, G. M. & Frisch, U.)(Springer, Nice, France, 1994).[6] D. Brockmann and I. M. Sokolov, ChemicalPhysics 284 (2002) 409.[7] D. Brockmann and T. Geisel, Physical ReviewLetters 91 (2003) 048303.[8] D. Brockmann and T. Geisel, Physical ReviewLetters 90 (2003) 170601.

counted by a similar model[3] (Fig. 4). In thismodel the Boltzmann factor is identified withthe visual salience, i.e. the attractivity, of a lo-cation in a scene: s(x)=exp(–ßV(x)/2). Wewere able to show that a process with inter-mediate Lévy index µ =1 is optimal for visualsearch tasks.Most importantly, our theory can be appliedin population dynamical contexts, particularyspatially extended models for the spread ofinfectious diseases. We are currently investi-gating the interplay of spatially variable pop-ulation densities with scale free superdiffu-sive dispersal of individuals and paradigmatic

reaction kinetics for local outbreaks of infec-tions. The combination of fractional Fokker-Planck equations mentioned above with localexponential growth due to the disease dy-namics yields spatio-temporal pattern whichdiffer vastly from those observed for ordinarydiffusion (see Fig. 5). As our approach can beapplied to realistic geographies we hope thatit will serve as a starting point for the devel-opment of more realistic models for thespread of disease and that general contain-ment strategies for emergent infections can bedevised.

Figure 4: Human saccadiceye-movements.

Left: A natural scenepresented to two observers

whose eye movements wererecorded (middle). Very

similar trajectories can begenerated by a topologically

superdiffusive process(right).

Figure 5: Spatiotemporal patterns of the spread ofinfectious diseases. a) A generic diffusive spatiallyextended model for the spread of a disease.Typically these models exhibit wave fronts whichpropagate at a constant speed. b) Spatialheterogeneity reflected by a position dependentpopulation density leads to a randomizaion of thediffusive wave front (c) which nevertheless retainsits overall shape. If infected agents perform scalefree superdiffusion (Lévy flights) the spatiotemporal patterns differ considerably (d).


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Nonlinear Dynamics

The application of mathematical modeling tothe spread of epidemics has a long historyand was initiated by Daniel Bernoulli’s workon the effect of cowpox inoculation on thespread of smallpox in 1760. Most studies con-centrate on the local temporal development ofdiseases and epidemics. Their geographicalspread is less well understood, although im-portant progress has been achieved in a num-ber of case studies. The key question, as wellas difficulty, is how to include spatial effectsand quantify the dispersal of individuals. To-day’s volume, speed, and globalization oftraffic (Fig. 1), increasing international tradeand intensified human mobility promote acomplexity of human travel of unprecedenteddegree.The severe acute respiratory syndrome(SARS) which spread around the globe in amatter of months in 2003 has not onlydemonstrated that the geographic spread ofmodern epidemics vastly differs from historicones but also the potential threat of emergentinfectious diseases such as Hanta, West Nileand Marburg fever which can be contained totheir endemic region only with increasing dif-ficulty. Particularly in the light of an immi-nent H5N1 influenza A pandemic the knowl-edge of dynamical and statistical properties ofhuman travel is of fundamental importanceand acute.

The spread of SARS on the global aviationnetwork – a case study

The application of spatially extended modelsto the geographic spread of human infectiousdisease by means of reaction-diffusion equa-tions has been motivated by the spread of his-toric pandemics such as the bubonic plague(1347–1350). A characteristic of the spread ofthe ›Black Death‹ was a wave front whichpropagated at a speed of approximately4–5km/per day, a direct consequence of the

local proliferation of the disease in combina-tion with diffusive motion of infected individ-uals who could travel at most a few km/dayat that time. In contrast, the rapid worldwidespread of the severe acute respiratory syn-drome (SARS) in 2003 (Fig. 2), showed clearlythat modern epidemics cannot be accountedfor by conventional reaction diffusion modelsas humans can travel from any point on theglobe to any other in a matter of days and notypical length scale for travel can be identi-fied. In a recent project [1] we focused on the keymechanisms of the worldwide spread of mod-ern infectious diseases. In particular we in-vestigated to what extend the worldwide avi-ation network plays a role in disseminatingepidemics. To this end we compiled approxi-mately 95% of the entire aviation traffic,which amounts to nearly 2 million flights perweek between the 500 largest airports world-wide. Some of the questions we aimed to an-swer were: Is it possible to describe theworldwide spread of an epidemic based on aconceptionally lean model which incorpo-rates the worldwide aviation network? If so,

2.1.3.10 Human Travel and the Spread of Modern Epidemics

Dirk Brockmann, Lars Hufnagel

Figure 1: The worldwide civil aviation network. Lines connect the 500 largest airports.Bright lines indicate high, dark lines low traffic between connected nodes. The entiredepicted traffic comprises 95% of the worldwide traffic.

how reliable are forecasts put forth by themodel? How important are fluctuations?What facilitates the spread? And, last but notleast, what containment strategies and con-trol measures can be devised as a result ofcomputer simulations based on such amodel?Our model consists of two part: a local infec-tion dynamics and the global traveling dy-

namics of individuals. The local dynamics isdescribed by the SIR reaction kinetic schemein which individuals are initially susceptible(S), become infected (I) and recover (R) fromthe disease, become immune and cannot beinfected a second time. The associated reac-tion kinetics

S + Iα→ 2I I

ß

→ R (1)

is defined by the two reaction rates α and ß,the ratio of which is the basic reproductionnumber Ro, which is the average number ofsecondary infections caused by one infectedindividual during the infectious period. IfRo>1, an epidemic outbreak occurs. ForSARS, which spread around the world in2003, a value Ro≈2– 4 was found. We as-sumed that the above SIR model governs thedynamics of the disease in each urban areasurrounding an airport. Furthermore we as-sumed that the transport between urban ar-eas is directly proportional to the traffic fluxof passengers between them. Both con-stituents of our model are treated on astochastic level, taking full account of fluctua-tions of disease transmission, latency, and re-covery on the one hand and of the geo-graphical dispersal of individuals on the other(Fig. 3). Furthermore, we incorporate nearlythe entire civil aviation network.

Figure 2: A) geographic spread of SARS in May 2003as reported by the World Health Organization(WHO) and the Center for Disease Control andPrevention (CDC). The number of infecteds per coun-try are encoded by color. B) The expected spread aspredicted by the model after a time of 90 days.Depicted ist the expectation value of the number ofinfecteds after 10000 simulations with an initialoutbreak in Hong Kong.

Figure 3: A) The SIR reaction kinetic model for thedynamics of local outbreaks. B) Dispersal betweenpopulations. C) The percentage of infectedindividuals in a population as a function of time for abasic reproduction number of Ro=2. The red curvesare simulations of the full stochastic reaction kinetics,the blue curve depicts the mean field dynamics.


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Nonlinear Dynamics

Fig 2. depicts a comparison of the spread ofSARS in May 2003 as reported by the WorldHealth Organization and simulations of ourmodel. Despite some differences the overallprediction of our model is surprisingly closeto the observed global spread of SARS. Thedegree of agreement seems particularly sur-prising if one recalls the conceptual simplicityof our model and the fact that we incorporatefluctuations in the infection dynamics as wellas the spatial dispersal. In2 we investigatedthe reason why predictions based on theglobal travel on the aviation network is in-deed possible. We were able to show that thestrong heterogeneity of the network reflectedby a wide range of airport capacities, fluxesbetween airports and particularly a widerange of connectivities decreases the effectsof internal fluctuations. Furthermore, wewere able to show that a containment strat-egy, which focuses on the most frequentedconnections, has practically no impact as op-posed to a strategy which focuses on the mostconnected nodes in the network.

The scaling laws of human travelWhereas the global aspects of disease dynam-ics can be accounted for by an comprehensiveknowledge of the aviation network, such anapproach is insufficient if a description forsmaller length scales is required. In order tounderstand and predict the spread of diseaseon a wide range of length scales, we need toknow the statistical rules that govern humantravel from a few to a few thousands kilome-ters. Quantitative studies, however, prove tobe very difficult, because people move overshort and long distances, using variousmeans of transportation (planes, trains, auto-mobiles, etc.). Compiling a comprehensivedataset for all the means of transportation onextended geographical areas is difficult if notimpossible.In a recent project3 we approached the prob-lem from an unusual angle. We evaluateddata collected at the online bill tracking sys-tem www.wheresgeorge.com in order to assessthe statistical properties of the geographic cir-

culation of money with a high spatiotemporalprecision. The idea behind this project was touse the dispersal of money as a proxy for hu-man travel as bank notes are primarily trans-ported from one place to another by travelinghumans.Wheresgeorge.com, which started in 1998without any scientific motivation, is a popu-lar US internet game in which participantscan register individual dollar bills for fun andmonitor their geographic circulation hence-forth. Since its beginning a vast amount ofdata has been collected at the website, over80 millions of dollar bills have been registeredby over 3 million registered users.Based on a dataset of over a million individ-ual displacements we found that the dispersalof dollar bills is anomalous in two ways. First,the probability p (δ r ) of traveling a distanceδr in a short period of time δΤ < 4 days de-cays as a power law, i. e.

with an exponent ß≈0.6 . This exponent im-plies that no typical distance can be definedas mean as well as variance of the displace-ment are divergent. Surprisingly this behaviordoes not depend strongly on local propertiessuch as the population density of the UnitedStates. Irrespective of the initial entry loca-tion, an asymptotic powerlaw was observed(see Fig. 5). This observation lead us to conjecture thatthe trajectories of dollar bills are reminiscentof Lévy flights4, a superdiffusive random walkcharacterized by a power law in the singlestep distribution with an exponent ß<2 . Theposition x N of a Lévy flight scales with thenumber of steps according to

x N ~ N 1/ß

for ß<2 unlike the ordinary ›square root‹scaling x N ~ N 1/2 exhibited by ordinary ran-dom walks. Employing the Lévy flight modelwe computed the time Teq for an initially lo-calized ensemble of dollar bills to redistribute

p (δr ) ~1

δr 1+ß

equally within the United States and obtainedTeq ≈70 days. However, the dispersal datashowed clearly that even after one year, billsdo not equilibrate within the United Statesand despite the clear evidence for the powerlaw in the short time dispersal the Lévy flightpicture seemed incomplete.We thus developed the idea that the dispersalof money can be described by a process inwhich long jumps in space compete with longperiods of rest at successive locations. Wemodeled the process as a continuous timerandom walk5 (CTRW) in which spatial dis-placements are interspersed with random pe-riods of rest which are distributed accordingto a power law as well, i.e.

(2)with an exponent α < 1 . A powerlaw in thewaiting time usually leads to subdiffusivemotion as the total time elapsed scales withthe number of steps according to

TN ~N 1/α V which implies that the number ofsteps increase sublineary with time, i.e.N~T α .In combination with the scaling of po-sition with the number of steps such an am-bivalent CTRW scales with time according to

x( t)~ t α / ß

This implies that the superdiffusive dispersalis attenuated by the long periods of rest. Wewere able to compute the asymptotics for theprocess which is given by

Wr(x,t)=t–2α /ßLα ,ß(x/tα /ß)

φ (δT) ~1

δT 1+α

Figure 5: Probability p(r) of travelling a distance r

in a short time δT<4 days. In blue, green and redtrajectories with initial entries in large cities,

small cities and small towns respectively. Between 10 and 3500km p(r) is a powerlaw

with an exponent ß≈0.6.

Figure 4: Short time trajectories of

individual dollar bills thatwere inititally reported inSeattle (blue), New York

(yellow) and Houston (red).Lines connect the initial

entry location and thelocation where the bill was

reported less than a week after inital entry.


Projects


Nonlinear Dynamics

in which Lα ,ß is a universal scaling function ofthe process which depends on the two expo-nents only. Comparing to the data he foundthat for α=ß=0.6 the model agrees very wellwith the data (Fig. 6). The dynamical equation for this ambivalentCTRW has the form

∂tαW(x,t)=Dα , ß ∂ß

|x|W(x,t)

In which the ordinary derivates ∂ and ∂2x are

replaced by fractional generalizations ∂tα and

∂ß|x|. These operators are nonlocal singular in-

tegral operators accounting for the spatial andtemporal anomalies of the process. The dis-persal of money is the first example of such abifractional anomalous process in nature. Existing models for the geographic spread ofinfectious diseases can now be checked forconsistency with our findings and a new classof models for the spread of epidemics can beconceived which are based on our results.

[1] L. Hufnagel, D. Brockmann, and T.Geisel, Proceedings of the NationalAcademy of Sciences of the United States ofAmerica 101 (2004) 15124.[2] D. Brockmann, L. Hufnagel, and T.Geisel, in SARS: A Case Study in EmergingInfections A. McLean et al. eds. (OxfordUniversity Press, Oxford, 2005) 81.

[3] D. Brockmann, L. Hufnagel, and T.Geisel, Nature 439 (2006) 462.[4] Lévy flights and related Topics inPhysics, M.F. Shlesinger, G.M. Zaslavsky,and U. Frisch (Springer, Nice, France,1994).[5] E. W. Montroll and G. H. Weiss,Journal of Math. Physics 6, (1965) 167.

Figure 6: Scaling properties of the dispersalof bank notes and comparisonwith the continuous time randomwalk model. The data collapse on asingle curve indicates that theprocess of dispersal exhibitsspatio-temporal scaling x( t)~ t 1 / µ

with an exponent µ =1within atime window of 10 days to 1 year.The black solid line represents theuniversal scaling function Lα ,ß ofthe continuous time random walkmodel for exponents α=ß=0.6 .The agreement with the observedscaling function is striking.

A fluid is called ›complex‹ if its constituentsare complex systems on their own: the macro-molecules in a polymer melt, the lamellae in afoam, the (dissipative) grains in the granu-late, or the bio-molecules in the cytoplasm.Can one predict, on the basis of the propertiesof these building blocks, the dynamic behav-ior of the fluid (the liquid crystal, the poly-mer, the foam, the granulate, the biomater-ial)? Are there general principles behind theemergence of large scale properties? Can thestudy of driven complex fluids yield deeperinsight into the principles of systems far fromequilibrium? These are just some of the ques-tions which lead us in our studies of the dy-namics of complex fluids.Aside from such rather fundamental consid-erations, complex fluids have particularlystrong importance to technological applica-tions. Granular materials, for instance, coverthe full range from toy model systems for irre-versibility to practical applications like landslides, food technology and chemical engi-neering. Emulsions, similarly, may providemicro reactors for applications in ›discrete mi-crofluidics‹, but the complex internal topol-ogy of lipid lamellae, which form between thedroplets in a micro-channel, touches on yetunanswered questions in the mathematics offoam structures. Transformations in thesetopologies may be induced in a controlled

manner, if the lamellae consist themselves ofcomplex fluids, such as liquid crystals or fer-rofluids. Biological matter, like the actin inthe cytoplasm, is further example of a com-plex fluid in confined geometry, where themesoscale building blocks of the fluid interactstrongly with the geometry of the confine-ment. This interaction can sometimes bedescribed by means of surprisingly simpleconcepts.The various mechanisms of self-assemblyand self-organization, which drive the con-stituents of a complex fluid to arrange intostructures on larger scale, are both interestingas genuinely non-equilibrium phenomenaand promising as possible tools for generatingnovel systems by self-assembly. Once we un-derstand the static and dynamic principleswhich are at work in these processes, the de-sign of self-organized ›soft‹ nano-machinesmay come within reach, pointing to noveltechnologies for times to come.


Dynamics of Complex Fluids2.2

2.2.1 Overview

Dynamics of Complex Fluids

Stephan Herminghaus




Prof. Dr. Stephan Herminghauswas born on June 23, 1959 in Wiesbaden, Germany.He received his PhD in Physics from the University ofMainz in 1989. After a post-doctoral stay at the IBMResearch Center San José in California, he moved tothe University of Konstanz, where he obtained hishabilitation in 1994 and became a Heisenbergfellow in 1995. Later he started an independentresearch group at the Max Planck Institute forColloids and Interfaces in Berlin (1996) and

launched a DFG Priority Program on WettingPhenomena. He declined an offer of a fullprofessorship at the Université de Fribourg, CH. In1999, he was appointed as a full professor at theUniversity of Ulm, where he also headed theGraduiertenkolleg 328. Since 2003 he is a Directorat the Max Planck Institute for Dynamics and Self-Organization in Göttingen. In 2005, he wasfurthermore appointed as an adjunct professor atthe University of Göttingen.

Dr. Christian Bahrstudied Chemistry at the Technical University Berlinand received his PhD in 1988. Research stays andpostdoctoral work took place at the RamanResearch Institute (Bangalore, India) and theLaboratoire de Physique des Solides of theUniversité Paris-Sud (Orsay, France). After hisHabilitation for Physical Chemistry at the TechnicalUniversity Berlin in 1992, he moved in 1996 to thePhysical Chemistry Institute of the University

Marburg as a holder of a Heisenberg-Fellowship.2001-2004 he worked as a software developer inindustrial projects. In 2004 he joined the group ofStephan Herminghaus at the MPI for Dynamics andSelf-Organization. Research topics compriseexperimental studies of soft matter, especiallythermotropic liquid crystals, phase transitions,structures of smectic phases, thin films, interfacesand wetting.

Dr. Martin Brinkmannstudied Physics and Mathematics at the Free Univer-sity of Berlin between 1990 and 1998 where hereceived his Diploma in Physics. After an internshipat the Dornier Labs (Immenstaad, Lake Constance)in 1999 he joined the theory group of Prof.Reinhard Lipowsky at the MPI of Colloids andInterfaces (Potsdam, Germany) to work on wettingof chemically patterned substrates. In 2003 hereceived his doctorate from the University of

Potsdam. During a postdoctoral stay in theBiological Nanosystems Group at theInterdisciplinary Research Institute in Lille (France)he explored wetting of topographic substrates as apossible way to manipulate small liquid droplets.Since the beginning of 2005 he investigates wettingof regular and random geometries in thedepartment Dynamics of Complex Fluids at the MPIfor Dynamics and Self-Organization.

Dr. Manfred Faubelwas born on 27.3.1944 in Alzey near Mainz. Physicsstudies at the University of Mainz (diploma 1969),and in Göttingen (PhD in 1976). Postdoctoral staysat the Lawrence Berkeley Laboratory, 1977, and inOkasaki at the Institute for Molecular Sciences inJapan, 1981. Employed by the MPI fürStrömungsforschung since 1973. Molecular beamsstudies of rotational state resolved scattering crosssections for simple benchmark collision systems,

such as Li+-H2, He-N2 and for reactive F-H2 scattering.Since 1986 exploration of the free vacuum surfaceof liquid water microjets. Photoelectronspectroscopy of aqueous solutions withsynchrotron radiation at BESSY/Berlin (1999 topresent), and, by laser desorption massspectrometry of very large ions of biomoleculesfrom liquid jets in vacuum (in a collaboration withMPI-BPC).

2.2.2 People


Dr. Peter Heinigstudied physics at Leipzig University and receivedhis Diploma in 2000. As a PhD student at the Max-Planck-Institute of Colloid and Interface Science inGolm he investigated the structure formation andwetting of two-dimensional liquid phases inLangmuir monolayers in the presence of long rangeinteractions. After he received his PhD in 2003 fromPotsdam University, and a postdoctoral stay atFlorida State University in Tallahassee, he joined the

group of Dominique Langevin in Orsay as apostdoctoral fellow within the franco-germannetwork »Complex Fluids from 3D to 2D«. Duringthis time he studied the dynamics and rheology offree standing thin liquid films. Since September2005 he is a Postdoc at the Max-Planck-Institute forDynamics and Self-Organization.

Dr. Thomas Pfohlstudied Chemistry at the Johannes-GutenbergUniversity, Mainz, and received his doctorate inPhysical Chemistry from the University of Potsdamin 1998. After his postdoctoral research at theMaterials Research Laboratory, University ofCalifornia, Santa Barbara, from 1998 to 2000, hebecame a research assistant at the Department ofApplied Physics at the University of Ulm from 2000until 2004. In 2001 he received a research grant to

lead his »Independent Emmy Noether JuniorResearch Group« by the DFG. Since 2004 he isproject leader »Biological Matter in MicrofluidicEnvironment« at the Department »Dynamics ofComplex Fluids« at the Max-Planck-Institute ofDynamics and Self-Organization.

Dr. Ralf Seemann studied physics at the University of Konstanz wherehe received his diploma in 1997. The diploma workwas carried out at the Max Planck Institute ofColloids and Interfaces in Berlin-Adlershof. Hereceived his doctorate in 2001 from the University ofUlm where he experimentally studied wetting andrheological properties of complex fluids. During astay as postdoctoral researcher at the University ofCalifornia at Santa Barbara, he explored techniques

to structure polymeric materials on the micro- andnano-scale. In 2002 he joined the group of StephanHerminghaus at the University of Ulm. He receivedthe science award of Ulm in 2003. Since 2003 he is agroup leader at the Max Planck Institute forDynamics and Self-Organization, Goettingen.Among others he is concerned with wetting oftopographic substrates and discrete microfluidics.

PD Dr. Holger Starkreceived his doctorate in theoretical physics fromthe University of Stuttgart in 1993. He pursued hispostdoctoral research at the University ofPennsylvania in Philadelphia in 1994 to 1996 with aresearch fellowship from the DeutscheForschungsgemeinschaft. After his habilitation atthe University of Stuttgart in 1999, he received aHeisenberg scholarship in 2000. In the years 2001to 2005, he was teaching and pursuing his research

at the University of Konstanz, where he also held aprofessorship during the summer semester 2004.He spent several research visits in the USA andJapan. Since 2006, Holger Stark is a group leader atthe Max-Planck Institute for Dynamics and Self-Organization. He currently holds a professorship atthe Ludwig-Maximilians University in Munich to de-liver Sommerfeld Lectures during the summersemester 2006.

People



The physical peculiarities of granular matterstem from its inherently dissipative nature.The grains in a slightly fluidized granulate, asin an hourglass, have an average center-of-mass kinetic energy corresponding to a fewGiga-Kelvin or more. When two of them col-lide, part of the kinetic energy is transferred totheir internal atomic degrees of freedom: theGiga-Kelvin heat bath is intimately coupled tothe room-temperature bath of the atoms. This

extreme non-equilibrium situation is at theheart of most of the intriguing features ofgranular matter. In dry granulates, the dissipative processesare somehow ›hidden‹ in the momentary im-pact events. Wet granular matter, in contrast,provides its dominant dissipation by virtue ofthe hysteretic nature of the liquid bridgeswhich form between adjacent grains: whentwo grains touch each other, a liquid bridge isformed and exerts an attractive force due tothe surface tension of the liquid. However, forthe bridge to disappear again, the grains mustbe withdrawn to a certain critical distance.That this dissipation can be dramatic is wellknown from the difference between the drysand in the desert, which almost behaves like

a liquid, and the wet sand on the beach fromwhich one may sculpture stable sand castles.Quite surprisingly, the yield stress of the wetmaterial turns out to be remarkably inde-pendent of the liquid content. Detailed stud-ies of this finding, including x-ray tomogra-phy(cf.Fig. 1) and numerical simulation ofconstant mean curvature structures betweenspheres, are described in the subsequent proj-ect (2.2.3.2).

A useful toy model of wet granular gasesemerges if one considers just two-body hys-teretic interactions between ideal hardspheres [1,2]. This simple model has provedquite successful in explaining most of thecharacteristic features of a wet granular pile.In simulations, we have established thatmany features of granular matter fluidized byvertical agitation may be recovered. Fig. 2shows a simulation at three different times: atthe very beginning, when the pile is still atrest (left), after some time, when the systemis fully fluidized (center), and after an ex-tended period of time when a quite interest-ing phenomenon, the granular Leidenfrost ef-fect, has fully developed (right) [3]. Thismodel system also exhibits surface melting

Figure 1: Distribution of liquid in awet granular system, as seenby x-ray tomography. Shownare sections through a wetpile of glass beads atdifferent water content. Left: 1%; center, 5.3%; right, 7.5%. Different colorsindicate disjoint liquidclusters. At 5.3%, manyliquid clusters are fullydeveloped. At 7.5%, almostall liquid belongs to a singlecluster which extends overthe whole sample.

2.2.3.1 Wet Granular Matter and Irreversibility

Ralf Seemann, Martin BrinkmannAxel Fingerle, Zoé Fournier, Klaus Röller, Mario Scheel, Vasily Zaburdaev

2.2.3 Projects


and other features analogous to phase transi-tions, which are also observed in experi-ments.This model has a number of interesting prop-erties. Its internal energy is a continuousfunction of time, and thus also its phase spacetrajectory is continuous, such that it can bedealt with using the extensive mathematicaltools developed for dynamic systems [6]. Inparticular, it has been found that the recentlydeveloped fluctuation theorems seem to holdfor granular systems, although the latter donot fulfill time reversibility as required by thestandard formulations of fluctuation theo-

rems. In our system, we can follow in detailhow dissipation takes place and try to allevi-ate the conditions for the fluctuation theo-rems such as to understand why they may ap-ply at all to granular systems. Furthermore,wet granular materials provide a class ofmodels general enough to cover standardgranular physics as well as the dynamics ofsticky gases, which serve as toy models forthe formation of planetesimals from primor-dial clouds. We could show that at high at-tractive force, the limit of the sticky gas isreached, with all of the well-known scalingrelations recovered. Our model may be morerealistic, however, because impacts will neverbe perfectly sticky in reality. At smaller attractive force, a wealth of newphenomena, including a symmetry-breakingphase transition, are found when merely ob-serving the free cooling of this dissipative gas.This is shown in Fig. 3, which shows thenumber of clusters as a function of simulationtime for a one-dimensional wet granular gas.The dashed line represents the limit of thesticky gas, which approaches the well-known-2/3 scaling at large times. The solid line re-presents the simulation. It exhibits a conden-sation transition after a longer quiescentplateau phase. During the plateau, the systemcools down until its granular temperature

Figure 2 : Granular dynamics

simulation of a pile ofspheres wetted by a liquid.

At intermediate times(center), the pile is wellfluidized. At large times

(right), a Leidenfrost typephenomenon occurs, charac-

terized by a solid plughovering over a hot granular

gas layer.

Figure 3:The number of clusters

(defined as grains connectedby liquid bridges) in a freely

cooling one-dimensionalgranular gas, as a function of

simulation time. Thecharacteristic peak

corresponds to a phasetransition which occurs

when the granulartemperature comes of the

same order as the hystereticenergy loss scale.

Projects



Random assemblies, such as granular piles,textiles, fleece, or fur, are ubiquitous in na-ture, technology, and everyday life. Theyshare the common feature of changing theirmechanical properties dramatically in pres-ence of a wetting liquid. Some of them suchas the hairy cuticula of some plants (e.g.Mullein, Verbascum Densiflorum B.) are thusspecially designed to avoid such moistening[1]. Most types of sand, the granular materialpar excellence, can be modeled as a randomassembly of spherical particles. Other para-digmatic shapes like prolate ellipsoids orcylindrical rods describe larger classes of ob-jects and may even serve for modelling fiberassemblies.The astonishing stability of a sand-castle canbe explained by the presence of numeroussmall water bridges in wet sand which spanbetween adjacent grains [2]. The interfacialtension of the liquid-air interface and the neg-ative Laplace pressure in these small liquidstructures create a cohesive stress in the as-sembly. During shear, one observes discontin-uous transitions between different capillarystates of the liquid, in the simplest case therupture and re-formation of bridges. This

mechanism opens up an additional path ofenergy dissipation during external agitationwhich, in a certain range of grain sizes, domi-nates over other dissipative mechanisms suchas interparticle friction. The implications ofthe discrete amounts of energy lost in capil-lary transitions for the collective behaviour ofwet granular material are discussed in thepreceding project 2.2.3.1. In general, the me-chanical behaviour of a wet random assembly

comes within the energy scale of the capillarybridges. When this happens, the latter affectthe dynamics strongly and lead to clustering.Finally, the sticky limit is approached fromabove. When one replaces the hysteresis inthe interaction force by a fixed energy losswhich is applied at each impact of two grains,the plateau and the peak vanish, thus demon-strating the importance of the hysteretic char-acter of the force.

[1] S. Herminghaus, Advances in Physics 54(2005) 221. [2] M. Schulz, B. M. Schulz and S.Herminghaus, Phys. Rev. E 67 (2003) 052301. [3] K. Roeller, Diploma Thesis, Ulm 2005. [4] A. Fingerle, S. Herminghaus and V.Zaburdaev, Phys. Rev. Lett. 95 (2005) 198001.[5] G. Gallavotti and E. G. D. Cohen, Phys.Rev. Lett. 74 (1995) 2694.[6] C. Jarzynski, Phys. Rev. Lett. 78 (1997)2690.[7] E. Ben-Naim et al., Phys. Rev. Lett. 83(1999) 4069.

2.2.3.2 Statics and Dynamics of Wet Random Assemblies

Martin Brinkmann, Ralf SeemannMario Scheel, Zoé Fournier

K. Mecke (Erlangen), B. Breidenbach (Erlangen), W. Goedel (Chemnitz), M. DiMichiel (Grenoble,France), A. Sheppard (Canberra, Australia)

Figure 1: X-ray tomographies of wet assemblies of submillimetric glass spheres. Theinner diameter of the glass tube containing the sample is about 9mm.An aqueous NaI solution was used as the wetting liquid. The left image shows a slicethrough a sample, the right image is a projection of a three dimensional volumeimage (glass spheres and container are suppressed). Pendular bridges betweenadjacent spheres in contact appear as rings in the right image.

under a shear or compression will be linkedto the local geometry of the assembly whichgoverns the appearance of specific capillarystates and the transitions between them. Experimental techniques such as x-ray to-mography or fluorescence microscopy can beutilized to image the liquid clusters in a threedimensional assembly. A wet random assem-bly of spheres can be easily prepared fromslightly polydisperse, submillimetric glassbeads and water. Figure 1 displays x-ray to-mographies of such a wet assembly containedin a small glass tube. The most prominentstructures at low water content are donut-shaped pendular bridges which grow and co-alesce into larger liquid structures as the liq-uid content is increased [3]. Figure 2 illus-trates experimentally observed pendularbridges(a,b) and the smallest type of liquidclusters(d,e) found between the glass beads.Surprisingly, this energetically driven reor-ganization of liquid does not lead to notice-able changes in the mechanical strength ofthe wet assembly. A beak-down of the shearresistance is observed beyond the percolationof liquid clusters [2,4]. If buoyancy is negligible, which typicallyholds for sub-milimetric liquid structures, the

shape of a pendular bridge between twospheres can be expressed in terms of analyticfunctions. All capillary states, however,which wet three or more spheres cannot betreated analytically and their study demandsfor numerical methods. The cluster shape andimportant physical quantities like the Laplacepressure of the cluster or the capillary forcesacting on individual spheres can be obtainedfrom a minimization of the interfacial energy,cf. Figure 2(c) and (f). All of the experimen-tally identified classes of liquid clusters re-semble those found in regular packings. Thiscan be explained by the remaining shortrange order in random assemblies of spheres.The question for the unexpected mechanicalstability in the liquid cluster regime is linkedto the evolution of the Laplace pressure dur-ing changes of the liquid content. The pro-posed qualitative dependence of the Laplacepressure on the cluster volume is depicted inFigure 3. Numerical minimizations providean appropriate tool to find an answer to thisopen question.Random assemblies of slender cylindricalrods typically exhibit a much smaller spacefilling when compared to assemblies of spher-ical particles. Other typical properties such as

Figure 2: The series of images (a-c) show pendular bridges between sphericalbeads; images (d-f) display liquid clusters wetting three beads. Micrographs(a) and (d) are obtained by fluorescence microscopy. Three dimensional shapesin (b) and (e) are extracted from x-ray tomographies; the shapes depicted in (c)and (f) are the results of numerical minimization of the interfacial energy atfixed volume.


Figure 3: Schematic course of the Laplace pressure -P of capillary states in an assembly of spheres for anincreasing volume V. At small liquid volume onlypendular bridges can be formed. Discontinuoustransitions to larger liquid clusters occur at highervolumes. The Laplace pressure of these states,however, will fluctuate around a certain mean level(shown as the black dotted line).

Projects



[1] A. Otten and S. Herminghaus,Langmuir 20 (2004) 2405.[2] S. Herminghaus, Advances in Physics54 (2005) 221.[3] M. M. Kohonen et al., Physica A 339(2004) 7.[4] Fournier et al., J. Phys. Condens. Matter17 (2005) 477.[5] M. Brinkmann et al., Appl. Phys. Lett.85 (2004) 2140. [6] M. Brinkmann and R. Blossey, Eur.Phys. J. E 14 (2004) 79.[7] R. Seemann et al., Proc. Natl. Acad. Sci.USA 102 (2005) 1848.

a broad pore size distribution and the smallcorrelation between contact points on a roddistinguishes them from random assembliesof spheres. The most important feature, how-ever, is the anisotropic nature of the capillaryinteraction between cylindrical rods. In exper-iments, one observes a strong tendency of thewet rods to align and to form stable bundles.Numerical minimizations and analytical argu-ments show that the liquid can be found in lo-calized, droplet-like states or in elongateddroplets, which we call filaments, if the rodsare close to parallel orientation. Similardroplet morphologies are found in the geome-try of a rectangular slot [5]. The discontinu-ous transition between filaments and dropletstates can be triggered by a change in the tiltangle and leads to a dissipation of energy

without breaking bridges. As outlined in thesubsequent project 2.2.3.3 such transitionsbetween elongated and localized liquid con-figurations are a generic feature of dropletswetting linear surface topographies [6,7].

2.2.3.3 Wetting of Topographic Substrates

Ralf Seemann, Martin BrinkmannEvgeny Gurevich, Krishnacharya Khare , Konstantina Kostourou

R. Lipowsky (Potsdam), J.-C. Baret (Eindhoven, The Netherlands), M. Decré (Eindhoven, TheNetherlands), B. Law (Kansas, USA), E. Kramer (Santa Barbara, USA), F. Lange (Santa Barbara, USA)

Alternatively to conventional microflu-idics, we consider systems with free liquid-liquid or liquid-vapor interfaces, which maytherefore be called open microfluidic systems.An important advantage of open structures isthat they are easy to clean and the liquid isfreely accessible. The concept is to confineliquid to certain regions of the system, to keepit away from others, to transport it along pre-fabricated connection lines, and to mix it ondemand. We do this by offering an appropri-ate surface topography to the liquid. In thisapproach, one takes advantage of the fact thatthe affinity of the liquid to corners andgrooves is strongly different as compared toplanar surfaces. If, for instance, the intrinsiccontact angle between the liquid and the sub-strate material is sufficiently small, the liquidwill strongly prefer to wet steps [1] or grooves

[2]. We explore the static wetting morpholo-gies and their manipulation varying the wet-tability or geometry of the grooves. Depending on control parameters such as thecontact angle, the liquid volume, and thegeometry of the grooves, a rich morphologicalbehavior of liquid droplets of variable size(volume) can be found [2-4]. In case of rec-tangular grooves droplet like morphologies(D) can be found for large contact angles orshallow grooves. For decreasing contact angleor increasing aspect ratio liquid filamentswith positive (F+) and liquid filaments withnegative Laplace pressure (F-) can be foundin experimental and numerical results asshown in Fig. 1. These liquid morphologiesare in excellent agreement with the analyti-cally derived morphology diagram, which isdepicted in Fig.2. Similar wetting morpholo-

gies can be found for chemically structured,plane substrates where hydrophilic stripes aresurrounded by a hydrophobic matrix [5] andfor wetting morphologies on wet random as-semblies as described in the preceeding pro-ject. However, liquid morphologies on planarsubstrates always exhibit a positive Laplacepressure. This seriously restricts the applica-

bility of chemically patterned substrates toopen microfluidics. As described in the fol-lowing for rectangular grooves, topographicstructures provide considerable advantages. To transport liquid along topographic groovesit is necessary to change the physical proper-ties of these structures dynamically, such asto induce transitions between different liquidmorphologies. This can result, if conceivedproperly, in controlled liquid transport. More-over, electrowetting allows to reversiblychange the apparent contact angle of an elec-trically conducting liquid on a solid substrate.The variation of the contact angle can be aslarge as several 10°. To minimize electro-chemical effects we apply an ac-voltage. Ifone starts with a droplet like wetting mor-phology and increases the applied voltage,the length of the liquid filament shows athreshold behavior for the filling when theline of zero mean curvature in the morpho-logical diagram is approached, c.f. Fig. 3. Thefinite lengths of the liquid filaments can bedescribed by a voltage drop along the fila-ment using an electrical transmission linemodel [6]. Moreover, the length of the liquidfilament is sensitive to the chemical contentof the liquid. This behavior gives us an easyhandle to manipulate and transport liquidalong grooves or sense the ionic content of aliquid and might enable the construction ofcomplex and highly integrated open microflu-idic devices. In case of rectangular grooves, the liquid fila-ments reversibly grow and shrink in length asfunction of the applied voltage. The advanc-ing and receding dynamics that defines theminimum switching time of the liquid fila-ments can be described exclusively by capil-lary forces, assuming the electrowetting-con-tact angle to vary along the liquid filamentsaccording to the voltage drop along the fila-ment [7].Although it is easier to produce triangulargrooves, they can not as easily be used totransport liquid reversibly along prefabricatedgrooves. Retracting an elongated liquid fila-ment from a triangular groove into its reser-voir by ramping down the applied voltage


Figure 2: Analytically derived morphology diagram as a function of grooveaspect ratio X and material contact angle θ. The solid line between theareas (F+) and (F-) denote liquid morphologies with zero mean curvature. The symbols denote experimental results from AFM scans. All experimentaldetermined morphologies are fully consistent with the thoreticalclassification.

Figure 1: a) - c) Numerically generated wetting morphologies and d) - f)Scanning force micrographs of polystyrene droplets wetting atopographically structured substrate with rectangular cross section. a) +d) droplet morphologies (D). b) + e) liquid filaments, (F+), with positiveLaplace pressure, PL > 0. c) + f) liquid filaments, (F-), with PL < 0. Liquidmorphologies with θ < 45° are in coexistence with liquid wetting thelower corner of the grooves.

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fails. When the contact angle of a liquid fila-ment suddenly increases above the fillingthreshold, the liquid filament becomes dy-

namically unstable and decays into isolateddroplets with well defined preferred distance[8].

Figure 4: Preferred droplet distance resulting from the dynamicinstability of liquid filaments with positive mean curvature intriangular grooves. The experimental data are shown as red squareswhereas the solid line denotes the theoretical expectation. The wedge angle of the triangular groove is indicated as dotted line.Inset: Optical micrograph of polystyrene droplets with a well definedspacing in triangular grooves.

[1] M. Brinkmann and R. Blossey, Eur.Phys. J. E 14 (2004) 79.[2] R. Seemann et al., PNAS 102 (2005)1848.[3] R. Seemann, E. J. Kramer and F. F.Lange, New Journal of Physics 6 (2004)111. [4] T. Pfohl et al., Chem. Phys. Chem. 4(2003) 1291.

[5] M. Brinkmann and R. Lipowsky, J.Appl. Phys. 92 (2002) 4298. [6] J.-C. Baret, M. Decré, S. Herminghaus,and R. Seemann, submitted to Langmuir.[7] J.-C. Baret et al., Langmuir 21 (2005)12218.[8] B. Law, E. Gurevich, M. Brinkmann, K.Khare, S. Herminghaus, and R. Seemann,submitted to Langmuir.

Figure 3: Spreading of liquid into grooves withrectangular cross section by electrowetting. Dueto the slanted interface only the fronts of theliquid channels are visible in the optical micro-graphs. The dataset in b) shows the length ofliquid filaments as function of the appliedacvoltage for various frequencies, which collapseon a single master curve when scaled with thefrequency of the applied ac-voltage. Fitting thetheoretical model to the master curve yields theconductivity of the liquid.

We employ monodisperse emulsions to com-partment liquids for microfluidic processing.Using this approach, some inherent problemsof conventional microfluidic systems, wheresingle phase liquids are transported throughmicrochannel networks, can be circum-vented[1]: for instance, axial dispersion canbe suppressed entirely due to the nature ofthe droplets carrying various chemical con-tents as individual compartments. And sec-ond, mixing of two components can be

achieved within each droplet separately, andis found to proceed quite efficiently by thetwisty flow pattern emerging within dropletswhen they are moved through a wavy chan-nel system [2]. If the volume fraction of thecontinuous phase is reduced to a few percentonly, the emulsion is called gel-emulsion dueto its macroscopic rheological properties.Here, the dispersed droplets (compartments)assemble to a well-defined topology, analo-gous to foam. Accordingly, the position of asingle droplet with a certain chemical contentis fully determined within an ensemble ofdroplets while being transported through mi-crofluidic channels.To control the volume of the compartmentsprecisely and to guarantee a well defined›foam like‹ structure for a given confiningchannel geometry, it is mandatory to usedroplets with excellent monodispersity. Wedeveloped a one-step, in situ method for theproduction of monodisperse gel emulsions,suitable for microfluidic processing [2], seeFig.1. The to be dispersed phase is injectedinto the continuous phase where it is guidedin a shallow channel and stabilized by thesurrounding continuous phase and the chan-nel walls. When the confining bottom wall›vanishes‹ at a topographic step, the continu-ous stream of the phase to be disperseddecays into single droplets. This step-emulsi-fication technique allows the in situ produc-tion of monodisperse gel-emulsions with vol-ume fraction up to 96%. The mutual proxim-ity of the single droplets, which follows fromthe small volume fraction of the continuousphase, allows for selectively induced coales-cence to initiate chemical reactions betweenadjacent compartments. This can be done byapplying a voltage pulse between two adja-cent droplets via electrodes intergrated into amicrofluidic channel, as shown in Fig. 2 [3].For aqueous droplets on the micrometer

Figure 2: Emulsion droplets united in a bamboo structure selectively coalesced byapplying a voltage between electrodes. The bright middle part shows the gapbetween the electrodes.


2.2.3.4 Discrete MicrofluidicsRalf Seemann

Craig Priest, Enkhtuul Surenjav, Magdalena Ulmeanu, Dmytro MelenevskyyT. Salditt (Göttingen), A. Griffith (Strasbourg, France)

Figure 1: Fabrication ofmonodisperse (gel-)emulsions in-situ in a

microfluidic device via stepemulsification. a) The streamof the to be dispersed phase

is stabilized between thecoflowing continuous phaseand the channel walls. At the

topographic step, theconfining bottom wall is

›removed‹ and the stream ofthe phase to be dispersed

breaks up into monodispersedroplets. b) + c) in-situ

fabricated gel-emulsion with75% and 93% dispersed

phase volume fraction,respectively.

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range, the diffusive mixing after coalescencewill occur on a millisecond time scale leadingto a well defined trigger for studying reactionkinetics. The motion of a gel emulsion in a solid chan-nel system is mainly governed by two physi-cal aspects of the system. One is the dynamicsof thin liquid films and three-phase contactsat solid surfaces, which has been investigatedin many studies in recent years [4-9]. Theother aspect concerns the mechanical proper-ties of the gel emulsion itself. It is well knownthat for rather dry foams, which correspondto small continuous phase volume fraction inour case, move within pipes by plug flow.This is due to the finite threshold stress re-quired to deform the foam network (e.g., thefinite energy required for a T1-transition).The flow resistance of the foamy emulsion ina channel with spatially constant cross sec-tion is thus solely determined by the interac-tion of the contact lines and Plateau borderswith defects at the walls, and by the flow re-sistance in the thin liquid films at the wall.However, when the channel (or pipe) geome-try is temporarily changed, or when thefoamy emulsion flows along a channel the

cross section of which varies along its axis,interesting topological transformations withinthe single compartments can be induced asdepicted in Fig. 3. If the shape of the channelis tailored appropriately, controlled manipula-tion of the emulsion droplets by the channelgeometry may be achieved, in order to posi-tion, sort, exchange, compile and redistributeliquid compartments, possibly with differentchemical contents. Besides the passive manipulation of foam liketopologies by the channel geometries, westudy the active manipulation of the resultingtopology by external stimuli. Figure 4 showsthe transition of a two row structure to a bam-boo structure, and the selective guiding ofdroplets by applying a magnetic field using aferrofluid as continuous phase, which is sen-sitive to magnetic fields. Replacing the fer-rofluid by a liquid crystal, the emulsion issensitive to temperature because the struc-ture of the continuous phase is depending ontemperature, as described in greater detail inthe subsequent project.Our approach may be called discrete mi-crofluidics, and is well suited for extensiveapplications in combinatorial chemistry, DNA

Figure 3:Interaction of mono-disperse gel-emulsions witha confining geometry. a) Depending on the ratioof channel to droplet size,the droplets are either splitin half at the y-junction, or afoam like topology with twoor more rows can beseparated or assembled likea zipper. b) 160° corner: thesequence of droplets is notaffected by the channelgeometry c) 140° corner: thesequence of droplets of thetop row is changed by oneposition relative to thebottom row.

[1] K. Jacobs, R. Seemann, and H.Kuhlmann, Nachrichten aus der Chemie 53(2005) 302.[2] C. Priest, S. Herminghaus and R.Seemann, Appl. Phys. Lett. 88 (2006)024106.[3] C. Priest, S. Herminghaus and R.Seemann, submitted to, Appl. Phys. Lett.[4] R. Seemann, S. Herminghaus and K.Jacobs, Phys. Rev. Lett. 86 (2001) 5534.[5] R. Seemann, S. Herminghaus and K.

Jacobs, Phys. Rev. Lett. 87 (2001) 196101.[6] S. Herminghaus, R. Seemann and K.Jacobs, Phys. Rev. Lett. 89 (2002) 056101.[7] J. Becker et al., Nature Materials 2(2003) 59.[8] R. Seemann, et al., J. Phys.: Condens.Matter 17 (2005) S267.[9]C. Neto et al., J. Phys.: Condens. Matter15 (2003) 3355.[10] T. Pfohl et al., Chem. Phys. Chem. 4(2003) 1291.


Figure 4: Using a ferrofluid as

continuous phase a) a tworow topology can be

switched to a bamboostructure by applying a

magnetic field. The localfield strength is indicated bythe white bars. b) Using thesame effect, droplets can be

selectively guided to anoutlet by applying a

magnetic field.

sequencing, drug screening, and any otherfield where similar chemical reactions have tobe induced with a large number of differentmolecules involved. Experiments to study thepolymerization of e.g. collagen as a functionof pH value are in preparation and explainedin project 2.2.3.8. Moreover, the lamellae can be used as confin-

ing geometry e.g. for lipids that form mem-branes in case the continuous phase volumefraction is minute. The usage of this well de-fined membrane topology in order to studythe exchange of molecules between singlecompartments or for the analysis of the lipidsby scattering techniques [10] is described inproject 2.2.3.6.

Projects



2.2.3.5 Wetting and Structure Formation at Soft Matter InterfacesChristian Bahr

Vincent Designolle, Wei Guo

The structure of soft matter systems is easilyinfluenced by external fields and forces. Forexample, a weak electric field is able tochange the molecular alignment, and thus theoptical properties, of a nematic liquid crystalphase. The presence of an interface may acton soft matter systems like a localized fieldand accordingly the structure near an inter-face often differs from the structure of the cor-responding volume phase. In many cases,such as the free surface of thermotropic liquidcrystals [1], this behaviour is especially pro-nounced near phase transitions, where onemay observe a spatially differentiated coexis-tence of two phases, one of which being pre-ferred by the interface. Understanding the be-havior of soft matter at interfaces is importantnot only from the viewpoint of basic researchbut also for many applications; examplesrange from emulsion paint over printer inkand liquid crystal displays to membrane sys-tems for drug delivery.This project is concerned with soft matter sys-tems containing thermotropic liquid crystalsas one component. The liquid crystal compo-nent provides an ›extra ingredient‹ to thesesystems namely the various phases and phasetransitions that are present in these materials.One emphasis of the project is the study ofthe interface between liquid crystals and wa-ter or aqueous surfactant solutions near thephase transitions of the liquid crystal. The re-sults will be of importance for basic aspects ofwetting as well as for the development of newsystems to be utilized in discrete microflu-idics. A second focal point is the study of liq-uid crystal nanostructures which are gener-ated by antagonistic boundary conditionsand/or spatial confinements which are pres-ent in, e.g., open microfluidic channels. For the study of liquid crystal/water inter-faces a phase-modulated ellipsometer wasconstructed and a suitable sample cell wasdesigned which enables the preparation of aplanar interface between the two volume

phases. First measurements were conductedwith the liquid crystal 8CB (octylcyano-biphenyl) at the interface to pure water andaqueous solutions of the surfactant CTAB(hexadecyltrimethylammonium bromide) inthe temperature range around the nematic –isotropic transition of 8CB (TNI=41°C). Ourresults [2] show, that at temperatures aboveTNI the interface is covered by a nematic wet-ting layer provided that the aqueous phasecontains CTAB with a concentration ca≥0.8µM. The thickness of the nematic layer showsa divergence-like increase when the volumetransition temperature TNI is approached fromabove and this behaviour becomes more pro-nounced with increasing surfactant concen-tration (Figure 1).The experimental data were analyzed withinthe framework of a phenomenological model,in which the Landau-de Gennes theory of thenematic – isotropic transition is extended by alinear coupling of the nematic order parame-ter to an ordering surface field V. Data ob-

tained for different ca values could be de-scribed by the Landau model by adjusting thevalue of V only, with all other parameters re-maining unchanged. In other words, the sur-factant concentration can be used for a directcontrol of the ordering interface field V. Therelation between V and ca is clearly nonlinear(Figure 2) and can be described by a fittingfunction which has the form of a Langmuir

Figure 1:Temperature dependence ofellipticity coefficient ρ andBrewster angle θB at theinterface between thethermotropic liquid crystal8CB and aqueous CTABsolutions with concen-trations ca = 0.8 µM (a), 3 µM(b), and 30 µM (c). TNI

designates the nematic -isotropic transitiontemperature of the volumeliquid crystal phase.

[1] R. Lucht and Ch. Bahr, Phys. Rev. Lett.78 (1997) 3487; R. Lucht et al., J. Chem.Phys. 108 (1998) 3716; R. Lucht, Ch. Bahrand G. Heppke, Phys. Rev. E 62 (2000)2324. [2] Ch. Bahr, Phys. Rev. E 73(2006)030702(R).[3] H. Stark, J. Fukuda and H. Yokoyama,Phys. Rev. Lett. 92 (2004) 205502; J.Fukuda, H. Stark and H.Yokoyama, Phys.Rev. E 69 (2004) 021714.[4] Q. Lei and C. D. Bain, Phys. Rev. Lett.92 (2004) 176103; E. Sloutskin et al.,Faraday Discuss. 129 (2005) 339. [5] V. Designolle et al., Langmuir 22(2006) 363.

adsorption isotherm indicating that the mag-nitude of V is linearly related to the amount ofadsorbed surfactant.Temperature and surfactant concentration en-able thus a comprehensive control of thestructure of the liquid crystalline interfacelayer which separates the two isotropic vol-ume phases. We will use this result for the de-velopment of new systems to be employed indiscrete microfluidics applications (for detailsconcerning discrete microfluidics see the pre-vious project) in which liquid crystal com-pounds are used as continuous phase of gelemulsions. For example, a gel emulsion ofwater droplets in an isotropic liquid crystalcould be prepared in which the lamellae sepa-rating the water cells can adopt an either liq-

uid crystalline or isotropic structure (depend-ing on temperature and surfactant concentra-tion); in this way even gel emulsions withsmectic lamellae could be prepared althoughit is hardly possible to disperse water dropletsin a smectic volume phase. Our results arealso of relevance for basic aspects of wetting,recent theoretical work [3] on wetting layersin isotropic liquid crystals (described in moredetail in project 2.2.3.10), and surfactant-in-duced interface transitions in other systemslike n-alkanes [4].Besides the study of liquid crystal/water in-terfaces we investigate structure formation inliquid crystal phases induced by antagonisticboundary conditions and/or spatial confine-ment. An example is the modulation of thesmectic-A/air interface by focal conic defectsin thin smectic films on silicon substrates. Afocal conic defect, which is generated by op-posite molecular alignment conditions at thesmectic-A/air and smectic-A/substrate inter-face, consists of an arangement of curvedequidistant smectic layers and leads to a de-pression of the free surface (Figure 3). UsingAFM we have measured the depression depthh as a function of temperature for differentsmectic compounds. Our results [5] showthat the behaviour of h strongly depends onthe type of the high-temperature phase abovethe smectic-A phase (nematic or isotropic)and on the nature of the corresponding phasetransition (second-order or first-order).


Figure 3: a) Schematic sketch of thesmectic layer structure in afocal conic defect which is

formed above a circulararea with diameter 2r inwhich the molecules are

aligned parallel to thesubstrate (at the air

interface, the moleculesalign always perpendicular

to the interface). b) AFM image of defect-

induced depressions in thesmectic-A/air interface.

The depth of thedepressions amounts to

250 nm, the lateraldimension of the shown

area is 25 µm.

a)

b)

Projects

Figure 2: Relation between interface

potential V and CTABconcentration ca in the

aqueous volume phase. Thesolid line is a fit using a

function possessing theform of a Langmuir

adsorption isotherm.

In biological cells, membranes act as barri-ers between reaction compartments and con-trol the transport of substances between cellorganelles, the cytoplasm and the environ-ment. The transport properties of biologicalmembranes are highly specific and are con-trolled by a number of different parameters,as electric potentials or concentration gradi-ents. The aim of this project is to make use ofthese membrane properties in order to controlinteractions between single reaction compart-ments, as for example water droplets in a wa-ter-in-oil (W/O) emulsion, fabricated usingmicrofluidic devices. Furthermore, the poten-tial of novel experimental methods for theanalysis of objects immersed in membranes,such as transmembrane proteins or nanos-tructures, is investigated. Gel-emulsions are emulsions with a smallvolume fraction of the continuous phase andform foam like structures with planar lamel-lae separating the emulsion droplets. A fur-ther decrease of the amount of continuousphase results in a thinning of the lamellae,possibly until a single bilayer of surfactantmolecules remains (Fig. 1). In order to studysingle lamellae in microchannels under staticand dynamic conditions, a microfluidic de-vice has been used (Fig. 2): In a cross-junc-tion of channels, water droplets in oily sur-roundings have been brought into contactsuch that a planar lamella is formed. The de-sign allows to apply an electric potentialacross the lamella and to measure the filmthickness by impedance measurement or theusage of voltage sensitive dyes. It was foundthat the thickness of the lamella depends onthe substances used and on the applied pres-sure. For this reason, the experimental conditions,under which black membranes are formed,were studied separately using the thin-film-technique developed by Scheludko. This

technique is commonly used to investigatefree standing liquid films. The film is formedin a circular opening within a porous plateand a pressure between the film phase andsurrounding phase is applied. The setup al-lows to observe the formation kinetics of thinfilms [1,2] and to precisely measure the filmthickness in dependence of the disjoiningpressure. Here, a Scheludko-setup has beenbuilt using a porous Teflon plate (porosity~10µm) and the oily film has been observedin aqueous surroundings using optical mi-



2.2.3.6. Membrane Assembly for NanosciencePeter Heinig, Ralf Seemann

Craig Priest, Magdalena Ulmeanu

Figure 1: Sketch of twoemulsiondroplets of awater-in-oilemulsion form-ing a blackmembrane

Figure 2: Microfluidicdevice forinvestigatingsingle lamellaein micro-channels.

croscopy. First experiments show that somesystems, as for example tetradecane/mono-olein/water, form stable black membranes. Closely packed monodisperse emulsions formcrystalline structures and exhibit a high geo-metrical order. This property of ›emulsioncrystals‹ can potentially be used for X-raystructure analysis of objects immersed in thelamellae between droplets or Plateau bordersof the crystal. It is obvious that the monodis-persity of the emulsion, as well as a precisecontrol of the thicknesses of the lamellae, isof crucial importance. The fabrication ofmonodisperse emulsions with a low volumefraction of the continuous phase is subject ofproject 2.2.3.4. Here, the rotating cup tech-nique has been applied (Fig. 3): The aqueousphase flows through a hydrophobized glass

capillary into a cup containing the oily phaseand a surfactant. Rotating the cup with con-stant angular velocity exposes the water toshear flow and highly monodisperse emul-sions can be created, reducing the polydisper-sity to less than 2% [3]. Oily phase from thegenerated emulsion was then removed byplacing it on a porous Teflon plate and by ap-plying an underpressure such that oil slowlyflows out of the emulsion. Figure 4 shows theformation of planar lamellae in a regularemulsion structure using water/tetrade-cane/monoolein. The functionality of theselamellae will be tested by adding ion channelproteins, which penetrate the lamellae assoon as black membranes are formed. Thelamellae then become permeable for specificions, and ion transport can be detected for ex-ample utilizing fluorescent ion indicators alsoused in project 2.2.3.8. Other microfluidic de-vices which allow to create monodisperseemulsions and to precisely control the vol-ume fraction of the continuous phase are un-der construction.


Figure 3: Rotating cuptechnique for

the fabricationof

monodisperseemulsions. Wa-

ter flowsthrough a

capillary in arotating cup

containing theoily phase.

Figure 4: Planar

lamellae in awater /tetra-

decane/monooleinemulsion.

The barrepresents

50 µm.

[1] P. Heinig and D. Langevin, Eur. Phys. J.E 18 (2005) 483.[2] P. Heinig, C. Márquez Beltrán and D.Langevin, Phys. Rev. E in press.[3] P.B. Umbanhowar, V. Prasad and D.A.Weitz, Langmuir 16 (2000) 347.

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The distinct physical properties and physico-chemical processes of liquid surfaces are de-termined ultimately by atomic phenomenaand molecular forces in liquids. Yet, macro-scopic measurements, even on scales rangingdown to nanometers, provide only very indi-rect and averaged information on individualmolecules in a liquid solution [1,2]. For atom-istic studies of the state and of the arrange-ment of individual molecules in an aqueoussurface we use photoelectron spectroscopy(Fig. 1a) which provides binding energies ofindividual atomic orbital energy levels for iso-lated molecules or solvated ions in the liquidfrom the analysis of the photoelectron kineticenergy spectra. In addition, the atomic or mo-lecular density of molecules in a liquid solu-tion can be determined by an intensity meas-urement of the atom-specific photoelectronemission lines. It has a surface layer probingdepth of approximately 0.5 nm.The photoelectron energy can be measuredwith high precision by deflecting the emittedphotoelectrons in well defined electrostaticfields in a vacuum environment (Fig. 1b).Thisis in conflict with the notable, high water va-por pressure of aqueous liquids (~10 mbar)and, therefore, a very thin, fast flowing, liquidjet was developed as a vacuum exposed freeliquid water surface. Sufficiently narrow liq-uid water jets, with diameters smaller thanmean free path in water vapor, evaporate invacuum without the occurrence of molecularcollisions and/or electron scattering or soft x-ray photon absorption events in the emergingvapor cloud. Because the experimental freevacuum surface of liquid water can be only afew 10 µm wide, a photon source with highbrilliance is required, which became availablerecently with modern synchrotron photonsources for the energy range of interest, be-tween 15 eV<hν <1000 eV. The principalsetup scheme for the liquid water jet photo-

electron spectroscopy is illustrated in Figure1b [1].Examples for synchrotron radiation photo-electron spectrum measurements on liquidwater are presented in Figure 2 [3]. The neatwater spectrum (bottom) is composed of theliquid water surface spectrum and of a contri-bution from the water vapor cloud evaporat-ing from the room temperature liquid jet. Itshows the four different valence bond elec-



2.2.3.7 Spectroscopy of Aqueous Surfaces

Manfred FaubelB. Winter (Berlin), I.V. Hertel (Berlin), P. Jungwirth (Prag, Czech R.), S. Bradforth (Los Angeles, USA),

B. Abel (Göttingen), A. Charvat (Göttingen)

Figure 1: Photoelectron emission from valence bands of molecules or frominner core electron energy levels of atoms can be used to determine thebinding energies and density of states distributions of all bound stateelectrons in a target (a). The electron binding energy is the differencebetween the incident photon energy and the observed photoelectron kineticenergy, BE =hν – Ekin. In chemically bond atom states and in condensed matterelectron binding energies show bonding specific energy shifts, calledchemical shift or solvation shift. They are induced by the electronic nature ofthe molecular interaction forces. For measurements on liquid aqueoussolutions with high vapor pressure (> 8 mbar for pure water at 0 C) a liquid mi-cro-jet with less than 10 µm diameter is used to maintain collision freemolecular beam vacuum conditions in the vapor cloud emerging from theliquid surface (b). The kinetic energy spectrum of emitted photoelectrons ismeasured in ultrahigh vacuum by an electrostatic electron energy analyzer.Intense, focused, monochromatic synchrotron radiation with 30 eV to 1000 eVphoton energy is used for the photoemission spectroscopy.

tron energy levels of the H2O moleculemarked by the upper scale insert in Fig. 2. Thenarrow peak designated 1b1g is a water vaporfeature. A pure vapor phase spectrum ismeasured separately and can be subtracted.The liquid phase spectrum exhibits a consid-erable broadening of the four principal or-bitals by the inhomogeneous molecular envi-ronment of the liquid water. In addition, theaverage liquid ionization peak energies arelowered by 1.6 to 1.9 eV with respect to thegas phase, which is theoretically understoodas a consequence of the condensed phase sur-roundings with a high dielectric constant. A more complex case for salt ion solvation inliquid water is investigated in Figure 2 (mid-dle and top) in photoelectron spectra from a 2mol solution of NaI, and for a 0.025 mol solu-tion of the surface active tetra-butyl-ammo-nium iodide salt (TBAI)[3]. The latter is sur-face enriched by a factor of 80 as compared tothe iodine in the ›normal‹ salt aqueous NaIsolution, and shows a very strong enhance-ment of the I– anion photoelectron peak inten-sity in relation to the absolute salt con-centration. A most remarkable and, still,unexplained experimental result is the inde-pendence of the observed electron bindingenergy of a given ion (Cl–, Br–, l–, Li+, Na+, K+,Cs+) with changing concentration of thesolute salt in aqueous solution and with dif-ferent counter-ions [4].


Figure 2: Photoemission spectra of (bottom) liquidwater, and (middle) 2 m NaI and (top) 0.025 m TBAI

aqueous solution measured at 100 eV photon energy.Ion emission is labeled. Electron binding energies arerelative to vacuum, and intensities are normalized to

the electron ring current. Nearly identical iodidesignals are observed for the two salt solutions, even

though the concentration of the surfactant is a factor80 lower. Energy differences of I¯(4d) peak positions

for the two solutions are not observed.

Figure 3 (Left): Snapshots from molecular dynamics simulations showing theinterfacial distribution of sodium cations and halide anions for the alkalihalide aqueous solutions. (Right) Plot of the respective number densitiesρ(z) of water oxygen atoms and ions vs distance z from the center of the slabsin the direction normal to the interface, normalized by the bulk waterdensity, ρ b. The colors of the curves correspond to the coloring of the atomsin the snapshots. Important to notice is that the small sodium cations arealways depleted from the surface, as is also true for the small fluoride anions.However, for increasing anion size and hence polarizability, the propensity ofanions to exist at the solution surface increases. For NaI solution, the two iondistributions are separated by ca. 3 Å.

Projects



Surface enrichment of solvate negative halo-gen ions was recently also investigated in anoceanographic context and is understood bynew molecular computer simulations of liq-uid aqueous salt solutions including ion po-larizability contributions to intermolecularforces in electrolyte solutions by Jungwirth[5]. Examples for computed salt ion distributionsnear the surface of a simulated liquid slab arepresented in Figure 3 for several alkali-halideaqueous solution systems. Theoretical elec-tron binding energies for individual anionsand cation species, also, were derived fromthis liquid aqueous solution simulation. Thusfar, these agree qualitatively with the liquidjet photoelectron spectroscopy experimental

data [6]. The ongoing analysis of the remain-ing discrepancies will lead to improvementsin the understanding of the intermolecularpotential models used in aqueous liquid solu-tion modelling.

[1] B. Winter and M. Faubel, ChemicalReviews, 2006, Web release date: March 8,2006 106, 1176.[2] D. Chandler, Introduction to ModernStatistical Mechanics, Oxford UniversityPress, 1987.[3] B. Winter et al., J. Phys. Chem. B 108(2004)14558.[4] R. Weber et al., J. Phys. Chem. B 108(2004) 4729.[5] P. Jungwirth and D. J. Tobias, J. Phys.Chem. B 105 (2001) 10468.[6] B. Winter et al., J. Am. Chem. Soc. 127(2005) 7203.

2.2.3.8 Biological Matter in Microfluidic EnvironmentThomas Pfohl

Rolf Dootz, Heather Evans, Sarah Köster, Alexander Otten, Dagmar SteinhauserM. Abel (Potsdam), J. Kierfeld (Potsdam), S. Roth (Hamburg), B. Struth (Grenoble, France)

J. Wong (Boston, USA)

Remarkable progress has been achieved inthe integration and analysis of chemical andbiological processes on the nanoliter-scale byusing microfluidic handling systems. Suchsystems require less reagent, resulting in amore efficient and cheaper experimentaldesign, and have led to advances in theminiaturization of biological assays and com-binatorial chemistry. Furthermore, due to theinteresting physics of fluid flow on the micro-and nanoscale, microfluidics constitute apowerful tool in particular for the investiga-tion of biological systems, whose dimensionsare generally also on these length scales. Ourexperiments are focused on the flow behaviorof individual macromolecules and the self-as-sembly of biological materials in micro- andnanochannels. These experiments enablestudies of the influence of geometric confine-

ment on static as well as dynamic propertiesof biological materials [1,2]. Our examinations of the self-assembly of indi-vidual biomolecules and their dynamics inmicroflow environments aim to better under-stand a variety of molecular properties, such

Figure 1: Single fluctuating actin filaments confined in parallel straight microchannels(left, width of 6 µm) and curved microchannels (right, width of 2.5µm).


as persistence length and bundle dimensions,in ambient conditions. Therefore, we analyzethe influence of confining geometries on ther-mal fluctuations of actin by means of fluores-cence microscopy. Actin is a semiflexible bio-logical macromolecule found within eukary-otic cells, and is responsible for a variety ofprocesses such as cellular motility and in par-ticular cellular morphology, as actin is a pri-mary component of the cytoskeleton. Fluores-cence microscopy is particularly well suited,in combination with a pulsed laser illumina-tion setup and CCD camera, for the collectionof image sequences whereby the fluctuationsof actin filaments can be quantified and sub-sequently analyzed. Furthermore, we observethe behavior of individual molecules (actin)and other objects (e.g. lipid vesicles) in spe-cific flow fields which are generated by thegeometries of the microfluidic devices. Theflow fields of channels containing a variety ofstructures, for example hyperbolic or zig-zaggeometries, can be precisely calculated usingfinite element method simulations [1,3]. Ad-ditionally, more complex mixing designs, forexample a reagent gradient, can be generatedby specific microfluidic designs. In caseswhere a reactant is added from the side chan-nels, measurements along the main jet streamprovide snapshots of the biomolecular inter-actions as a function of time. The dynamics offilament bundling and cytoskeletal networkformation can be observed in situ, as a conse-quence of the well-defined addition of linker

proteins to individual actin filaments withinmicrochannels. The evolution and non-equilibrium dynamicsof self-assembly processes of biological mate-rials in microflow can be studied on the mi-cro-, meso-, and nanoscale using characteri-zation techniques such as fluorescence mi-croscopy, as discussed previously, as well asother complementary methods such as confo-cal Raman microscopy and X-ray microdif-fraction. [4,5] The latter technique is particu-larly advantageous in studies of biomole-cules. Firstly, the X-ray beam is microfocusedsuch that the beam is only 20 µm in diameterat the sample. The small beam size permitsthe acquisition of X-ray patterns at specificspatial positions along and perpendicular to amicrochannel. Secondly, improved diffractionsignals are acquired owing to the increasedflux of the X-ray beam as well as the orienta-tion of the molecules within the microchan-nel. Finally, the collection of data in mi-croflow conditions significantly reduces is-sues regarding radiation damage of thebiomolecules. DNA condensation is a topic of biological aswell as physical interest, especially with re-spect to the hierarchical compaction of cellu-lar DNA into chromosomes via histone pro-teins. Crossed microchannel devices are usedto explore the interaction of DNA with his-tone-proteins as well as models for such moi-eties [6]. Hydrodynamic focusing of a stream

Figure 2: a) Overlay of the velocity field calculated by finite element methodsimulations and snapshots of an individual actin filament in elongational flow withendpoints and midpoints labeled 1,2,3 (channel width 40µm). b) Normalized extension Rij/Ls versus strain rate calculated combining experimentalresults and simulations.

Figure 3: Schematic representation of the scanningX-ray microdiffraction setup.

Projects

of a semidilute DNA solution can predictablystretch and orient the biomolecules, enablingthe study of the influence of confinement onstatic and dynamic properties of DNA [5].The compaction of DNA is initiated via theaddition of macroions (e. g. polyimine den-drimers) through the side channels, whereinthese molecules diffuse into the focusedstream at a rate proportional to their distancealong the reaction channel. By varying theobservation position along the microchannel,the evolution of the compaction process is ob-servable. Using X-ray microdiffraction we areable to obtain data of DNA nanostructureswith very high spatial resolution within a mi-crofluidic device [4,5]. The comparison of thecompaction of the DNA by histone-proteinswith model-histone-proteins can help to clar-ify to what extent the wrapping of DNA

around histones occurs ›actively‹ due to thespecial chemical structure of the histone-pro-teins, as opposed to the pure electrostatic in-teraction of negatively charged DNA withpositively charged macroions. Recently, we have extended our investiga-tions to studies of collagen and fibrin, twoubiquitous extracellular filamentous proteins.A pH-gradient generated in microfluidic de-vices results in the hierarchical self-assemblyof collagen, and the formation of collagen fib-rils can be predicted as a function of pH val-ues that are calculated using finite elementmodeling [7]. Using optimized microchannelgeometries, it is possible to form droplets ofaqueous materials in oil (see project 2.2.3.4).In the case of collagen, droplets of the proteinin monotonically increasing pH concentra-

tions can be formed in continuous flow condi-tions, permitting the controlled study of pHeffects on collagen fibril formation in a partic-ularly efficient design. Fundamental investi-gations of fibrin, the main protein in bloodclotting or hemostasis, probe the dynamic as-sembly of the protein as a function of a vari-ety of interaction parameters. The use of fib-rin ›compartments‹ also has many advan-tages, principally to dramatically reduce therequired volumes needed to extensivelyquantify effects of reactant concentrations onfibrin formation. The marriage of state-of-the-art microfluidic technologies with biologicalmacromolecules provides a virtually endlesssupply of notable subjects and new opportu-nities to answer fundamental biophysicalquestions.



[1] T. Pfohl et al., Chem. Phys. Chem. 4(2003) 1291.[2] M. C. Choi et al., Proceedings of theNational Academy of Sciences of the USA(PNAS) 101 (2004) 17340.[3] S. Köster, D. Steinhauser and T. Pfohl ,Journal of Physics: Condensed Matter 17(2005) S4091.

[4] A. Otten et al., Journal of SynchrotronRadiation 12 (2005) 745. [5] R. Dootz et al., Journal of Physics:Condensed Matter 18 (2006) 639.[6] H. M. Evans et al., Phys. Rev. Lett. 91(2003) 075501.[7] S. Köster et al., MRS Proceedings 898E(2005) 0989-L05-21.

Figure 4: The hydrodynamic focusing enables a time resolved analysis of the non-equilibrium dynamics of DNA compaction induced by polyvalent ions. 2-D X-raydiffraction patterns of the evolution of DNA compaction can be obtained with aspatial resolution of 20µm.


When we think about locomotion, we areguided by our everyday experience in amacroscopic world. However, there existmuch more organisms which move in the mi-croscopic world in an aqueous environment;one prominent example is the Escherichia Coli(E. coli) bacterium in the human stomach.When we swim, we drift by inertia. However,these organisms do not know inertia. As soonas they stop their swimming stroke, they alsostop moving. Due to the micrometer lengthscale, water appears very viscous to them; soReynolds number is very small and micro-or-ganisms had to invent mechanisms to moveforward that might look rather strange to us[1]. Within the newly founded priority pro-gram SPP1207 of the Deutsche Forschungsge-

meinschaft with the title Strömungsbeeinflus-sung in Natur und Technik, T. Pfohl, H. Stark,and their groups aim to contribute to the un-derstanding of the principles governing themotion of micro-organisms, the fluid trans-port on a micrometer scale, and biomimeticmaterials.According to Purcell [2], micro-organismshave to perform a periodic non-reciprocal mo-tion in time to move forward at very lowReynolds numbers. This means, under timereversal the motion is not the same. Sperm

cells, e.g., use a beating elastic filament,called flagellum, to propel themselves. Theparamecium possesses on its surface a wholecarpet of shorter filaments, now called cilia,whose collective motion in the so-calledmetachronal waves pushes it forward. Ciliaare also employed for fluid transport in thenose and lung, and to develop the left-rightasymmetry of the embryo at an early stage.Certain bacteria, e.g., E. coli, move forwardwith the help of a bundle of helical filamentsdriven by a marvelous nano motor. The proto-zoan African trypanosome propels itself by ascrewing motion of the whole chiral body.The group of H. Stark has recently addressedthe question where the bundling of the helicalflagella of E. coli bacteria comes from [3]. AsFig. 1 illustrates, to form a bundle the rota-tions of the single helices must be highly syn-chronized. We investigated if hydrodynamicinteractions, i.e., interactions due to the flowfields the rotating helices generate aroundthemselves (see next project), could be thereason for such a synchronization. We there-fore constructed two parallel rigid helicesfrom a sequence of spheres and drove themby constant and equal torques. We indeedfind that the helices synchronize to a phasedifference zero as in Fig. 1. However, it is im-portant that their orientations can jigglearound in space since strictly parallel helicesdo not synchronize. So synchronization isonly achieved when the helices possess someflexibility. In our case, it might mimic the flex-ibility of the hook connecting the flagellum tothe rotary motor.The flagella of sperm cells or cilia are drivenby internal motors [1]. The group of J. Bibettefrom the ESPCI in Paris has deviced a bio-mimetic flagellum or cilium that is insteadeasily actuated by an external magnetic field[4]. They take superparamagnetic particles ofmicron size that form a chain in a magneticfield. They then link the particles together

2.2.3.9 Locomotion in Biology at Low Reynolds NumberThomas Pfohl, Holger Stark

Erik Gauger, Michael Reichert, Eric StellamannsJ. Bibette (Paris), M. Engstler (München)

Figure 1:Two rotating helices can

only form a bundle whentheir rotations are highly

synchronized.

Projects



with, e.g., double-stranded DNA to obtain anelastic filament. Attached to a blood cell, theresulting swimmer is actuated by an externalmagnetic field with oscillating direction. Wehave modeled this artificial swimmer using abead-spring model that also possesses thebending energy of an elastic rod [5]. One ac-tuation cycle is illustrated in Fig. 2. Our nu-merical study helps to identify the optimumswimming speed and efficiency as a functionof magnetic field strength and frequency. Thesuperparamagnetic elastic filament can alsobe attached to a surface and, with an appro-priate time protocol of the magnetic field tocreate a non-reciprocal motion, used to trans-port fluid.In collaboration with the geneticist MarkusEngstler, LMU Munich, the group aroundT. Pfohl studies the influence of Africantrypanosome motility on the directionalmovement of proteins within its plasmamembrane. Trypanosomes have ingeniouslyadapted to their extreme environment by ac-tually exploiting for their survival the hostileflow conditions of the mammalian blood-stream. Evolution has provided these unicel-lular flagellates with a unique cell surface

coat consisting of a single type of variant sur-face glycoprotein (VSG). Host-derived anti-bodies are rapidly removed from the VSG

coat. The Engstler group has shown that a co-ordinated action of directional cellular motil-ity and plasma membrane recycling is neces-sary and sufficient for rapid removal of host-derived antibodies from the trypanosome cellsurface. We found that immunoglobulins at-tached to VSG act as molecular sails. Hydro-dynamic flow acting on the swimming cell se-lectively drags antibody-bound proteinswithin the plasma membrane towards theposterior pole of the cell, from where they arerapidly internalised by the localised andhighly efficient endocytosis machinery [6].Therefore, we develop microfluidic systemsfor mimicking the attack of host-derived anti-bodies as well as their removal in hydrody-namic flow. Surface protein movement andtrypanosome motility are simultaneously vi-sualized and measured using three-dimen-sional microscopy.

Figure 2: One actuation cycle of the simulated artificial swimmer. The superparamagneticelastic filament (blue) tries to follow the oscillating magnetic field (red arrow). Due to thefriction with the surrounding fluid, the filament bends and performs a ›paddle‹ motion. As a result, the load (yellow) is transported to the right.

[1] D. Bray, Cell Movements: FromMolecules to Motility, 2

nded., Garland

Publishing, New York (2001)


Colloidal dispersions consist of particlessuspended in a liquid or gaseous environ-ment. As milk, paint, fog, and drugs, theyplay an important role in our everyday life.Even the cell with its crowded constituents isregarded as a colloidal dispersion. A wholezoo of interactions like the electrostaticYukawa potential or depletion forces whoseproperties can be fine-tuned and also the factthat colloids strongly interact with light fields,e.g., in optical tweezers, make them an idealmodel system for statistical mechanics and toexplore the non-equilibrium. Colloids dis-persed in a complex fluid such as a nematic

liquid crystal experience new types of interac-tions that give rise to prominent structure for-mation into chains, hexagonal crystals, andcellular materials.

Hydroynamic InteractionsParticles suspended in a liquid are in constantBrownian motion or they move under the in-fluence of external forces. In both cases, theycreate a long-ranged flow field around them-selves that in turn influences the motion ofneighboring particles. These hydrodynamicinteractions (a complicated many-body prob-lem) constitute an inherent property of any

Figure 4: Schematic representation of amodel for estimation of the drag forceacting on a single VSG-antibodycomplex

Figure 3: Schematic drawing of the proposed mechanismof antibody removal. Top: host-derived antibodiesrecognise the variant surface glycoprotein (VSG) coat.Mid: hydrodynamic flow acting on the swimmingtrypanosome pushes the antibody-bound VSGs (VSGIgG)to the posterior cell pole. Bottom: from the flagellar pocketmembrane VSGIgG is internalized by the highly efficientendocytosis machinery (courtesy of M. Engstler).

[2] E. M. Purcell, Am. J. Phys. 45 (1977) 3.[3] M. Reichert and H. Stark, Eur. Phys. J. E. 17(2005) 493.[4] R. Dreyfus et al., Nature 437 (2005) 862.

[5] E. Gauger and H. Stark, submitted to Phys. Rev. E[6] M. Engstler, T. Pfohl, S. Herminghaus, M.Boshart, G. Wiegertjes, and P. Overath in prepara-tion

2.2.3.10 Colloids In and Out of EquilibriumHolger Stark

Andrej Grimm, Matthias Huber, Michael Reichert, Michael SchmiedebergC. Bechinger, C. Lutz, J. Roth (Stuttgart), T. Gisler, S. Martin, G. Maret, K. Sandomirski (Konstanz),

J. Bibette (Paris, France), J. Fukuda, H. Yokoyama (Tsukuba, Japan), T. Lubensky (Philadelphia, USA),A. Mertelj (Ljubljana, Slovenia), M.-F. Miri (Zanjan, Iran)

Projects

colloidal dispersion even of swarming bacte-ria. It is therefore of interest to explore theirproperties in detail. Together with S. Martin and T. Gisler, our ex-perimental colleagues from the University ofKonstanz, we have devised a method to ex-plore especially the hydrodynamic couplingof translating and rotating spheres [1,2]. Fig-ure 1 illustrates the correlated translationaland rotational motion of nearby birefringentparticles trapped in optical tweezers. This ex-perimental verification of our theoretical pre-dictions [2] is the first explicit demonstrationof hydrodynamic interactions between trans-lating and rotating spheres.Hydrodynamic interactions mediate collec-tive motions that can be periodic or even tran-siently chaotic. To explore this property, weconsidered particles that circle on a ringdriven by a constant force. A linear stabilityanalysis reveals that regular clusters of thesehydrodynamically interacting particles (e.g.,three particles forming an equilateral trian-gle) exhibit a saddle-point instability, how-ever only when they are allowed to makesmall excursions into the radial direction [3].Three particles enter a characteristic limit cy-cle as illustrated in Fig. 2. Adding a strongenough sawtooth potential to the constantdriving force creates a tilted potential land-scape with potential wells [4]. Whereas a sin-gle particle now performs a ›stick-slip‹ mo-tion, two neighboring particles use hydrody-namic interactions to move in a deterministic›caterpillar-like‹ motion over the potentialbarriers that is initiated or terminated by ther-mal fluctuations. This illustrates that the sys-tem is an excellent model to study non-equi-librium processes.

Liquid-Crystal ColloidsReplacing the isotropic host liquid of colloidaldispersions by an anisotropic fluid such as anematic liquid crystal (where rodlike mole-cules align on average along a common direc-tion also called director) introduces an ap-pealing system whose new phenomena haveintensively been studied in recent years [5]. Together with colleagues from Japan, we

used the Landau-Ginzburg-de Gennes free en-ergy functional to demonstrate that wettingphenomena above the isotropic-nematicphase transition [6], as illustrated in project2.2.3.5, also occur around colloidal particles[7]. They can even be used to constructtetravalent colloids that could arrange intocolloidal crystals with diamond lattice struc-ture known to possess a large photonic bandgap [8].Between two partices a bridge of condensednematic phase forms close to the nematic-isotropic phase transition (see Fig.3) [9].These capillary bridges induce a very strongtwo-particle interaction, as verified by carefulexperiments of a group from Ljubljana. It alsoshows hysteresis similar to the one intro-duced in project 2.2.3.1. If the surfaces of theparticles do not induce strong nematic order-ing, theory and experiments demonstrate theoccurrence of a weaker Yukawa interaction.



Figure1: Translation-rotation crosscorrelation of two sphericalbirefringent particlestrapped in optical tweezers.At equal times, the particles’positions and orientationsare not correlated sincethere are no staticinteractions. With increasingtime difference, correlationsdue to hydrodynamicinteractions build up andultimately decay to zero(experimental data, courtesyof S. Martin and T. Gisler,University of Konstanz).

Figure 2: Characteristic limit cycle ofthree colloidal particles(bright) driven along acircular trap in counter-clockwise direction. The trapand the constant drivingforce are realized by a fastlyspinning optical tweezer(experimental data, courtesyof C. Lutz and C. Bechinger,University of Stuttgart).

Colloidal Adsorbates on QuasicrystallineSubstrates

Together with colleagues from the Universityof Stuttgart [J. Roth (theory) and C. Bechinger(experiment)], we have proposed a projectthat uses colloids as model system to studyhow quasicrystalline substrates enforce the

controlled growth of quasicrystalline films.Quasicrystals possess a long-range positionalorder with a non-crystallographic point groupsymmetry such as a five-fold symmetry axis.Besides having been a subject of intense fun-damental research that explores the new fea-tures of quasicrstals, they are also of techno-


Figure 4: A Brownian particle in a two-dimensional quasicrystalline potential (created by thesuperposition of five plane waves along the edges of a pentagon, see inset) exhibits subdif-fusion over several decades in time where it explores the complex potential landscape to reachthermal equilibrium (lower red curve). It then enters normal diffusion (not shown). Withincreasing phasonic drift velocity (indicated by the arrow), the subdiffusive regime vanishesand the particle assumes a normal diffusive regime with a much larger diffusion constantcompared to the static potential.

Figure 3: Two-particle interaction potential as a result of the formation of a bridge of conden-sed nematic phase (see inset) above the nematic-isotropic phase transition. A typical energyunit for 350 nm particles is 1500 thermal energies. Starting from the nematic-isotropic phasetransition, temperature increases with the arrow.

Projects



logical importance due to their good corro-sion resistance, low coefficient of friction, andgood wear-resistance.Based on the Alexander-McTague theory formelting and on Monte-Carlo simulations, weexamined the influence of a one-dimensionalquasicrystalline substrate potential on thestructure of the ›adsorbed‹ colloids [10]. Wefind the following interesting but counterintu-itive feature: a rhombic (distorted trigonal)phase that forms under the influence of thesubstrate potential melts again when the po-tential strength is further increased. Ab-solutely crucial for the melting is the quasi-periodicity of the substrate potential. Still thestructure of the resulting ›modulated liquid‹needs to be explored.

Besides phononic hydrodynamic modes (uni-form translations for zero wave vector), qua-sicrystals also possess phasonic degrees offreedom. Due to a uniform ›phasonic drift‹ ina two-dimensional quasicrystalline potential(created by the superposition of five planewaves along the edges of a pentagon), localminima appear and vanish continuously. Fig-ure 4 demonstrates how a Brownian particlein such a dynamic potential landscape be-haves. The phasonic drift constantly pumpsenergy into the particle and keeps it far fromequilibrium. We currently explore how thissystem can be used to study fundamentalquestions arising far from thermal equilib-rium.

[1] A. Mertelj et al., Europhys. Lett. 59 (2002) 337;M. Schmiedeberg and H. Stark, Europhys. Lett. 69(2005) 135.[2] M. Reichert and H. Stark, Phys. Rev. E 69 (2004)031407.[3] M. Reichert and H. Stark, J. Phys.: Condens.Matter 16 (2004) S4085.[4] C. Lutz et al., Europhys. Lett. 74 (2006) 719.[5] H. Stark, Phys. Rep. 351 (2001) 387; P. Poulin etal., Science 275 (1997) 1770 .

[6] H. Stark, J. Fukuda and H. Yokoyama, J. Phys.:Condens. Matter 16 (2004) S1911. [7] J. Fukuda, H. Stark and H. Yokoyama, Phys. Rev.E 69 (2004) 021714.[8] M. Huber and H. Stark, Europhys. Lett. 69 (2005)135.[9] H. Stark, J. Fukuda and H. Yokoyama, Phys. Rev.Lett. 92 (2004) 205502.[10] M. Schmiedeberg, J. Roth and H. Stark, submit-ted to Phys. Rev. Lett.

Nonlinear out-off-equilibrium systems im-pact all levels of our everyday lives from ecol-ogy, sociology and economics, to biology,medicine, chemistry and physics. Typicallythese systems show self-organization andcomplex, sometimes unpredictable spatio-temporal dynamics. Although different in de-tail, the temporal and spatial structure ofthese systems can often be described by uni-fying principles. Searching for and understanding these princi-ples is at the center of our group’s research.To achieve this goal, we are focusing on well-defined problems in the physics of fluid dy-namics, of cellular biology, and of materials.Currently we are investigating experimentallyand theoretically pattern formation and spa-tiotemporal chaos in thermal convection. Incollaboration with researchers from the Inter-national Collaboration for Turbulence Re-search, we study particle transport in the fullydeveloped turbulence of simple and complexfluids with its implication to fundamental the-ories, but also to practical issues like turbu-lent mixing and particle aggregation. We col-laborate with cardiologists at the VeterinarySchool at Cornell University and the HeartCenter at the University of Göttingen in theinvestigation of the dynamics of the mam-malian heart at the cellular and organ scale.In collaboration with groups at the University

of California at San Diego, Cornell University,and Göttingen we conduct experiments inbiophysics and nano-biocomplexity using mi-cro-fluidic devices to probe and to understandthe spatio-temporal dynamics of intra-cellularand extra-cellular processes. In material sci-ence/geophysics we are investigating withina wax-model spatio-temporal processes thatresemble the dynamics of Earth’s mid-oceanridges. Our research has been and will continue to betruly interdisciplinary from engineering, ma-terial science, geophysics, and applied mathe-matics, to chemistry, biology, and medicine. Itfits well into the collaborative structure of theinstitute with Nonlinear Dynamics on the oneside and Dynamics of Complex Fluids on theother.On the following pages each individual topicwill be shortly discussed to give a more de-tailed picture of the research programs of theLaboratory of Fluid Dynamics, Pattern Forma-tion and Nanobiocomplexity.


Fluid Dynamics, Pattern Formation and Nanobiocomplexity

2.3

2.3.1 Overview

Eberhard Bodenschatz




2.3.2 People

Prof. Dr. Eberhard Bodenschatz

received his doctorate in theoretical physics from

the University of Bayreuth in 1989. In 1991,

during his postdoctoral research at the

University of California at Santa Barbara, he

received a faculty position in experimental

physics at Cornell University. From 1992 until

2005, during his tenure at Cornell he was a

visiting professor at the University of California at

San Diego (1999-2000). In 2003 he became a

Scientific Member of the Max Planck Society and

an Adjunct Director (2003-2005)/ Director (since

2005) at the Max Planck Institute for Dynamics

and Self-Organization. He continues to have

close ties to Cornell University, where he is

Adjunct Professor of Physics and of Mechanical

and Aerospace Engineering (since 2005).

Dr. Carsten Beta

studied Chemistry at the Universities of

Tübingen and Karlsruhe and at the Ecole

Normale Supérieure in Paris (France). In 2001,

he joined the Department of Gerhard Ertl at the

Fritz Haber Institute of the Max Planck Society in

Berlin and in 2004 received his doctorate in

Physical Chemistry from the Free University

Berlin. He then moved to the USA as a

postdoctoral research fellow in the group of

Eberhard Bodenschatz at Cornell University and

as a visiting scientist at the University of

California at San Diego. He is currently a group

leader at the Max Planck Institute for Dynamics

and Self-Organization in Göttingen.

Barbara Kasemann

Born in Schmallenberg, Germany. Professional

training as biological technical assistant (BTA) at

the Marine Fishery Regional Office in Albaum.

Fabrication of monoclonal antibodies related to

neuron degenerative diseases at Boehringer

Mannheim. Subsequently, project manager for

cell culture and animal experiment models at the

Fraunhofer Inst. for Biomed. Engineering IBMT,

St. Ingbert. Research and development on CD 34

cells at a subsidiary of ASTA Medica,

Frankfurt/M. Controlling and quality manage-

ment (GMP) in a biotech. comp., focusing on the

development of transplant techniques for blood

stem cells. Research laboratory manager at the

MPI for Dynamics and Self-Organization and

deputy representative/coordinator for the

institute’s new building and research facilities.

Dr. Stefan Luther

received his doctorate in experimental physicsfrom the University of Göttingen in 2000. From2001–2004, he was a research associate at theUniversity of Enschede, The Netherlands,where he worked on turbulent multiphaseflow.Since 2004, he is group leader at the MaxPlanck Institute for Dynamics and

Self-Organization and visiting scientist at Cornell University, Ithaca NY, USA.In July 2006 he will move to Göttingen.

Dr.-Ing.Holger Nobach

received his doctorate in electrical engineering

from the University of Rostock in 1997. During his

postdoctoral research, between 1998 and 2000

on an industrial research program with Dantec

Dynamics in Copenhagen and between 2000

and 2005 at the Technical University of

Darmstadt, he developed measurement

techniques for flow investigations. Since 2005 he

is a scientist at the Max Planck Institute for

Dynamics and Self-Organization. He works on

experimental investigation of turbulent flows

with improved and extended optical

measurement systems at the Cornell University.

In July 2006 he will move to Göttingen.

Dr. Nicholas T. Ouellette

originally from Cambridge, Massachusetts,

received his B.A. with High Honors in Physics

and Computer Science from Swarthmore

College in 2002. He did his graduate work in

Physics at Cornell University working with

Eberhard Bodenschatz studying Lagrangian

particle tracking in intense turbulence, receiving

his Ph.D. in 2006. He will continue to work on

Lagrangian turbulence in both Newtonian and

dilute polymer solutions as well as the dynamics

of heavy particles in turbulence at the Max


Organization.

Dr. Gabriel Seiden

Born in Haifa, Israel. Earned his B.A. degree in

physics in 2000 from the Technion-Israel

Institute of Technology, where he also studied

for his direct-track PhD in physics. His

dissertation theme was the phenomenon of

pattern formation in rotating suspensions. He is

currently a postdoc researcher working with

Eberhard Bodenschatz at the Max Planck

Institute for Dynamics and Self-Organization. His

current research is on optical forcing in Rayleigh-

Bénard convection and wax modeling of plate

tectonics.

Dr. Dario Vincenzi

received his Ph.D in Physics from the University

of Nice–Sophia Antipolis in 2003. His

dissertation work dealt with turbulent transport.

In 2004, he was lecturer at the Department of

Mathematics of the University of Nice–Sophia

Antipolis. In January 2005, he became a member

of the Max Planck Institute for Dynamics and

Self-Organization, Göttingen, and joined the

Bodenschatz group as a post-doctoral research

associate in the Laboratory of Atomic and Solid

State Physics at Cornell University. He is currently

working on theoretical modeling of dilute

polymer solutions and viscoelastic flows.

In July 2006 he will move to Göttingen.

Dr. Haitao Xu

received his Ph.D in Mechanical Engineering

from Cornell University in 2003. His dissertation

work is on collisional granular flows. In

September 2003, he joined Eberhard

Bodenschatz group as a pos-doctoral research

associate in the Laboratory of Atomic and Solid-

State Physics at Cornell University and worked on

experimental investigation of fluid turbulence.

In July 2006, he becomes a member of the Max


Organization, Göttingen.

People


People

From systems as varied as the pumping ofblood in the heart to the formation of clouds,to the dynamics of the interstellar medium,turbulence dominates fluid flow in the worldaround us. And yet, even though turbulenceimpacts a whole host of scientific fields, welack a complete understanding of the subject. Fluid flow can be described in two compli-mentary ways: the Eulerian perspective con-siders the motion of the fluid as it sweeps pasta fixed point in the flow, while the Lagrangianperspective follows the motion of individualparcels of fluid. Eulerian measurements havebeen possible for many years, and have pro-vided a great deal of insight into the structureof turbulence. On the basis of Eulerian meas-urements, a rich phenomenology of turbu-lence has been developed. The Lagrangianperspective, however, is more fundamentalfor many problems in turbulence, both practi-cal and basic [1]. Relating Eulerian and La-grangian measurements is currently an un-solved problem, in a large part because La-grangian measurements have not beenpossible until very recently.Our group has pioneered the use of high-speed particle tracking for Lagrangian meas-urements, first by adapting the silicon stripdetector technology used in high-energy par-ticle accelerators [2-4] and more recently byusing high-speed commercial digital cameras[5,6]. We use these systems to track the si-multaneous motions of hundreds of tracerparticles added to a flow (Fig. 1). Under suit-able conditions, these tracer particles are verygood approximations to true fluid elements,giving us direct Lagrangian information. By analyzing the statistics of pairs of tracerparticles, we have recently revisited the old

problem of pair dispersion in turbulence [6].Pair dispersion is a fundamental componentof turbulent mixing and transport. In turbu-lence the mean-square separation of a particlepair will grow faster than what would be ex-

Figure 1: Particle tracks measured byour camera system in intenseturbulence.



Figure 2: The time evolution of the mean-square particle separation. Weobserve clear power-law scaling. Data are shown for fifty different initialpair separations. When we simply plot the mean-square separation intime, we find many different curves (inset). When we scale by Batchelor’spredicted t2 power law, we find an excellent scale collapse.

2.3.3.1 Particle Tracking Measurements in Intense TurbulenceHaitao Xu

Kelken Chang, Holger Nobach, Nicholas T. OuelletteL. R. Collins (Cornell, USA), M. Kinzel (Darmstadt), Z. Warhaft (Cornell, USA)

International Collaboration for Turbulence Research

2.3.3 Projects

pected from Brownian motion. Richardson fa-mously predicted that, at small scales, itshould in fact grow as the third power of time[7]; subsequently, Batchelor refined Richard-son’s work, identifying a regime in which theinitial separation of the particle pair remainsimportant and where the mean-square sepa-ration should grow as time squared [8]. In our

measurements in intense laboratory turbu-lence, we have found excellent agreementwith Batchelor’s t2 law, with no hint ofRichardson’s law (Fig. 2). These results sug-gest that significantly more intense turbu-lence, perhaps more intense than exists any-where naturally on Earth, would be requiredto observe a significant Richardson regime.Our results have important implications fordesigners of models of pollutant transport orweather modeling.Turbulence is generally modeled as a cascadeprocess, where energy is injected into theflow at large length and time scales and cas-cades down to smaller scales where it is con-verted to heat by molecular viscosity. In theintermediate range of scales where the energyloss is negligible, known as the inertial range,the statistics of the turbulence are expected tobe universal for all turbulent flows, regardlessof the large-scale forcing or geometry. Kol-mogorov’s phenomenological model, knownsimply as K41, has been very successful in ex-plaining inertial range statistics [9], but in thepast several decades strong discrepancieshave been found with the K41 model for high-order Eulerian statistics. These discrepanciesare attributed to the ›burstiness‹ of turbu-lence, a phenomenon known as intermit-tency. Deviations from the K41 model are typ-ically measured from the statistics of thestructure functions, namely the moments ofthe velocity increments. K41 predicts that thestructure functions should scale as powerlaws in the inertial range; this behavior is re-produced in experiments and simulations,but the exponents of the power laws are sig-nificantly different from the K41 predictions.We have recently measured the Lagrangianstructure function scaling exponents (Fig. 3),and have also found strong intermittency ef-fects [10].Many models have been proposed to accountfor intermittency. One of the most successfulreinterprets the turbulent cascade as a multi-fractal process, implying that turbulent en-ergy transfer has a fractal structure with awhole spectra of allowed fractal dimensions.Using our particle tracking system, we have

Figure 4: Directly measured multifractal dimension spectra shown forthree different turbulence levels. The solid, dashed, and dot-dashed linesare previously-proposed models.

Figure 3: Scaling exponents of the Lagrangian structure functions in theinertial range as a function of structure function order. The solid line isthe K41 prediction; the strong deviation of the measured scalingexponents from the K41 prediction shows the effects of intermittency.Data is shown for three different turbulence levels; open symbols denotedata points that may not be fully statistically converged.


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recently measured multifractal dimensionspectra (Fig. 4), and have found more featuresin the dimension spectrum than were pre-dicted [11].In the future, we will extend our particletracking techniques to new flows, such as theGöttinger Wind Tunnel, as well as to thetracking of heavy particles, of great interest tothe cloud physics community. We are alsostudying the effects of long-chain polymers,known to reduce turbulent drag at bound-aries, on bulk turbulence.

[1] P. K. Yeung, Annu. Rev. Fluid Mech. 34(2002)115.[2] A. La Porta et al., Nature 409 (2001) 1017.[3] G. A. Voth et al., Rev. Sci. Instr. 12 (2001) 4348.[4] G. A. Voth et al., J. Fluid Mech. 469 (2002) 121.[5] N. T. Ouellette, H. Xu, and E. Bodenschatz,Exp. Fluids 40 (2006) 301.[6] M. Bourgoin et al., Science 311 (2006) 835.[7] L. F. Richardson, Proc. R. Soc. Lond. A 110(1926) 709.[8] G. K. Batchelor, Q. J. R. Meteorol. Soc. 76(1950) 133.[9] A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30(1941) 301.[10] H. Xu et al., Phys. Rev. Lett. 96 (2006) 024503.[11] H. Xu, N. T. Ouellette, and E. Bodenschatz,Phys. Rev. Lett. 96 (2006)114503.

2.3.3.2 Development of Fluid Dynamics Measurement Techniques

Holger NobachKelken Chang, Nicholas T. Ouellette, Haitao Xu

S. Ayyalasomayajula (Cornell, USA), M. Kinzel (Darmstadt), C. Tropea (Darmstadt)

Experimental investigations of fluid me-chanics and the verification of statistical tur-bulence models require measurement tech-niques that allow access to the fundamentalflow quantities. Time series of the flow veloc-ity can be measured with pressure tubes andhot-wire probes. To measure more quantities,like temporal or spatial derivatives, extendedmeasurement probes are required. With amulti-hot-wire probe (five arrays with fourhot-wires and one cold-wire each [1,2]) it ispossible to measure the velocity fluctuationvector, all nine components of the spatial ve-locity gradient tensor and all three temporalvelocity derivatives. However, these measure-ment techniques strongly affect the flow fielddue to the presence of measurement probesinside the flow.Modern optical measurement techniques likeLaser Doppler Velocimetry (LDV, Fig. 1) orParticle Imaging Velocimetry (PIV, Fig. 2) al-low the access to flow quantities without dis-turbing the flow field. Based on the observa-tion of small tracer particles, the LDV tech-nique provides a time series of the velocity ina small measurement volume, while the PIV

technique yields an instantaneous, spatiallyresolved flow field. For both techniques thereexist extensions of the basic principles that al-low the measurement of all three velocitycomponents, spatial derivatives or time-aver-aged, spatial statistics. However, these techniques are restricted tomeasurements at fixed points in space (Euler-ian measurements). To measure Lagrangianstatistics, individual particle tracks must befollowed in time and space simultaneously.This can be realized with a high-speed parti-cle imaging and tracking systems, consistingof several digital high-speed cameras as em-ployed in our laboratory ([3], Fig. 3). Here we develop improved LDV and PIV sys-tems to provide complimentary measure-ments to the hot-wire probes and the particletracking measurements. For both techniques,LDV and PIV, recent developments [4-6] showthat the measurement of particle accelerationas an additional quantity is possible. Main is-sues for both techniques are the improvementof the accuracy and the resolution (temporal,spatial as well as in signal amplitude).In case of PIV, image deformation techniques

Figure 1: Laser Doppler Velocimetry

Figure 2: Particle Image Velocimetry

Figure 3: High-speed Particle Imaging and Tracking

have the potential to improve the spatial reso-lution [7-9]. Unfortunately, even with ad-vanced windowing techniques that remove it-eration instabilities [10], we recently foundambiguities that yield strong fluctuations ofthe estimated velocity field and, hence, limitthe accuracy [11]. In order to overcome thislimitation and to realize better spatial resolu-tion of the PIV technique, the reason of thisambiguity must be identified and methodsmust be found, which are robust against thisinfluence [12,13].The laser Doppler measurement of particleacceleration would give a much-needed alter-native to particle tracking techniques. In col-laboration with the TU Darmstadt, we wereable to successfully use a commercial LDVsystem to measure both, particle velocity andacceleration in backward scatter [14-16]. Be-cause of the small measurement volume of anLDV system, the alignment procedures andthe signal processing require the highest pos-sible accuracies. Only this allows for accelera-tion measurement with sufficient resolution.Our first test measurement of the probabilitydensity of particle accelerations in a turbu-lence tank quantitatively agrees with the pre-vious measurement of the Bodenschatz groupusing silicon strip detectors (Fig. 4). This newtechnique now provides an alternative meas-urement system, which can be used atsmaller flow scales. Although the system per-formed well there is much room for improve-ments. In addition, the system needs to bemodified so that it can be used inside the Göt-tinger High Pressure Turbulence Tunnel.

[1] A. Tsinober, E. Kit, and T. Dracos, J.Fluid Mech. 242 (1992) 169.[2] A. Tsinober, L. Shtilman, and H.Vaisburd, Fluid Dyn. Res. 21 (1997) 477.[3] N.T. Ouellette, H. Xu, and E.Bodenschatz, Exp. in Fluids 40 (2006) 301.[4] B. Lehmann, H. Nobach, and C.Tropea, Meas. Sci. Technol. 13 (2002) 1367.[5] K.T. Christensen and R.J. Adrian, InProc. 4th Int. Symp. on PIV ’01, Göttingen,Germany, paper 1080 (2001).[6] P. Dong et al., Exp. in Fluids 30 (2001)626.[7] H. Nobach, N. Damaschke, and C.Tropea, Exp. in Fluids 39 (2005) 299.


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[8] H. Nobach et al., In Proc. 6th Int.Symp. on PIV ‘05, Pasadena, California,USA (2005).[9] H. Nobach and C. Tropea, Exp. inFluids 39 (2005) 614.[10] J. Nogueira, A. Lecuona, and P.A.Rodriguez, Exp. in Fluids 27 (1999) 107.[11] H. Nobach and E. Bodenschatz, Meas.Sci. Technol. (submitted).[12] H. Nobach and E. Bodenschatz, InProc. 13th Int. Symp. on Appl. of LaserTechn. to Fluid Mech., Lisbon, Portugal,paper 26.3 (2006).[13] H. Nobach and E. Bodenschatz, In

Proc. 14. Fachtagung »Lasermethoden inder Strömungsmesstechnik«, Braunschweig,Germany, paper 4 (2006).[14] H. Nobach, M. Kinzel, and C. Tropea,In Proc. 7th Int. Conf. on Optical Methodsof Flow Investigation, Proc. SPIE 6262,Moscow, Russia (2005).[15] M. Kinzel et al., In Proc. 13th Int.Symp. on Appl. of Laser Techn. to FluidMech., Lisbon, Portugal, paper 17.4 (2006).[16] M. Kinzel et al., In Proc. 14.Fachtagung »Lasermethoden in derStrömungs-messtechnik«, Braunschweig,Germany, paper 1 (2006).

Figure 4: Probability density distribution of LDV acceleration measurements in a water tank at Rλ = 500

2.3.3.3 The Goettinger Turbulence TunnelHolger Nobach

Kelken Chang, Nicholas T. Ouellette, Haitao XuInternational Collaboration for Turbulence Research

The investigation of fundamental principlesof turbulent flows and the exploration of tur-bulence phenomena are major interests of thegroup. Important questions concern scalingand the validity of scale-independent con-stants. Computational fluid dynamics cansubstitute experiments only for small Rey-nolds numbers. Therefore, experimental facil-ities generating turbulent flow fields at highReynolds numbers are essential for the re-search.

To achieve Reynolds numbers up toReλ ∼ 10,000, which is close to the highest val-ues on Earth, a wind tunnel with sulfur hexa-fluoride (SF6) and air as working fluids, pres-surized at 15bar, is being built in Göttingen.The wind tunnel is upright and consists oftwo measurement sections with a cross-sec-tional area of 2 m2 and with lengths of 10 and6m, respectively. The high turbulence levelsare generated by active grids that will be in-stalled at the beginning of each test section.The measurements will provide new insightsinto turbulence that will be indispensable for

understanding turbulent dispersion and re-lated problems in the atmospheric and envi-ronmental sciences, micrometeorology andengineering.Measurement techniques such as hot-wireanemometry, laser Doppler velocimetry andhigh-speed optical particle tracking will beimplemented in the wind tunnel.The hot-wire instrument consists of a multi-hot-and-cold-wire probe (five arrays with fourhot-wires and one cold-wire each), allowingthe measurement of the velocity fluctuationvector , all nine components of the spatialvelocity gradient tensor and all threetemporal velocity derivatives . Theimplementation of the hot-wire technique inthe pressurized wind tunnel requires an auto-matic three-dimensional calibration insidethe tunnel at the operation parameters of thetunnel.The three-dimensional laser Doppler systemcan be used directly for three-dimensionalparticle (Lagrangian) acceleration measure-ments. The relatively small measurement vol-ume yields a high spatial resolution and re-duces systematic deviations due to temporalor spatial averaging. The limits of the achiev-able resolution, given by systematic devia-tions due to a divergence of the fringe systemand random deviations due to signal noise,can be balanced by an accurate adjustment ofthe system (all optical components can be ad-justed separately). The signals are recordedby high-speed AD-cards and processed offlinein a computer using custom software. In testmeasurements a resolution of about 200 m/s2

could be verified.The optical particle tracking system consistsof multiple high-speed cameras observing thethree-dimensional traces of small particles ina certain fluid volume. The cameras take im-ages at rate up to 37,000 fps at a resolution of255x255 pixels. To extract the particle traces,

→∂u /∂ t

→∇ u

→u

Figure 1: Schematic of the

experimental hall


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the image sequences are processed in a com-puter cluster. The cameras can be mountedon a rail system, which is moving at the meanspeed of the flow. This allows the observationof tracer particles over several meters, whichincreases the observation time significantly,independent of the mean velocity. Other researchers from the International Col-laboration for Turbulence Research (ICTR)will also use the tunnel. They will employcomplimentary measurement technologies.ICTR is mainly an experimental group thatuses a combination of proven and most mod-ern technology to investigate problems of tur-

bulence. It was born out of the realizationthat progress in turbulence requires to go be-yond the financial, technical, and manpowercapabilities of a single researcher or a singleresearch group. Very much analog to investi-gations in High Energy Physics, by joiningforces the members of ICTR are providing ac-cess to shared facilities in measurement tech-nology and a variety of turbulence generators.The MPIDS with the best facility worldwidewill be a cornerstone of ICTR. We expect that30% of the tunnel will be used by outside col-laborators who will be housed during theirstay in the guest apartments.

Figure 2: A sketch of the pressurized SF6 wind tunnel.

Dario VincenziL. R. Collins (Cornell, USA), Shi Jin (Cornell, USA)

International Collaboration for Turbulence Research

2.3.3.4 Polymer solutions and viscoelastic flows

Dilute polymer solutions exhibit physicalbehaviors that distinguish them from ordi-nary Newtonian fluids. The elasticity of poly-mers, combined with fluid turbulence, pro-duces very complex memory effects. Evensmall concentrations (a few parts per millionof added polymers) can considerably changethe large-scale behavior of a turbulent flow.One of the most striking effects is drag reduc-tion: the injection of polymers in a turbulentflow can reduce the energy dissipation evenby 80% [1]. Since the pioneering work ofToms [2], this technology is routinely used inoil pipelines to reduce pumping costs(http://www.alyeska-pipe.com).The modeling of turbulent flows of polymersolutions represents a major challenge since it

couples hydrodynamic turbulence and poly-mer dynamics in solution, two problems that,even separately, are not fully understood. A starting point for the theoretical descriptionof dilute polymer solutions is the dynamics ofisolated polymer molecules. While to date thestationary dynamics of a single, isolated poly-mer has received much attention [3], less isknown about non-equilibrium dynamics. Wehave analytically solved the relaxation dy-namics of a polymer molecule both in lami-nar and random flows [4–6]. By means ofFokker-Planck methods, we have computedthe polymer relaxation time towards the sta-tionary regime as a function of the velocitygradient. Our analysis brings to evidence animportant slowdown of dynamics in the vici-

Figure 1: (a) Polymer relaxation time in a random flow, trel, rescaled by the relaxation time in theabsence of flow, τ , vs. the Weissenberg number Wi. The Weissenberg number is defined as the productof τ by a characteristic extension rate of the flow, and measures the strength of the turbulence relativeto the restoration force of the polymer. The relaxation time is maximal in the vicinity of the coil–stretchtransition (Wi=1/2). The maximum value strongly increases when the drag coefficient of the polymerin the stretched state,ζs, is sufficiently larger than the drag coefficient in the coiled state, ζc. Thedashed curve refers to polyacrylamide; (b) Rescaled maximum relaxation time for the followingpolymers: DNA (º» , ,£ ,Ç), polystyrene (×), polyethyleneoxide (p), Escherichia Coli DNA (r),polyacrylamide (¾).


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nity of the so-called coil–stretch transition.For the elongational flow, this is related toconformation hysteresis [3]. For randomflows, we have shown that hysteresis is notpresent. Nonetheless, the amplification of therelaxation time persists, albeit to a lesser ex-tent, due to the large heterogeneity of poly-mer configuration. In both cases, the depend-ence of the drag force on the polymer configu-ration plays a prominent role (Fig. 1). Thisconclusion suggests that the conformation-dependent drag should be included as a basicingredient of continuum models of polymersolutions.The dynamics of an isolated polymer in aflow field forms the basis of constitutive mod-els for numerical simulation of viscoelasticflows [3]. Direct numerical simulation (DNS)has recently emerged as an important tool foranalyzing drag reduction in channel flows,boundary layers and homogeneous turbu-lence. In the context of two-bead models, thepolymer conformation results from the coun-terbalance of the flow stretching and theaction of entropic forces restoring extendedpolymers into the equilibrium configura-tion[7].The advantage DNS has over laboratory ex-periments is that it yields information aboutthe polymer orientation and the flow simulta-neously, making it easier to understand themechanism(s) of turbulent drag reductionand how they depend upon the polymer pa-rameters. However, despite the successes ofDNS, it is clear that it will not be a useful toolfor designing large-scale systems, as the

Reynolds numbers that are required are muchlarger than can be achieved. A possible ap-proach is to renounce resolving small scalesand concentrate on the mean evolution. Thatapproach leads to a closure problem since thestretching and restoration terms in the equa-tions of motion cannot be expressed as ex-plicit functions of the mean polymer confor-mation because of polymer-turbulence statis-tical correlations. In collaboration withengineers at the Sibley School of Mechanicaland Aerospace Engineering at Cornell Univer-sity, we have presented a systematic closureapproximation for the stretching term in theevolution equation for the mean polymer con-formation [8]. This term plays an importantrole in non-Newtonian turbulence by estab-lishing the mean stretch of the polymer due tothe background turbulent fluctuations. By as-suming the velocity gradient in the frame ofreference moving with the polymer is Gauss-ian and short-correlated in time, it was possi-ble to derive an analytical closure for thestretching term. DNS were used to tune thecoefficients appearing in the closure providedby the analytical work. The final closure withtuned coefficients is in excellent agreementwith the simulations (Fig. 2). We presentlyare extending the model to homogeneous tur-bulent shear flow. Additionally, we are seek-ing a closure for the mean restoration term. Inthis case, knowledge of the distribution ofstretch by the isolated polymer can be used toobtain an approximate closure in terms of themean conformation tensor.

Figure 2: Left: Snapshot of thevorticity field from directnumerical simulations of 2DNavier–Stokes turbulence.Right: Plot of the stretchingterm vs. time. The points arefrom direct numericalsimulations and the solidline is the theoreticalprediction.

[1] J.L. Lumley, Annu. Rev. Fluid Mech. 1 (1969)367.[2] B. Toms, Proc. Int. Rheo. Congress 2 (1948) 135.[3] E.S.G. Shaqfeh, J. Non-Newtonian Fluid Mech.130 (2005) 1.[4] M.M. Afonso and D. Vincenzi, J. Fluid Mech. 540(2005) 99.[5] D. Vincenzi and E. Bodenschatz, J. Phys. A:

Math. Gen. (2006), under review.[6] A. Celani, A. Puliafito, and D. Vincenzi, Phys.Rev. Lett. (2006), under review.[7] R.B. Bird et al., Dynamics of Polymeric Liquids,Wiley, New York (1987).[8] D. Vincenzi et al., Phys. Rev. Lett. (2006), underreview.

2.3.3.5 Experiments on Thermal Convection

Gabriel SeidenWill Brunner, Jonathan McCoy, Hélène Scolan, Stephan Weiß

S. E. Lipson (Technion, Israel), W. Pesch (Bayreuth)

Fluid motion driven by thermal gradients(thermal convection) is a common and mostimportant phenomenon in nature. Convec-tion not only governs the dynamics of theoceans, the atmosphere, and the interior ofstars and planets, but it is also important inmany industrial processes. For many years,the quest for the understanding of convectiveflows has motivated many experimental andtheoretical studies. In spatially extended sys-tems convection usually occurs when a suffi-ciently steep temperature gradient is appliedacross a fluid layer. The convection structuresappear often in regular arrangement, whichwe call a pattern. It is the investigation ofsuch convection patterns that is at the centerof this project. Pattern formation is commonalso in many other non-equilibrium situationsin physics, chemistry, or biology. The ob-served patterns are often of striking similarityand indeed their understanding in terms ofgeneral, unifying concepts continues to be amain direction of research.Many fundamental aspects of patterns andtheir instabilities have been studied inten-sively over the past 20 years in the context ofRayleigh-Bénard convection (RBC) [1]. In atraditional RBC-experiment a horizontal fluidlayer of height d is confined between twothermally well conducting, parallel plates.

When the temperature difference between thebottom plate and the top plate exceeds a cer-tain critical value the conductive motionlessstate is unstable and convection sets in. Themost ideal pattern is that of straight, parallelconvection rolls with a horizontal wavelengthof ~2d. In the less well-known case of In-clined Layer Convection (ILC) the standardRayleigh-Bénard cell is inclined at an anglewith respect to the horizontal, resulting in abasic state which is characterized not only byheat conduction, but also by a plane parallelshear-flow with cubic velocity profile. Thisshear-flow not only breaks the isotropy in theplane of the layer, but also, at large anglesand when inclined and heated from above,causes a transition from a thermal to a hydro-dynamic shear-flow instability. For ILC weobserved an intricate phase space, filled withnonlinear, spatio-temporally chaotic states[2].In our experimental investigations we use apressurized gas cell to study forcing and con-trol of thermal convection in horizontal andinclined fluid layers. As explained in detail in[1], compressed gases have the advantageover other fluids in that they enable an exper-imental realization of large aspect-ratio sam-ples (length/height <150) with short relax-ation times (<2sec). In addition, the Prandtl


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number can be tuned from 0.17 to 150. ThePrandtl number gives the relative importanceof the nonlinearities in the heat conductionequation and the Navier-Stokes equation. Ourcurrent investigations are restricted to Prandtlnumbers <1.5, where non-relaxational, spa-tio-temporally chaotic behavior can be ob-served very close to the onset of convection.We use spatially periodic and spatio-temporalforcing schemes of various geometries tostudy the influence of modulations on patternformation. We are particularly interested ininvestigating the spatio-temporal chaoticstates like Spiral Defect Chaos [3] or undula-tion chaos [2]. Two types of forcing schemesare applied – one uses micro-machined sur-faces, as shown schematically in Fig. 1, andthe other uses a thermal imprinting techniquethat is improved but similar to the one pio-neered by Busse and Whitehead [4]; we illu-minate the cell with infrared light, which at awavelength of 2.7 µm is absorbed by the CO2

gas. A considerable body of literature on time peri-odic forcing of hydrodynamic patterns, partic-ularly convective patterns, has accumulated.Time periodic forcing can generate hexagonsin a system where a roll pattern is expected;standing waves in a system where travelingwaves are expected; and even four-mode su-perlattices. Spatially periodic forcing, on the

other hand, has received far less attention. Inparticular, there is no spatial counterpart tothe extensive investigations of RBC subjectedto time periodic forcing. Similarly, while tem-poral forcing of a spatiotemporally chaoticstate has been investigated, the response ofspatiotemporal chaos to spatial forcing re-mains an open question. In one of our ongoing experiments we forcewith a parallel array of micromachined walls(see Fig. 1) a wavevector, which lies outsideof the stability region for ideal parallel rolls,but still close to the critical wavenumber ofthe unforced system. Above onset with in-creasing temperature difference we first ob-serve a pattern of ideal rolls, which give wayto localized convection states consisting ofkinks and anti-kinks, as shown in Fig. 2A.These are moving mostly along the rolls withkinks (or anti-kinks) rowing up or kink/an-tikink-pairs annihilating. As a function oftemperature difference, there exist regions inparameter-space, where kinks (or antikinks)row up and generate a continuous obliquepattern, as shown in Fig. 2B. An analysisshows that a resonance triad of the forcingmode with two oblique modes that lie withinthe stability region generates these extendedpatterns.Currently we use two apparatuses. The onewith the micro-machined bottom plate is at



Figure 1: Schematic of the convection cell withmicromachined bottom plate (to scale). The fluidheight is typically 0.5 mm.

Figure 2: False color image of shadowgraph images of convection patterns. (A) Forced pattern withoblique kinks and anti-kinks. The kinks/anti-kinks move preferentially from left to right or viceversa. (B) Extended oblique pattern formed from a bound state of kinks.

Cornell University and will move in Nov. 2006to Göttingen after Jonathan McCoy graduates.The other has already been moved to Göttin-gen. It has been CE certified and also modi-fied to allow for the optical forcing experi-ments.

[1] E. Bodenschatz, W. Pesch, and G.Ahlers, A. Rev. Fluid Mech. 32 (2000) 709.[2] K.E. Daniels and E. Bodenschatz, Phys.Rev. Lett. 88 (2002) 4501.[3] K.E. Daniels, R.J. Wiener, and E.Bodenschatz, Phys. Rev. Lett. 91 (2003)114501.[4] S.W. Morris et al., Phys. Rev. Lett. 71(1993) 2026.[5] F.H. Busse and J.A. Whitehead, J. FluidMech. 47 (1971) 305.

2.3.3.6 Wax Modeling of Plate TectonicsGabriel Seiden

Will Brunner, Hélène Scolan, Stephan Weiß

The time scale of plate tectonics is on the or-der of hundreds of millions of years, making itdifficult to observe the dynamical processesinvolved. In addition, most of the interestingphenomena occur on the ocean-floors under2 to 4 km of water. The only available meansfor studying the details of the dynamics arethrough numerical simulations and physicalmodeling. Current numerical simulations re-main far from capturing the full complexity ofthe problem, which involves coupled multi-scale physical processes including fracture,phase transitions, and flow of complex fluids.This may leave physical modeling as an alter-

native. Physical models, in turn, may not cap-ture every aspect of the physics (e. g., pres-sure, rheology, etc.) and often do not obey dy-namic similarity in every detail. Our recentexperiments [1] have shown that wax modelsmay indeed be used to simulate certain uni-versal features of mid-ocean ridge dynamics.At fast and intermediate spreading rate weobserved behavior similar to that of Earth. Wefound transform faults, microplates and asimilar across rift height variation. Our wax-analog experimental model simu-lates the divergence of two brittle lithosphericplates above a ductile mantle, exactly as it oc-


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curs beneath the sea at the mid-ocean ridges.The experimental apparatus (Fig. 1) consistsof a 1m long, 30 cm wide and 10 cm deep rec-tangular aluminum tank onto which twothreaded rods are fastened. These rods carrytwo skimmers, which are partially immersedin the top layer of the wax and can be drivenapart along the rods via a stepper motor. Thetank is heated from below and from the sidesin order to melt the wax in the interior of thetank, and cooled from above by a vent to al-low for a thin crust to form. The experiment isinitiated with a cut with a sharp knife to di-vide the wax surface into two plates. Activat-ing the motor causes the skimmers to diverge,dragging with them the two wax plates andcausing fluid wax from below to up-well intothe rift between the plates, just as ductilemantle rock up-wells beneath a mid-oceanridge. Like oceanic microplates, wax microplatesoriginate from overlapping spreading centers.Figure 2 depicts the nucleation of such a cen-ter on a spreading rift. A time series of thesubsequent evolution of a wax microplate isshown in Fig. 3. The resemblance to the ac-tual phenomenon is quite striking, as can beseen in Fig. 4 where we compare the topologi-cally of the actual phenomenon with the waxmicroplate. Our wax-to-earth kinematic scal-ing relations indicate that the dimensions ofthe wax microplates are consistent with esti-mates for oceanic microplates [1,3], confirm-ing the validity of the model. Moreover, closeobservation have enabled us to develop a the-ory for the nucleation of overlapping spread-ing centers and to further establish the geo-logical model of microplates [1]. In particular,this formulation enables one to infer the timeevolution of the pseudofaults, given the cur-rent phase-angle of its tip (see Fig. 4).Further results of our wax experiments com-pare favorably with other observations frommid-ocean ridges. The topography of mid-ocean ridges is known to vary with thespreading rate. Slower spreading rifts (<25mm/yr half spreading rate) form deep rift val-leys (1-2 km deep), while faster spreading

rifts (>40mm/yr half spreading rate) form asmall peak (axial high) at the rift axis. The to-pography at intermediate rates is a shallowvalley within an overall axial high. All threetypes of behavior are observable in the waxwith the same trend in spreading rates. Forspreading rates >80 µm/s we found a shal-low ridge with a height to width ratio of ap-proximately 0.03. This ratio is very similar tothe one reported for fast spreading oceanicrifts. The wax in the rift region was observedto be paste-like. If a hole was cut at the rift,the liquid wax would neither well up nor re-cede: the rift was at the same pressure as theliquid. Consequently, the across-rift topogra-phy can only be explained by a downward



Figure 1: Scheme of experimentalapparatus used in theinvestigation of theformation and evolution ofwax microplates.

Figure 2:Nucleation of an overlappingspreading center, precursorof a wax microplate. The leftcolumn consists of a timeseries of images at highmagnification. The rightcolumn consists ofinterpretive drawings of theevolution of the rift into anoverlapping geometry.

bending of the solidifying crust in the vicinityof the rift axis. For between 60 µm/s and80 µm/s the rift was flat, and at lower spread-ing rates the rift formed a valley. All the features described above are similar tothat of Earth. However, at this point it is un-clear what causes this behavior. The answermust lie in the rheological properties of thesolidifying wax. These are very poorlyknown, a fact that hinders a more compre-hensive and quantitative theoretical formal-ism. To this end we constructed an experi-mental apparatus (Fig. 4) designed to investi-gate the complex viscosity dependence of thedifferent waxes used to model plate tectonics.These measurements, together with quantita-tive studies of the thermal and flow fields in arefined version of the wax-tectonics appara-tus, will enable us to test numerical modelsthat later, in a refined form, can be applied toEarth or other planets.

Figure 4:Comparison between a wax-

microplate and the Eastermicroplate.

(a) Schematic diagramillustrating the kinematics of

microplates. The lettersindicate points on the

pseudofaults that wereformerly at the rift tips,

showing how the microplategrows with time.

The current positions aremarked as (d) and (D). (b)Image of a wax microplate

with model fit and riftmarkers overlayed as in (a).

(c) Bathymetry of the Eastermicroplate [4]. Colorsdenote elevation with

respect to sea-level.

Figure 3:Time series of wax-

microplate dynamicalevolution. Interval between

frames is 15 s. The spreadingrate is 70 µms-1.

The left column consists ofimages of the microplates.

The right column images areidentical to the ones on the

left, but with pseudofaultpairs and spreading ridge

overlayed in red.Figure 5. The experimental apparatus used for themeasurement of the viscosity of the wax as afunction of temperature. A small ball at the tip of athin rod is immersed in the molten wax underconstant load. The viscosity is calculated from themeasured terminal velocity.

[1] H. Schouten, K.D. Klitgord, and D.G.Gallow, J. Geophys. Res. 98 (1993) 6689.[2] R.F. Katz, R. Ragnarsson, and E.Bodenschatz, New J. Phys. 7 (2005) 37.[3] R.L. Larson et al., Nature 356 (1992)571.[4] W.F.H. Smith and D.T. Sandwell,Science 277 (1997) 1957.


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Figure 1:Onset of cardiac arrhythmiaobserved in an ECGrecording (top). The normalsinus rhythm (NSR)undergoes a transition toventricular fibrillation (VF)via a short episode ofventricular tachycardia (VT).Numerical simulations(bottom) show thecorresponding hypothesizedelectrical activation patternssuggesting a transition fromplanar waves to spiral wavesand spatiotemporal chaos.

2.3.3.7 Nonlinear Dynamics and Arrhythmia of the HeartStefan Luther

Michael Enyeart, Gisa Luther, Amgad SquiresR. Gilmour (Cornell, USA), B. Pieske (Göttingen)

Heart disease is one of the most prevalentdiseases in the world and is the leading causeof death in industrialized countries. In Ger-many alone, heart rhythm disorders cause ap-proximately 100,000 sudden deaths annually.Sudden cardiac death occurs unpredictably asa result of fast-developing electromechanicalmalfunctions of the heart. During normalfunctioning, the contraction of the heart is pe-riodically triggered by planar electrical activa-tion waves propagating across the heart fol-lowed by a refractory period. Numerical sim-ulations and measurements suggest thatduring ventricular tachycardia (VT) the planewave undergoes a transition to fast rotating,three-dimensional spiral waves (which areanalogous to vortices in the Ginzburg-Landaumodel). Subsequently, spiral wave breakupresults in a spatiotemporal chaotic statecalled ventricular fibrillation (VF, see Fig. 1).Ventricular fibrillation inhibits the synchro-nized contraction of the heart due to lack ofspatiotemporal coherence. The blood flowstops and as a consequence the organism dieswithin minutes. It is the topic of this research program to in-vestigate the following questions: How is VT

or VF created? Is there only one type of VT orVF? How can VT or VF be efficiently removedwithout harming the organism? What ionicchannels can be identified/altered that causeVT or VF? What treatment (medication, genetherapy) can be found to avoid VT or VF? Progress in this field requires a close interplayof time resolved three-dimensional measure-ments of wave propagation with mathemati-cal modeling.

Numerical Simulations: Return Maps andIonic Models

We have found evidence, both from experi-ments and from computer simulations, thatthe initiation and breakup of spiral waves incardiac tissue is related to a period doubling

bifurcation of cardiac electrical properties. Atrapid heart rates, electrical alternans devel-ops, a beat-to-beat long-short alternation inthe duration of the cardiac action potential. Inboth the experiments and the computer mod-els, rapid periodic pacing produced spa-tiotemporal heterogeneity of cellular electri-cal properties. These behaviors resulted fromthe interplay between local period two dy-namics (alternans) and conduction velocitydispersion. This activity can be understood interms of a period doubling bifurcation of asimple uni-dimensional return map (calledthe duration restitution relation) relating theduration of an action potential to the rest in-terval that preceded it [2]. In addition of sim-ulating this simple model, we also investigateionic models that produce a more detailedrepresentation of cardiac action potentials.The ionic model is solved by taking into ac-count a realistic heart geometry and tissueheterogeneity such as fiber orientation asshown in Fig. 2. The model equations aresolved numerically using finite differencesand Cartesian coordinates. An auxiliary vari-able, the phase field, indicates the presence orabsence of tissue at each grid point.

Experiment: Optical Mapping andIntramural Probes

The electrical activation of the heart surfacecan be measured optically using voltage sen-

sitive dyes at high spatial and temporal reso-lution [3]. However, electrical activation trig-gers contractile motion, which in turn causessubstantial distortions of the optical signal asshown in Fig. 3. These artifacts prevent an ac-curate measurement of the action potentialduration and diastolic interval and thus biasthe restitution relation. Hitherto approachesto prevent motion artifacts are based on me-chanical or pharmacological immobilizationof the tissue and are known to change its elec-trophysiological properties. Therefore, mo-tion artifacts pose a severe limitation to theoptical mapping technique. We have devel-oped a numerical technique that reliably re-moves the effect of contractile motion fromoptical action potential measurements [4]. Itis based on image registration using locallyaffine transformations that compensate mo-tion and deformation effects. Figure 3 shows atime series with substantial motion artifactsand the corresponding restored signal. In ad-dition, the measured displacement field pro-vides valuable information on the surfacestrain. Our new technique removes a signifi-cant limitation to the optical mapping tech-

nique and provides the basis for studies of ex-citation-contraction coupling [5].Optical mapping measures electrical activa-tion of cardiac tissue on its surface. The mainchallenge is, however, to measure the three-dimensional propagation of the action poten-tials in the tissue. Currently, we are develop-ing fiber optical probes that can be insertedinto the heart wall. Up to 4 multimode fibersare bundled and provide optical measure-ment of cardiac action potentials at varioustissue depths. During an experiment, severalof these fibers are inserted into the ventricularwall. Data from the intramural and surfacemeasurements are used to characterize car-diac activation during tachycardia and fibril-lation. Wave breaks, spiral or scroll wavecores can be identified as phase singularitiesor defects. This approach is illustrated inFig. 4. These phase singularities are the or-ganizing structures of tachycardia and fibril-lation. First encouraging experimental resultsindicate that our approach allows for locatingscroll waves in the heart wall and to followthem in time. This new method can now beused to address the questions raised above.

Figure 2:Numerical simulation of the

electrical activation ofcardiac tissue using the

canine ventricular model(CVM) and realistic

geometry. Panels (a-c) showthe time evolution of anexcitation propagating

across the ventricles. Blueindicates polarized tissue,

red depolarized tissue.

Figure 3:Contractile motion of

cardiac tissue results insubstantial artifacts in action

potential recordings (redtrace). These distortions

impede meaningful signalanalysis such as action

potential durationmeasurements. The green

trace shows thecorresponding restored

times series with recoveredaction potential

morphology.


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Figure 4: Top row: Experimental reentry pattern obtained during ventricular fibrillation usingoptical surface mapping with voltage sensitive dye. Field of view 2.5x2.5 cm2. (a) Normalizedtransmembrane potential. Color code same as panel (a). (b) Phase. (c) Position of phasesingularities. The circles indicate the positions of phase singularities in all panels, where red andgreen indicate clockwise and counter clockwise rotation, respectively.Bottom row: Numerical example of a complex activation pattern in two-dimensional tissue of size5.5x5.5 cm2. (d) Normalized transmembrane potential. Blue indicates polarized tissue, reddepolarized tissue. (e) Phase. (f) Position of phase singularities given by the zero crossing of real(red) and imaginary part (blue) of the complex signal.

[1] J.F. Fox et al., Circ. Res. 90 (2002) 289.[2] J.F. Fox, E. Bodenschatz, and R.F. Gilmour, Phys.Rev. Lett. 89 (2002) 138101.

[3] I.R. Efimov et al., Circ. Res. 95 (2004) 21.[4] G.E. Luther et al., to be submitted to Circ. Res.[5] D.M. Bers, Nature 418 (2002) 198.

Chemotaxis – the directed movement of acell in response to chemical stimuli – is a fun-damental phenomenon in many biologicaland medical processes including morphogen-esis, immune response, and cancer metasta-sis. Over the past thirty years, major researchefforts were undertaken to advance the un-derstanding of how a cell senses, responds,and moves towards a chemical signal. In par-ticular, the last decade has witnessed a rapidadvance in deciphering the G-protein linkedsignaling pathways that govern the direc-tional response of eukaryotic cells to chemo-attracting agents [1,2]. However, for a thor-ough understanding of the complex phenom-enon of chemotaxis the molecular details ofintracellular signaling and the macroscopicmigration of a cell have to be merged into anoverall model. While many of the key components of intra-cellular biochemical networks could be iden-tified in recent years, a complete picture of di-rectional sensing and chemotaxis is mostlyhampered by the lack of quantitative data.For the actual movement of a cell in gradientsof chemoattractant as well as for the intracel-lular reaction networks almost none of thedynamical characteristics have been preciselydetermined. It is the aim of the Chemotaxisand Cell Migration project to provide quanti-

tative insight into the governing parametersof directional cell movement. A solid know-ledge of the length and time scales for bothcell migration and intracellular spatiotempo-ral dynamics of signaling networks is expec-ted to considerably advance our understand-ing of a vast number of biological and med-ical processes that depend on chemotacitcmotion. Our approach combines the work on a well-established model organism for chemotaxiswith novel experimental techniques that al-low the precise spatiotemporal addressing ofthis organism in easily tunable, highly con-trolled chemical environments. Chemotaxishas been studied for a large variety of biologi-cal systems ranging from prokaryotic cells tomammalian leukocytes and neutrophils. Forour current projects we choose the eukaryoteDictyostelium discoideum, one of the mostprominent biological model systems forchemotactic behavior [3]. Our experiments on D. discoideum are per-formed with microfluidic devices. Micrometersized flow chambers combine a number ofadvantages that make them optimally suitedfor cell dynamics experiments: Due to strictlylaminar flow conditions the chemical envi-ronment can be precisely controlled on thelength scale of individual cells and arbitrary

Figure 1:Layout of the microfluidic channel network used togenerate a linear concentration gradient. The color

coding displays the concentration from a 2-dimensional numerical simulation of the Navier-Stokes and drift-diffusion equation in the shown

geometry using FEMlab 3.1. Black lines mark in- andoutlets that were not part of the numerical

simulation.

2.3.3.8 Chemotaxis and Cell MigrationCarsten Beta

Albert Bae, Toni Fröhlich, Barbara Kasemann, Katharina Schneider, Danica WyattH. Levine (UCSD, USA), W. F. Loomis (UCSD, USA), W.-J. Rappel (UCSD, USA)

C. Franck (Cornell, USA), G. Gerisch (MPIBC), H. Ishikawa (MPIBC)


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sequences of stimuli can be applied with hightemporal resolution. Besides, only biocom-patible materials are used, they are wellsuited for the combination with optical imag-ing techniques, and the microfabricationprocess follows well established and highlyreproducible protocols. As an example, Fig. 1 shows a microfluidicnetwork for the built-up of a well-defined lin-ear gradient between a minimal and a maxi-mal concentration level. Through a cascade ofsuccessive dividing and remixing ten equidis-tant concentration levels are generated andunited inside the main channel to form a lin-ear concentration gradient. Compared to tra-ditional chemotaxis assays like micropipettesetups or diffusion chambers, a microfluidicdevice allows for a well defined and tempo-rally stable concentration profile while a slowcontinuous fluid flow ensures that wasteproducts and signaling substances releasedby the cells are washed away. In this setup,cell motility and chemotactic response can besystematically investigated as displayed inFig. 2 for D. discoideum cells in linear gradi-ents of the chemoattractant cAMP (cyclicadenosine 3’,5’-monophosphate). The experi-ments show a chemotactic response and anincreased motility for gradients between 10-3

and 10 nM/µm [4]. Besides conventional mi-crofluidic devices, we also combine microme-ter sized flow channels with the use of cagedsubstances. This approach leads to a highlyversatile setup allowing for a wealth of newsingle cell experiments. An additional UVlight beam is coupled into the imaging lightpath and allows to release caged chemoattrac-tants by photoactivation inside a microfluidicchamber in the vicinity of a cell. In combina-tion with differently shaped pin holes, theuncaging light spots can be individuallytuned to generate arbitrary concentration pro-files of released signaling substances, see e.g.Fig. 3. In this context, particular attention hasto be paid to the deformation of the concen-

Figure 2: Average velocitycomponents vx (reddiamonds) and vy (=chemotactic velocity, bluediamonds) as well as motility(red squares) measured fordifferent cAMP gradients.

Figure 3: Photoactivation of cageddye by a square shaped (a)and a triangular (c)uncaging light spot, flow isrunning from right to left.Intensity profilesdownstream of the squareshaped (b) and of thetriangular (d) uncagingspots along the linesindicated in (a) and (c),respectively.One pixel corresponds to0.83 microns

tration distribution close to a cell. The inter-play of flow profile and cell geometry can leadto nontrivial effects that are studied usingboth experimental 3D-imaging techniquesand numerical finite element simulations (seeFig. 4).A second focus of our project emphasizes theuse of fluorescently labeled biomolecules incell constructs to study the internal dynamicsof chemotactic cells. In the framework of co-operations with the group of Prof. William F.Loomis (Division of Biological Sciences, Uni-versity of California at San Diego) and thegroup of Prof. Günther Gerisch (MPI for Bio-chemistry, Martinsried), a library of cell linesis available in which different proteins, that

are known to be part of the chemotactic sig-naling pathways, are expressed together witha fluorescent marker. These constructs allowimaging of the spatiotemporal dynamics ofprotein distributions inside individual cells asthey experience stimulation. As an example,Fig.5 shows the uniform translocation of theGFP-marked Lim protein to the cell cortex inresponse to a uniform stimulus with 10 µMcAMP. In these experiments, we use state-of-the-art fluorescence microscopy imagingtechniques including a multi-channel laserscanning confocal microscope and total inter-nal reflection fluorescence microscopy(TIRF).

Figure 4:Deviations from an ideal,

unperturbed concentrationgradient in the vicinity of a

half-sphere in a microfluidicchannel (from a numerical

3D finite element simulationusing FEMlab 3.1) with alaminar flow. The Péclet

number Pe=200.

[1] P.J.M. Van Haastert and P.N. Devreotes,Nature Reviews 5 (2004) 626.[2] C.A. Parent and P.N. Devreotes, Science284 (1999) 765.[3] R.H. Kessin, Dictyostelium: Evolution,Cell Biology, and the Development ofMulticellularity, Cambridge University Press(Cambridge, 2001).[4] L. Song et al., Eur. J. Cell Biol., in press

Figure 5: Globaltranslocation of the GFP-

marked Lim protein to thecell cortex in response to a

uniform stimulus with cAMP.The bottom side length

corresponds to 41.4 microns.


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The cell culture laboratory is one of the de-partment’s core research facilities. It providesexpertise in diverse applications of cell char-acterization, diagnosis, and culturing. It of-fers extensive services and training to the re-search groups. The laboratory’s interdiscipli-nary work focuses on the development ofmyocardial cell cultures. Applying principlesof engineering and life science we are devel-oping methods for two and three-dimensionalaggregation of cardiomyocytes. The engi-neered myocardial tissue will allow for theinvestigation of fundamental mechanism ofarrhythmia in a controlled physico-chemicalenvironment. By combining cell cultureexperiments with biophysically realistic com-puter models we hope to gain further insightinto cardiac cell and tissue function andpathology. The cell culture laboratory hasbeen established in 2005. This report de-scribes the equipment, the current research,and outlines the future work.

EquipmentThe cell culture laboratory is a fully equippedresearch facility certified according to genetechnology safety class S1. Our laboratoryprovides outstanding imaging facilities for di-verse applications. A collaborative agreementwith Olympus provides cutting edge micro-scope and imaging systems for research andtraining.Our equipment includes a confocal and twoepifluorescence microscopes, and two realtime imaging and TIRFM systems (Olympus,Delta Vision). The confocal microscope offersseveral advantages over conventional opticalmicroscopy, including controllable depth offield, the elimination of image degrading out-of-focus information, and the ability to collectserial optical sections from thick specimen.The TIRFM Systems allow for ultra sensitive

fluorescence microscopy at the cell surface,providing high contrast imaging with mini-mal background noise. The cell culture laboratory comprises a class2 microbiological cabinet including standardequipment such as UV illumination, vacuumpump, pipettors etc. The cell cultures aregrown adherent to a surface or in suspension.An incubator provides a controlled CO2 at-mosphere at constant temperature. The cellsare preserved and stored in liquid nitrogenand in a -80°C freezer. A laboratory dishwasher, drying cabinet, and autoclave areavailable for cleaning and sterilization ofglassware. The autoclave is also used for ger-micidal treatment of biological waste. For di-agnosis and cell analysis an ELISA Reader andmycoplasma test are available.

Cardiac myocytesCurrently we are investigating and comparingvarious approaches to obtain and cultivatecardiomyocytes from embryonic chicken andthe P19 cell line. In order to obtain a primary cell culture fromembryonic chicken, the heart is excised anddissected. The tissue is enzymatically dissoci-ated into individual cardiac myocytes. Forcultivation the cells are placed onto differentsubstrates, e.g. glass or plastic. Cell adhesionis improved by covering the surfaces withproteins. After two days the cells begin tobeat spontaneously. The properties of cell ad-hesion strongly depend on the substrate. Wefound that the cell adhesion is significantlyimproved on the semi-permeable membraneLumox50. We have completed cell morpho-logical tests, and electrophysiological charac-terization will follow. Currently, we are evaluating the P19 cell line.This cell line was derived from an embryonalcarcinoma induced in a C3H/He strain

2.3.3.9 The Cell Culture Laboratory – Myocardial Tissue Engineering

Barbara KasemannStefan Luther, Katharina Schneider

Olympus Deutschland GmbH (Hamburg), B. Busse (Zell-Kontakt, Nörten-Hardenberg),E.-K. Sinner (MPIPR, Mainz)

mouse. The pluripotent P19 cells can be in-duced to differentiate into neuronal, glial,skeletal, and cardiac cells. The first resultswith cardiac cells obtained from this cell lineare very encouraging and further electrophys-iological experiments are under way. Thiswork is done in collaboration with Dr. Eva-Kathrin Sinner (Max Planck Institute for Poly-mer Research, Mainz).

Future ResearchThe successful development of cell culturesrequires accurate control of the cells’ physico-chemical environment. Lacking a microvas-cular structure, the growth of functional cellaggregates is limited by diffusion to a few celllayers. Microfluidic technology providesmeans to overcome this limitation. The goalof our research is the development of micro-fluidic two- and three-dimensional tissuescaffolds that provide a controlled mechani-cal and physico-chemical cellular environ-ment. This challenging interdisciplinary proj-ect involves physics, engineering and life sci-ence in effort to affect the advancement ofmedicine. When applied to cardiac myocytes, our ap-proach will provide a simplified yet realisticmodel of cardiac tissue. By controlling the cellenvironment, such that regions are locally de-pleted from oxygen, we will obtain a modelfor diseased tissue such as myocardial infarctand ischemia and reperfusion damage. It willprovide experimental insight into the role ofdynamical vs. structural heterogeneities forthe development and sustaining of cardiac ar-rhythmia.

Figure 1. Cell dissociation and preparation.

Figure 2: Cell diagnosis and characterization.

Figure 3:Training on the Olympus TIRFM System.


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Associated Scientists

Associated Scientists2.4

2.4.1 People

PD Dr. Folkert Müller-HoissenFolkert Müller-Hoissen received his doctorate intheoretical physics from the University of Göttingenin 1983. After postdoc positions at the MPI forPhysics in Munich and the Yale University in NewHaven, USA, he returned to the University ofGöttingen as a Wissenschaftlicher Assistent, passedthe Habilitation in 1993 and became a Privatdozent.Since 1996 he carries on his research inmathematical physics at the MPI for Fluid

Dynamics, which meanwhile evolved into the MPIfor Dynamics and Self-Organization. Since 2000 heis also außerplanmäßiger Professor at the Universityof Göttingen.

PD Dr. Reinhard SchinkeReinhard Schinke received his doctorate intheoretical physics from the University ofKaiserslautern in 1976. After a one year postdoctoralposition at the IBM research laboratory in San Jose(Cal.) he took a position at the MPI fürStrömungsforschung in the department for Atomicand Molecular Interactions in 1980. He received hishabilitation in theoretical chemistry from theTechnical University of Munich in 1988. His research

centers around the understanding of elementaryprocesses in the gas phase like chemical reactions,photodissociation and unimolecular reactions. He isauthor of the monography »PhotodissociationDynamics« (Cambridge University Press, 1993) andreceived the Max-Planck research award in 1994and the Gay-Lussac/Humboldt award in 2002.


The investigation of elementary reactions inthe gas phase (exchange reactions, photodis-sociation, unimolecular dissociation etc.) isimportant for understanding complicatedprocesses, for example, in combustion andin the atmosphere. Theoretical studies aimat reproducing detailed experimental data byab initio methods, explaining measured dataon the basis of fundamental equations andmaking predictions for experiments, whichare difficult to perform in the laboratory. Thetools are global potential energy surfaces(PES's), calculated in the Born-Oppenheimerapproximation by solving the electronicSchrödinger equation, and the solution ofthe nuclear Schrödinger equation for the in-tramolecular dynamics of the atoms on thesePES's [1,2].

In recent years we concentrated on one par-ticular molecule, ozone, which plays a cen-tral role in atmospheric chemistry. Both thephotodissociation of O3,

O3 + hv → O + O2 (1)and the recombination

O + O2 + M → O3 + M , (2)where M is necessary to carry away the ex-cess energy, have been investigated. Al-though both processes appear to be seem-ingly simple, there are many open questions,which can be solved only by state-of-the-artquantum mechanical calculations.The photoabsorption cross section of ozonein the wavelength region from the near ir tothe uv shows four different bands: Wulf,Chappuis, Huggins and Hartley. Each bandcorresponds to one (or several) particularelectronic states which are excited by thephoton. Calculations have been completedor are in progress for all bands. The quanti-tative description of process (1) requires thecalculation of PES's of all electronic statesinvolved, each being a function of the threeinternal coordinates of O3. In addition, thenon-Born-Oppenheimer coupling elementsare required if more than one state is in-volved. Figure1 shows one-dimensional cutsalong the dissociation coordinate of all statesof ozone, which possibly take part in thephotodissociation [3,4]. For a total of 10states global PES's have been determined.Quantum mechanical dynamics calcula-tions, i.e., solving either the time-independ-ent or the time-dependent Schrödinger equa-tion, yield the absorption spectrum and thefinal rotational-vibrational product state dis-tributions. In addition they reveal, in combi-nation with classical mechanics calcula-tions, the dissociation mechanisms and ex-

Reinhard SchinkeSergei Y. Grebenshchikov, Mikhail V. Ivanov

2.4.2.1 Elementary Gas-Phase Reactions

2.4.2 Projects

Figure 1: Potential cuts for the singlet

and triplet A' (a) and thesinglet and triplet A'' (b)states of ozone along thedissociation coordinate.

From Zhu et al., Chem. Phys.Lett. 384, 45 (2004).

Projects

planations for certain prominent featureslike diffuse vibrational structures and predis-sociation lifetimes [5,6]. Figure 2 shows cal-culated rotational state distributions of O2

for several vibrational states in comparisonwith measured results. Current work con-cerns the influence of spin-orbit coupling inthe Wulf band and non-adiabatic coupling inthe Hartley band and its influence on disso-ciation lifetimes.The recombination of ozone in collisions ofO atoms and O2 molecules is a very compli-cated process and despite many experimen-tal and theoretical efforts it is not yet fullyunderstood. Questions concern the tempera-ture dependence of the formation rate coeffi-cient, and thus the formation mechanism(energy transfer or chaperon mechanism orboth), and its surprisingly strong isotope de-pendence. The latter effect leads to a non-statistical distribution of isotopomers in theatmosphere as has been measured in the1980'ies by means of balloon experiments[7]. The isotope dependence has created agreat deal of interest among theorists be-cause it seems to reveal a fundamental reac-tion mechanism. Up to now there is no satis-factory explanation on the basis of real abinitio calculations; a status report criticallyreviews all the dynamical calculations in thelast decade to explain this effect [8]. Themore realistic calculations, each of whichhowever makes some model assumptions,hint at the difference of zero-point energiesin the different channels in which the highlyvibrationally excited ozone complexes candissociate (Figure 3) [9]. In our current workwe attempt to perform rigorous quantummechanical calculations for state-specificlifetimes [2] of different isotopomers, whichappear to be the key for the ozone isotope ef-fect.



Figure 2: Comparison of experimental (•), classical (°) and quantummechanical (—) rotational state distributions of O2 for photolysis at 240 nm.From Qu et al., J. Chem. Phys. 123, 074305 (2005).

Figure 3: Comparison of relative formation rates as function of the zero-point energy difference between reactant and product channels, ∆ZPE.The data points correspond to (from left to right): 8+66, 7+66, 6+66, 6+77,and 6+88. T = 300 K and low pressures. runscaled trajectory results;

° scaled trajectory results (η = 1.14); •experimental results; £ statisticalRRKM calculations (ηGM = 1.18). The scaled trajectory data for 8+66 and6+88 agree with the experimental results and therefore are not discern-able. From Schinke and Fleurat-Lessard, J. Chem. Phys. 122, 094317(2005).


Projects

[1] R. Schinke, Photodissociation Dynamics.Cambridge University Press, Cambridge, (1993).

[2] S.Yu. Grebenshchikov, R. Schinke and W.L.Hase, in Unimolecular Kinetics, N. Green ed.(Elsevier, Amsterdam, 2003).

[3] Z.-W. Qu, H. Zhu and R. Schinke, Chem. Phys.Lett. 377 (2003) 359.

[4] H. Zhu et al., Chem. Phys. Lett. 384 (2004) 45.[5] Z.-W. Qu et al., J. Chem. Phys. 121 (2004) 11731.

[6] Z.-W. Qu et al., J. Chem. Phys. 123 (2005)074305.

[7] K. Mauersberger et al., Adv. At. Mol. Opt.Physics 50 (2005) 1.

[8] R. Schinke et al., Ann. Rev. Phys. Chem. 57 (2006)625-661.[9] R. Schinke and P. Fleurat-Lessard, J. Chem.

Phys. 120 (2005) 094317.

2.4.2.2 Mathematical Physics

Folkert Müller-Hoissen A. Dimakis (Aegean, Greece)

Solitons and ›integrable‹ systems.Continuum physics and classical field theoryis mathematically modelled with, typicallynonlinear, partial differential equations(PDEs). These exhibit very peculiar phenom-ena, ranging from chaos to organizationalbehavior. The latter is typically related to theexistence of symmetries of the respectivePDE beyond those given by special groups ofcoordinate transformations. An extreme caseis met if a PDE possesses an infinite numberof (independent) symmetries, in which casethe PDE extends to an infinite tower of ›com-patible‹ PDEs, a so-called hierarchy [1]. Themost famous example is given by the Korte-weg-deVries (KdV) equation which pos-sesses ›multi-soliton solutions‹: an arbitrarynumber of solitary waves flow through eachother and regain their initial form after-wards. By now quite a number of PDEs withproperties similar to the KdV equation havebeen found and frequently recovered as cer-tain limits of physical models. Several beau-tiful (including some rather miraculous)mathematical techniques have been devel-oped to unravel the essential structure ofsuch equations. All this is covered nowadaysunder the heading of ›integrable systemstheory‹. For equations in this class there aretypically methods to obtain exact solutions(e.g., via Bäcklund transformations, or the

powerful inverse scattering method). This isextremely important in particular in areas ofphysics where relevant exact solutions areextremely difficult to find and numericalmethods difficult to apply, which is not onlythe case in general relativity.Despite enormous progress, this field is stillfar from a kind of completion. Neither arethere satisfactory ›integrability tests‹, nor dowe understand well enough the relations be-tween the various existing notions of ›inte-grability‹ and the extent to which they canbe applied and still generalized. On the otherhand, it is quite natural that this field is notreally bounded, but rather continues to ex-tend into various directions, in particular to-wards handling equations which are not›completely integrable‹. Our project is not confined to a particularcorner of this field. Presently particular em-phasis is put on generalizations of ›inte-grable equations‹ to the case of noncommu-tative dependent variables, like matrices offunctions. This covers also the case of sys-tems of coupled equations and thus achievesa certain unification. In the following webriefly describe three of our most recent re-search achievements.The ubiquitousness of the famous Kadomt-sev-Petviashvili (KP) hierarchy, which gen-eralizes the KdV hierarchy, in mathematics

Projects



(in particular differential and algebraicgeometry) and physics (from hydrodynamicsto string theory) still remains a bit of a mys-tery. In a recent work [2] we showed that, forany weakly nonassociative algebra, gener-ated by a single element, the KP hierarchyshows up in the algebraic structure of com-muting derivations. As a consequence, anysuch algebra leads to a solution of the KP

hierarchy, and in particular the multi-solitonsolutions are obtained in this way. Theessential and amazing point is that thenonassociative structure achieves to decou-ple the KP hierarchy of PDEs into a hierarchyof ordinary differential equations (though ina nonassociative algebra), which is easy tosolve. Integrable models with dependentvariables in nonassociative algebras of a spe-cial type already appeared in the work ofSvinolupov [3] and collaborators.Starting from work of Okhuma and Wadati[4], an analysis of the algebraic structure ofthe soliton solutions of the (noncommuta-tive) KP hierarchy led us to the proof of acorrespondence between its equations and acertain set of identities in an abstract alge-bra, carrying in particular a quasi-shuffleproduct [5,6]. This algebra expresses thebuilding laws of the KP hierarchy equations.There are more identities in this algebra andit turned out that these correspond to exten-sions of the KP hierarchy in the case wherethe product between dependent variables isdeformed in the sense of deformation quan-tization (see also [7,8] for explorations of de-formed hierarchies). Soliton solutions of thedeformed equations are deformations of or-dinary solitons and the deformation parame-ters should be fixed in some physical model.So far objects of this type made their appear-ance only in the context of string theory. Anindependent motivation for further explo-rations of this framework stems from the factthat surprising relations between differentintegrable systems show up. For example,the simplest deformation equation of the(deformed) KdV equation has the form ofthe Heisenberg ferromagnet equation [7].A central role in the mathematics of inte-

grable hierarchies is played by the Gelfand-Dickey formalism [1]. The latter, however,introduces an infinite number of auxiliarydependent variables and it is often desirableto turn the hierarchy equations into a formwhich only makes reference to the relevantdependent variables. We developed a con-venient and unifying formalism to achievethis. The results are representations of hier-archies in terms of functional equations de-pending on auxiliary parameters [9,10]. Inseveral cases of scalar equations (with com-muting dependent variables), correspondingrepresentations of hierarchies are availablein terms of Hirota τ -functions (in particularas so-called ›Fay identitities‹). In contrast,our formalism also covers the noncommuta-tive case. Furthermore, it provides bridgesbetween the Gelfand-Dickey formalism andin particular approaches to integrable sys-tems as formulated by Bogdanov andKonopelchenko [11], and Adler, Bobenkoand Suris [12] (discrete zero curvature repre-sentation).

Development and applications ofnoncommutative geometry.

›Noncommutative geometry‹ is a mathemati-cal framework which primarily aims at gen-eralizations of concepts of differential geom-etry from a manifold (respectively, the alge-bra of smooth functions on it) to a(noncommutative) associative algebra [13].In particular, it provides a setting for ›dis-crete geometry‹, based on directed graphs(digraphs). The latter play an important rolein many areas of mathematics and appliedsciences. In particular, they provide a frame-work for discretizations and discrete analogsof continuum models. The observation [14]that directed graphs are in correspondencewith differential calculi on discrete sets setthe stage for a formulation of discrete mod-els in close analogy with continuum models,if the latter possess a convenient formula-tion in terms of differential forms. A differ-ential calculus (more generally on an asso-ciative algebra) is an analog of the calculusof differential forms on a manifold. The


Projects

aforementioned examples are ›noncommuta-tive‹ in the sense that differentials and func-tions satisfy nontrivial commutation rela-tions. The basic rules of the calculus of dif-ferential forms, i.e. the Leibniz rule and thenilpotency of the exterior derivative, are pre-served, however. Illuminating examples ofapplications are the following.

• The Wilson action of lattice gauge the-ory results from the Yang-Mills actionby deformation of the continuum differ-ential calculus to a differential calculusassociated with a hypercubic latticegraph [15, 16].

• Some discrete integrable models are ob-tained from continuum models via sucha deformation of the continuum differ-ential calculus, carried out such thatcertain ›integrability aspects‹ are pre-served [17, 18]. The well-known inte-grable Toda lattice results in this way asa deformation of the linear wave equa-tion in 1+1 dimensions.

A differential calculus provides the basis forthe introduction of geometric concepts, likemetric, connection and curvature. In inte-grable systems theory, for example, the con-dition of vanishing curvature plays a crucial

role. Noncommutative geometry supplies uswith corresponding generalizations (see also[19]), and thus new possibilities.Over the years we further developed this for-malism aiming at applications ranging fromdiscretization (or rather discrete versions) ofgauge theories and General Relativity tosome kind of ›integrable‹ network models.More recent contributions to this project in-clude the development of gauge theory anddifferential geometry on (bicovariant) grouplattices [20, 21]. In the case of this specialclass of digraphs, we established a clear geo-metric interpretation of the a priori ratherabstract algebraic generalizations of contin-uum geometric concepts. In particular, thisframework allows the formulation of dis-crete analogs of differential geometric equa-tions, including those of gravity theories.A special class of differential calculi associ-ated with automorphisms of the underlyingalgebra has been the subject of some otherpublications [22, 23]. This generalizes rele-vant examples like the differential calculusassociated with a hypercubic lattice graphmentioned above, but even covers examplesof bicovariant differential calculi on quan-tum groups.

[1] L.A. Dickey, Soliton Equations and HamiltonianSystems, World Scientific (2003)[2] A. Dimakis and F. Müller-Hoissen, nlin.SI/0601001[3] S.I. Svinolupov, Theor. Math. Phys. 87 (1991) 611.[4] K. Okhuma and M. Wadati, J. Phys. Soc. Japan 52(1983) 749.[5] A. Dimakis and F. Müller-Hoissen, J. Phys. A:Math.Gen. 38 (2005) 5453.[6] A. Dimakis and F. Müller-Hoissen, Czech. J. Phys.55 (2005) 1385.[7] A. Dimakis and F. Müller-Hoissen, J. Phys. A:Math.Gen. 37 (2004) 4069.[8] A. Dimakis and F. Müller-Hoissen, J. Phys. A:Math.Gen. 37 (2004) 10899.[9] A. Dimakis and F. Müller-Hoissen, nlin.SI/0603018[10] A. Dimakis and F. Müller-Hoissen,nlin.SI/0603048[11] L.V. Bogdanov and B.G. Konopelchenko, J. Math.Phys. 39 (1998) 4701.[12] V.E. Adler, A.I. Bobenko and Yu.B. Suris, Comm.Math. Phys. 233 (2003) 513.[13] [13] J. Madore, in An Introduction toNoncommutative Differential Geometry and its Physical

Applications, (Cambridge University Press, Cambridge1999)Applications, Cambridge University Press (1999)[14] A. Dimakis and F. Müller-Hoissen, J. Math. Phys.35 (1994) 6703.[15] A. Dimakis, F. Müller-Hoissen and T. Striker, J.Phys. A: Math. Gen. 26 (1993) 1927.[16] A. Dimakis, F. Müller-Hoissen and T. Striker,Phys. Lett. B 300 (1993) 141.[17] A. Dimakis and F. Müller-Hoissen, J. Phys. A:Math. Gen. 29 (1996) 5007.[18] A. Dimakis and F. Müller-Hoissen, Lett. Math.Phys. 39 (1997) 69.[19] A. Dimakis and F. Müller-Hoissen, J. Phys. A 29(1996) 7279.[20] A. Dimakis and F. Müller-Hoissen, J. Math. Phys.44 (2003) 1781.[21] A. Dimakis and F. Müller-Hoissen, J. Math. Phys.44 (2003) 4220.[22] A. Dimakis and F. Müller-Hoissen, J. Phys. A:Math. Gen. 37 (2004) 2307.[23] A. Dimakis and F. Müller-Hoissen, Czech. J. Phys.54 (2004) 1235.

Projects


Publications

1996

H.-U. Bauer, R. Der, and M. Herrmann,»Controlling the magnification factor of self-organizing feature maps«, Neural Comp. 8 (1996)757.

H.-U. Bauer, M. Riesenhuber, and T. Geisel,»Phase diagrams of self-organizing maps«, Phys.Rev. E 54 (1996) 2807.

H.-U. Bauer et al., »Self-organizing neuronalmaps«, Bericht 102 (1996) 1.

H.-U. Bauer, and M. Riesenhuber, »Calculatingconditions for the emergence of structure in self-organizing maps«, in Proc. CNS 96 (1996).

H.-U. Bauer et al., »Selbstorganisierende neurona-le Karten«, Spektrum der Wissenschaft 4 (1996)38.

U. Ernst et al., »Identifying oscillatory and sto-chastic neuronal behaviour with high temporalprecision in macaque monkey visual cortex«, inProc. CNS 96 (1996).

K. Pawelzik et al., »Orientation contrast sensitivi-ty from long-range interactions in visual cortex«,in Proc. NIPS 96 (1996).

R. Fleischmann et al., »Nonlinear dynamics ofcomposite fermions in nanostructures«, Europhys.Lett. 36 (1996) 167.

F. Hoffsümmer et al., »Sequential bifurcation anddynamic rearrangement of columnar patternsduring cortical development«, in Proc. CNS 96 (J.Bower ed.) (1996).

R. Ketzmerick, »Fractal conductance fluctuationsin generic chaotic cavities«, Phys. Rev. B 54(1996) 10841.

K. Pawelzik, J. Kohlmorgen, and K.-R. Müller,»Annealed Competition of Experts for aSegmentation and Classification of SwitchingDynamics«, Neural Comp. 8 (1996) 340.

M. Riesenhuber, H.-U. Bauer, and T. Geisel,»Analyzing phase transitions in high-dimensionalself-organizing maps«, Biol. Cyb. 75 (1996) 397.

M. Riesenhuber, H.-U. Bauer, and T. Geisel, »On-center and off-center cell competition generates

oriented receptive fields from non-oriented stim-uli in Kohonen's self-organizing map«, in Proc.CNS 96 (1996).

M. Riesenhuber, H.-U. Bauer, and T. Geisel,»Analyzing the formation of structure in high-dimensional self-organizing reveals differences tofeature map models«, in Proc. ICANN 96, SpringerVerlag (1996) 415.

J. H. Smet et al., »Magnetic focusing of compositefermions through arrays of cavities«, Phys. Rev.Lett. 77 (1996) 2272.

J. H. Smet et al., »Evidence for quasi-classicaltransport of composite fermions in an inhomoge-neous effective magnetic field«, Semicond. Sci.Technol. 11 (1996) 1482.

F. Wolf et al., »Organization of the visual cortex«,Nature 382 (1996) 306.

1997

H.-U. Bauer, and T. Villmann, »Growing a hyper-cubical output space in a self-organizing featuremap«, IEEE Trans. Neur. Netw. 8 (1997) 218.

H.-U. Bauer, D. Brockmann, and T. Geisel,»Analysis of ocular dominance pattern formationin a high-dimensional self-organizing-mapmodel«, Network 8 (1997) 17.

H.-U. Bauer et al., »Analysis of SOM-based mod-els for the development of visual maps«, inProceedings to the WSOM '97 (L. P. Oy ed.),Helsinki University of Technology (1997) 233.

H.-U. Bauer, and W. Schöllhorn, »Self-organizingmaps for the analysis of complex movement pat-terns«, Neural Processing Lett. 5 (1997) 193.

D. Brockmann et al., »Conditions for the jointemergence of orientation and ocular dominancein a high-dimensional self-organizing map«, inProc. CNS 97 (J. Bower ed.) (1997).

D. Brockmann et al., »SOM-model for the devel-opment of oriented receptive fields and orienta-tion maps from non-oriented ON-center OFF-cen-ter inputs«, in Artificial Neural Networks - ICANN97 (J.-D. Nicoud ed.), Springer (1997) 207.

2.5.1 Nonlinear Dynamics (1996–2006)

2.5 Publications


K. Pawelzik et al., »Geometry of orientation pref-erence map determines nonclassical receptivefield properties«, in Proc. ICANN 97 (1997).

M. Herrmann, H.-U. Bauer, and T. Villmann,»Topology preservation in neural maps«, inESANN 97 (1997) 205.

D. W. Hone, R. Ketzmerick, and W. Kohn, »TimeDependent Floquet Theory and Absence of anAdiabatic Limit«, Phys. Rev. A 56 (1997) 4045.

R. Ketzmerick et al., »What determines thespreading of a wave packet?« Phys. Rev. Lett. 79(1997) 1959.

J. H. Smet et al., »Enhanced soft-wall effects forcomposite fermions in magnetic focusing andcommensurability experiments«, Physica E 1(1997) 153.

D. Springsguth, R. Ketzmerick, and T. Geisel,»Hall Conductance of Bloch Electrons in aMagnetic Field«, Phys. Rev. B 56 (1997) 2036.

1998

M. Bethge, K. Pawelzik, and T. Geisel, »TemporalCoding and Synfire Chains in Chaotic Networks«,in Göttingen Neurobiology Report 1998,Proceedings of the 26th Göttingen NeurobiologyConference (R. Wehner ed.), Thieme, 2 (1998)757.

U. Ernst, K. Pawelzik, and T. Geisel, »Analysingthe Context Dependence of Receptive Fields inVisual Cortex«, in Perspectives in NeuralComputing: ICANN 98 (T. Ziemke ed.), Springer-Verlag, 1 (1998) 343.

U. Ernst, K. Pawelzik, and T. Geisel, »Orientationpreferences geometry modulates nonclassicalreceptive field properties«, in New Neuroethologyon the Move - Proceedings of the 26th GöttingenNeurobiology Conference (R. Wehner ed.), Thieme(1998) 759.

U. Ernst, K. Pawelzik, and T. Geisel, »Delay-induced multistable synchronization of biologicaloscillators«, Phys. Rev. E 57 (1998) 2150.

U. Ernst et al., »Orientation contrast enhance-ment modulated by differential long-range inter-action in visial cortex«, in ComputationalNeuroscience: Trends in Research (CNS 97),Plenum Press (1998) 361.

J. Eroms et al., »Magnetotransport in large diame-ter InAs/GaSb antidot lattices«, Physica B 256-258 (1998) 409.

C. W. Eurich, U. Ernst, and K. Pawelzik,»Continuous Dynamics of Neuronal Delay

Adaption«, in Perspectives in Neural Computing,International Conference on Artificial NeuralNetworks, ICANN 98 (T. Ziemke ed.), Springer-Verlag, 1 (1998) 355.

M. Herrmann, K. Pawelzik, and T. Geisel, »Self-Localization by Hidden Representations«, inProceedings for the 8th International Conferenceon Artificial Neural Networks, ICANN 98 (T.Ziemke ed.), Springer, 2 (1998) 1103.

M. Herrmann, K. Pawelzik, and T. Geisel, »Self-localization of a robot by simultaneous self-organization of place and direction selectivity«, inProceedings Second International Conference onCognitive and Neural Systems, Boston 1998(1998) 79.

R. Ketzmerick, K. Kruse, and T. Geisel, »AvoidedBand Crossings: Tuning Metal-InsulatorTransitions in Chaotic Systems«, Phys. Rev. Lett.80 (1998) 137.

R. Ketzmerick et al., »A covering property ofHofstadter's butterfly«, Phys. Rev. B 58 (1998)9881.

J. Lin et al., »Irregular synchonous activity in sto-chastically-coupled networks of integrate-and-fireneurons«, Network 9 (1998) 333.

S. Löwel et al., »The layout of orientation andocular dominance domains in area 17 of strabis-mic cats«, European Journal of Neuroscience 10(1998) 2629.

N. Mayer et al., »Orientation Maps From NaturalImages«, in Proceedings of the 26th GöttingenNeurobiology Conference (R. Wehner ed.),Thieme, 2 (1998) 759.

N. Mayer et al., »A Cortical Interpretation ofASSOMs«, in Proceedings of the 8th InternationalConference on Artificial Neural Networks, ICANN98 (T. Ziemke ed.), Springer, 2 (1998) 961.

K. Pawelzik et al., »Orientation PreferenceGeometry Modulated Nonclassical Receptive FieldProperties«, in New Neuroethology on the Move -Proceedings of the 26th Göttingen NeurobiologyConference, Georg-Thieme-Verlag (1998) 759.

H.-E. Plesser, »Noise turns Integrate-Fire Neuroninto Bandpass Filter«, in New Neuroethology onthe Move, Proceedings of the 26th GöttingenNeurobiology Conference (R. Wehner ed.), Thieme(1998) 760.

M. Riesenhuber et al., »Breaking RotationalSymmetry in a self-organizing map model for ori-entation map development«, Neural Computation10 (1998) 717.

A. S. Sachrajda et al., »Fractal conductance fluc-tuations in a soft wall stadium and a SinaiBilliard«, Phys. Rev. Lett. 80 (1998) 1948.


Publications

J. H. Smet et al., »Composite fermions in magnet-ic focusing and commensurability experiments«,Physica B 249 (1998) 15.

T. Villmann, and M. Herrmann, »MagnificationControl in Neural Maps«, in European Symposiumon Artificial Neural Networks, ESANN 98, D facto(1998) 191.

F. Wolf, and T. Geisel, »Spontaneous pinwheelannihilation during visual development«, Nature395 (1998) 73.

J. X. Zhong, and T. Geisel, »Level fluctuations inquantum systems with multifractal eigenstates«,Phys. Rev. E 59 (1998)

1999

H.-U. Bauer, M. Herrmann, and T. Villmann,»Neural Maps and topographic VectorQuantization«, Neural Networks 12 (1999) 659.

D. Brockmann, and T. Geisel, »The Lévy-FlightNature of Gaze Shifts«, in Proceedings of the 27thGöttingen Neurobiology Conference (U. Eysel ed.),Thieme, I (1999) 876.

M. Diesmann, M.-O. Gewaltig, and A. Aertsen,»Stable Propagation of Synchronous Spiking inCortical Neural Networks«, Nature 402 (1999)529.

T. Dittrich et al., »Spectral Statistics in ChaoticSystems with two Identical Connected Cells«, J.Phys. A 32 (1999) 6791.

T. Dittrich et al., »Spectral correlations in SystemsUndergoing a Transition from Periodicity toDisorder«, Phys. Rev. E 59 (1999) 6541.

S. Dodel, J. M. Herrmann, and T. Geisel,»Components of brain activity - Data analysis forfMRI«, in Proc. ICANN 99, 2 (1999) 1023.

B. Elattari, and T. Kottos, »One-dimensionalLocalization in the Presence of Resonances«,Phys. Rev. B 59 (1999) 5265.

U. Ernst, »Struktur und Dynamik lateralerWechselwirkungen im primären visuellenKortex«, PhD thesis, MPI fürStrömungsforschung, Göttingen (1999).

U. Ernst, K. Pawelzik, and M. V. T. a. Sahar-Pikielny, »Relationships Between Cortical Mapsand Receptive are Determined by Lateral CorticalFeedback«, in Proceedings of the 27th GöttingenNeurobiology Conference, Georg-Thieme-Verlag(1999) 168.

U. Ernst et al., »Relation Between Retinotopicaland Orientation Maps in Visual Cortex«, NeuralComputation 11 (1999) 375.

U. Ernst et al., »Theory of Nonclassical ReceptiveField Phenomena in the Visual Cortex«,Neurocomputing 26-27 (1999) 367.

J. Eroms et al., »Skipping orbits and enhancedresistivity in large-diameter InAs/GaSb antidotlat-tices«, Phys. Rev. B 59 (1999) 7829.

C. W. Eurich, and U. Ernst, »Avalanches ofActivity in a Network of Integrate-and-FireNeurons with Stochastic Input«, in Icann'99,Ninth International Conference on NeuralNetworks, IEE Conference Publication No. 470(1999) 545.

C. W. Eurich et al., »Dynamics of Self-OrganizedDelay Adaptation«, Phys. Rev. Lett. 82 (1999)1594.

S. Grün et al., »Detecting Unitary Events withoutDiscretization of Time«, Journal of NeuroscienceMethods 94 (1999) 67.

J. M. Herrmann, F. Emmert-Streib, and K.Pawelzik, »Autonomous robots and neuroetholo-gy: emergence of behavior from a sense of curios-ity«, in Proceedings of the 1st InternationalKhepera Workshop (U. Rückert ed.), HNIVerlagschriftenreihe, 64 (1999) 89.

J. M. Herrmann, and K. Pawelzik, »Simultaneousself-organization of place and direction selectivityin a neural model of self-localization«,Neurocomputing 26-27 (1999) 721.

J. M. Herrmann, K. Pawelzik, and T. Geisel, »Self-organization of predictive presentations«, in Proc.ICANN 99 (1999) 186.

W. Just, and H. Kantz, »Some Considerations onPoincaré Maps for Chaotic Flows«, J. Phys. A 33(1999) 163.

M. Kaschube et al., »The Variability ofOrientation Maps in Cat Visual Cortex«, inProceedings of the International Conference onArtificial Neural Networks (ICANN99) (A. Murrayed.), IEE, 1 (1999) 79.

M. Kaschube et al., »Quantifying the Variability ofPatterns of Orientation Columns in Cat's Area 17:Correlation-Lengths and Wavelengths«, inProceedings of the 27th Göttingen NeurobiologyConference, Thieme, 1 (1999) 480.

R. Ketzmerick, K. Kruse, and T. Geisel, »Efficientdiagonalization of kicked quantum systems«,Physica D (1999) 247.

T. Kottos, F. M. Izrailev, and A. Politi, »Finite-Length Lyapunov Exponents and Conductance for


Quasi 1D disordered Solids«, Physica D 131(1999) 155.

T. Kottos, and U. Smilansky, »Periodic OrbitTheory and Spectral Statistics for QuantumGraphs«, Annals of Physics 274 (1999) 76.

T. Kottos et al., »Chaotic Scattering ofMicrowaves«, Radio Science (1999)

S. Löwel, and F. Wolf, »Pattern Formation in theDeveloping Visual Cortex«, in Transport andStructure in Biophysics and Chemistry: LectureNotes in Physics (J. Parisi ed.), Springer Verlag(1999).

N. Mayer, J. M. Herrmann, and T. Geisel,»Receptive field formation in BD cats depends onhigher order statistics«, in Proceedings of the 27thGöttingen Neurobiology Conference (1999) 905.

H.-E. Plesser, »Aspects of Signal Processing inNoisy Neurons«, PhD thesis, UniversitätGöttingen, Göttingen (1999).

H.-E. Plesser, and T. Geisel, »Markov analysis ofstochastic resonance in a periodically driven inte-grate-and-fire neuron«, Phys Rev E 59 (1999)7008.

H.-E. Plesser, and T. Geisel, »Bandpass Propertiesof Integrate-Fire Neurons«, Neurocomputing26/27 (1999) 229.

S. Rathjen et al., »Variability and SpatialInhomogeneity of Patterns of OrientationColumns in Cat Striate Cortex«, in Society forNeuroscience Abstracts (1999) 278.

S. Rotter, and M. Diesmann, »Exact DigitalSimulation of Time-Invariant Linear Systems withApplications to Neuronal Modeling«, Biol. Cyb. 81(1999) 381.

O. Scherf, »Selbstorganisation neuronalerStrukturen durch Kooperation und Wettbewerb -Theorie der Bildung von Augendominanzmusternund Zeitreihenanalyse mit neuronalen Modellen«,PhD thesis, Johann-Wolfgang-Goethe-Universität,Frankfurt (1999).

O. Scherf et al., »Theory of ocular dominance pat-tern formation«, Phys. Rev. E 59 (1999)

F. Wolf, »Forschung und wissenschaftlichesRechnen«, (H. H. T. Plesser ed.), Gesellschaft fürwissenschaftliche Datenverarbeitung, Göttingen(1999) 109.

F. Wolf, and T. Geisel, »Pattern Formation in theDeveloping Visual Cortex: Topological Defects,their Generation, Motion, and Annihilation«,Statistical Mechanics of Biocomplexity: LectureNotes in Physics 527 (1999) 174.

2000

D. Bibitchkov, J. M. Herrmann, and T. Geisel,»Dynamics of associative memory networks withsynaptic depression«, in Proceedings of DYNN2000 (2000) 106.

D. Bibitchkov, J. M. Herrmann, and T. Geisel,»Synaptic depression in associative memory net-works«, in Proceedings of the IJCNN 2000 (2000).

D. Brockmann, and T. Geisel, »The ecology ofgaze shifts«, Neurocomputing 32-33 (2000) 643.

D. Cohen, F. Izrailev, and T. Kottos, »Wavepacketdynamics in energy space, RMT and quantum-classical correspondence«, Phys. Rev. Lett. 84(2000) 2052.

D. Cohen, and T. Kottos, »Quantum-mechanicalnon-perturbative response of driven chaoticmesoscopic systems«, Phys. Rev. Lett. 85 (2000)4839.

M. Diesmann, M.-O. Gewaltig, and A. Aertsen,»Analysis of spike synchronization in feed-for-ward cortical neural networks«, in Society forNeuroscience Abstracts (2000) 2201.

T. Dittrich et al., »Classical and quantum trans-port in deterministic Hamiltonian ratchets«,Ann.Phys., Leipzig 9 (2000) 755.

S. Dodel, J. M. Herrmann, and T. Geisel,»Comparison of temporal and spatial ICA in fMRIdata analysis«, in ICA 2000 Proceedings (2000)543.

S. Dodel, J. M. Herrmann, and T. Geisel,»Localization of brain activity - blind separationfor fMRI data«, Neurocomputing 32-33 (2000)701.

B. Elattari, and T. Kottos, »Effect of resonances onthe transport properties of two-dimensional disor-dered systems«, Phys. Rev. B 62 (2000) 9880.

U. Ernst et al., »Lateral Intracortical Interactionsand Random Inhomogeneities: A Key to theSpontaneous Emergence of Cortical Maps in V1«,in FENS Conference 2000 (2000).

C. Eurich et al., »Delay Adaptation in theNervous System«, Neurocomputing 32 (2000) 741.

D. Fliegner, A. Retey, and J. A. M. Vermaseren,»A parallel version of form 3«, in Proceedings ofACAT 2000 (2000).

T. Geisel, R. Ketzmerick, and K. Kruse, »QuantumChaos in Extended Systems: Spreading WavePackets and Avoided Band Crossings«, in NewDirections in Quantum Chaos, Proceedings ofEnrico Fermi School (U. Smilansky ed.) (2000)101.


Publications

S. Grün, and M. Diesmann, »Evaluation of high-er-order coincidences in multiple parallel process-es«, in Society for Neuroscience Abstracts (2000)2201.

J. M. Herrmann, K. Pawelzik, and T. Geisel,»Learning predictive representations«,Neurocomputing 32-33 (2000) 785.

B. Huckestein, R. Ketzmerick, and C. H.Lewenkopf, »Quantum transport through ballisticcavities: soft vs. hard quantum chaos«, Phys. Rev.Lett. 84 (2000) 5504.

L. Hufnagel et al., »Metal-insulator transitions inthe cyclotron resonance of periodic nanostruc-tures due to avoided band crossings«, Phys. Rev.B 62 (2000) 15348.

W. Just, »On the eigenvalue spectrum for time-delayed Floquet problems«, Physica D 142 (2000)153.

W. Just et al., »Influence of stable Floquet expo-nents on time-delayed feedback control«, Phys.Rev. E 61 (2000) 5045.

M. Kaschube et al., »Building cortical architec-tures for peripheral and central vision«, in Societyfor Neuroscience Abstracts, 26 (2000) 1084.

M. Kaschube et al., »Quantifying the Variability ofPatterns of Orientation Domains in the VisualCortex of Cats«, Neurocomputing 32-33 (2000)415.

M. Kaschube et al., »Cortical architectures forperipheral and central vision«, European Journalof Neuroscience 12 (2000) 488.

R. Ketzmerick et al., »New class of eigenstates ingeneric Hamiltonian systems«, Phys. Rev. Lett. 85(2000) 1214.

R. Ketzmerick et al., »Bloch Electrons in aMagnetic Field - Why does Chaos send Electronsthe Hard Way ?« Phys. Rev. Lett. 84 (2000) 2929.

T. Kottos, and U. Smilansky, »Chaotic scatteringon graphs«, Phys. Rev. Lett. 85 (2000) 968.

K. Kruse, and F. Jülicher, »Actively contractingbundles of polar filaments«, Phys. Rev. Lett. 85(2000) 1778.

K. Kruse, R. Ketzmerick, and T. Geisel, »QuantumChaos and Spectral Transitions in the KickedHarper Model«, in Statistical and DynamicalAspects of Mesoscopic Systems. Proceedings of theXVI. Sitges Conference on Statistical Mechanics (J.M. Rubi ed.), Springer, Berlin (2000) 47.

S. Löwel et al., »Substantial genetic influence onvisual cortical orientation maps«, in Society forNeuroscience Abstracts, 26 (2000) 820.

S. Löwel et al., »Genetically controlled features ofvisual cortical orientation maps«, EuropeanJournal of Neuroscience 12 (2000) 127.

N. Mayer, »Die Entwicklung rezeptiver Felder undneuronaler Karten im visuellen Kortex«, PhD the-sis, Universität Göttingen, Göttingen (2000).

N. Mayer, J. M. Herrmann, and T. Geisel, »Thetime course of the emergence of orientation selec-tivity«, in European Journal of Neuroscience, 12,suppl. 11 (2000) 127.

N. Mayer, J. M. Herrmann, and T. Geisel, »TheImpact of Receptive Field Shape on Cortical MapFormation«, in Proc. of the 7th Int. Conf. on Neur.Inf. Processing (2000) 1443.

N. Mayer, J. M. Herrmann, and T. Geisel,»Retinotopy and spatial phase in topographicmaps«, Neurocomputing 2000 32-33 (2000) 447.

A. Ossipov, T. Kottos, and T. Geisel, »Statisticalproperties of phases and delay times of the one-dimensional Anderson model with one openchannel«, Phys. Rev. B 61 (2000) 11411.

H. E. Plesser, and W. Gerstner, »Escape RateModels for Noisy Integrate-and-Fire Neurons«,Neurocomputing 32-33 (2000) 219.

H. E. Plesser, and W. Gerstner, »Noise in inte-grate-and-fire neurons: from stochastic input toescape rates.« Neural Computation 12 (2000) 367.

A. Riehle et al., »Dynamical Changes andTemporal Precision of Synchronized SpikingActivity in Monkey Motor Cortex DuringMovement Preparation«, Journal of Physiology(Paris) 94 (2000) 569

H. Schanz, and U. Smilansky, »Periodic-orbit the-ory of Anderson localization on graphs«, Phys.Rev. Lett. 84 (2000) 1427.

H. Schanz, and U. Smilansky, »Spectral Statisticsfor Quantum Graphs: Periodic Orbits andCombinatorics«, Philosophical Magazine 80(2000)

F. Schmüser, W. Just, and H. Kantz, »On the rela-tion between coupled map lattices and kineticIsing models«, Phys. Rev. E 61 (2000) 3675.

M. Schnabel, and T. Wettig, »Fake symmetry tran-sitions in lattice Dirac spectra«, Phys. Rev. D 62(2000) 034501.

D. Springsguth, »Spektrum und Transport fürBloch-Elektronen im Magnetfeld«, PhD thesis,Johann-Wolfgang-Goethe-Universität Frankfurt(2000).

F. Steinbach et al., »Statistics of resonances andof delay times in quasiperiodic Schrödinger equa-


tions«, Phys. Rev. Lett. 85 (2000) 4426.

T. Tetzlaff et al., »The prevalence of colinear con-tours in the real world«, European Journal ofNeuroscience 12 (2000) 286.

M. Timme, T. Geisel, and F. Wolf, »System ofunstable attractors induces desynchronizationand attractor selection in neural networks withdelayed interactions«, in Society for NeuroscienceAbstracts (2000) 1969.

M. Timme, T. Geisel, and F. Wolf, »Unstable syn-chronization in networks of integrate-and-fireneurons«, European Journal of Neuroscience 12(2000) 194.

M. Weiss, T. Kottos, and T. Geisel, »Scaling prop-erties of one-dimensional Anderson models in anelectric field: Exponential vs. factorial localiza-tion«, Phys. Rev. B 62 (2000) 1765.

M. Weiss, and T. Nilsson, »Protein sorting in theGolgi apparatus: A consequence of maturationand triggered sorting«, FEBS Lett. 486, 2 486(2000) 2.

F. Wolf, and T. Geisel, »A general theory of pin-wheel stability«, in Society for NeuroscienceAbstracts (2000).

F. Wolf, and T. Geisel, »Are pinwheels essential ?«European Journal of Neuroscience 12 (2000) 75.

F. Wolf et al., »How can squint change the spac-ing of ocular dominance columns?« J. Physiol. 94(2000) 525.

2001

D. Bibitchkov, J. M. Herrmann, and T. Geisel,»Pattern and sequence storage with dynamicsynapses«, in 28th Göttingen NeurobiologyConference, Göttingen, Thieme Verlag (2001) 854.

D. Cohen, and T. Kottos, »Parametric dependentHamiltonians, wavefunctions, random-matrix the-ory, and quantal-classical correpondence«, Phys.Rev. E 63 (2001) 36203.

M. Diesmann et al., »State Space Analysis ofSynchronous Spiking in Cortical NeuralNetworks«, Neurocomputing 38-40 (2001) 565.

T. Dittrich, B. Mehlig, and H. Schanz, »SpectralSignatures of Chaotic Diffusion in Systems withand without Spatial Order«, Physica E 9 (2001)494.

S. Dodel, J. M. Herrmann, and T. Geisel,»Emergent Neural Computational ArchitecturesBased on Neuroscience - Towards Neuroscience-Inspired Computing. Lecture Notes in Computer

Science 2036«, (D. J. Willshaw ed.), Springer(2001) 39.

S. Dodel, J. M. Herrmann, and T. Geisel,»Temporal Versus Spatial PCA and ICA in DataAnalysis for fMRI«, in 28th GöttingenNeurobiology Conference, Göttingen, ThiemeVerlag (2001) 897.

S. Dodel, M. Herrmann, and T. Geisel, »Is brainactivity spatially or temporally correlated?«NeuroImage 13 (2001) 110.

U. A. Ernst et al., »Intracortical Origin of VisualMaps«, Nature Neuroscience 4 (2001) 431.

M.-O. Gewaltig, M. Diesmann, and A. Aertsen,»Cortical Synfire-Activity: Configuration Spaceand Survival Probability«, Neurocomputing 38-40(2001) 621.

M. O. Gewaltig, M. Diesmann, and A. Aertsen,»Propagation of cortical synfire activity: survivalprobability in single trials and stability in themean«, Neural Networks 14 (2001) 657.

J. M. Herrmann, »Dynamical Systems forPredictive Control of Autonomous Robots«,Theory in Biosciences 120 (2001) 241.

L. Hufnagel, »Transport in Hamilton-Systemen:Von der Klassik zur Quantenmechanick«, PhDthesis, MPI für Strömungsforschung, Göttingen(2001).

L. Hufnagel et al., »Superballistic Spreading ofWave Packets«, Phys. Rev. E 64 (2001) 12301.

L. Hufnagel, R. Ketzmerick, and M. Weiss,»Conductance fluctuations of generic billiards:Fractal or isolated?« Europhys. Lett. 54 (2001)703.

M. Kaschube et al., »The prevalence of colinearcontours in the real world«, Neurocomputing 38-40 (2001) 1335.

M. Kaschube et al., »2-D Analysis of Patterns ofOcular Dominance Columns in Cat PrimaryVisual Cortex«, in 28th Göttingen NeurobiologyConference, Göttingen, Thieme Verlag (2001) 546.

M. Kaschube et al., »2-D Analysis of OcularDominance Patterns in Cat Primary VisualCortex«, in Society for Neuroscience Abstracts(2001) 821.

R. Ketzmerick, L. Hufnagel, and M. Weiss,»Quantum Signatures of Typical ChaoticDynamics«, Adv. Sol. St. Phys. 41 (2001) 473.

T. Kottos, and D. Cohen, »Failure of randommatrix theory to correctly describe quantumdynamics«, Phys. Rev. E 64 (2001) 065202.

T. Kottos, and H. Schanz, »Quantum graphs: A


Publications

model for Quantum Chaos«, Physica E 9 (2001)523.

K. Kruse, S. Camalet, and F. Jülicher, »Self-propa-gating Patterns in Active Filament Bundles«, Phys.Rev. Lett. 87 (2001) 138101.

N. Mayer, J. M. Herrmann, and T. Geisel, »ACurved Feature Map Model of Visual Cortex«, in28th Göttingen Neurobiology Conference,Göttingen, Thieme Verlag (2001) 851.

N. Mayer, J. M. Herrmann, and T. Geisel,»Signatures of Natural Image Statistics in CorticalSimple Cell Receptive Fields«, Neurocomputing38-40 (2001) 279.

A. Ossipov et al., »Quantum mechanical relax-ation of open quasiperiodic systems«, Phys. Rev.B 64 (2001) 224210.

K. Pichugin, H. Schanz, and P.Seba, »EffectiveCoupling for Open Billiards«, Phys. Rev. E 64(2001) 056227.

H. E. Plesser, and T. Geisel, »Stochastic resonancein neuron models: Endogenous stimulation revis-ited«, Phys. Rev. E 63 (2001) 031916.

H. Schanz et al., »Classical and quantumHamiltonian ratchets«, Phys. Rev. Lett. 87 (2001)070601.

M. Schnabel, F. Wolf, and T. Geisel, »Universalfine structure of orientation pinwheels«, inProceedings of the 28th Göttingen NeurobiologyConference, Thieme, 1 (2001) 258.

F. Steinbach, »Statistische Eigenschaften offenerund geschlossener Quantensysteme: vonQuantenchaos bis Quasiperiodizität«, PhD thesis,Georg-August-Universität, Göttingen (2001).

T. Tetzlaff, T. Geisel, and M. Diesmann, »Theground state of synfire structures«, in Proceedingsof the 28th Göttingen Neurobiology Conference,Thieme Verlag (2001) 260.

M. Timme, T. Geisel, and F. Wolf,»Synchronization and Desynchronization inNeural Networks with General Connectivity«, inSoc. Neurosci. Abstr., 27 (2001) 821.

M. Timme, T. Geisel, and F. Wolf, »Mechanismsof synchronization and desynchronization in neu-ral networks with general connectivity«, inProceedings of the 28th Göttingen NeurobiologyConference (G. W. Kreutzberg ed.), 1 (2001) 595.

M. Timme, F. Wolf, and T. Geisel, »Complex net-works of pulse-coupled oscillators: Exact stabilityanalysis of synchronous states«, in WE-HeraeusSeminar »Synchronization in Physics andNeuroscience« (2001).

M. Timme, F. Wolf, and T. Geisel, »Unstable syn-

chronization and switching among unstableattractors in spiking neural networks«, in 265.WE-Heraeus Seminar »Synchronization in Physicsand Neuroscience« (2001).

M. Timme, F. Wolf, and T. Geisel, »Unstableattractors in networks of pulse-coupled oscilla-tors«, in Europhysics Conference Abstracts, 25 F(2001) 20.

M. Timme, F. Wolf, and T. Geisel, »Unstableattractors in networks of biological oscillators«, inEuropean Dynamics Days 2001 - Book of Abstracts(2001) 51.

M. A. Topinka et al., »Coherent branched flow ina two-dimensional electron gas«, Nature 410(2001) 183.

M. Weiss, T. Kottos, and T. Geisel, »Taming chaosby impurities in two-dimensional oscillatorarrays«, Phys. Rev. E 63 (2001) 056211.

M. Weiss, T. Kottos, and T. Geisel, »Spreadingand localization of wavepackets in disorderedwires in a magnetic field«, Phys. Rev. B 63 (2001)R81306.

2002

A. Bäcker et al., »Isolated resonances inconductance fluctuations and hierarchical states«,Phys. Rev. E 66 (2002) 016211.

G. Berkolaiko, H. Schanz, and R. S. Whitney,»The Leading Off-Diagonal Correction to the FormFactor of Large Graphs«, Phys. Rev. Lett. 88(2002) 104101.

D. Bibitchkov, J. M. Herrmann, and T. Geisel,»Pattern storage and processing in attractor net-works with short-time synaptic dynamics«,Network: Comput. Neural Syst. 13 (2002) 115.

D. Bibitchkov, J. M. Herrmann, and T. Geisel,»Effects of short-time plasticity on the associativememory«, Neurocomputing 44-46 (2002) 329.

D. Brockmann, and I. M. Sokolov, »Lévy Flightsin External Force Fields: From Models toEquations«, Chemical Physics 284 (2002) 409.

S. Dodel, J. M. Herrmann, and T. Geisel,»Functional Connectivity by Cross-CorrelationClustering«, Neurocomputing 44-46 (2002) 1065.

C. W. Eurich, J. M. Herrmann, and U. A. Ernst,»Finite-size effects of avalanche dynamics«, Phys.Rev. E 66 (2002) 006137.

R. Fleischmann, and T. Geisel, »MesoscopicRectifiers based on Ballistic Transport«, Phys. Rev.Lett. 89 (2002) 016804.


S. Großkinsky, M. Timme, and B. Naundorf,»Universal Attractors of Reversible Aggregate-Reorganization Processes«, Phys. Rev. Lett. 88(2002) 245501.

S. Gruen, M. Diesmann, and A. Aertsen,»’Unitary Events’ in Multiple Single NeuronSpiking Activity. II. Non-Stationary Data«, NeuralComputation 14 (2002) 81.

L. Hufnagel et al., »Eigenstates Ignoring RegularAnd Chaotic Phase-Space Structures«, Phys. Rev.Lett. 89 (2002) 154101.

M. Kaschube et al., »Quantifying the Variability ofOrientation Maps in Ferret Visual Cortex«, inSociety for Neuroscience Abstracts (2002).

M. Kaschube et al., »Building cortical architec-tures for central and peripheral vision«, in FENSAbstr., 1 (2002) A051.13.

M. Kaschube et al., »Genetic Influence onQuantitative Features of NeocorticalArchitecture«, Journal of Neuroscience 22 (2002)7206.

T. Kottos, and M. Weiss, »Statistics of Resonancesand Delay Times: A Criterion for Metal-InsulatorTransitions«, Phys. Rev. Lett. 89 (2002) 056401.

K. Kruse, »A dynamic model for determining themiddle of Escherichia coli«, Biophys. J. 82 (2002)618.

K. Kruse, and K. Sekimoto, »Growth of finger-likeprotrusions driven by molecular motors«, Phys.Rev. E 66 (2002) 031904.

N. Mayer, J. M. Herrmann, and T. Geisel,»Curved Feature Metrics in Models of VisualCortex«, Neurocomputing 44-46 (2002) 533.

B. Naundorf, and J. Freund, »Signal detection bymeans of phase coherence induced through phaseresetting«, Phys Rev E 66 (2002) 040901.

A. Ossipov, T. Kottos, and T. Geisel, »Signaturesof Prelocalized States in Classically ChaoticSystems«, Phys. Rev. E 65 (2002) 055209(R).

M. Schnabel, T. Geisel, and F. Wolf, »Universalfine structure of orientation pinwheels«, inVerhandlungen der Deutschen PhysikalischenGesellschaft (2002).

T. Tetzlaff, T. Geisel, and M. Diesmann, »Theground state of cortical feed-forward networks«,Neurocomputing 44-46 (2002) 673.

M. Timme, F. Wolf, and T. Geisel, »Prevalence ofUnstable Attractors in Networks of Pulse-CoupledOscillators«, Phys. Rev. Lett. 89 (2002) 154105.

M. Timme, F. Wolf, and T. Geisel, »Coexistence ofRegular and Irregular Dynamics in Complex

Networks of Pulse-Coupled Oscillators«, Phys.Rev. Lett. 89 (2002) 258701.

M. Weiss, L. Hufnagel, and R. Ketzmerick,»Universal Power-Law Decay in HamiltonianSystems?« Phys. Rev. Lett. 89 (2002) 239401.

F. Wolf et al., »Pronounced Variability of the Sizeof Cat Primary Visual Cortex«, in Society forNeuroscience Abstracts (2002).

2003

G. Berkolaiko, H. Schanz, and R. S. Whitney,»Form Factor for a Family of Quantum Graphs«, J.of Physics A 36 (2003) 8373.

D. Brockmann, »Superdiffussion inInhomogeneous Scale-free Enviroments«, Where'sGeorge-August Universität, Göttingen (2003).

D. Brockmann, and T. Geisel, »Particle Dispersionon Rapidly Folding Random Hetero-Polymers«,Phys. Rev. Lett. 91 (2003) 048303.

D. Brockmann, and T. Geisel, »Lévy Flights inInhomogeneous Media«, Phys. Rev. Lett. 90(2003) 170601.

D. Cohen, and T. Kottos, »Non-perturbativeresponse: Chaos versus Disorder«, J. of Phys. A:Math. and General 36 (2003) 10151.

S. Gruen, A. Riehle, and M. Diesmann, »Effect ofcross-trial nonstationarity on joint-spike events«,Biological Cybernetics 88 (2003) 335.

M. Kaschube et al., »Localizing the ticklish spotsof cortical orientation maps«, in 2nd Symposiumof the Volkswagen Stiftung »Dynamics andAdaptivity of Neuronal Systems - IntegrativeApproaches to Analyzing Cognitive Functions«(2003).

M. Kaschube et al., »The Pattern of OcularDominance Columns in Cat Primary VisualCortex: Intra- and Interindividual Variability ofColumn Spacing and its Dependence on GeneticBackground«, European Journal of Neuroscience18 (2003) 3251.

M. Kaschube et al., »Are orientation preferencemaps attractors of a developmental dynamics?« inSociety for Neuroscience Abstracts, 29 (2003).

T. Kottos, and D. Cohen, »Quantum irreversibilityof energy spreading«, Europhys. Lett. 61 (2003)431.

T. Kottos, A. Ossipov, and T. Kottos, »Signaturesof Classical Diffusion in Quantum Fluctuations of2D Chaotic Systems«, Phys. Rev. E 68 (2003)066215.


Publications

T. Kottos, and U. Smilansky, »Quantum Graphs: ASimple Model for Chaotic Scattering«, Journal ofPhysics A: Mathematical and General 36 (2003)3501.

N. Mayer, J. M. Herrmann, and T. Geisel,»Shaping of Receptive Fields in Visual CortexDuring Retinal Maturation«, Journal ofComputational Neuroscience 15 (2003) 307.

C. Mehring et al., »Activity dynamics and propa-gation of synchronous spiking in locally connect-ed random networks«, Biological Cybernetics 88(2003) 395.

A. Ossipov, T. Kottos, and T. Geisel, »Fingerprintsof classical diffusion in open 2D mesoscopic sys-tems in the metallic regime«, Europhys. Lett. 62(2003) 719.

T. Prager, B. Naundorf, and L. Schimansky-Geier,»Coupled three-state oscillators«, Physica A 325(2003) 176.

H. Schanz, »Reaction Matrix for Dirichlet Billiardswith Attatched Waveguides«, Physica E 18 (2003)429.

H. Schanz, and T. Kottos, »Scars on QuantumNetworks Ignore the Lyapunov Exponent«, Phys.Rev. Lett. 90 (2003) 234101.

H. Schanz, M. Puhlmann, and T.Geisel, »Shotnoise in Chaotic Cavities from ActionCorrelations«, Phys. Rev. Lett. 91 (2003) 134101.

M. Schnabel et al., »The ticklish spots of corticalorientation maps«, in Proceedings of the 29thGöttingen Neurobiology Conference (2003) 611.

T. Tetzlaff et al., »The spread of rate and correla-tion in stationary cortical networks«,Neurocomputing 52-54 (2003) 949.

M. Timme et al., »Pinwheel generation with shift-twist symmetry«, in Society for NeuroscienceAbstracts, 29 (2003).

M. Timme, F. Wolf, and T. Geisel, »Unstableattractors induce perpetual synchronization anddesynchronization«, Chaos 13 (2003) 377.

M. Weiss, L. Hufnagel, and R. Ketzmerick, »Cansimple renormalization theories describe the trap-ping of chaotic trajectories in mixed systems?«Phys. Rev. E 67 (2003) 046209.

F. Wolf, and T. Geisel, »Universality in VisualCortical Pattern Formation«, Journal of Physiology– Paris 97 (2003) 253.

2004

D. Cohen, and T. Kottos, »Quantum dissipationdue to the interaction with chaos«, Phys. Rev. E69 (2004) 055201.

M. Denker et al., »Breaking Synchrony byHeterogeneity in Complex Networks«, Phys. Rev.Lett. 92 (2004) 074103.

M. C. Geisler et al., »Detection of a Landau Band-Coupling-Induced Rearrangement of the Hofstad-ter Butterfly«, Phys. Rev. Lett. 92 (2004) 256801.

M. Hiller et al., »Quantum Reversibility: Is therean Echo«, Phys. Rev. Lett. 92 (2004) 010402.

L. Hufnagel, D. Brockmann, and T. Geisel, »Forecast and Control of epidemics in a globalizedworld«, PNAS 101 (2004) 15124.

M. Kaschube et al., »Sensitive locations in orien-tation preference maps«, in Society forNeuroscience Abstracts, 30 (2004).

T. Kottos, and H. Schanz, »Statistical Properties ofResonance Width for Open Quantum Systems«,Waves in Random Media 14 (2004) S91.

T. Kottos, and M. Weiss, »Current Relaxation inNonlinear Random Media«, Phys. Rev. Lett. 93(2004) 190604.

K. Kreikemeier et al., »Large-scale reorganizationof orientation preference maps in visual cortex(area 18) of adult cats induced by intracorticalmicroststimulation (ICMS): an optical imagingstudy.« in FENS Abstracts, 2 (2004).

K. Kreikemeier et al., »Space-time characteristicsof orientation preference map (OPM) plasticity invisual cortex of adult cats induced by intracorti-cal microstimulation (ICMS)«, in Society forNeuroscience Abstracts, 30 (2004).

A. Ossipov, and T. Kottos, »Superconductor-poximity effect in hybrid structures: Fractalityversus Chaos«, Phys. Rev. Lett. 92 (2004) 017004.

K. F. Schmidt et al., »Plasticity of orientationpreference maps in adult visual cortex: is thererecovery?« in FENS Abstracts, 2 (2004).

K. F. Schmidt et al., »Adult plasticity: long-termrearrangement of orientation maps in cat visualcortex«, in Society for Neuroscience Abstracts, 30(2004).

M. Schnabel et al., »Signatures of shift-twistsymmetry in the layout of orientation preferencemaps«, in Society for Neuroscience Abstracts, 30(2004).

M. Timme, F. Wolf, and T. Geisel, »Topological


Speed Limits to Network Synchronization«, Phys.Rev. Lett. 92 (2004) 074101.

A. Zumdieck et al., »Long Chaotic Transients inComplex Networks«, Phys. Rev. Lett. 93 (2004)244103.

2005

P. Ashwin, and M. Timme, »When instabilitymakes sense«, Nature 436 (2005) 36.

D. Brockmann, L. Hufnagel, and T. Geisel,»Dynamics of Modern Epidemics«, in SARS: ACase Study in Emerging Infections (R. Weiss ed.),Oxford University Press (2005).

D. Cohen, T. Kottos, and H. Schanz, »Quantumpumping: The charge transported due to a trans-lation of a scatterer«, Phys. Rev. E 71 (2005)035202.

J. M. Herrmann, H. Schrobsdorff, and T. Geisel,»Localized activations in a simple neural fieldmodel«, Neurocomputing 65-66 (2005) 679.

M. Kaschube et al., »Orientation preference mapshave sensitive spots«, in Proceedings of the 30thGöttingen Neurobiology Conference (2005).

M. Kaschube et al., »Interareal coordination ofcolumn development in cat visual cortex«, inSociety for Neuroscience Abstracts (2005).

M. Kaschube et al., »Predicting sensitive spots invisual cortical orientation preference maps.« in11th Magdeburg International NeurobiologicalSymposium »Learning and Memory: cellular andSystematic Views« (2005).

K. Kreikemeier et al., »Space-time characteristicsof orientation preference map (OPM) plasticity invisual cortex of adult cats«, in Proceedings of the30th Göttingen Neurobiology Conference (2005).

A. Levina, J. M. Herrmann, and T. Geisel,»Dynamical Synapses Give Rise to a Power-LawDistribution of Neuronal Avalanches«, inNIPS*2005 (2005).

A. Méndez-Bermúdez et al., »Trends in Electro-Optics Research«, Nova Science Publishers,Hauppauge (2005) 231.

B. Naundorf, T. Geisel, and F. Wolf, »Actionpotential onset dynamics and the response speedof neuronal populations«, Journal ofComputational Neuroscience 18 (2005) 297.

B. Naundorf, T. Geisel, and F. Wolf, »Dynamicalresponse properties of a canonical model fortype-I membranes«, Neurocomputing 65 (2005)421.

M. Puhlmann et al., »Quantum decay of an openchaotic system: A semiclassical approach«,Europhysics Letters 69 (2005) 313.

H. Schanz, »Phase-Space Correlations of ChaoticEigenstates«, Phys. Rev. Lett. 94 (2005) 134101.

H. Schanz, T. Dittrich, and R. Ketzmerick,»Directed chaotic transport in Hamiltonian ratch-ets«, Phys. Rev. E 71 (2005) 026228.

H. Schanz, and M. Prusty, »Directed chaos in abilliard chain with transversal magnetic field«,Journal of Physics A: Mathematical and General38 (2005) 10085.

K. F. Schmidt et al., »Adult plasticity: Long-termchanges of orientation maps in cat visual cortex«,in Proceedings of the 30th Göttingen NeurobiologyConference (2005).

K. F. Schmidt et al., »Adult plasticity: Activity-dependent short- and long-term changes of func-tional maps in cat visual cortex«, in 11thMagdeburg International NeurobiologicalSymposium »Learning and Memory: cellular andSystematic Views« (2005).

M. Schnabel et al., »Signature of shift-twistSymmetry in the layout of orientation preferencemaps«, in Proceedings of the 30th GöttingenNeurobiology Conference (2005).

M. Schnabel et al., »Shift-twist Symmetry in natu-ral images and orientation maps«, in Society forNeuroscience Abstracts, 31 (2005).

M. Voultsidou, S. Dodel, and J. M. Herrmann,»Neural Networks Approach to Clustering ofActivity in fMRI Data«, IEEE Trans. Med. Imaging12 (2005) 987.

M. Weiss, P. Ashwin, and M. Timme, »Unstableattractors: existence and robustness in networksof oscillators with delayed pulse coupling«,Nonlinearity 18 (2005) 2035.

F. Wolf, »Symmetry, Multistability, and Long-Range Interactions in Brain Development«, Phys.Rev. Lett. 95 (2005) 208701.

F. Wolf, »Symmetry Breaking and PatternSelection in Visual Cortical Development«, inÉcole d'Été de Physique des Houches, 2003,Methods and Models in Neurophysics, Elsevier,Amsterdam (2005) 575.

2006

D. Brockmann, L. Hufnagel, and T. Geisel, »Thescaling laws of human travel«, Nature 439 (2006)462.

M. Hiller et al., »Wavepacket Dynamics, Quantum


Publications

Reversibility and Random Matrix Theory«, Annalsof Physics 321 (2006) 1025.

J. A. Méndez-Bermúdez, T. Kottos, and D. Cohen,»Parametric invariant random matrix model andthe emergence of multifractality«, Physical ReviewE 73 (2006) 036204.

B. Naundorf, F. Wolf, and M. Volgushev, »Uniquefeatures of action potential initiation in corticalneurons«, Nature 440 (2006) 1060.

M. Prusty, and H. Schanz, »Signature of DirectedChaos in the Conductance of a Nanowire«, Phys.Rev. Let. 96 (2006) 130601.

M. Schnabel et al., »Signatures of shift-twist sym-metry in natural images and orientation maps«,in FENS Abstracts (2006).

M. Timme, T. Geisel, and F. Wolf, »Speed of syn-chronization in complex networks of neural oscil-lators: Analytic results based on Random MatrixTheory«, Chaos 16 (2006) 015108.


2003

J. Becker et al., »Complex dewetting scenarioscaptured by thin film models«, Nature Materials 2(2003) 59.

J. Buehrle, S. Herminghaus, and F. Mugele,»Interface profiles near three-phase contact linesin electric fields«, Phys. Rev. Lett. 91 (2003)086101.

H. M. Evans et al., »Structural polymorphism ofDNA-dendrimer complexes«, Phys. Rev. Lett. 91(2003) 075501.

M.A.Z. Ewiss et al., »Molecular dynamics andalignment studies of silica-filled 4-pentyl-4'-cyanobiphenyl (5CB) liquid crystal«, LiquidCrystals 30 (2003) 1.

D. Geromichalos et al., »Dynamic aspects of wet-ting in granular matter«, Contact AngleWettability and Adhesion 3 (2003) 385.

D. Geromichalos et al., »Mixing and condensationin a wet granular medium«, Phys. Rev. Lett. 90(2003) 168702.

S. Herminghaus, K. Jacobs, and R. Seemann,»Viscoelastic dynamics of polymer thin films andsurfaces« Eur. Phys. J. E 12 (2003) 101.

S. Herminghaus, »Harnessing the unstable«,Nature Materials 2 (2003) 11.

A. Klingner, S. Herminghaus, and F. Mugele,»Self-excited oscillatory dynamics of capillarybridges in electric fields«, Appl. Phys. Lett. 82(2003) 4187.

C. Neto et al., »Satellite hole formation duringdewetting: Experiment and simulation«, J. Phys.: Condens. Matter 15 (2003) 3355.

C. Neto et al., »Correlated dewetting patterns inthin polystyrene films«, J. Phys.: Condens. Matter15 (2003) 421.

T. Pfohl et al., »Trends in microfluidics with com-plex systems«, Chem. Phys. Chem. 4 (2003) 1291.

T. Pfohl and S. Herminghaus, »Mikrofluidik mitkomplexen Flüssigkeiten«, Physik Journal 2(2003) 35.

M. Schulz, B. Schulz, and S. Herminghaus,»Shear-induced solid-fluid transition in a wet gra-nular medium«, Phys. Rev. E 67 (2003) 052301.

R. Seemann, »Zerreißprobe für dünnePolymerfilme - Neue Erkenntnisse warum undwie dünne Flüssigkeitsfilme aufbrechen«,Chemie.de, 19. August 2003.

A. Thoss et al., »Kilohertz sources of hard x raysand fast ions with femtosecond laser plasmas.«,Journal of the Optical Society of America - OpticalPhysics B 20 (2003) 224.

A.A.M. Ward et al., »Effect of cyclic deformationson the dynamic-mechanical properties of Silica-filled Butyl Rubber«, Macromol. Mater. Eng. 288(2003) 971.

A.A.M. Ward et al., »Studies on the dielectricbehavior of Silica-filled Butyl Rubber Vulcanizatesafter cyclic deformation«, J. of Macromol. ScienceB 42 (2003) 1265.

2004

B. Abel et al., »Characterization of extreme utl-traviolet light-emitting plasmas from laser excitedfluorine containing liquid polymer jet target« J.Appl. Phys. 95 (2004) 7619.

A. Charvat et al., »New design for a time-of-flightmass spectrometer with a liquid beam laser des-orption ion source for the analysis of biomole-cules«, Rev. Sci. Instrum. 75 (2004) 1209.

M. Chul Choi et al., »Ordered patterns of liquidcrystal toroidal defects by microchannel confine-ment«, Proceedings of the National Academy ofSciences of the USA (PNAS) 101 (2004) 17340.

S. Herminghaus, R. Seemann. and K. Landfester,»Polymer Surface Melting Mediated by CapillaryWaves«, Phys. Rev. Lett. 93 (2004) 017801.

M. Kohonen et al., »On Capilary Bridges in WetGranular Materials«, Physica A 339 (2004) 7.

A. Otten and S. Herminghaus: »How plants keepdry: a physicist’s point of view«, Langmuir 20(2004) 2405.

M. Scheel, D. Geromichalos, and S. Herminghaus,»Wet granular matter under vertical agitation«, J.Phys.: Condens. Matter 16 (2004) 1.

B. Struth et al., »Application of microfocussing ata none specific beamline«, SRI 2003 Proceedings,AIP Conference Proceedings 705 (2004) 804.

2.5.2 Dynamics of Complex Fluids (2003–2006)


Publications

R. Weber et al., »Photoemission from aqueousalkali-iodine salt solutions, using EUV synchro-tron radiation«, J. Phys. Chem. B 108 (2004)4729.

B. Winter et al., »Full valence band photoemis-sion from liquid water, using EUV synchrotronradiation«, J. Phys. Chem. A 108 (2004) 2625.

B. Winter et al., »Molecular structure of surfaceactive salt solutions: photoelectron spectroscopyand molecular dynamics simulations of aqueousTetrabutyl-Ammonium Iodide«, J. Phys. Chem. B108 (2004) 14558.

M.A. Zaki Ewiss et al., »Wetting behaviour of5CB and 8CB and their binary mixtures above theisotropic transition«, Liquid Crystals 31 (2004)557.

2005

B. Abel et al., »Applications, features, and mecha-nistic aspects of liquid water beam desorptionmass spectrometry«, International Journal ofMass Spectrometry 243 (2005) 177.

A. Ahmad et al., »New multivalent cationic lipidsreveal bell curve for transfection efficiency versusmembrane charge density: lipid-DNA complexesfor gene delivery«, Journal of Gene Medicine 7(2005) 739.

J.-C. Baret et al., »Electroactuation of Fluid UsingTopographical Wetting Transitions«, Langmuir 21(2005) 12218.

M. Brinkmann, J. Kierfeld, and R. Lipowsky,»Stability of liquid channels or filaments in thepresence of line tension«, J. Phys. Condens.Matter 17 (2005) 2349.

T. v. Dorfmüller et al., Bergmann-Schaefer:Lehrbuch der Experimentalphysik: Gase,Nanosysteme, Flüssigkeiten, 2. Aufl, Hrsg. v. K.Kleinermanns, Walter de Gruyter -Verlagsgruppe,Berlin 2005.

K. Ewert et al., »Cationic lipid-DNA complexesfor non-viral gene therapy: relating supramolecu-lar structures to cellular pathways«, ExpertOpinion on Biological Therapy 5 (2005) 33.

A. Fingerle, S. Herminghaus, and V. Zaburdaev,»Kolmogorov-Sinai Entropy of the Dilute WetGranular Gas«, Phys. Rev. Lett 95 (2005) 198001.

Z. Fournier et al., »Mechanical properties of wetgranular materials«, J. Phys.: Condens. Matter 17(2005) S477.

P. Heinig and D. Langevin, »Domain shape relax

ation and local viscosity in stratifying foamfilms«, Eur. Phys. J. E 18 (2005) 483.

S. Herminghaus, »A Generic Mechanism ofSliding Friction between Charged Soft Surfaces«,Phys. Rev. Lett. 95 (2005) 264301.

S. Herminghaus (edtr.), J. Phys.: Condens. Matter17 (2005) (special issue on wetting).

S. Herminghaus, »Dynamics of wet granular mat-ter«, Advances in Physics 54 (2005) 221.

K. Jacobs, R. Seemann, and H. Kuhlmann«Trendbericht: Mikrofluidik« Nachrichten aus derChemie 53 (2005) 302 (eingeladener Beitrag).

S. Köster et al., »Microaligned collagen matricesby hydrodynamic focusing: controlling the pH-induced self-assembly«, MRS Proceedings 898E(2005) 0989-L05-21.

S. Köster, D. Steinhauser, T. Pfohl, »Brownianmotion of actin filaments in confining microchan-nels«, J. Phys.: Condens. Matter 17 (2005) S4091.

R. Lipowsky et al., »Droplets, bubbles, and vesi-cles at chemically structured surfaces«,J. Phys. Condens. Matter 17 (2005) S537.

R. Lipowsky et al., »Wetting, budding, andfusion-morphological transitions of soft surfaces«, J. Phys. Condens. Matter 17 (2005) S2885.

F. Mugele et al., »Electrowetting: A ConvenientWay to Switchable Wettability Patterns«,J. Phys.: Condens. Matter 17 (2005) S559.

A. Otten et al., »Microfluidics of soft matterinvestigated by small angle x-ray scattering«,Journal of Synchrotron Radiation 12 (2005) 745.

R. Seemann et al., »Wetting morphologies atmicrostructured surfaces«, Proc. Natl. Acad. Sci.USA 102 (2005) 1848.

R. Seemann et al., »Dynamics and structure for-mation in thin polymer melt films«, J. Phys.:Condens. Matter 17 (2005) S267.

B. Winter et al., »Effect of bromide on the interfa-cial structure of aqueous tetrabutylammoniumiodide: Photoelectron spectroscopy and moleculardynamics simulations«, Chemical Physics Letters410 (2005) 222.

B. Winter et al.,«Electron Binding Energies ofAqueous Alkali and Halide Ions: EUVPhotoelectron Spectroscopy of Liquid Solutionsand Combined Ab Initio and Molecular DynamicsCalculations«, J. Am. Chem. Soc. 127 (2005)2703.


2006

S. Arscott et al., »Capillary filling of miniaturizedsources for electrospray mass spectrometry«, J.Phys.: Condens. Matter 18 (2006) S677.

Ch. Bahr, »Surfactant-induced nematic wettinglayer at a thermotropic liquid crystal/water inter-face«, Phys. Rev. E 73 (2006) 030702(R).

J.-C. Baret and M. Brinkmann, »Wettability con-trol of droplet deposition and detachment«, Phys.Rev. Letters 96 (2006) 146106.

V. Designolle et al., »AFM study of defect-induceddepressions of the smectic-A/air interface«,Langmuir 22 (2006) 362.

R. Dootz et al., »Evolution of DNA compaction inmicrochannels«, J. Phys.: Condens. Matter 18(2006) S639.

R. Dootz et al., »Raman and surface enhancedRaman microscopy of microstructured PEI/DNAmultilayers«, Langmuir 22 (2006) 1735.

K. Ewert et al., »A columnar phase of dendriticlipid-based cationic liposome-DNA complexes forgene delivery: hexagonally ordered cylindricalmicelles embedded in a DNA honeycomb lattice«,Journal of the American Chemical Society 128(2006) 3998.

M. Fischer, P. Heinig and P. Dhar, »The viscousdrag of spheres and filaments moving in mem-branes or monolayers«, to appear in J. Fluid.Mech (2006).

C. Lutz et al., »Surmounting Barriers: The Benefitof Hydrodynamic Interactions«, Europhys. Lett. 74(2006) 719.

C. Priest, S. Herminghaus, and R. Seemann,»Generation of monodisperse gel emulsions in amicrofluidic device«, Applied Physics Letters 88(2006) 024106.

M. Schmiedeberg and H. Stark, »Superdiffusion ina Honeycomb Billiard«, Phys. Rev. E. 73 (2006)031113.

R. Seemann et al., »Freezing of Polymer ThinFilms and Surfaces: The Small Molecular WeightPuzzle«, to appear in J. Pol. Sci. B (2006).

R. Seemann, S. Herminghaus, and K. Jacobs,»Structure Formation in thin Liquid Films:Interface Forces Unleashed«, to appear inSpringer, Heidelberg, New York (2006)

B. Winter and M. Faubel, »Photoemission fromliquid aqueous solutions«, Chemical Reviews 106(2006) 1176.

B. Winter et al., »Electron binding energies ofhydrated H3O+ and OH-: Photoelectron spec-troscopy of aqueous acid and base solutions com-bined with electronic structure calculations«,Journal of the American Chemical Society 128(2006) 3864.


Publications

2003

A.M. Crawford, N. Mordant, and E. Bodenschatz,»Comment on Dynamical Foundations ofNonextensive Statistical Mechanics«, arXiv:physics/0212080 (2003).

K.E. Daniels and E. Bodenschatz, »Statistics ofDefect Motion in Spatiotemporal Chaos inInclined Layer Convection«, Chaos 13 (2003) 55.

K.E. Daniels, R.J. Wiener, and E. Bodenschatz,»Localized Transverse Bursts in Inclined LayerConvection«, Phys. Rev. Lett. 91, (2003) 114501.

B.L. Sawford et al., »Conditional andUnconditional Acceleration Statistics inTurbulence«, Phys. Fluids 15 (2003) 3478.

2004

K.E. Daniels, C. Beck, and E. Bodenschatz,»Defect Turbulence and Generalized StatisticalMechanics«, Physica D 193 (2004) 208.

C. Huepe et al., »Statistics of Defect Trajectoriesin Spatio-Temporal Chaos in Inclined LayerConvection and the Complex Ginzburg-LandauEquation«, Chaos 14 (2004) 864.

S. Luther, J. Rensen, and S. Guet, »Aspect RatioMeasurement Using a Four-Point Fiber-OpticalProbe«, Exp. Fluids 36 (2004) 326.

N. Mordant, A.M. Crawford, and E. Bodenschatz,»Experimental Lagrangian AccelerationProbability Density Function Measurement«,Physica D 193 (2004) 245.

N. Mordant, A.M. Crawford, and E. Bodenschatz,»Three-Dimensional Structure of LagrangianAcceleration in Turbulent Flows«, Phys. Rev. Lett.93 (2004) 214501.

D.S. Rhoads et al., »Using Microfluidic ChannelNetworks to Generate Gradients for Studying CellMigration«, In Cell Migration: DevelopmentalMethods and Protocols (J.-L. Guan, ed.),Humana Press, Totowa, NJ 294 (2004) 347.

E.A. Variano, E. Bodenschatz, and E.A. Cowen,»A Random Synthetic Jet Array DrivenTurbulence Tank«, Exp. Fluids 37 (2004) 613.

C. Voelz and E. Bodenschatz, »Experiments withDictyostelium Discoidium Amoebae in Different

Geometries«, in Dynamics and Bifurcation ofPatterns in Dissipative Systems G. Dangelmayrand I. Oprea (eds.), World Scientific Series onNonlinear Science 12, World Scientific(Singapore) (2004) 372.

T. Walter, E. Bodenschatz, and W. Pesch,»Dislocation Dynamics in Rayleigh-BénardConvection«, Chaos 14 (2004) 933.

2005

M.M. Afonso and D. Vincenzi, »Non LinearElastic Polymers in Random Flow«, J. Fluid Mech.540 (2005) 99.

J. Bluemink et al., »Asymmetry Induced ParticleDrift in Rotational Flow«, Phys. Fluids 17 (2005)072106.

A.M. Crawford, N. Mordant, and E. Bodenschatz,»Joint Statistics of the Lagrangian Accelerationand Velocity in Fully Developed Turbulence«,Phys. Rev. Lett. 94 (2005) 024501.

S. Guet, S. Luther, and G. Ooms, »Bubble Shapeand Orientation Determination with a Four-PointOptical Fiber Probe«, Exp. Therm. Fluid Sci. 29(2005) 803.

R.F. Katz, R. Ragnarsson, and E. Bodenschatz,»Tectonic Microplates in a Wax Model of Sea-Floor Spreading«, New J. Phys. 7 (2005) 37.

R.F. Katz and E. Bodenschatz, »Taking Wax for aSpin: Microplates in an Analog Model of PlateTectonics«, Europhysics News 5 (2005) 155.

S. Luther et al., »Data Analysis for Hot-FilmAnemometry in Turbulent Bubbly Flow«, Exp.Therm. Fluid Sci. 29 (2005) 821.

H. Nobach, K. Chang, and E. Bodenschatz,»Transformation von zeitlichen in räumlicheStatistiken - zwei Alternativen zur Taylor-Hypothese«. Tagungsband 13. Fachtagung»Lasermethoden in der Strömungsmesstechnik«,6.-8. Sept. 2005, Cottbus.

H. Nobach et al., »Full-Field Correlation-BasedImage Processing for PIV«, Proc. 6th InternationalSymposium on Particle Image Velocimetry,Pasadena, California, USA, September 21-23,2005.

J. Rensen et al., »Hot-Film Anemometry in TwoPhase Flows I: Bubble-Probe Interaction«,

2.5.3 Fluid Dynamics, Pattern Formation and Nanobiocomplexity (2003–2006)


Int. J. Multiphase Flow 31 (2005) 285.J. Rensen, S. Luther, and D. Lohse, »The Effect ofBubbles on Developed Turbulence«, J. FluidMech. 548 (2005) 153.

A.M. Reynolds et al., »On the Distribution ofLagrangian Accelerations in Turbulent Flows«,New J. Phys. 7 (2005) 58.

B. Utter, R. Ragnarsson, and E. Bodenschatz,»Experimental Apparatus and Sample PreparationTechniques for Directional Solidification«, Rev.Sci. Inst. 76 (2005) 013906.

B. Utter and E. Bodenschatz, »Double DendriteGrowth in Solidification«, Phys. Rev. E 72 (2005)011601.

T.H. van der Berg et al., »Drag Reduction inBubbly Taylor-Couette Turbulence«, Phys. Rev.Lett. 94 (2005) 044501.

H. Varela et al., »Transitions to ElectrochemicalTurbulence«, Phys. Rev. Lett. 94 (2005) 174104.

H. Varela et al., »A Hierarchy of Global CouplingInduced Cluster Patterns? During the OscillatoryH2-Electrooxidation Reaction on a Pt Ring-Electrode«, Phys. Chem. Chem. Phys. 7 (2005)2429.

2006

M. Bourgoin et al., »The Role of Pair Dispersionin Turbulent Flow«, Science 311 (2006) 835.

A. Celani, A. Mazzino, and D. Vincenzi,»Magnetic Field Transport and Kinematic DynamoEffect: A Lagrangian Interpretation«, Proc. R. Soc.A 462 (2006) 137.

S. Luther and J. Rensen, »Hot-Film Anemometryin Two Phase Flows II: Local PhaseDiscrimination«, to appear in Int. J. MultiphaseFlow (2006).

N.T. Ouellette, H. Xu, and E. Bodenschatz, »AQuantitative Study of Three-DimensionalLagrangian Particle Tracking Algorithms», Exp.Fluids 40 (2006) 301.

N.T. Ouellette et al., »Small-Scale Anisotropy inLagrangian Turbulence«, New J. Phys. (2006) inpress.

L. Song et al., »Dictyostelium DiscoideumChemotaxis: Threshold for Directed Motion«, inpress in Eur. J. Cell Biol. (2006).

R. Toegel, S. Luther, and D. Lohse, »ViscosityDestabilizes Bubbles«, Phys. Rev. Lett. 96 (2006)114301.

T.H. van der Berg, S. Luther, and D. Lohse,»Energy Spectra in Microbubbly Turbulence»,Phys. Fluids 18 (2006) 038103.

T.H. van der Berg et al., »Bubbly Turbulence«, J.of Turbulence 7 (2006) 1.H. Xu et al., »High Order Lagrangian VelocityStatistics in Turbulence«, Phys. Rev. Lett. 96(2006) 024503.

D. Vincenzi et al., »Statistical Closures forHomogeneous Shear Flow Turbulence of DilutePolymer Solutions«, in Progress in Turbulence 2 -Springer Proceedings in Physics 109 (2006) inpress.

N.T. Ouellette et al., »An Experimental Study ofTurbulent Relative Dispersion«, New J. Phys.(2006), in press

H. Xu, N.T. Ouellette, and E. Bodenschatz,»Multifractal Dimension of LagrangianTurbulence«, International Collaboration forTurbulence Research, Phys. Rev. Lett. 96 (2006)114503.

2003

B. Abel et al., »Comment on ’Rate coefficients forphotoinitiated NO2 unimolecular decomposition:energy dependence in the threshold regime’«,Chem. Phys. Lett. 368 (2003) 252.

T. Azzam et al., »The bound state spectrum ofHOBr up to the dissociation limit: Evolution ofsaddle-node bifurcations«, J. Chem. Phys. 118(2003) 9643.

D. Babikov et al., »Quantum origin of an anom-alous isotope effect in ozone formation«, Chem.Phys. Lett. 372 (2003) 686.

D. Babikov et al., »Metastable states of ozone cal-culated on an accurate potential energy surface«,J. Chem. Phys. 118 (2003) 6298.

D. Babikov et al., »Formation of ozone:Metastable states and anomalous isotope effect«,J. Chem. Phys. 119 (2003) 2577.

P. Fleurat-Lessard et al., »Theoretical investiga-tion of the temperature dependence of the O+O2

exchange reaction«, J. Chem. Phys. 118 (2003)610.

P. Fleurat-Lessard et al., »Isotope dependence ofthe O+O2 exchange reaction: Experiment andtheory«, J. Chem. Phys. 119 (2003) 4700.[Erratum: 120 (2004) 4993].

S. Yu. Grebenshchikov, »Van der Waals states inozone and their influence on the threshold spec-trum of O3(X1A1). I. Bound states«, J. Chem.Phys. 119 (2003) 6512.

S. Yu. Grebenshchikov, R. Schinke, and W. L.Hase, »State-specific dynamics of unimoleculardissociation«, in Comprehensive ChemicalKinetics, 39 Unimolecular Kinetics, Part 1. TheReaction Step, N. J. B. Green, ed. (Elsevier,Amsterdam, 2003).

M. V. Ivanov, and R. Schinke, »Two-dimensionalneutral donors in electric fields«, J. Phys: Condensed Matter 15 (2003) 5909.

V. Kurkal, P. Fleurat-Lessard, and R. Schinke,»NO2: Global potential energy surfaces of theground (2A1) and the first excited (2B1) electronicstates«, J. Chem. Phys. 119 (2003) 1489.

L. Poluyanov, and R. Schinke, »Theory ofMolecular Bound States including Σ - πVibronic Interaction«, Chem. Phys. 288 (2003)123.

Z.-W. Qu, H. Zhu, and R. Schinke, »The ultra-vio-let photodissociation of ozone revisited«, Chem.Phys. Lett. 377 (2003) 359.

R. Schinke, P. Fleurat-Lessard, and S. Yu.Grebenshchikov, »Isotope dependence of the life-time of ozone complexes formed in O+O2 colli-sions«, Phys. Chem. Chem. Phys. 5 (2003) 1966.R. Siebert, and R. Schinke, »The vibrational spec-trum of cyclic ozone«, J. Chem. Phys. 119 (2003)3092.

M. Tashiro, and R. Schinke, »The effect of spin-orbit coupling in complex forming O(3P) + O2

collisions«, J. Chem. Phys. 119 (2003) 10186.

K.-L. Yeh et al., »A time-dependent wave packetstudy of the O+O2 (v = 0, j = 0) exchange reac-tion«, J. Phys. Chem. A 107 (2003) 7215.

2004

S. F. Deppe et al., »Resonance spectrum and dis-sociation dynamics of ozone in the 3B2 electroni-cally excited state: Experiment and theory«, J.Chem. Phys. 121 (2004) 5191.

M. V. Ivanov, and R. Schinke »Two-dimensionalanalogs of the H2

+ ion in stationary electricfields«, Phys. Rev. B 69 (2004) 165308-1.

M.V. Ivanov, S. Yu. Grebenshchikov, and R.Schinke »Intra- and intermolecular energy trans-fer in highly excited ozone complexes«, J. Chem.Phys. 120 (2004) 10015.

M. Joyeux, R. Schinke, and S. Yu.Grebenshchikov »Semiclassical dynamics of thevan der Waals states in O3(X1A1)«, J. Chem. Phys.120 (2004) 7426.

Z.-W. Qu et al., »The Huggins band of ozone:Unambiguous electronic and vibrational assign-ment«, J. Chem. Phys. 120 (2004) 6811.

Z.-W. Qu, »The Huggins band of ozone: A theo-

2.5.4.1 PD Dr. Reinhard Schinke (2003–2006)


Publications

2.5.4 Associated Scientists


retical analysis«, J. Chem. Phys. 121, (2004)11731.

R. Schinke, and P. Fleurat-Lessard »On the transi-tion-state region of the O(3P) + O2(3Σ -

g) potentialenergy surface«, J. Chem. Phys. 121 (2004) 5789.

R. Schinke, »Quantum mechanical studies of pho-todissociation dynamics using accurate globalpotential energy surfaces«, In ConicalIntersections: Electronic Structure, Dynamics andSpectroscopy, W. Domcke ed. (2004) 473.

H. Zhu et al., »On spin-forbidden processes in theultra-violet photodissociation of ozone«, Chem.Phys. Lett. 384 (2004) 45.

2005

L. Adam et al., »Experimental and theoreticalinvestigation of the reactionNH(X3Σ)+H(2S) →N(4S)+H2(X1Σ +

g)«, J. Chem.Phys. 122 (2005) 114301-1.

W. L. Hase, and R. Schinke »Role of computation-al chemistry in the theory of unimolecular reac-tion rates«, In Theory and Applications ofComputational Chemistry: The first 40 years, C.E.Dykstra et al. eds. (Elsevier, New York, 2005)397.

M. V. Ivanov, and R. Schinke, »Temperaturedependent energy transfer in Ar – O3 collisions«,J. Chem. Phys. 122 (2005) 234318-1.

M. Joyeux et al., «Intramolecular dynamics alongisomerization and dissociation pathways«, Adv.Chem. Phys. 130 (2005) 267.

K. Mauersberger et al., »Assessment of the ozoneisotope effect«, Adv. Atom. Mol. and Opt. Phys.50 (2005) 1.

Z.-W. Qu et al., »Experimental and theoreticalinvestigation of the reactionsNH(X3Σ)+D(2S)→ND(X3Σ)+H(2S) andNH(X3Σ)+D(2S)→N(4S)+HD(X1Σ +

g)«, J. Chem.Phys. 122 (2005) 204313-1.

Z.-W. Qu. et al., »The photodissociation of ozonein the Hartley band: A theoretical analysis«, J.Chem. Phys. 123 (2005) 074305-1.

Z.-W. Qu, H. Zhu, and R. Schinke, »Infrared spec-trum of cyclic ozone: A theoretical investigation«,J. Chem. Phys. 123 (2005) 204324-1.

Z.-W. Qu et al., »The triplet channel in the pho-todissociation of ozone in the Hartley band:Classical trajectory surface hopping analysis«, J.Chem. Phys. 122 (2005) 191102-1.

R. Schinke, and P. Fleurat-Lessard, »The effect of

zero-point energy differences on the isotopedependence of the formation of ozone: A classi-cal trajectory study. J. Chem. Phys. 122 (2005) 094317.

H. Zhu et al., »The Huggins band of ozone.Analysis of hot bands«, J. Chem. Phys. 122 (2005)024310-1.

2006

S. C. Farantos et al., »Reaction paths and elemen-tary bifurcation tracks: the diabatic 1B2-state ofozone«, International Journal of Bifurcation andChaos, in press.

S. Yu Grebenshchikov et al., »Absorption spec-trum and assignment of the Chappuis band ofozone«, submitted to J. Chem. Phys., in press.

M. V. Ivanov, and R. Schinke, »Recombination ofozone via the chaperon mechanism«, J. Chem.Phys. 124 (2006) 104303-1.

L. Lammich et al., »Electron-impact dissociationand transition properties of a stored LiH2

- beam«,European J. Physics, to be published.

R. Schinke et al., „Dynamical studies of theozone isotope effect: A status report«, Ann. Rev.Phys. Chem. 57 (2006).


Publications

2003

A. Dimakis, and F. Müller-Hoissen, »Riemanniangeometry of bicovariant group lattices«, J. Math.Phys. 44 (2003) 4220.

A. Dimakis, and F. Müller-Hoissen, »Differentialgeometry of group lattices«, J. Math. Phys. 44(2003) 1781.

2004

A. Dimakis, and F. Müller-Hoissen,»Automorphisms of associative algebras and non-commutative geometry«, J. Phys. A: Math. Gen.37 (2004) 2307.

A. Dimakis, and F. Müller-Hoissen, »Extension ofnoncommutative soliton hierarchies«, J. Phys. A:Math. Gen. 37 (2004) 4069.

A. Dimakis, and F. Müller-Hoissen, »Explorationsof the extended ncKP hierarchy«, J. Phys. A:Math. Gen. 37 (2004) 10899.

A. Dimakis, and F. Müller-Hoissen, »Differentialcalculi on quantum spaces determined by auto-morphisms«, Czech. J. Phys. 54 (2004) 1235.

A. Dimakis, and F. Müller-Hoissen, »Extension ofMoyal-deformed hierarchies of soliton equations«,in XI International Conference SymmetryMethods in Physics, C. Burdik, O. Navratil and S.Posta (eds.), Joint Institute for Nuclear Research(Dubna) (2004).

2005

A. Dimakis, and F. Müller-Hoissen, »An algebraicscheme associated with the noncommutative KPhierarchy and some of its extensions«, J. Phys. A:Math. Gen. 38 (2005) 5453.

A. Dimakis, and F. Müller-Hoissen, »Algebraicidentities associated with KP and AKNS hierar-chies«, Czech. J. Phys. 55 (2005) 1385.

A. Dimakis, and F. Müller-Hoissen,»Nonassociativity and integrable hierarchies«,Nlin.SI/0601001.

A. Dimakis, and F. Müller-Hoissen, »Functionalrepresentations of integrable hierarchies«,Nlin.SI/0603018.

A. Dimakis, and F. Müller-Hoissen, »Functionalrepresentations of derivative NLS hierarchies«,Nlin.SI/0603048.

2.5.4.2 PD Dr. Folkert Müller-Hoissen (2003–2006)

The service groups of the institute are headedby the Institute Manager relieving the Boardof Directors and its Managing Director from arange of management tasks. The InstituteManager and her team are supporting the sci-entific departments and ensure that all staffand guests enjoy an excellent research envi-ronment. Next to financial affairs, human re-sources, grant administration, and coordina-tion with the central administration, the Insti-tute Management is in charge of the library,the information technology services, the facil-ity management including machine and elec-tronics shops, and all outreach activities.


Services and Infrastructure

3. Services and Infrastructure

Based on the requests from scientific depart-ments the mechanical design group developsand engineers solutions for scientific appara-tuses. The group uses the most advanced soft-ware tools that allow the design of complexparts in three dimensions. This includes thethree-dimensional assembly and simulationof the assembled components. Once the tech-nical design has been finished, technicaldrawings are generated or the design is di-rectly entered into the CAD engine that gener-ates instruction sets that are understood bythe CNC-machines.The design group works in tight collaborationwith the electronics shop that designs all elec-trical components including digital and ana-log electronics. The design group also certi-fies in collaboration with the mechanical andelectronic shop the conformity of the appara-tuses with the European and German laws.New parts and electronics are manufacturedin the respective workshop. The machineshop also assembles components and appara-

tuses. It is equipped with conventional aswell as computer controlled lathes, millingand EDM (electrical discharge) machines.The associated metalshop manufacturesframes and other large metal parts, and it hasstate of the art welding equipment for han-dling steel and aluminum.The machine and electronics shops are alsoresponsible for the maintenance and repair ofthe existing machines and apparatuses. In ad-dition, the staff provides a one-week coursethat trains graduate students and scientists inthe save use of the Research Shop. Thisranges from basic tasks like drilling, cutting,tapping, or filing to the advanced use of mod-ern machinery like that of milling machines,and a computer controlled lathe. Upon suc-cessful completion of the course the personmay work independently in the ResearchWorkshop. The institute is also training a to-tal of six apprentices in the machine and elec-tronics shop.

3.1 Design and Engineering

Figure 1: MPIDS at Bunsenstraße.


1. Design

2. Manufacturing 3. The apparatus

4. Installation 5. Ready for science

Figure 2: From Design to laboratory use.



The central IT service group maintains a vari-ety of centralized resources and fulfills the ITneeds of the institute. Examples are networkinfrastructure, user and security manage-ment, centralized software distribution andinstallation, and the implementation andmanagement of high availability file servers.Each department operates their own comput-ing facilities that are tailored to their specificapplications and thus allow the flexibility ofsmall organisational units and a rapid re-sponse to changing scientific needs. Further-more information technology proliferates allareas, from administration and public rela-tions, over the design and manufacture in theinstitute’s workshops, to teaching, communi-cation, and outreach – computer based serv-ices and equipment are utilized throughoutand need installation, integration and man-agement.A special focus of the IT service group is tomaintain the IT infrastructure of tomorrow.The implementation of the most modernserver technology often requires a tight col-

laboration with the software and hardwaremanufacturers. In addition, the thermal loadfrom compute clusters is steadily increasingdue to ever increasing densities of compo-nents. The IT-group is meeting this challengeby tailoring in collaboration with an outsidecompany the next generation air-conditionedserver racks.

3.2 Computing Facilities and IT-Services

Figure 3: 64bit HPC Linux cluster withHA AIX file server in air-conditioned racks. Thesystems shown provide 112CPUs, 872GB RAM and morethan 25TB disk space

The members of the facility managementteam are in charge of all technical and infra-structural issues. They are supporting the de-partments during the installation of specialexperimental equipment or constructions andcare for the unobstructed handling of all facil-ities. Special challenges on manpower arisefrom the fact that with the new experimentalhall at the Fassberg additional maintenance isnecessary until the move in 2009. In addition,the guesthouses will be renovated and mod-ernized in the years to come.

3.3 Facility Management

Figure 4:Members of the MPIDSFacility Management Team


The Administration supports all depart-ments in performing their personal and finan-cial management tasks. This includes: pur-chasing, accounting and bookkeeping, con-tract management, payroll accounting,calculation of travel expenses, administrationof sponsored research and the managementof 10 guest apartments and 14 guestroomswithin 3 guesthouses. To perform these tasksthe administration is using modern officetools such as SAP.

3.4 Administration

3.5 Library

The library of the institute provides re-searchers, guests and visitors with all neces-sary printed and online accessible informa-tion focusing on the main research topics of

the institute. Due to the fact that the MaxPlanck Institute for Dynamics and Self-Orga-nization has been founded only in November2004 as the successor of the 80-year old MaxPlanck Institute for Flow Research, the exist-ing inventory mainly contains literature fromthe former institute and some books evenhave antiquarian value. Due to the upcomingmove of the institute the inventory of thelibrary will be included into the Otto HahnLibrary at the Max Planck Campus as soon asthe Library extension of the Otto HahnLibrary has been built. Currently the institute library together withthe library of the department »NonlinearDynamics« contains more than 7,700 vol-umes, subscribes to 24 printed research jour-nals, and is part of the Max Planck electroniclibrary system. The library is supported by abookbinding shop.

Figure 6: MPIDS Institute Library

Figure 5: Members of the MPIDS Administration Team



3.6 Outreach Activities

All departments of the institute value highlythe dissemination of their research results tothe general public both locally and at the na-tional/international level. Major findings arehighlighted in internationally distributedpress releases that are usually coordinatedwith the central press office of the MaxPlanck Society.

The institute is also actively reaching out tothe local community with multiple activities.We initiated the column »Frag’ den Wis-senschaftler« (Ask the Scientist) in coopera-tion with the weekly regional newsprint andadvertising paper Extra Tip. The Extra Tip isdistributed every Sunday free of charge to190,000 households in the larger Göttingenarea. Since January 2006 »Frag’ den Wis-senschaftler« has been published weekly. Thegeneral public (typically students from Grade7–13) can ask questions about topics fromscience in general. A scientist from the insti-tute (or other Göttinger research institutions)answers the question at a simple but precise

level. The answer is then published togetherwith a picture and a short introduction of thecorresponding scientist. Previous published»Frag’ den Wissenschaftler« questions andanswers can be found at the website of thejournal http://www.extratip-goettingen.de/fraeg-den-wissenschaeftler.html and that ofthe institute.

To better inform young people about science,the institute offers internships to studentsfrom local high-schools and to undergradu-ates that come from Germany and abroad.The institute also regularly participates in theworldwide initiative Girl‘s Day. In 2006 forthe first time, a special one-day program hadbeen offered and 10 girls and boys, mainlychildren of staff members, had the opportu-nity to inform themselves about different jobswithin the machine shops, the bookbindingshop, the administration, and the researchlaboratories.

Figure 7: MPIDS Girl´s Days, April 2006

On an international level the institute is par-ticipating in the »Science Tunnel«, which is atravelling science exhibition about today’ssearch for new knowledge. The show wasdeveloped by the Max Panck institutes un-der the leadership of the Max Planck Soci-ety. Two ›identical‹ double pendula werebuilt next to each other. To give the same ini-tial conditions the pendula can be held by amagnetic switch and released. After they arereleased it is very simple to observe the dif-ference in their motion and the chaotic be-havior. The machine shop and the electronicshop built the apparatus that can be easilyoperated by the visitors of the show. In 2005the Science Tunnel was exhibited in Miraka

(Japan, National Museum of Emerging Sci-ence and Innovation, September 16th to No-vember 17th 2005) and now is displayed inSingapore (Singapore Science Center, March24th to June 18th 2006) and later in Shang-hai (Shanghai Science and Technology Mu-seum, August 11th to October 8th 2006).As international contacts and research staysat foreign institutions are an important partof the everyday life of today’s scientist, ›net-working‹ is important. The MPIDS is part ofan initiative that is establishing an ALUMNI

network using the novel IT-tools of the pub-lic relation office of the Max Planck Society.This will allow an easier maintenance of thecontacts to its former members.

Figure 8 a,b:»MPIDS - Double Pendula«at the Science TunnelExhibition 2005


Bunsenstraße 10

D - 37073 Göttingen

Departments: Nonlinear Dynamics (Prof. Geisel)

Dynamics of Complex Fluids (Prof. Herminghaus)

Services: Institute Management, Administration, Facility Management, Electronic and

Mechanic Workshop, IT-Services, Library, Outreach Office, Stock Rooms, Lecture

Hall, and Guest Houses.

By plane

From Frankfurt am Main Airport (FRA): Use the railway station at the airport. Trains to

Göttingen (direct or via Frankfurt main station) leave twice an hour during daytime (travel

time: 2 hours).

From Hanover Airport (HAJ): Take the suburban railway (S-Bahn) to the Central Station

(»Hannover Hauptbahnhof«). From here direct ICE trains to Göttingen depart every 1/2 hour.

By train

Göttingen Station is served by the following ICE routes: Hamburg-Göttingen-Munich,

Hamburg-Göttingen-Frankfurt, and Berlin-Göttingen-Frankfurt.

From Göttingen railway station:

From the Göttingen station you can take a Taxi (5 minutes) or walk (20 minutes). If you

walk, you need to leave the main exit of the station and walk to the right. Follow the main

street, which after the traffic lights turns into Bürgerstraße. Keep walking until you come to

the Bunsenstraße. Turn right – you will reach the entrance gate of the MPIDS after about

300m.

By car

Leave the freeway A7 (Hanover–Kassel) at the exit »Göttingen«, which is the southern exit.

Follow the direction »Göttingen Zentrum« (B3). After about 4 km you will pass through a

tunnel. At the next traffic light, turn right (direction »Eschwege« B27) and follow the

»Bürgerstraße« for about 600 m. The fourth junction to the right is the »Bunsenstraße«. You

will reach the institute’s gate after about 300m.

How to get to the Max Planck Institute for Dynamics and Self-Organization

Location 1

Location 1

Location 2

Am Faßberg 17

D - 37077 Göttingen

Department: Fluid Dynamics, Pattern Formation and Nanobiocomplexity

(Prof. Bodenschatz)

Services: Experimental Hall, Clean Room, and Cell Biology Laboratories.

By plane

From Frankfurt am Main Airport (FRA): Use the railway station at the airport. Trains to

Göttingen (direct or via Frankfurt main station) leave twice an hour during daytime (travel

time: 2 hours).

From Hanover Airport (HAJ): Take the suburban railway (S-Bahn) to the Central Station

(»Hannover Hauptbahnhof«). From here direct ICE trains to Göttingen depart every 1/2 hour.

By train

Göttingen Station is served by the following ICE routes: Hamburg-Göttingen-Munich,

Hamburg-Göttingen-Frankfurt am Main, and Berlin-Göttingen-Frankfurt.

From Göttingen railway station:

On arrival at Göttingen station take a Taxi (15 minutes) or the bus (35 minutes). At platform

A take the bus No. 8 (direction: »Geismar-Süd«) or No 13 (direction: »Weende-

Ost/Papenberg« ). At the second stop »Groner Straße« change to bus No. 5 (direction

»Nikolausberg« and get off at the »Faßberg« stop, which is directly in front of the entrance of

the Max Planck Campus (MPISDS and MPI for Biophysical Chemistry). Ask at the gate to get

directions.

By car

Leave the freeway A7 (Hanover-Kassel) at the exit »Göttingen-Nord«, which is the northern

of two exits. Follow the direction for Braunlage (B 27). Leave town – after about 1.5 km at

the traffic light (Chinese restaurant on your right) turn left and follow the sign

»Nikolausberg«. The third junction on the left is the entrance to the Max Planck Campus

(MPIDS and MPI for Biophysical Chemistry). Ask at the gate to get directions.

Location 2

Documents

Max Planck Institute · integration. The mission of the Max Planck Institute for Dynamics and Self-Organization (MPIDS) is the investigation of the physics of such phenomena. Founded