Upload
sarah-bryant
View
214
Download
1
Tags:
Embed Size (px)
Citation preview
11
Transport phenomena and structure formation at micro/nanometerscale in
biomedicine and material science Daniel Vizman, West University of Timisoara, Faculty of Physics Victor Sofonea, Center for Fundamental and Advanced Technical
Research, Romanian Academy – Timisoara Branch Titus Beu, Babes-Bolyai University, Faculty of Physics, Cluj- Napoca Adrian Neagu, “Victor Babes” University of Medicine and Pharmacy,
Timisoara
22
MOLECULARLEVEL (~10-9m)
MESOSCALE (10-6m)
MACROSCALE(>10-3m)
ParticlePosition momentum,
interaction forces
Distribution functionBoltzmann Equation
Challenge: Multiscale simulation Challenge: Multiscale simulation
Continuum media mechanics mass, momentum, energy
equations
•Monte Carlo•Molecular Dynamics
•Lattice Boltzmann•Phase Field
•Finite Element•Finite Volume
33
MONTE CARLO SIMULATIONSMONTE CARLO SIMULATIONSMONTE CARLO SIMULATIONSMONTE CARLO SIMULATIONS
The biological tissue is represented on a cubic lattice. Cell rearrangements are obtained by random sampling.
Probability of acceptance
Monte Carlo simulations yield energetically favourable tissue conformations by minimizing the total energy of adhesion.
UNIVERSITATEA DE MEDICINĂ ŞI FARMACIE “VICTOR BABEŞ” TIMIŞOARA,
CENTRUL DE MODELARE A SISTEMELOR BIOLOGICE ŞI ANALIZA DATELOR
(CMSBAD)
UNIVERSITATEA DE MEDICINĂ ŞI FARMACIE “VICTOR BABEŞ” TIMIŞOARA,
CENTRUL DE MODELARE A SISTEMELOR BIOLOGICE ŞI ANALIZA DATELOR
(CMSBAD)
1P 0 if E
)exp( TEEP otherwise
ET = effective measure of cell motility.
44
EXAMPLEEXAMPLEEXAMPLEEXAMPLE
Spontaneous emergence of tubular structures:
TE7.001
Aggregate:
•200 m diameter
•Rint/Rext = 0.8
•2060 cells
•2109 nodes occupied by gel
TE5.102
TE3.012
0 Type
1 Type
2 Type
Neagu A. et al. Phys. Rev. Lett. 95:178104-1– 4.
20 000 MCS 100 000 MCS
55
Ion channels – proteins that control the passage of ions (Na+, K+ etc) across cell membranes
Molecular dynamics – solving Newton’s law for all particles
The electrolyte – 1M NaCl solution: 600 H2O molecules, 8 Na+ and 8 Cl-
Water – rigid molecules:• Site-site intermolecular potential TIP4P• Rigid-body dynamics – rotation about CM – quaternions
Periodic boundary conditions
Coulomb interactions – Ewald sum technique with lattice-based charge distribution and Fast Fourier Transform – increases speed substantially
Titus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of Physics
Molecular Dynamics Simulation of biological ion channels
66
Titus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of PhysicsTitus Beu, University ”Babeş-Bolyai”, Faculty of Physics
The model membrane channel
similar to nicotine acetycloline receptor 388 interaction sites: charges (-0.5e, -0.35e, +0.35e, +0.5e, neutral)
+ Lennard-Jones interactions
11 20-atom rings11 20-atom rings
relative rotation 9relative rotation 9°°
77
SNAPSHOSNAPSHOTT
88
Phase space discretized Boltzmann equations with BGK approximation
Equilibrium distribution functions
Boltzmann equation:
)],(),([ 1 )],( [1 ),(e),( teqift
if
ift
iTBkt
if
it
ift
xxxueFxx
the force term
relaxation time
collisionsttftf
mt
),( ),(
vr,vr,Fv vr
F
22422
2)(2
1 cc
iciniw
eqif
uuueue
Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,
Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,
Lattice Boltzmann method
99
Approach: development of appropiate numerical schemes; implementation of diffuse reflection boundary conditions; parallel computing
thermal transpiration
Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,
Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,
Objective: investigation of two - dimensional, non - isothermal fluid flow phenomena in micro – electro – mechanical systems (MEMS)
1010
pressure-driven
Flow
Rarefaction effects in micro-channels
Velocity slip and temperature jump in Couette flow
Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,
Center for Fundamental and Advanced Technical Research Romanian Academy – Timisora Branch,
1111
forward
Process paramete
rs
e.g. geometry, heating power
Crystalproperties
defined by application,
e.g. LED, Laser diode
Growthcondition
s
e.g. temperature T and stress vm
distribution
T(x,y,t,t) vm
Formation of crystal defects
b
desired (doping),
undesired (e.g. dislocation)
inverse
goal: understanding of relation between crystal properties and the conditions (parameters) of the crystal growth process
Faculty of Physics, West University of Timisoara Faculty of Physics, West University of Timisoara
1212
global 3D
Global 3D-modeling is very expensive.
2D axi-symmetricproblem: 3D-phenomena
partial 3DSTHAMAS3D – developed in collaboration with Fraunhofer Institute, Erlangen, Germany
Reduction of the complexity
• by using symmetry effects (e.g. axi-symmetric) • simplification of geometry (partial model)
Faculty of Physics, West University of Timisoara Faculty of Physics, West University of Timisoara
Development of Simulation Programs for Crystal Growth
1313
0.1
1
10
100
1000
10000
100000
1000000
Perfo
rman
ce [G
Flop
/s]
N=1
N=500
Sum
N=10
1 TFlop/s
1 PFlop/s
ASCI
Earth Simulator
Challenges in Computational Power Challenges in Computational Power
•Computing speeds advances (uni- and multi-processor systems), Grid Computing• Systems Software•Applications Advances (parallel & grid computing)•Algorithms advances (parallel &grid computing, numeric and non-numeric techniques: dynamic meshing, data assimilation)
NANOSIM – cluster at West University of Timisoara, Faculty of Physics
1414
Conclusions Conclusions
•Challenge is to integrate what is happening on the atomic level with the mesoscopic and macroscopic classical level. Collaboration between scientists ‘working at every level’ is strongly necessary
•Theoretical and computational skills can be learned by training, meaningful applications is achieved only with experience. User friendly software should be developed.
•Grids and Service Oriented Architectures are necessary (worldwide networks of interconnected computers that behave as a single entity) to increase computational power
•Local hardware infrastructure development necessary
•While computational experiment is much less expensive than real experiment it is necessary to develop an application oriented computational culture and community
1515
Acknowledgements Acknowledgements
The authors would like to acknowledge the Romanian Ministry of Education and Research for the financial
assistance under CEEX 11/2005