Honoring Alfonso Castro

The 2012 MSU-UAB Conference on Differential Equations and Computational Simulations is dedicated to Alfonso Castro, Professor of Mathematics at Harvey Mudd College, CA. Alfonso received his B.S. and M.S. degrees from Colombia, Bogota and Ph. D. from University of Cincinnati, OH in 1977. Professor Castro is a world renowned expert in the area of Partial Differential Equations. In particular his interest lies in variational methods, inverse problems and water waves (solitons). He has more than 80 articles in reputed journals and supervised 13 PhD students at various institutions. His research, for example, involves understanding the temperature distribution in a star which requires balancing heat diffusion, generation and radiation. In recent years, he has fully classified the radial solutions to this problem. The fundamental nature of his research allows him to involve mathematics majors interested in differential equations in his research program.

He served as the program director of National Science Foundation from 1989 to 1991. He is in the editorial board of many journals. Most notably, he is the Co-founder and Managing Editor of the open access journal Electronic Journal of Differential Equations.

Please join us in wishing Alfonso happy birthday and celebrating such an outstanding

career.

Alfonso Castro

Table of Contents Honoring Alfonso Castro 1 Table of Contents 2 Conference Program 3 McCool Hall Floor Plan 12-13 Invited Principal Speakers 14-17 Abstracts for Principal Talks (separate table of contents: A1 - A5) 18 Abstracts for Contributed Talks (separate table of contents: B1 – B28) 19 Proceedings Instructions for Authors 20 EJDE Flyer 21 Conference Flyer 22 Department of Mathematics and Statistics at MSU 23-24 UAB Mechanical Engineering Department 25-26 Center for Computational Sciences at MSU 27-28 High Performance Computing Collaboratory at MSU 29 Conference Organizing Committee 30 Conference Proceedings Editors 31

Conference Program

Wednesday, Oct 3, 2012 5:45PM Transportation from other hotels to Holiday Inn Express

6:00PM-9:00PM Registration/Reception : State Room, Holiday Inn Express

9:00PM Transportation from Holiday Inn Express to other hotels

Thursday, Oct 4, 2012 8:00AM & 8:30AM Transportation from hotels to McCool Hall

8:00AM-5:30PM Registration : Atrium, McCool Hall

8:15AM-9:00AM Breakfast : Atrium, McCool Hall

9:00AM-9:30AM Opening Ceremony: 124, McCool Hall

Introduction: Roy Koomullil, Deptartment of Mechanical Engineering, UAB

Dedication of the conference to Prof. Alfonso Castro, Harvey Mudd College

Welcoming Remarks: Jerry Gilbert, Provost, MSU Bharat Soni, Head, Department of Mechanical Engineering, UAB Seong-Gon Kim, Director, CCS, HPCC, MSU Mohsen Razzaghi, Head, Department of Mathematics & Statistics, MSU

Program Announcements: Jerome Goddard II, Program Chair

9:30AM-10:30AM Principal Lecture 1: 124, McCool Hall

“Multiple solutions to a nonlinear Choquard equation,” Monica Clapp, Instituto de Matemáticas, Universidad Nacional Autónoma de México Chaired by: Alfonso Castro, Department of Mathematics, HMC

10:30AM-10:50AM Break: Atrium, McCool Hall

10:50AM-11:50AM Principal Lecture 2: 124, McCool Hall

“Pattern formation in mesophases”, Jorge Vinals, Minnesota Supercomputing Institute, University of Minnesota Chaired by: Mark Novotny, Department of Physics, MSU

11:50AM-1:10PM Lunch : Atrium, McCool Hall

1:10PM-2:10PM Principal Lecture 3: 124, McCool Hall “Time analyticity of solutions to linear parabolic systems and mathematical finance,” Peter Takác, Institut für Mathematik, Universität Rostock. Chaired by: Seth Oppenheimer, Department of Mathematics and Statistics, MSU

2:10PM-2:30PM Break: Atrium, McCool Hall

2:30PM-3:30PM Principal Lecture 4: 124, McCool Hall “No artificial numerical viscosity: from the 2/3 rule to entropy stable approximations of Navier-Stokes and related equations”, Eitan Tadmor, Center for Scientific Computation and Mathematical Modeling, University of Maryland Chaired by: Seongjai Kim, Department of Mathematics and Statistics, MSU

3:30PM-3:50PM Break : Atrium, McCool Hall

3:50PM-5:10PM Parallel Session A1 – A4 : 126, 128, 130, 232, McCool Hall

5:20PM Transportation from McCool Hall to Banquet Hall

6:00PM-8:30PM Reception and Conference Banquet : Plymouth Bluff Reception Dinner Remarks on Alfonso Castro by John Neuberger, Northern Arizona University Cake presentation, champagne and toast to Alfonso Castro, Harvey Mudd College Closing Remarks: Hyeona Lim, Mississippi State University

8:30PM Transportation back to hotels

Friday, Oct 5, 2012 8:15AM & 8:40AM Transportation from hotels to McCool Hall

8:30AM-5:30PM Registration : Atrium, McCool Hall

8:30AM-9:00AM Breakfast : Atrium, McCool Hall

9:00AM-10:00AM Principal Lecture 5: 124, McCool Hall

“Control aspects of compressible Navier-Stokes system”, Mythily Ramaswamy, Centre for Applicable Mathematics, TIFR Chaired by: Maya Chhetri, Department of Mathematics and Statistics, UNCG

10:00AM-10:15AM Break: Atrium, McCool Hall

10:15AM-11:15AM Principal Lecture 6: 124, McCool Hall

“The development of adaptive high-order CFD methods for aerospace applications”, Zhi J Wang, Department of Aerospace Engineering, University of Kansas Chaired by: David Thompson, Department of Aerospace Engineering, MSU

11:15AM-11:30AM Break : Atrium, McCool Hall

11:30AM-12:50PM Parallel Session B1 – B4 -- 126, 128, 130, 232, 234, McCool Hall

12:50PM-2:00PM Lunch : Atrium, McCool Hall

2:00PM-3:00PM Principal Lecture 7: 124, McCool Hall

“Computational chemistry for practical applications”, David A. Dixon, Department of Chemistry, University of Alabama Chaired by: Roy Koomullil, Department of Mechanical Engineering, UAB

3:00PM-3:15PM Break : Atrium, McCool Hall

3:15PM-4:15PM Principal Lecture 8: 124, McCool Hall

“On the variational characterization of the Fučík spectrum: venturing outside of Castro's strip”, Steve Robinson, Dept. of Mathematics, Wake Forest University Chaired by: Jerome Goddard II, Department of Mathematics, AUM

4:15PM-4:25PM Break : Atrium, McCool Hall

4:25PM-5:45PM Parallel Session C1 – C4 -- 126, 128, 130, 232, McCool Hall

5:45PM Transportation from McCool Hall to High Performance Computing Collaboratory (HPC2)

6:00PM-8:00PM Hawg Barbeque Cook-Out at the HPCC

8:00PM Transportation back to hotels

Saturday, Oct 6, 2012 8:15AM & 8:40AM Transportation from hotels to McCool Hall

8:30AM-5:30PM Registration : Atrium, McCool Hall

8:30AM-9:00AM Breakfast : Atrium, McCool Hall

9:00AM-10:00AM Principal Lecture 9: 124, McCool Hall “Discontinuous Galerkin finite element methods for high order nonlinear partial differential equations”, Chi-Wang Shu, Division of Applied Mathematics, Brown University Chaired by: Hyeona Lim, Department of Mathematics and Statistics, MSU

10:00AM-10:10AM Concluding Remarks: Hyeona Lim, Mississippi State University

10:10AM-11:10AM Principal Lecture 10: 124, McCool Hall

“Computational mechanics in highway & race track safety”, Dean Sicking, Dept. of Structural Engineering, Nebraska Transportation Center, University of Nebraska-Lincoln Chaired by: Roy Koomullil, Department of Mechanical Engineering, UAB

11:10AM-11:30PM Break: Atrium, McCool Hall

11:30PM-12:50PM Parallel Session D1 – D4 : 126, 128, 130, McCool Hall

12:50PM-2:00PM Lunch : Atrium, McCool Hall

2:15PM Transportation back to hotels

Parallel Sessions

Thursday, Oct 4, 2012, 3:50PM-5:10PM Session A1: 126, McCool Hall Chair: Jaffar Ali , Florida Gulf Coast University

3:50PM-4:10PM Jaffar Ali Positive solutions for a classes of elliptic bi-variate systems with combined nonlinear effects Florida Gulf Coast University

4:10PM-4:30PM Nsoki Mavinga Nonresonance on the boundary and strong solutions of elliptic equations with nonlinear boundary conditions Swarthmore College

4:30PM-4:50PM Vasilios Alexiades Nanosecond laser ablation modeling University of Tennessee

4:50PM-5:10PM Harihar Khanal Time-stepping for laser ablation Embry-Riddle Aeronautical University

Session A2: 128, McCool Hall Chair: Chuanxi Qian, Mississippi State University

3:50PM-4:10PM Andrew Kerr Numerov-type method for the numerical solution of elliptic partial differential equations Austin Peay State University

4:10PM-4:30PM Cory Medlin Predictor not needed Austin Peay State University

4:30PM-4:50PM Fidele F. Ngwane Solving oscillatory problems using a block hybrid trigonometrically fitted method with two off-step points

USC Salkehatchie

4:50PM-5:10PM Volodymyr Borodin A semi-analytic approach to the construction of Green's functions for the Laplace equation posed in multiply-connected regions Middle Tennessee State University

Session A3: 130, McCool Hall Chair: Bela Soni, Jackson State University

3:50PM-4:10PM Bela Soni Simulation of airflow, fluid-structure interaction and aerosol deposition in lung airway Jackson State University

4:10PM-4:30PM Christopher Moore A modified tait equation of state to model cavitating water and its implementation in Loci/BLAST CAVS, Mississippi State University

4:30PM-4:50PM Luis Cueva-Parra Lattice Boltzmann simulation of nanofluid melting with natural convection

Auburn University at Montgomery

4:50PM-5:10PM M.K. Wolverton Feasibility study on sensitivity analysis for first-order flow effects due to perturbations in geometry in human upper airways CAVS, Mississippi State University

Session A4: 232, McCool Hall Chair: Abraham Abebe, University of North Carolina Greensboro

3:50PM-4:10PM Abraham Abebe Interactive treatment planning in cancer radiotherapy University of North Carolina Greensboro

4:10PM-4:30PM Chuan Li Parallel computing techniques in DelPhi to solve the Poisson-Boltzmann equation and calculate electrostatic energies of biological marcromolecules

Clemson University

4:30PM-4:50PM Marisabel Rodriguez Evolution of within-host antibiotic resistance in Gonorrhea

University of Texas-Pan American

4:50PM-5:10PM Shan Zhao Fast simulations of pseudo-time coupled nonlinear biomolecular solvation systems University of Alabama

Friday, Oct 5, 2012, 11:30AM-12:50PM Session B1: 126, McCool Hall Chair: Eunkyung Ko, McDaniel College

11:30AM-11:50AM Dagny Butler Existence of alternate steady states in a phosphorous cycling model Mississippi State University

11:50AM-12:10PM Maya Chhetri Positive solutions for a class of p-Laplacian superlinear semipositone problems University of North Carolina Greensboro

12:10PM-12:30PM Lakshmi S Kalappattil A uniqueness result for semipositone problems on exterior domains Mississippi State University

12:30PM-12:50PM Eunkyung Ko Uniqueness and multiplicity results for singular nonlinear eigenvalue problems McDaniel College

Session B2: 128, McCool Hall Chair: Xiangsheng Xu, Mississippi State University

11:30AM-11:50AM Nar Rawal Criteria for the existence of principal eigenvalue of time periodic nonlocal dispersal operator Auburn University

11:50AM-12:10PM Matthew Fury Well-posed approximations of nonlinear evolution problems in a Hilbert space Penn State Abington

12:10PM-12:30PM Dhruba Adhikari Eigenvalues and balls in the range of perturbations of maximal monotone operators Southern Polytechnic State University

12:30PM-12:50PM Shruti Dubey Existence of solutions to partial functional differential equations of fractional order with nonlocal conditions Indian Institute of Technology

Session B3: 130, McCool Hall Chair: Arundhati Bagchi Misra, Saginaw Valley State University

11:30AM-11:50AM Arundhati Bagchi Misra Nonlocal speckle denoising model based on non-linear partial differential equations Saginaw Valley State University

11:50AM-12:10PM Harish P Bhatt Comparative study of numerical methods for a multi-dimensional non-linear reaction-diffusion Brusselator system Middle Tennessee State University

12:10PM-12:30PM Ritesh Kumar Dubey Bounds on total variation and second order accuracy at extrema SRM University

12:30PM-12:50PM Mohammad Gandomkar A new numerical integration method based on Kriging interpolation Isfahan University of Technology

Session B4: 232, McCool Hall Chair: Ray Treinen, Texas State University San Marcos

11:30AM-11:50AM Ray Treinen Uniqueness and non-uniqueness of solutions to the floating ball problem Texas State University San Marcos

11:50AM-12:10PM Jeremy LeCrone Stability and bifurcation of equilibria for the axisymmetric surface diffusion flow Vanderbilt University

12:10PM-12:30PM Xiaoming He Immersed finite element methods for parabolic equations with moving interface Missouri S&T

12:30PM-12:50PM David M. Lavallee Application of lambda-2, Q-, and delta-criterion vortex detection techniques to experimental airfoil data Mississippi State Univerisity

Session B5: 234, McCool Hall Chair: Laalitha Liyanage, CAVS, Mississippi State University

11:30AM-11:50AM Laalitha Liyanage First principles study of magnetic properties of Zn-Sn substituted M-type Sr-hexaferrite CAVS, Mississippi State University

11:50AM-12:10PM Noureddine Hannoun Partition analysis for the spectral volume method University of Science and Technology Houari Boumediene

12:10PM-12:30PM Zachariah Sinkala Inverse problem for Fokker-Planck equations Middle Tennessee State University

12:30PM-12:50PM Richard C Ewool The application of explicit stabilized numerical methods on a mathematical model for tumor angiogenesis in the cornea Middle Tennessee State University

Friday, Oct 5, 2012, 4:25PM-5:45PM Session C1: 126 McCool Hall Chair: Shantia Yarahmadian, Mississippi State University

4:25PM-4:45PM Shantia Yarahmadian Dynamic instability of microtubules in three states Mississippi State University

4:45PM-5:05PM Peng Feng Global bifurcation of positive solutions to some quasilinear elliptic problem Florida Gulf Coast University

5:05PM-5:25PM Bonnie Roberson Weak Allee effect, grazing, and S-shaped bifurcation curves Mississippi State University

5:25PM-5:45PM Alicia Prieto Langarica From discrete to continuous models of cell movement: an application to medical implants Youngstown State University

Session C2: 128 McCool Hall Chair: Hai Dang, Mississippi State University

4:25PM-4:45PM Xiaoqian Gong Duffing-van der Pol oscillator system University of Texas Pan American

4:45PM-5:05PM Jose M Vega-Guzman The minimum-uncertainty squeezed states for quantum harmonic oscillators Arizona State University

5:05PM-5:25PM Falko Baustian Pricing American options as a free boundary problem and regularity results Universität Rostock

5:25PM-5:45PM Satyanarayana Engu Higher order approximations in the Burgers equation Tata Institute of Fundamental Research

Session C3: 130 McCool Hall Chair: Seongjai Kim, Mississippi State University

4:25PM-4:45PM Seongjai Kim Surface reconstruction for nonuniformly sampled data: A PDE-based approach Mississippi State University

4:45PM-5:05PM Samuel N. Jator Stabilized Adams type method with a block extension for the valuation of options Austin Peay State University

5:05PM-5:25PM Xiao Liang Efficient exponential time differencing methods for non-linear Schrodinger equations Middle Tennessee State University

5:25PM-5:45PM Ehigie Julius A Legendre-collocation based continuous second derivative BDF formula for stiff problems University of Lagos

Session C4: 232 McCool Hall Chair: Eric M. Collins, Mississippi State University

4:25PM-4:45PM Eric M. Collins Fast and accurate evaluation of complex equations of state

Mississippi State University

4:45PM-5:05PM M. Faridul Alam Prediction of vortical structures in unsteady separated transitional/turbulent flows using hybrid RANS/LES modeling methodology CAVS, Mississippi State University

5:05PM-5:25PM Marcelo Disconzi On the fluid motion with free boundary and strong surface tension

Vanderbilt University

5:25PM-5:45PM Yuanzhen Shao Analytic solution of the surface diffusion flow

Vanderbilt University

Saturday, Oct 6, 2012, 11:30AM-12:50PM Session D1: 126 McCool Hall Chair: John R. Graef, University of Tennessee at Chattanooga

11:30AM-11:50AM John R. Graef Solutions of a nonlinear fourth order periodic boundary value problem for difference equations University of Tennessee at Chattanooga

11:50AM-12:10PM Zhaosheng Feng Burgers--KdV equation with time delay University of Texas-Pan American

12:10PM-12:30PM Jerome Goldstein New asymptotic energy results for damped waves

University of Memphis

12:30PM-12:50PM Jinglong Ye Nonexistence results for classes of 3x3 elliptic systems Mississippi Valley State University

Session D2: 128 McCool Hall Chair: Suzanne Shontz, Mississippi State University

11:30AM-11:50AM Suzanne Shontz A space-filling curve mesh element- and vertex-reordering technique for efficient multicore finite element simulations Mississippi State University

11:50AM-12:10PM Wenchao Wang The oscillation behavior of 3D elasticity exact solution for orthotropic hollow cylinder IDC Technical Services

12:10PM-12:30PM Morteza Kiani Application of Fourier series to demonstrate the energy absorption phenomenon in aluminum tubes under impact loading CAVS, Mississippi State University

12:30PM-12:50PM Jigarkumar Patel Computational study of a dynamic contact problem University of Texas at Dallas

Session D3: 130 McCool Hall Chair: Adrian Sescu, Mississippi State University

11:30AM-11:50AM Adrian Sescu Synthesis of non-Gaussian turbulent velocity fields by random distributions of distorted Hill's vortices

Mississippi State University

11:50AM-12:10PM Arjun Shanker Physics based grid refinement and uncertainty quantifications for hybrid RANS/LES turbulent simulations HPCC, Mississippi State University

12:10PM-12:30PM Maurin Lopez Development of a simple phenomenological linear eddy-viscosity RANS model for computational fluid dynamics simulations of transitional flow

CAVS, Mississippi State University

12:30PM-12:50PM Varun Chitta A four-equation variant of the k-kL-w Model sensitized to rotation and curvature effects CAVS, Mississippi State University

McCool Hall Floor Plan (First Floor)

McCool Hall Floor Plan (Second Floor)

Invited Principal Speakers

Monica Clapp Professor of Mathematics Instituto de Matemáticas Universidad Nacional Autónoma de México

Mónica Clapp was born in Mexico. She studied Mathematics at the Universidad Nacional Autónoma de México (UNAM) and got her PhD at the University of Heidelberg in 1979. She is currently full professor at UNAM. She started doing research in Algebraic Topology, but after some years her mathematical interests moved towards Nonlinear Partial Differential Equations, which is her current field of research. She is particularly interested in variational problems and in the application of topological and geometrical tools to obtain existence and multiplicity results.

David Dixon Robert Ramsay Chair & Professor of Chemistry

Department of Chemistry University of Alabama

Dr. David A. Dixon received a B.S. in chemistry from Caltech in 1971. He received a PhD from Harvard University in physical chemistry in 1976 where he worked on molecular orbital theory with Prof. William Lipscomb (Nobel Prize, Chemistry, 1976) and crossed molecular beam chemistry with Prof. Dudley Herschbach (Nobel Prize, Chemistry, 1986). He is currently the Robert Ramsay Chair the Department of Chemistry at The University of Alabama where he has been since Jan. 1, 2004. Prior to moving to UA, he was Associate Director for Theory, Modeling, & Simulation (TM&S) in the William R. Wiley Environmental Molecular Science Laboratory at the Pacific Northwest National Laboratory where he managed the Molecular Sciences Computing Facility including the Molecular Sciences Software Suite, and computational chemistry and biology efforts from 1995 to 2002 and a Battelle Fellow from 2002-2003. He spent more than 12 years at DuPont’s Central Research at the Experimental Station in Wilmington, Delaware with a specific focus on chlorofluorocarbon replacements (eliminating atmospheric ozone depleting substances), fluoropolymers, catalysis, and main group chemistry in support of the Company’s different businesses. He was on the chemistry faculty at the University of Minnesota from 1977-1983 before he moved to DuPont. The overall goal of the work in his research group is to develop computational chemistry approaches on advanced computer systems and then apply them to address a range of important national problems with a focus on energy and the environment. Dr. Dixon has published over 600 papers on a wide range of topics and is considered a world leader in the application of numerical simulation methods to chemical problems.

Mythily Ramaswamy Professor of Mathematics & Dean Centre for Applicable Mathematics Tata Institute of Fundamental Research (TIFR)

Mythily Ramaswamy had her Master’s degree from Bombay University and was awarded the Diplôme (Diplôme de Docteur de 3ème Cycle) and Docteur de l’Université from Université Pierre et Marie Curie, Paris, France. She has been at the TIFR, Centre for Applicable Mathematics Bangalore and is currently Professor and Dean. Her main area of research is in the analysis of solutions of partial differential equations (PDEs). This includes questions related to existence, uniqueness and

qualitative properties of solutions. She has obtained important results in bifurcation and symmetry of positive solutions and their uniform a priori estimates. She is also interested in applications of PDEs and has worked on optimal control problems arising in hybrid engineering systems. Recently she has been concentrating on control of systems governed by PDEs. Her research contribution includes numerous publications, collaborative Indo‐French projects and the guidance of Masters and PhD students. She has been a visiting professor at many institutions and Universities all over the world. She is a fellow of the Indian Academy of Sciences, Bangalore, as well as the National Academy of Sciences, Allahabad. In 2004, the State Government of Karnataka conferred Mythily Ramaswamy the Dr. Kalpana Chawla Award for Science and Technology.

Steve Robinson Professor of Mathematics

Department of Mathematics Wake Forest University

Stephen Robinson is a professor of mathematics at Wake Forest University where he has worked since 1991. He has 34 publications primarily in the area of Nonlinear Boundary Value Problems, with some side excursions into applications such as Mathematical Biology and Medical Imaging.

Dean Sicking Professor & Director Midwest Roadside Safety Facility University of Nebraska-Lincoln Dr. Dean L. Sicking began developing roadside safety systems in 1980, shortly after obtaining a BSME degree from Texas A&M. His list of “firsts” include development of the, first crash cushion with reusable energy absorbers, first energy absorbing guardrail terminal, first trailer-truck mounted attenuator, first crashworthy culvert grate system, and the first guardrail system compatible with light trucks and SUV’s. His roadside safety features have been installed along

virtually every mile of all major rural highways in the nation and sales of his proprietary products have exceeded $1 billion. Dr. Sicking also led the development of the SAFER Barrier for use on high speed race tracks. NASCAR and IRL have not had any serious injury or fatal crashes involving the SAFER Barrier since it was installed system wide in 2004. In recognition of his contributions to roadside and race track safety, Dr.Sicking was awarded the 2005 National Medal of Technology by President George W. Bush.

Chi-Wang Shu Theodore B. Stowell University Professor of Applied Mathematics

Division of Applied Mathematics Brown University

Chi-Wang Shu obtained his BS degree from the University of Science and Technology of China in 1982 and his PhD degree from the University of California at Los Angeles in 1986. He came to Brown University as an Assistant Professor in 1987, moving up to Associate Professor in 1992 and Full Professor in 1996. He was the Chair of the Division of Applied Mathematics between 1999 and 2005, and is now the Theodore B. Stowell University Professor of Applied Mathematics. His research interest includes high order finite difference, finite element and spectral methods for solving hyperbolic and other convection dominated partial differential equations, with applications to areas such as computational fluid dynamics, semi-conductor device simulations and computational cosmology. He served as the Managing Editor of Mathematics of Computation between 2002 and 2012, is now the Chief Editor of Journal of Scientific Computing and the Co-Chief Editor of Methods and Applications of Analysis, and he currently serves in the editorial boards of 12 other journals. His honors include the First Feng Kang Prize of Scientific Computing in 1995 and the SIAM/ACM Prize in Computational Science and Engineering in 2007. He is an ISI Highly Cited Author in Mathematics and a SIAM Fellow.

Eitan Tadmor Distinguished University Professor Department of Mathematics University of Maryland Dr. Eitan Tadmor is a Distinguished University Professor at the University of Maryland, College Park and the Director of the university Center for Scientific Computation and Mathematical Modeling (CSCAMM). He received his Ph.D. in Mathematics from Tel Aviv University in 1979. Tadmor began his scientific career at CalTech, 1980-1982. He held professorship positions at Tel-Aviv University, 1983-1998, where he chaired the department of Applied Mathematics from 1991-

1993, and at UCLA, 1995-2004, where he was the founding co-director of the NSF Institute for Pure and Applied Mathematics (IPAM) from 1999-2001. Since 2002, he has served on the faculty of the Department of Mathematics and the Institute for Physical Sciences and Technology (IPST) at the University of Maryland. Tadmor’s primary research interests include analysis of time-dependent problems, the development of novel, high-resolution algorithms for the approximate solution of these problems, and the interplay between analytical theory and computational aspects of such algorithms with applications to shock waves, kinetic transport, self-organized dynamics, propagation of critical thresholds and image processing. Tadmor serves on the editorial boards of more than a dozen leading international journals and has given numerous invited lectures, including plenary addresses in the international conferences on hyperbolic problems in 1990 and 1998 and an invited lecture in the 2002 International Congress of Mathematicians. Tadmor is on the ISI list of most cited researchers in mathematics. He published more than 150 research papers, mostly in Numerical Analysis and Applied Partial Differential Equations.

Peter Takác

Professor of Mathematics & Chair Department of Applied Mathematics

Universität Rostock Peter Takác is a professor of Mathematics & chair for the Department of Applied Mathematics. He received his Ph. D. in Mathematics from the University of Minnesota, Minneapolis. Peter has held several visiting positions at institutions such as, Argonne National Laboratory, Chicago, Illinois, University of Toulouse, France, and the IMA, University of Minnesota. In addition to his authoring 85+ publications and two successful books, Peter has given numerous invited talks and seminars. His research has been continuously supported through grants awarded from organizations such as the U.S. NSF, DFG – German Research Society, DAAD – German Academic Exchange Service, and D.L.R. – German Aerospace. Peter serves on the editorial board of several journals including, International Journal of Mathematics and Mathematical Sciences. His research interests include partial differential equations and modern functional analytic methods with numerous applications to problems such as: degenerate and singular diffusion equations, nonlinear eigenvalue problems with the p-Laplacian, and the nonlinear Boltzmann equation.

Jorge Vinals Director & Professor of Physics Minnesota Supercomputing Institute University of Minnesota Jorge received his Ph.D. in Physics at the University of Barcelona. He did post-doctoral work at Temple University in Philadelphia and at Carnegie Mellon in Pittsburgh, from which Jorge moved to the Supercomputer Research Institute at Florida State University. The Institute was later turned into a university institute, and he held then the position of Associate Professor and Program Director. In 2004, Jorge moved to McGill University in Montreal, as a Canada Research Chair in the Department of Physics, and director of the McGill Institute for Advanced Materials. Just two

years ago, he joined the University of Minnesota as a Professor of Physics and the director of the Minnesota Supercomputing Institute. His research interests are in the area of nonlinear dynamics and nonequilibrium pattern formation, with applications to materials science and soft matter. Current research focuses on the development of mesoscopic models for complex soft matter, their computational analysis, and the study of the rheology of phases with partially broken symmetries.

Zhi J Wang Spahr Professor and Chair of Aerospace Engineering

Department of Aerospace Engineering University of Kansas

Z.J. Wang, Spahr Professor and Chair of Aerospace Engineering at the University of Kansas (KU), received his Ph.D. in Aerospace Engineering from the University of Glasgow in 1990. Then he conducted post-doctoral research in Glasgow and Oxford before joining CFD Research Corporation in Huntsville, Alabama in 1991 as a Research Engineer, and later becoming a Technical Fellow. In 2000, he joined the faculty of Michigan State University. In 2005 he returned to Aerospace Engineering at Iowa State University. In 2012, he became a member of the KU faculty. He has been active in CFD research since early 1990es with over 160 journal and conference publications. His research areas include adaptive high-order methods for the Navier-Stokes equations, algorithm and flow solver development for structured and unstructured, overset and adaptive Cartesian grids, computational aeroacoustics, large eddy simulation of transitional and bio-inspired flow problems, climate modeling and simulation, high performance computing on CPU and GPU clusters, geometry modeling and grid generation. He was an invited lecturer of the von Karman Institute Lecture Series on High-Order CFD Methods in 2005 and 2008. He is an Associate Fellow of AIAA, and an Associate Editor of the AIAA Journal. He was awarded the degree of Doctor of Science in Engineering by the University of Glasgow in 2008.

Abstracts for Principal Talks

Contents

Monica Clapp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

David A. Dixon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Mythily Ramaswamy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Stephen B. Robinson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Chi-Wang Shu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Dean Sicking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Eitan Tadmor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Peter Takac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Jorge Vinals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Z. J. Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

i

Multiple solutions to a nonlinear Choquard equationMonica ClappUniversidad Nacional Autonoma de Mexico, Mexicomclapp@matem.unam.mx

Coauthors: Silvia Cingolani (Politecnico di Bari), Simone Secchi (Universita di Milano-Bicocca), Dora Salazar (Universidad Nacional Autonoma de Mexico).

We consider the generalized Choquard equation

−∆u+ V (x)u = (|x|−α ∗ |u|p)|u|p−2u, u in H10 (Ω),

where Ω is an exterior domain in RN , N ≥ 3, V is a scalar potential, α in (0, N) andp in [2, (2N − α)/(N − 2)).

The special case

−∆u+ u = (|x|−1 ∗ |u|2)u, u in H1(R3),

is commonly referred to as the stationary Choquard equation. It arises in an approximationto Hartree-Fock theory for a one component plasma, and has many interesting applicationsin the quantum theory of large systems of non-relativistic bosonic atoms and molecules. Thisequation was also introduced by Penrose in his discussion on the self-gravitational collapseof a quantum mechanical wave-function. In this context it is usually called the Schrodinger-Newton equation.

We shall give an overview and present some recent multiplicity results for this problem,some of them obtained in colaboration with Silvia Cingolani (Politecnico di Bari) and SimoneSecchi (Universita di Milano-Bicocca), and others with Dora Salazar (Universidad NacionalAutonoma de Mexico).

Computational chemistry for practical applicationsDavid A. DixonUniversity of Alabamadadixon@bama.ua.edu

Advances in theory, algorithms, software, and computer architectures have made it pos-sible to calculate reliably the properties of a broad range of molecular systems with practicalapplications. The focus is on the prediction of such properties, especially thermodynamicproperties in the gas phase and aqueous solution, using correlated molecular orbital (MO)theory and density functional theory (DFT) coupled with self-consistent reaction field ap-proaches. A brief overview of the methods will be presented. Examples of the use of thesemethods for applications in chemical hydrogen storage systems, homogeneous and heteroge-neous catalysis, heavy metal chemistry, and environmental chemistry will be described.

1

Control aspects of compressible Navier-Stokes systemMythily RamaswamyT.I.F.R Centre for Applicable Mathematics, Indiamythily@math.tifrbng.res.in

Compressible Navier-Stokes system is a coupled system of differential equations for den-sity and velocity of a fluid. For the system linearized around a constant steady state, in oneand two dimensions, questions of controllability, stabilizability and optimal control will beanalyzed. Use of these results in exploring the stabilizability of the full nonlinear system willbe indicated.

On the variational characterization of the Fucık spectrum: venturing outside ofCastro’s stripStephen B. RobinsonWake Forest Universitysbr@wfu.edu

Coauthors: Pavel Drabek

It is well known that the nonlinear eigenvalue problem

∆u = au+ − bu−, x ∈ Ω,u|∂Ω = 0

(1)

plays an important role in understanding nonlinear oscillators such as the famous TacomaNarrows Bridge. Fucık and Dancer were the first to explore these problems in detail inthe 1970s, and so the pairs (a, b) ∈ R2 such that (1) has a nontrivial solution are calledthe Fucık-Dancer Spectrum or just the Fucık Spectrum. Much progress has been made incharacterizing these spectral values using minimax arguments reminiscent of the RayleighQuotient characterization of the associated linear problem (a = b = λ). In this talk wereview some of that work, in particular the results of Schechter and of Castro and Chang,and we present some recent extensions of their work. The previously cited work characterizesspectral curves that lie within a vertical strip λk < a < λk+1. We demonstrate that the curvescan be extended outside of this strip. Finally, we discuss the solvability of the resonanceproblems that result when a forcing term is added to the eigenvalue problem.

2

Discontinuous Galerkin finite element methods for high order nonlinear partialdifferential equationsChi-Wang ShuBrown Universityshu@dam.brown.edu

Discontinuous Galerkin (DG) finite element methods were first designed to solve hyper-bolic conservation laws utilizing successful high resolution finite difference and finite volumeschemes such as approximate Riemann solvers and nonlinear limiters. More recently the DGmethods have been generalized to solve convection dominated convection-diffusion equations(e.g. high Reynolds number Navier-Stokes equations), convection-dispersion (e.g. KdV equa-tions) and other high order nonlinear wave equations or diffusion equations. In this talk wewill first give an introduction to the DG method, emphasizing several key ingredients whichmade the method popular, and then we will move on to introduce a class of DG methods forsolving high order PDEs, termed local DG (LDG) methods. We will highlight the importantingredient of the design of LDG schemes, namely the adequate choice of numerical fluxes,and emphasize the stability of the fully nonlinear DG approximations. Numerical exampleswill be shown to demonstrate the performance of the DG methods.

Computational Mechanics in Highway & Race Track SafetyDean SickingUniversity of Nebraska-Lincolndsicking@unl.edu

Approximately 12,000 people die each year as a result of ran-off-road crashes. Unfor-tunately, more than 25% of these fatalities are associated with vehicles striking a roadsidesafety device, erected to prevent serious injury and fatal crashes. Although the frequencyof serious crashes on high-speed race tracks is much lower, a great deal of public scrutiny isfocused on the motorsports industry when a driver sustains a serious or fatal injury. The ad-vent of modern computational mechanics programs, especially explicit finite element codes,has produced dramatic improvements in the performance of roadside safety features. Thispresentation will summarize the development of energy absorbing barriers for racing appli-cations, new roadside guardrail designs, and impact attenuators designed to accommodatehead-on impacts. The strengths and remaining weaknesses associated with existing explicitfinite element programs will be discussed in the context of analyzing the impact performanceof roadside and race track safety hardware.

3

No artificial numerical viscosity: from the 2/3 rule to entropy stable approxima-tions of Navier-Stokes and related equationsEitan TadmorUniversity of Marylandtadmor@cscamm.umd.edu

Entropy stability plays an important role in the dynamics of nonlinear systems of con-servation laws and related convection-diffusion equations. What about the correspondingnumerical framework? we present a general theory of entropy stability for difference ap-proximations of such nonlinear equations. Our approach is based on comparing numericalviscosities to certain entropy conservative schemes. It yields precise characterizations of en-tropy stability which is enforced in rarefactions while keeping sharp resolution of shocks. Wedemonstrate this approach with a host of first- and second-order accurate schemes rangingfrom scalar examples to Euler and Navier-Stokes equations. In particular, we present a fam-ily of energy-stable schemes for the shallow-water equations, with a well-balanced descriptionof moving equilibria states. Numerical experiments provide a remarkable evidence for thedifferent roles of viscosity and heat conduction in forming sharp monotone profiles in theimmediate neighborhoods of shocks and contacts.

Time analyticity of solutions to linear parabolic systems and mathematical fi-nancePeter TakacUniversitat Rostock, Germanypeter.takac@uni-rostock.de

We begin by a brief presentation of a well-known mathematical model for Europeanoption pricing in a market with stochastic volatility. European options are used for marketcompletion. We explain the connection between a complete market and the analyticity ofthe weak solution to a general, strongly parabolic linear Cauchy problem of second order inRN × (0, T ) with analytic coefficients (in space and time variables). The analytic smoothingproperty is expressed in terms of holomorphic continuation of global (weak) L2-type solutionsto the system. Given 0 < T ′ < T ≤ ∞, we sketch a proof that any L2-type solutionu : RN × (0, T ) → RM possesses a bounded holomorphic continuation u(x + iy, σ + iτ) intoa complex domain in CN ×C defined by (x, σ) ∈ RN × (T ′, T ), |y| < A′ and |τ | < B′, whereA′, B′ > 0 are constants depending upon T ′. The proof uses the extension of a solution toan L2-type solution in a domain in CN × C, such that this extension satisfies the Cauchy-Riemann equations. The holomorphic extension is thus obtained in a Hardy space H2.

4

Pattern formation in mesophasesJorge VinalsUniversity of Minnesotavinals@umn.edu

Mesophases are ordered phases of symmetry that is intermediate between unstructuredfluids and fully ordered crystalline solids. These phases are quite common in many areasof condensed matter, especially in physical systems that self-assemble at the mesoscale. Wediscuss a few mathematical models that describe these phases, including their non equilib-rium properties, the formation and evolution of topological defects, and domain coarsening.We also discuss show to extend the models to account for hydrodynamic flows, and a fewresults on the rheology of block copolymer lamellar phases.

The development of adaptive high-order CFD methods for aerospace applicationsZ. J. WangUniversity of Kansaszjw@ku.edu

A current breakthrough in computational fluid dynamics (CFD) is the emergence ofadaptive high-order (order > 2) methods. The leader is the discontinuous Galerkin (DG)method, amongst several other methods including the multi-domain spectral, spectral volume(SV), spectral difference (SD) methods. Recently, the correction procedure via reconstruction(CPR) formulation was developed to unify these methods under a single framework. All themethods possess the following properties: k-exactness on arbitrary grids, and compactness,which is especially important for parallel computing on clusters of CPUs and GPUs. In thistalk, I will describe the CPR formulation, and explain its connection to the DG, SV and SDmethods. In addition, the application of high-order methods to compute transitional flowover a SD7003 wing and flow over flapping wings will be presented. The talk will concludewith several remaining challenges in the research on high-order methods.

5

Abstracts for Contributed Talks

Contents

Abraham Abebe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Dhruba Adhikari . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

M. Faridul Alam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Vasilios Alexiades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Jaffar Ali . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Alexis Erich S. Almocera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Falko Baustian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Harish P Bhatt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Volodymyr Borodin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Dagny Butler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Maya Chhetri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Varun Chitta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Eric M. Collins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Luis Cueva-Parra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Marcelo Disconzi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Ritesh Kumar Dubey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Shruti Dubey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Satyanarayana Engu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Richard C Ewool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Peng Feng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Zhaosheng Feng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Matthew Fury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Mohammad Gandomkar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Jerome Goldstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Xiaoqian Gong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

John R. Graef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Noureddine Hannoun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Xiaoming He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Samuel N. Jator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Ehigie Julius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Lakshmi S Kalappattil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

i

Andrew Kerr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Harihar Khanal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Morteza Kiani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Seongjai Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Eunkyung Ko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Alicia Prieto Langarica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

David M. Lavallee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Jeremy LeCrone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Chuan Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Xiao Liang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Laalitha Liyanage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Maurin Lopez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Nsoki Mavinga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Cory Medlin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Arundhati Bagchi Misra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Christopher Moore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Janpou Nee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Fidele F. Ngwane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Jigarkumar Patel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Nar Rawal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Bonnie Roberson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Marisabel Rodriguez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Adrian Sescu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Arjun Shanker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Yuanzhen Shao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Suzanne Shontz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Zachariah Sinkala . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Bela Soni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Ray Treinen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Christophe Troestler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Jose M Vega-Guzman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Wenchao Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

M.K. Wolverton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Shantia Yarahmadian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Jinglong Ye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Shan Zhao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

ii

Interactive treatment planning in cancer radiotherapyAbraham AbebeUniversity of North Carolina at Greensboroanabebe@uncg.edu

Coauthors: Sarah Couzens, Laura Norena, , Mohammad Shakourifar, Wenling Shang, PooyanShirvani Ghomi, Giulio Trigila, Masoud Zarepisheh.

Cancer is the second greatest cause of death in USA. Cancer patients are treated withradiotherapy since it has been proven effective as treatment for many cancer types. Onetherapy technique for cancer is Intensity Modulated Radiation Therapy (IMRT). The goalis to deliver a given amount of radiation (prescribed by the physician) to the tumor whilelimiting the amount of radiation absorbed by the healthy organs. In this talk we present analgorithm and numerical results for the treatment planning of cancer radiotherapy. The algo-rithm is based on the so called moments approach in which a given Dose Volume Histogram(DVH) is approximated with a set of constraints on the moments of the dose distribution.

Eigenvalues and balls in the range of perturbations of maximal monotone oper-atorsDhruba AdhikariSouthern Polytechnic State Universitydadhikar@spsu.edu

Coauthors: Athanassios G. Kartsatos

Let X be an infinite dimensional real reflexive locally uniformly convex Banach space withlocally uniformly covex dual space X∗ and G ⊂ X open and bounded. Let T : X ⊃ D(T )→2X

∗be maximal monotone and strongly quasibounded, S : X ⊃ D(S) → X∗ maximal

monotone, and C : X ⊃ D(C) → X∗ strongly quasibounded w.r.t. S and such that itsatisfies a generalized (S+)-condition w.r.t. S. Assume that D(S) = L ⊂ D(T ) ∩ D(C),where L is a dense subspace of X, and 0 ∈ T (0), S(0) = 0. With the help of the topologicaldegree theory for T + S + C recently developed by the authors, the eigenvalue problem ofthe form T + S + C(λ, ·) 3 0 will be discussed. In addition, the problem of existence of apathwise connected set in the range of the operator T + S +C will also be discussed. Thesetheories have applications in the study of a class of time-dependent problems involving threeoperators.

1

Prediction of vortical structures in unsteady separated transitional/turbulentflows using hybrid RANS/LES modeling methodologyM. Faridul AlamMississippi State Universitymfa38@cavs.msstate.edu

Coauthors: D. Keith Walters, David Thompson

In addition to their local characteristic structures, unsteady, separated turbulent flowphenomena generate vortical structures called ’turbulent eddies/scales.’ These turbulentscales cover a wide spectrum that ranges from smaller eddies of near wall boundary layerto larger eddies in regions of separated flow. Prediction of these vortical structures is im-portant in order to capture flow physics accurately and requires an appropriate turbulencemodeling approach. Theoretically, Direct Numerical Simulation (DNS) is the most accu-rate approach for predicting turbulent flows. DNS resolves all spatial and temporal scalesof the turbulence spectrum. However, due to its immense computational expense, DNS isyet not feasible for real world flow problems. The most popularly used approach, based onthe Reynolds-averaged Navier-Stokes (RANS) equations, resolves only the mean flow andmodels all turbulent scales. RANS uses significantly less computational resources due to itshigh degree of phenomenological modeling, which reduces its generality. The Large-EddySimulation (LES) modeling approach stands in the middle with regard to accuracy and com-putational cost. LES resolves the large scale motion in the separated flow region and modelsthe smaller scales in the boundary layer. Although LES offers more accuracy than RANS inthe separated flow regions, LES requires much more computational expenses for boundarylayer prediction relative to RANS. As an alternative approach, a hybrid RANS/LES (HRL)modeling methodology combines the characteristics of both RANS and LES in such a waythat it offers more accuracy than RANS at a reduced cost relative to LES. In this study,a new HRL modeling methodology, the Dynamic Hybrid RANS/LES (DHRL) model, isdeveloped and tested to predict the vortical structures for two fully-turbulent flow cases.The results are compared to those obtained using the Delayed Detached Eddy Simulation(DDES) model, which is a widely accepted HRL model. A transition-sensitive RANS modelis also incorporated in the DHRL model to predict laminar-to-turbulent transitional flowphenomena, in addition to fully-turbulent flow prediction. Results of a canonical transi-tional flow test case are presented to show the viability of the transition-sensitive DHRLmodel.

Nanosecond laser ablation modelingVasilios AlexiadesUniv. of Tennesseealexiades@utk.edu

Coauthors: David Autrique (Physics, Univ. of Kaiserslautern, Germany)

Laser ablation is increasingly important in science and technology, in applications rangingfrom chemical analysis via mass spectroscopy, to pulsed laser deposition and nanoparticle

2

manufacturing. We outline a hydrodynamic model describing energy, momentum, and massconservation in the target material, in the plume and the plasma. In 1-D numerical simu-lations we explore the effects of different laser intensities and wave lengths on copper withnanosecond Gaussian pulse.

Positive solutions for a classes of elliptic bi-variate systems with combined non-linear effectsJaffar AliFlorida Gulf Coast Universityjahameed@fgcu.edu

Coauthors: R. Shivaji

In this talk, existence and multiplicity of positive solutions to the 3x3 bi-variate linearand quasi-linear elliptic system will be discussed. The reaction term of our system includesboth positone and semi-positone cases.

Limiting dynamics of a two-predator one-prey model with a Beddington-DeAngelis functional responseAlexis Erich S. AlmoceraUniversity of the Philippines Diliman, Philippinesalalmocera@gmail.com

Coauthors: Lorna S. Almocera (Sciences Cluster, University of the Philippines, Cebu) PollyW. Sy (Institute of Mathematics, College of Science, University of the Philippines Diliman)

We consider a population model of two competing predator species that exploit theirconsumption of a single renewable prey. Each predator-prey interaction is modeled by aBeddington-DeAngelis functional response. We investigate on how the parameters can de-termine the limiting behavior of any solution in the model. By solving differential inequali-ties, we obtain parametric conditions that suffice for a competitor to independently becomeextinct, hence being ”inadequate”. Furthermore, we show that competitive exclusion holdswhenever the losing competitor is inadequate. Given the extinction of at least one competi-tor, we analyze subsystems to calculate the limiting value of the solution. In case neithercompetitor is inadequate, we establish conditions where all three species can survive. Specif-ically, by solving differential inequalities, we find that a competitor can survive at a very lowdensity. In addition, we use a Lyapunov function to establish coexistence through a globalstability of the positive equilibrium point.

3

Pricing American options as a free boundary problem and regularity resultsFalko BaustianUniversitat Rostock, Germanyfalko.baustian@uni-rostock.de

Options are important assets in financial markets. With the Black-Scholes model it ispossible to derive the price function of an option as a solution of a PDE. European Optionshave been widely investigated. American options are a bit more complicated. They canbe exercised at every time before the maturity. The corresponding PDE is a free boundaryproblem and, thus, much more complicated to solve than a standard boundary value problem.

The price function of a European option satisfies a linear parabolic equation. For Americanoptions we get a similar equation, but only on a domain with a free boundary dependingon the solution. We transform the problem to a PDE on a half plane. This gives us on onehand the advantage of a fixed boundary and on the other hand we get an nonlinear term.We consider the resulting equation

(∂τ −B)v(ξ, τ) = ∂τv(0, τ)/v(0, τ)(∂ξv(ξ, τ) + v(ξ, τ)) + µv0(ξ) for ξ ∈ R+, τ ∈ [0, T ]

where B is the parabolic Black-Scholes operator and give some regularity results. We applythe implicit function theorem to prove these results.

Comparative study of numerical methods for a multi-dimensional non-linearreaction-diffusion Brusselator system.Harish P BhattMiddle Tennessee State Universityharishbht24@gmail.com

Coauthors: Abdul Q. M. Khaliq

Non-linear reaction-diffusion systems arise frequently in the study of chemical and biolog-ical phenomenon and most usually modeled by time dependent partial differential equationsexhibiting oscillation. To understand the complex dynamic behavior of the system, we needto depend on the numerical approaches due to the cumbersome works associated with get-ting an analytical solution of such systems. In this work, we try to compare the meshfree (Radial Basis Functions), mesh based (Finite Difference), and time stepping approachin terms of their accuracy, rate of convergence, and computational efficiency for solvingmulti-dimensional initial-boundary value problems governed by a non-linear time dependentsystem of PDEs. The system is known as a reaction-diffusion Brusselator system. We uselinearly implicit Crank-Nicolson (LICN) and Peaceman-Rachford ADI method as a meshbased approach, multiquadric radial basis function as a mesh free approach, and exponen-tial time differencing locally one dimensional (ETD-LOD) as a time stepping approach tocompute the approximate solution of reaction-diffusion Brusselator system.

4

A semi-analytic approach to the construction of Green’s functions for the Laplaceequation posed in multiply-connected regionsVolodymyr BorodinTennessee State Universityvb2m@mtmail.mtsu.edu

Boundary-value problems are considered as posed in multiply-connected regions on sur-faces of revolution. Green’s functions for such problems are targeted and their constructionis managed with the aid of the so-called resolving Green’s functions which are supposedto be available in advance. The latter represent Green’s functions for problem stated forthe corresponding simply-connected regions. Construction of the resolving Green’s func-tions is possible by means of the analytic technique provided in [1]. The numerical partof semi-analytic approach is based on the method of functional equations. This results inintegral type functional equations whose solution are accomplished numerically. Graphicalillustrations are presented.

The present project was supported by the Computational Science Program at MiddleTennessee State University, and the author greatly appreciates that support.

[1] Melnikov Yu.A., ”Influence Functions and Matrices”, Marcel Dekker, New York, 1999

Existence of alternate steady states in a phosphorous cycling modelDagny ButlerMississippi State Universitydg301@msstate.edu

Coauthors: Ratnasingham Shivaji (University of North Carolina Greensboro) & Sarath Sasi(Mississippi State University)

We consider the existence of multiple positive solutions to the steady state reactiondiffusion equation with Dirichlet boundary conditions of the form:

−∆u = λ[K − u+ cu4

1 + u4], x ∈ Ω

u = 0, x ∈ ∂Ω.

Here ∆u = div(∇u)

is the Laplacian of u, 1λ

is the diffusion coefficient, K and c are positiveconstants, and Ω ⊂ RN is a smooth bounded region with ∂Ω in C2. This model describesthe steady states of phosphorus cycling in stratified lakes. Also, it describes the colonizationof barren soils in drylands by vegetation. In this paper, we discuss the existence of multiplepositive solutions leading to the occurrence of an S-shaped bifurcation curve. We prove ourresults by the method of sub-super solutions.

5

Positive solutions for a class of p-Laplacian superlinear semipositone problemsMaya ChhetriUniversity of North Carolina at Greensboromaya@uncg.edu

Coauthors: Pavel Drabek and R. Shivaji

We consider an elliptic problem of the form

−∆pu = λ f(u); Ωu > 0; Ωu = 0; ∂Ω ,

where λ > 0 is a parameter, Ω is a strictly convex bounded domain in RN ;N ≥ 2 with C2

boundary ∂Ω and 1 < p ≤ 2. The nonlinearity f : [0,∞)→ R is a continuous function thatis semipositone (f(0) < 0) and p-superlinear at infinity. We use degree theory combinedwith re-scaling argument and uniform L∞ apriori estimate to prove that the problem has apositive solution for λ small. We extend this result to systems case as well.

A four-equation variant of the k-kL-w Model sensitized to rotation and curvatureeffectsVarun ChittaMississippi State Universityvc217@msstate.edu

Coauthors: Tej P. Dhakal and D. Keith Walters

A new four-equation eddy-viscosity turbulence model sensitized to both flow transitionand curvature effects is presented. The model is based on the k-w framework and has four ad-ditional transport equations. The first three transport equations are similar to the equationsfrom the previously documented transition-sensitive k-kL-w model and the fourth transportequation is similar to the v2 equation from the previously documented curvature-sensitiveSST k-w-v2 model. The pretransitional low-frequency velocity fluctuations which are theprecursors to transition are represented by the third transport equation (kL), and the fourthscalar transport equation (v2) introduces the physical effects of curvature and rotation onthe turbulence structure. The model has been implemented into the commercial flow solverFLUENT, and is tested on several two-dimensional problems involving rotation or curvatureeffects and flow transition effects. The test cases include flat plate boundary layers with andwithout applied pressure gradients, cylinder test cases with different Reynolds numbers andelliptic airfoil test cases with different angles of attack. To evaluate the predictive-capabilityof several different RANS-based turbulence modeling approaches towards this class of flow-field, the results obtained are compared to the standard SST k-w model, transition-sensitivek-kL-w model and curvature-sensitive SST k-w-v2 model. The results from the test casespresented here demonstrate the ability of the new model to successfully resolve both flowtransition and curvature effects with reasonable engineering accuracy, for only a small in-crease in computational cost.

6

Fast and accurate evaluation of complex equations of stateEric M. CollinsMississippi State Universityemc@cavs.msstate.edu

Coauthors: Ed Luke

One of the most common operations encountered in computational fluid dynamics (CFD)solvers is the evaluation of the caloric and thermal equations of state (EOS) which are re-quired to compute thermodynamic state variables from the conserved values that are typ-ically being advanced by the simulation. The complexity of these calculations can varywidely depending on the nature of the fluid under consideration. We present a method forgenerating an interpolated representation of the EOS that is fairly inexpensive to evaluateregardless of the complexity of the actual underlying state equations. This approach has theadvantage of being agnostic towards the original representation; whether it be a complexanalytic expression, expensive iterative method, or interpolated from empirical data.

Lattice Boltzmann simulation of nanofluid melting with natural convectionLuis Cueva-ParraAuburn University at Montgomerylcuevapa@aum.edu

Coauthors: Augustine Bertagnolli

A Lattice Boltzmann model is employed for simulating melting with natural convectionof a nanofluid. The domain is a 2D box, initially filled up with a frozen nanofluid, then wekeep one of the lateral boundaries at higher than melting temperature while the other one iskept below freezing temperature. The other two boundaries, top and bottom are adiabatic.We compare the liquid/solid interface temporal and spatial evolution with that of the purebase fluid. The effects of the nanoparticles are studied.

On the fluid motion with free boundary and strong surface tensionMarcelo DisconziVanderbilt Universitymarcelo.disconzi@vanderbilt.edu

Coauthors: David G. Ebin (SUNY Stony Brook)

We consider the initial value problem for the motion of an incompressible inviscid fluidwithin a bounded domain in Rn and with free boundary. Assume that the domain at timezero, denoted by U, has constant mean curvature. We prove that when the surface tensiongoes to infinity, solutions of the free boundary Euler equations converge to solutions ofthe Euler equations in the fixed domain U. This provides mathematical justification to theintuitive idea that a domain with high surface tension is essentially ”rigid”.

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Bounds on total variation and second order accuracy at extrema.Ritesh Kumar DubeySRM University, Indiariteshkd@gmail.com

In this work we give total variation bounds on some uniformly second order accurateschemes for hyperbolic conservation laws. These bounds show that these it is possible tohave second order TVD approximation at points of extrema as well in steep gradient region.Numerical tests are also reported to support the theoretical bounds.

Existence of solutions to partial functional differential equations of fractionalorder with nonlocal conditionsShruti DubeyIndian Institute of Technology, Indiashrurkd@gmail.com

The study of ordinary and partial differential equation of fractional order is of consid-erable importance as they frequently appear in the various applications in fluid dynamics,aerodynamics, biology, physics and engineering. In fact, such type of equations efficientlydescribe many physical phenomena. In the present work, we consider a partial functionaldifferential equations of fractional order in a Banach space with nonlocal condition. Nonlocalconditions are usually more precise for physical measurments than the classical conditionsand therefore the considered problem can be applied with better effect. The fractionalderivative is described in the Caputo sense. The theory of resolvent operators, the fractionalpowers of operators, fixed point techniques are used to establish the existence and regularityof local mild solution. Then the existence of local classical solutions is shown. Finally anexample is given to illustrate the application of the abstract results.

Higher order approximations in the Burgers equationSatyanarayana EnguTata Institute of Fundamental Research, Indiasatya@math.tifrbng.res.in

The aim of this paper is to study the large time asymptotics for solutions of the viscousBurgers equation subject to a class of initial conditions. Using generalization of the truncatedmoment problem to a complex measure space, we construct asymptotic N-wave approximatesolution. We prove that constructed solution differs from the true solution by an error oforder O(t−(n+1)+1/2p) in Lp norm. This process allows us to obtain the convergence of anyhigher order in Lp norm by suitably improving the constructed solution.

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The application of explicit stabilized numerical methods on a mathematicalmodel for tumor angiogenesis in the cornea.Richard C EwoolMiddle Tennesse State Universtiyrce2m@mtmail.mtsu.edu

Coauthors: Zachariah Sinkala

We consider the onset of tumor-induced angiogenesis in the cornea and how inhibitorscan possibly slow down the growth of tumor by restricting signaling factors to blood vesselsthat can grow and vascularize the tumor mass. The resulting partial differential equationsthat describes this process follows from H.A.Harrington et al. The spatial discretization ofthis system of PDEs results in a large system of ordinary differential equations. In our study,we use a special class of time integration numerical methods known as the Explicit StabilizedRunge-Kutta methods. Our choice for this method is because the Explicit Stabilized Runge-Kutta methods work very well for mildly stiff PDEs like that of our model . We used threedifferent Explicit Stabilized Runge-Kutta methods namely DUMKA, ROCK2 and ROCK4to solve the system numerically using Fortran as our computational tool. We compared thecpu times of DUMKA, ROCK2 and ROCK4 methods on the model and also checked whetherour results were consistent with the biological process.

Global bifurcation of positive solutions to some quasilinear elliptic problemPeng FengFlorida Gulf Coast Universitypfeng@fgcu.edu

We study the structure of positive solutions for an m-Laplacian boundary value problemarising in the study of thin films. The boundary value problem involves singular nonlineari-ties. We obtain the precise global bifurcation diagram of the solutions.

Burgers–KdV equation with time delayZhaosheng FengUniversity of Texas-Pan Americanzsfeng@utpa.edu

Coauthors: Zengji Du

In this talk, we are concerned with the existence of traveling wave solution to the Burgers-KdV equation with time delay by applying the geometric method of differential manifolds aswell as the implication function theorem, and establish the existence of a homoclinic orbitto the origin in a two-dimensional inertial manifold.

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Well-posed approximations of nonlinear evolution problems in a Hilbert spaceMatthew FuryPenn State Abingtonmaf44@psu.edu

We prove regularization for the ill-posed, semilinear evolution problem du/dt =A(t,D)u(t) + h(t, u(t)), 0 ≤ s ≤ t < T , with initial condition u(s) = x in a Hilbert spacewhere A(t,D) is an operator depending on both time t and a positive self-adjoint operatorD in the space. As in recent literature focusing on linear equations, regularization is estab-lished by approximating the solution u(t) of the problem by the solution of an approximatewell-posed problem. We will provide an outline of the regularization using a few differentapproximations of the operators A(t,D), and finally demonstrate our theory with applica-tions to a wide class of nonlinear partial differential equations in L2 spaces including thenonlinear backwards heat equation with a time-dependent diffusion coefficient.

A new numerical integration method based on Kriging interpolationMohammad GandomkarIsfahan University of Technology, Iranmgd gandomkar@me.iut.ac.ir

Coauthors: S. H. Dibajianb;M. Farzinc; S. H. Hashemolhoseinid

In this article a numerical integration approach is proposed to analyze quasistatic prob-lems based on weak formulation in meshless methods. In the present method the integrationover global domain is performed at integration points and the weights are obtained by ageostatistical approach which is developed based on Kriging interpolation. Absolutely nobackground mesh is needed in this approach. Kriging interpolation is also used to obtainstiffness matrix and also a diagonal mass matrix which is an important advantage for explicittime integrations. Several numerical examples in structural domain validate the performanceof the new approach.

New asymptotic energy results for damped wavesJerome GoldsteinUniversity of Memphisjgoldste@memphis.edu

Coauthors: Gisele Goldstein, Genni Fragnelli, Silvia Romanelli, Gustavo Perla M, & GuillermoReyes.

We discuss three kinds of new asymptotic results for wave equations with strong damping.(1) Equipartition of energy. (2) Overdamping. (3) Asymptotic parabolicity.

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Duffing-van der Pol oscillator systemXiaoqian GongUniversity of Texas Pan Americanjiaxiaoqian666@126.com

In this talk, we study a nonlinear Duffing-van der Pol–type oscillator system by meansof the first-integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and thedamped Duffing oscillator, etc. as particular cases. Firstly, we apply the Division Theoremfor two variables in the complex domain, which is based on the ring theory of commutativealgebra, to find a quasi-polynomial first integral to an equivalent autonomous system. Thenthrough a certain parametric condition, we derive a general first integral of Duffing–van derPol–type oscillator system.

Solutions of a nonlinear fourth order periodic boundary value problem for dif-ference equationsJohn R. GraefUniversity of Tennessee at Chattanoogajohn-graef@utc.edu

Coauthors: Lingju Kong and Min Wang

The authors consider the fourth order periodic boundary value problem

∆4u(t− 2)−∆(p(t− 1)∆u(t− 1)) + q(t)u(t) = f(t, u(t)), t ∈ [1, N ]Z,

∆iu(−1) = ∆iu(N − 1), i = 0, 1, 2, 3,

where N ≥ 1 is an integer, p ∈ C([0, N ]Z,R), q ∈ C([1, N ]Z,R), and f ∈ C([1, N ]Z × R,R).They obtain sufficient conditions for the existence of one and two solutions of the problem.The analysis is based mainly on the variational method and critical point theory.

Partition analysis for the spectral volume methodNoureddine HannounUniversity of Science and Technology Houari Boumediene, Algerianhannoun@usthb.dz

Coauthors: Vasilios Alexiades (Mathematics, Univ. of Tennessee)

The Spectral Volume Method has been developed by Z. J. Wang as a higher order al-ternative to the traditional Finite Volume Method, which is so popular in the numericalsimulation of physical problems governed by systems of conservation laws. High order accu-racy is achieved by partitioning a basic grid element (the spectral volume SV) into a set ofcontrol volumes (CV). The polynomial approximation of the solution is then cast in termsof the solution CV-averaged values. The choice of a partition is a crucial aspect for the

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success of the method. We investigate several partitions for the two-dimensional triangularelement and provide results in terms of the Lebesgue constant and the reconstruction matrixcondition number.

Immersed finite element methods for parabolic equations with moving interfaceXiaoming HeMissouri S&Thex@mst.edu

Coauthors: Tao Lin, Yanping Lin, Xu Zhang

Three Crank-Nicolson-type immersed finite element (IFE) methods are presented forsolving parabolic equations whose diffusion coefficient is discontinuous across a time depen-dent interface. Instead of the body-fitting mesh needed by the traditional finite elements forsolving interface problems, these IFE methods can use a structured mesh because IFEs canhandle interface jump conditions without requiring the mesh to be aligned with the inter-face. Several disadvantages of the body-fitting mesh for time-dependent interface problemswill be discussed. And then a fixed structured mesh for IFEs will be utilized to resolvethese problems. Numerical examples are provided to demonstrate features of the three IFEmethods.

Stabilized Adams type method with a block extension for the valuation of optionsSamuel N. JatorAustin Peay State UniversityJators@apsu.edu

Coauthors: Dong Nyonna; Drew KERR

We construct a continuous stabilized Adams type method (CSAM) that is defined for allvalues of the independent variable on the range of interest. This continuous scheme has theability to provide a continuous solution between all the grid points with a uniform accuracycomparable to that obtained at the grid points. Hence, discrete schemes which are recoveredfrom the CSAM as by-products are combined to form a stabilized block Adams type method(SBAM). The SBAM is then extended on the entire interval and applied as a single blockmatrix equation for the valuation of options on a non-dividend-paying stock by solving asystem resulting from the semi-discretization of the Black-Scholes model. The stability ofthe SBAM is discussed and the convergence of the block extension of the SBAM is given. Anumerical example is given to show the accuracy of the method.

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A Legendre-collocation based continuous second derivative BDF formula for stiffproblemsEhigie JuliusUniversity of Lagos, Nigeriajehigie@unilag.edu.ng

Coauthors: Prof. S. A. Okunuga (University of Lagos) Prof S. N. Jator (Austin Peay StateUniversity, Clarksville, TN, USA)

Special numerical methods are required to simulate stiff models without solutions. In thispaper, a 2-point Block multistep formula is derived from a Legendre-Collocation based con-tinuous second derivative backward differentiation formula with special quadratures, which iscapable of simulating stiff models arising from natural phenomenon whether PDEs or ODEs.The method is self-starting and stiffly stable. The method is applied in block form as simul-taneous numerical integrators over non-overlapping intervals. Numerical results obtainedusing the proposed block form reveal that it is highly competitive with existing methods inthe literature.

A uniqueness result for semipositone problems on exterior domainsLakshmi S KalappattilMississippi State Universitylk154@msstate.edu

Coauthors: Alfonso Castro, R. Shivaji

We study nonnegative radial solutions to the problem−∆u = λK(|x|)f(u), x ∈ Ω,

u = 0 if |x| = r0,

u→ 0 as |x| → ∞,

where λ is a positive parameter, ∆u = div(∇u)

is the Laplacian of u, Ω = x ∈ Rn;n >2, |x| > r0 and K belongs to a class of functions such that limr→∞K(r) = 0. For classes ofnonlinearities f that are negative at the origin and sublinear at ∞ we discuss a uniquenessresult when λ is large.

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Numerov-type method for the numerical solution of elliptic partial differentialequationsAndrew KerrAustin Peay State Universityakerr@my.apsu.edu

Coauthors: Beth Oglesby Glapa (Austin Peay State University) Samuel N. Jator (AustinPeay State University)

One commonly used approach to approximating solutions for time-dependent partialdifferential equations (PDE) is replacing the spatial derivatives by algebraic approximationsthrough a central difference method. However, for time-independent PDEs, this approachis not very common. We convert the Laplace equation into a system of ordinary differentialequations (ODE) by replacing one of the spatial derivatives using the central differencemethod. The resulting system of ODEs is then solved using a Numerov-type method. Wecompare these solutions to Laplace’s equation generated by our Numerov-type method tothe central difference method.

Time-stepping for laser ablationHarihar KhanalEmbry-Riddle Aeronautical Universityharihar.khanal@erau.edu

Coauthors: D. Autrique (Physics, Univ. of Kaiserslautern, Germany),

V. Alexiades (Math, Univ. of Tennessee)

Laser ablation is used in many areas of science and technology including medicine, archae-ology, chemistry, environmental and materials sciences. We outline a computational modelfor radiative and collisional processes during laser ablation, and compare the performance ofvarious low and high order time-stepping algorithms.

Application of Fourier series to demonstrate the energy absorption phenomenonin aluminum tubes under impact loadingMorteza KianiMississippi State Universitymk532@msstate.edu

Coauthors: Shantia Yarahmadian, Keiichi Motoyama, Mohammad Sepehrifar

By using Fourier analysis, we have developed a new computational approach to deter-mine the energy absorption capacity in aluminum tubes. The dynamic crash responses ofaluminum tubes are determined through experimental methods or from the finite elementsolutions of the related PDEs for the structural dynamics and material failure in the struc-ture. Using the proposed computational approach will reduce the cost of the experimentsand will reduce the time consumption and effort in FEM simulation. The proposed method

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can be adopted for the analysis of the other structures under impact.

Surface reconstruction for nonuniformly sampled data: A PDE-based approachSeongjai KimMississippi State Universityskim@math.msstate.edu

Coauthors: William T. Cordell, Hakran Kim, and Jeffrey L. Willers

The article is concerned with image reconstruction for arbitrarily spaced data using cur-vature interpolation. Image reconstruction is a challenging problem when no constraint isimposed on data locations. In the literature, various methods have been studied for thereconstruction of nonuniformly sampled data in terms of the approximation theory, incorpo-rating spline and wavelet spaces. However, the problem is ill-posed and numerical methodsbecome overly expensive as the number of sample points increases. This article develops aneffective partial differential equation (PDE)-based algorithm, called the recursive curvatureinterpolation method (R-CIM). The new method utilizes a curvature-related informationwhich is estimated from an intermediate surface of the nonuniform data and plays a roleof driving force for the reconstruction of a reliable image surface. The R-CIM is an inter-polator, converges to a piecewise smooth image, possesses a minimum oscillatory behavior,and finishes all the computational tasks in O(N) operations, where N is the number of gridpoints. Examples are given to prove the claim; the suggested algorithm outperforms theinverse-distance weighting method, one of the most popular surface construction methodsfor scattered data.

Uniqueness and multiplicity results for singular nonlinear eigenvalue problemsEunkyung KoMcDaniel Collegeeko@mcdaniel.edu

Coauthors: Alfonso Castro and Ratnasingham Shivaji

We study positive solutions to the singular boundary value problem

−∆u = λf(u)

uβin Ω,

u = 0 on ∂Ω,

where λ is a positive parameter, β ∈ (0, 1) and Ω is a bounded domain in RN , N ≥ 1.

Here f ∈ C([0,∞), (0,∞)) is nondecreasing and satisfies limu→∞f(u)uβ+1 = 0. We discuss the

existence of multiple positive solutions for a certain range of λ and a uniqueness result forλ 1. A simple model that will satisfy our hypotheses is f(u) = e

αuα+u for α 1. We

extend our multiplicity result to classes of systems, including p−Laplacian systems, whenthe nonlinearities satisfy certain combined sublinear conditions at infinity.

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From discrete to continuous models of cell movement: an application to medicalimplantsAlicia Prieto LangaricaYoungstown State Universityaprietolangarica@ysu.edu

Coauthors: Dr. Hristo Kojouharov

Mathematical modeling of cell movement can help attain a deeper understanding of vitalprocesses such as embryogenesis, angiogenesis, tumor metastasis, and immune reactions tomedical implants. In this work, cell movement and growth in response to external stimulusand the interactions between cells and the stimulus are considered. In order to model therandom nature of the movement, a discrete model is created to simulate cells moving in thepresence of a growing and moving stimulus distribution. The model also includes the deple-tion of the stimulus under the presence of cells. The discrete model is then upscaled, basedon transition probabilities of the individuals at each site, to obtain a corresponding con-tinuous differential equation model. Under traditional modeling assumptions the proposedcontinuous model reduces to previously developed models in the literature. Next, a set ofnumerical experiments are presented showing very good agreement between the continuousand discrete models for a variety of different values of the parameters. Potential applicationsof the new mathematical models for reducing medical implant-associated infection are alsodiscussed.

Application of lambda-2, Q-, and delta-criterion vortex detection techniques toexperimental airfoil dataDavid M. LavalleeMississippi State Universitydml148@cavs.msstate.edu

Coauthors: David Thompson & Redha Wahidi

The common vortex detection techniques using Lambda-2, Q-, and Delta-criterion wereapplied to experimentally-obtained data from a NACA 4412 airfoil in a water channel atRe=56,000, angle of attack = 4 degrees, and measurements taken at 5 frames/second usinga volumetric three-component velocimetry (V3V) system. Using consistent thresholdingamong the three methods, the three methods were compared. Lambda-2 and Q tend toshow very similar structures, whereas Delta seems to be more inclusive than either of theother two methods.

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Stability and bifurcation of equilibria for the axisymmetric surface diffusion flowJeremy LeCroneVanderbilt Universityjeremy.lecrone@vanderbilt.edu

Coauthors: Gieri Simonett

The surface diffusion flow is a fourth-order quasilinear evolution law which models themotion of some surfaces in the presence of high temperatures. I will focus on the setting oftwo-dimensional surfaces which exhibit symmetry about a fixed axis of rotation and satisfyperiodic boundary conditions. I will discuss equilibria of the flow in this setting and analyticmethods involved with stability/instability and bifurcation results.

Parallel computing techniques in DelPhi to solve the Poisson-Boltzmann equa-tion and calculate electrostatic energies of biological marcromoleculesChuan LiClemson Universitychuanli@clemson.edu

Coauthors: Lin Li, Emil Alexov

Modelling the electrostatic potential and the corresponding energies plays an essential rolein molecular biology and is nontrivial due to the irregular shape of biological macromolecules.In a continuum case, it requires solving the Poisson-Boltzmann equation (PBE). The DelPhiprogram utilizes finite difference method to solve PBE and has been widely recognized in thebiological community. Here we report recent developments of parallel computing techniquesimplemented in DelPhi. These techniques, including one to effectively parallelize the Gauss-Seidel/SOR iterations, make the parallelized DelPhi several-fold faster than the serial codewithout compromising the accuracy and without introducing any assumptions. Furtherwe demonstrate the advantages of the parallelized DelPhi by computing the electrostaticpotential and energies of large supramolecular structures.

Efficient exponential time differencing methods for non-linear Schrodinger equa-tionsXiao LiangMiddle Tennessee State Universityxl2h@mtmail.mtsu.edu

Coauthors: A.Q.M. Khaliq

The non-linear Schrodinger (NLS) equation and its higher order extension (HONLS equa-tion) are widely used in simulating phenomena in areas of fiber optics and wave mechanics.Solitons achieved by these equations describe the energy conservation in these phenomena.Efficient nonlinear numerical schemes are needed to solve these equations for further analysisof the physical models. Based on Cox and Matthew’s exponential time differencing (ETD)

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approach, a fourth-order strongly-stable method having real distinct poles is developed andapplied to solve the non-linear part of the NLS and HONLS equations. A computationallyefficient version of the method is constructed using partial fraction splitting technique. Thisapproach requires solving several backward Euler type linear systems at each time step. Forthe linear part, the split-step Fourier method is used to simplify the linear systems. Todetermine the computational efficiency we calculate the minimum CPU time required for agiven scheme to achieve a specified error. Numerical experiments are presented to demon-strate that the fourth-order ETD method is always more efficient than other methods, suchas the Fourier split-step method and fourth-order Runge Kutta method.

First principles study of magnetic properties of Zn-Sn substituted M-type Sr-hexaferriteLaalitha LiyanageMississippi State Universitylaalitha@cavs.msstate.edu

Coauthors: Sungho Kim, Yang Ki Hong, Steven C. Erwin, Seong-Gon Kim

Site occupancy and magnetic properties of Zn-Sn substituted M-type Sr-hexaferriteSrFe12x(Zn0:5Sn0:5)xO19 with x = 1 were studied using density functional theory and gen-eralized gradient approximation (GGA). Using the hybrid functionals and GGA+U methodthe description of strongly correlated 3d electrons of Fe was improved. Our results show thatZn and Sn atoms prefer to occupy 4f1 and 4f2 sites respectively. Favorable Zn-Sn substitutedconfiguration show an increase in saturation of magnetization (Ms), and a decrease in mag-netic anisotropy energy (MAE), over the pure M-type Sr-hexaferrite (x = 0). Experimentalobservations agree with the decrease of MAE and the increase of Ms for Zn-Sn substitutedSr-hexaferrite.

Development of a simple phenomenological linear eddy-viscosity RANS modelfor computational fluid dynamics simulations of transitional flowMaurin LopezMississippi State Universitymal278@msstate.edu

Coauthors: D. Keith Walters

The motion of single-phase, Newtonian fluids is governed by the Navier-Stokes equation,a well known partial differential equation that is notoriously difficult to solve. Computa-tional fluid dynamics (CFD) offers one approach, in which the variables describing the flow(velocity and pressure) are computed numerically at discrete spatial and temporal locations.One type of CFD, direct numerical simulation (DNS), is based on a highly resolved solutionin which all length and time scales of the motion are included in the simulation. For highReynolds number flows, which exhibit a very large range of scales, this approach is unfea-sible for all but the most powerful high performance computers, even for relatively simpleproblems. As an alternative, statistical methods are often employed to dramatically reduce

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the computational cost. The most common of these is the use of the Reynolds-averagedNavier-Stokes (RANS) equations, supplemented by a relatively simple mathematical modelto represent the effects of unresolved scales of motion. A key challenge for RANS modelingis transitional flow, in which the flow changes regime from a smooth orderly state (laminar)to a rapidly fluctuating state (turbulent), due to instabilities related to the nonlinearity ofthe advective term in the Navier-Stokes equation. Several RANS models for transitional flowhave been developed, but one drawback of these models is their complexity, which is oftenbased on the empiricism required to predict flow features for which the physics are not yetcompletely understood. One of the current goals for CFD researchers is the development ofnew transitional RANS models with high accuracy in the prediction of transitional boundarylayers for a wide range of applications, but with low consumption of computational resourcesand relative model simplicity. In this study we present a new model concept for predictionof boundary layer transition using a linear eddy-viscosity RANS approach, based on a de-scription of the transition process previously discussed by Walters (2009). We compare theunderlying physics and initial results of this new methodology with other currently used, ro-bust models like that presented by Walters and Cokljat (2008), in order to show the inherentsimplicity and relative accuracy of the new model.

Nonresonance on the boundary and strong solutions of elliptic equations withnonlinear boundary conditionsNsoki MavingaSwarthmore Collegemavinga@swarthmore.edu

Coauthors: M. Nkashama

We are concerned with the solvability of linear second order elliptic partial differentialequations with nonlinear boundary conditions by imposing asymptotic nonresonance condi-tions of nonuniform type with respect to the Steklov spectrum on the boundary nonlinearity.We cast the problem in terms of nonlinear compact perturbations of the identity on appro-priate trace spaces in order to prove the existence of strong solutions. We obtain a prioriestimates for possible solutions to a homotopy on suitable trace spaces and use topologicaldegree arguments.

Predictor not neededCory MedlinAustin Peay State Universitycmedlin31@gmail.com

Coauthors: Anne French, Sean Cather, Lin Nyguen

The standard Adams-Moulton / Adams-Bashforth method is based on a predictor-corrector algorithm. The Adams-Bashforth component of the method is the predictor andstarting values needed to start the method are supplied by a one-step method such as theRunge-Kutta Method. In this paper, we present a self-starting Adams method of order 5

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for solving second order differential equations. Numerical results are performed to show theadvantage of this approach over the standard algorithm.

Nonlocal speckle denoising model based on non-linear partial differential equa-tionsArundhati Bagchi MisraSaginaw Valley State Universityabmisra@svsu.edu

Coauthors: Hyeona Lim, Department of Mathematics and Statistics, Mississippi State Uni-versity, Mississippi State, MS 39762

Image denoising is among the most fundamental problems in image processing. A largerange of methods covering various fields of mathematics are available for denoising an image.The initial denoising models are derived from energy minimization using nonlinear partialdifferential equations (PDEs). The filtering based models have also been used for quite along time where the denoising is done by smoothing operators. The most successful amongthem was the very recently developed nonlocal means method proposed by Buades, Colland Morel in 2005. Though the method is very accurate in removing noise, it is very slowand hence quite impractical. In 2008, Gilboa and Osher extended some known PDE andvariational techniques in image processing to the nonlocal framework. The motivation behindthis was to make any point interact with any other point in the image. Using nonlocal PDEoperators, they proposed the nonlocal total variation method for Gaussian noise. In thispaper we develop a nonlinear PDE based accelerated diffusion speckle denoising model. Forfaster convergence, we use the Split Bregman scheme to find the solution to this new model.The new model shows more accurate results than the existing speckle denoising model. It isalso faster than the original nonlocal means method.

A modified tait equation of state to model cavitating water and its implementa-tion in Loci/BLASTChristopher MooreMississippi State Universitycdm168@msstate.edu

Coauthors: E. Luke, D. Thompson, R. Weed, J. Kang

Cavitation of water can occur due to a variety of circumstances from propeller rotationto reflection of shock waves caused by underwater blasts. Prior to this effort, the Taitequation of state (EoS) was the only EoS for water that was available within Loci/BLAST,and while the Tait EoS performs well at high pressures, it does not model cavitation. Anew extension for the Tait EoS, named the Modified Tait Eos, was developed for lowerpressures that can be used to simulate the effects of cavitating water. Simulations of onedimensional open- and close-ended shock tube problems were performed to validate thecavitation model. Simulation results for the open-ended shock tube compared well to resultsfound in literature; however, the close-ended shock tube results differed greatly. The EoS

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was then used in axisymmetric simulations of an underwater blast and detonation of a mineburied in saturated soil to assess its applicability to real blast problems. Excellent correlationwith results found in literature was shown for the underwater blast case. A mine impulsependulum simulation was performed using 22.33

UNCLASSIFIED: Dist A. Approved for public release

Solution behavior of certain types of elliptic equationsJanpou NeeChienKuo Technology University, Taiwanjpnee@ctu.edu.tw

Coauthors: Hsi-Chuan Huang Department of Automation Engineer and Institute of Mecha-tronoptic System,ChienKuo Technology University, Changhua, Taiwan, R.O.C.

This main purpose of this article is to study the behavior of the solution of generalizedelliptic equations from the model of micro electromechanical system. The results show thatthe range of the parameter k concerning touchdown voltage of the device is related to thegeometry of the device.

Solving oscillatory problems using a block hybrid trigonometrically fitted methodwith two off-step pointsFidele F. NgwaneUSC Salkehatchiengwanef@mailbox.sc.edu

Coauthors: Samuel N. Jator:

Department of Mathematics and Statistics, Austin Peay State University Clarksville, TN37044

A continuous hybrid method using trigonometric basis (CHMTB) with two ‘off-step’point is developed and used to produce three discrete hybrid methods which are simulta-neously applied as numerical integrators by assembling them into a block hybrid methodwith trigonometric basis (BHMTB) for solving oscillatory initial value problems (IVPs).The stability property of the BHMTB is discussed and the performance of the method isdemonstrated on some numerical examples to show accuracy and efficiency advantages.

Computational study of a dynamic contact problemJigarkumar PatelThe University of Texas at Dallasjigar jcp1@yahoo.com

Coauthors: Dr. Janos Turi

In this paper, we describe a computational framework to study the influence of a normalcrack on the dynamics of a cantilever beam. Due to the opening and closing of the crack

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during beam vibrations contact boundary conditions are assumed at the crack location. Inthe numerical implementation, the contact conditions lead to the consideration of a linearcomplementarity problem. We have introduced a very effective method for the solving linearcomplementarity problem. Numerical experiments are included.

Criteria for the existence of principal eigenvalue of time periodic nonlocal dis-persal operatorNar RawalAuburn Universitynsr0005@auburn.edu

Coauthors: Wenxian Shen

Nonlocal and random dispersal operators have been widely used to model duffusion sys-tems in applied sciences. I will talk about some criteria for the existence of a principaleigenvalue of the time periodic nonlocal dispersal operator. It will be shown that a timeperiodic nonlocal dispersal operator possesses a principal eigenvalue provided that the timeaverage of the underlying media satisfies some vanishing condition with respect to the spacevariable at maximum point.

Weak Allee effect, grazing, and S-shaped bifurcation curvesBonnie RobersonMississippi State Universitybjr76@msstate.edu

Coauthors: Emily Poole and Brittany Stephenson

We study a one-dimensional reaction-diffusion model arising in population dynamicswhere the growth rate is a weak Allee type. In particular, we consider the effects of grazingon the steady states and discuss the complete evolution of the bifurcation curve of positivesolutions as the grazing parameter varies. We obtain our results via the quadrature methodand Mathematica computations. In particular, we establish that the bifurcation curve isS-shaped for certain ranges of the grazing parameter. We also prove this occurrence of anS-shaped bifurcation curve analytically.

Evolution of within-host antibiotic resistance in GonorrheaMarisabel RodriguezThe University of Texas-Pan Americanmrodriguezy5@broncs.utpa.edu

Coauthors: Beverly Burgett, Samantha Ryan, William Tressel, Oscar Patterson, and StephenWirkus.

In the past decades, Gonorrhea, a sexually transmitted bacterial infection caused byNeisseria gonorrhoeae, has become resistant to a wider range of antibiotics. In this paper,

22

we consider the competition dynamics of multiple N. gonorrhoeae bacterial strains within ahost in an effort to better understand the development of antibiotic resistance and exam-ine individual-patient treatment regimes to determine conditions for within-host antibiotic-resistance emergence. To that aim, we propose a phenomenological model that takes intoaccount essential ideas such as the effects of different treatment levels, the mutation ratesof bacteria, and the response of the immune system. Numerical simulations also provide amore integral view of how model parameters affect the emergence of within-host resistance.

Synthesis of non-Gaussian turbulent velocity fields by random distributions ofdistorted Hill’s vorticesAdrian SescuMississippi State Universityadrian.sescu@msstate.edu

Coauthors: Charles Meneveau, Johns Hopkins University; Carlos Rosales, UniversidadTecnica Federico Santa Marıa, Chile

Hill’s spherical vortex is a simple analytical solution to the Helmholtz equation describingthe motion of an inviscid incompressible fluid. In this work, we focus on synthesizing a non-Gaussian turbulent velocity field using a random distribution of deformed Hill’s sphericalvortices. Studying synthetic turbulence is particularly useful not only in generating initialor/and inflow conditions to numerical simulations of turbulent flows, but also in providingnew insights into the basic structure of turbulence. A distortion is performed that uses amapping that breaks the spherical symmetry of the vortex, with the goal of introducingskewness in the velocity increments. The divergence-free condition is satisfied by performingthe distortion on the streamfunction itself, instead of on the velocity field. The amplitudes ofthe eddies are chosen from a given energy spectrum with the wave number being a functionof the eddy size. Statistical analysis shows that the synthetic non-Gaussian velocity fieldresembles some of the properties observed in real turbulence.

Physics based grid refinement and uncertainty quantifications for hybridRANS/LES turbulent simulationsArjun ShankerMississippi State Universityas1789@msstate.edu

Coauthors: S. Bhushan, D. McLaurin

The objective of this study is to develop and validate: (a) physics based unstructured gridrefinement, and (b) simulation uncertainty quantification (UQ) methodologies for URANSand hybrid RANS/LES simulations. An adaptive grid refinement methodology is beingdeveloped using the turbulence length scale as a metric for refinement. Turbulence lengthscale is adopted since it is the basic parameter for turbulence simulations, and determines thechoice of modeling such as URANS, hybrid RANS/LES (HRL), LES or DNS. The proposedgrid refinement strategy seeks to resolve the turbulence length scales uniformly in the URANS

23

and LES regions to reduce modeling error. The uncertainties in the URANS simulations willbe obtained using available Richardson extrapolation based correction factor method; andwill use the mesh refinement module to generate systematically refined grids. The URANSmethod is extended to HRL simulations using additional grid refinement in the LES region.The grid refinement and UQ methodology will be validated for canonical simulations, suchas flow over a sphere, jet flow, using an in-house solver LOCI/Chem.

Analytic solution of the surface diffusion flowYuanzhen ShaoVanderbilt Universityyuanzhen.shao@vanderbilt.edu

The problem of the surface diffusion flow is to look for a family of moving hypersufacesΓ(t) subject to the geometric evolution law that the normal velocity is equal to the Laplace-Beltrami of the mean curvature. By parametrizing them on a reference manifold, it leadsto a fourth order nonlinear evolution equation. We can show by means of a parametrizeddiffeomorphism on the reference manifold and implicit function theorem that there existsa unique local solution Γ(t) : t ∈ [0, T ) for some T > 0 such that it is analytic on themanifold ∪t∈(0,T )Γ(t) × t. If time allows, I may also discuss about the analytic solutionsof the averaged mean curvature flow or sefan problem.

A space-filling curve mesh element- and vertex-reordering technique for efficientmulticore finite element simulationsSuzanne ShontzMississippi State Universitysshontz@math.msstate.edu

Coauthors: Shankar Prasad Sastry, Emre Kultursay, Mahmut Kandemir

Finite element methods for unstructured meshes used to numerically solve partial dif-ferential equations often suffer from low cache utilization due to unstructured data accesspatterns. We reorder the mesh vertices and elements using space-filling curves to improvethe cache utilization in shared-memory, multicore processors. Our technique also improvesthe performance of the preconditioner associated with the discretized finite element system.Our results indicate performance improvements on shared-memory, multicore machines ofup to 48 cores.

24

Inverse problem for Fokker-Planck equationsZachariah SinkalaMiddle Tennessee State UniversityZachariah.Sinkala@mtsu.edu

Coauthors: Richard C. Ewool

In this work we look at the Inverse problems involving Fokker-Planck equations in whichsome coefficients are unknown. One has to determine unknown coefficients along with thesolution in Fokker-Planck equations. One of the features is that those problems may not bewell-posed. A challenging question is how to impose additional data in order to solve theproblem properly. There are many applications in ecology and in cancer biology.

Simulation of airflow, fluid-structure interaction and aerosol deposition in lungairwayBela SoniJackson State Universitybela bahen.j.soni@jsums.edu

Coauthors: Shahrouz Aliabadi

The respiratory system is one of the most complex dynamic systems in the human body.Bronchial tube flow and particle deposition simulations can increase an understanding of thehazardous health effects of the inhalation of harmful particles. In this study, we simulateflows, particle deposition, and structural deformation in idealized lung geometry of the smallbronchial tube model using our hybrid (finite element/finite volume), matrix free, parallelCaMEL solver. Realistically, the airflow in lung airway is not simply a steady-state. There-fore, the unsteady nature of airflow associated with inhale-exhale breathing is also consideredin this study. These unsteady breathing patterns cause deformation of the lung airway es-pecially in smaller bronchial tubes. During inhalation the tubes expand, while exhalationcauses narrowing of the tubes. In order to capture the tube deformation, fluid-structureinteraction analysis of lung airway was carried out.

Uniqueness and non-uniqueness of solutions to the floating ball problem.Ray TreinenTexas State Universityrt30@txstate.edu

Consider a ball of density d floating at the interface of a fluid of density d`. The dominantforces are due to surface tension and gravity. A variational argument gives the usual necessaryconditions of the Young-Laplace equation with Neumann type boundary conditions, however,there is a new additional condition on the free boundary which can be seen as a forcebalance equation. We explore this condition and illustrate how it leads to uniqueness ornon-uniqueness.

25

Multiplicity and symmetry of positive solutions to semi-linear elliptic problemswith Neumann boundary conditionsChristophe TroestlerUniversity de Mons, BelgiumChristophe.Troestler@umons.ac.be

Coauthors: Denis Bonheure, Christopher Grumiau

In this talk we will examine how the number of positive solutions to −∆u+u = |u|p−2u onΩ, with Neumann boundary conditions, changes as the exponent p increases. In particular,when Ω is a ball, we will show that this problem possesses an arbitrarily large number ofpositive solutions (in the subcritical as well as in the supercritical range) and degeneratesolutions provided p is large enough.

The minimum-uncertainty squeezed states for quantum harmonic oscillatorsJose M Vega-GuzmanArizona State Universityjmvega@asu.edu

We construct explicitly a six-parameter family of the minimum-uncertainty squeezedstates for the harmonic oscillator in non-relativistic quantum mechanics. They are derivedby the action of corresponding maximal kinematical invariance group on the standard groundstate solution. We show that the product of the variances attains the required minimumvalue 1/4 only at the instances that one variance is a minimum and the other is a maximum,when the ’squeezing’ of one of the variances occurs. Some applications to quantum opticsand cavity quantum electrodynamics are mentioned.

The oscillation behavior of 3D elasticity exact solution for orthotropic hollowcylinderWenchao WangIDC Technical Serviceswenchao25@gmail.com

Coauthors: Shantia Yarahmadian

The three dimensional elasticity exact solution for orthotropic hollow cylinder is devel-oped by authors. The accurate results are difficult to achieve by comparing with FEAsimulation. The main reason is an oscillation behavior of the solution for the differentialequation system found by authors recently. A study for this special behavior is presentedhere which help to identify the applicable field of 3D exact elasticity solution for this problem.

26

Feasibility study on sensitivity analysis for first-order flow effects due to pertur-bations in geometry in human upper airwaysM.K. WolvertonMississippi State Universitymkw21@cavs.msstate.edu

Coauthors: D. Thompson, G. Burgreen, D. Lavallee

The upper airways of humans are highly individualized, necessitating patient-specificdata for many medical and engineering applications. This requirement severely limits theutility of computational tools in a clinical setting. The aim of this project is to evaluate theapplicability of a base geometric model to be used in computational fluid dynamics (CFD)simulations for flow in the upper airways of humans. This study was accomplished usinga first-order sensitivity analysis of flow response to parametric changes in the geometry ofthese airways.

Dynamic instability of microtubules in three statesShantia YarahmadianMississippi State Universitysyarahmadian@math.msstate.edu

Microtubules are intercellular filaments. Throughout a unique phenomenon of undergoingstochastic growth and shrinkage, they act as a molecular machine. This phenomenon is calleddynamic instability. A PDE model for this dynamic instability in three states, (growth, pauseand shrinkage) has been developed. With this model, we will study the Green’s functionsand extinction rate of the microtubules.

Nonexistence results for classes of 3x3 elliptic systemsJinglong YeMississippi Valley State Universityjinglong.ye@mvsu.edu

Coauthors: R. shivaji

−∆u = λf(v, w);x ∈ Ω

−∆v = µg(u,w);x ∈ Ω

−∆w = σh(u, v);x ∈ Ω

u = v = w = 0;x ∈ ∂Ω,

where Ω is a ball in RN , N > 1 and ∂Ω is its boundary, λ , µ , σ are positive parametersbounded away from zero, and f , g, h are smooth functions that are negative at the origin(semipositone system) and satisfy certain linear growth conditions at infinity.We establish

27

nonexistence of positive solutions when two of the parameters λ , µ , σ are large. Our proofsdepend on energy analysis and comparison methods.

Fast simulations of pseudo-time coupled nonlinear biomolecular solvation sys-temsShan ZhaoUniversity of Alabamaszhao@as.ua.edu

Recently, we have introduced a pseudo-time coupled PDE model for biomolecular solva-tion analysis. A smooth solvent-solute interface is considered to characterize the dielectricboundary between macromolecules and the surrounding aqueous environment. A nonlinearPoisson-Boltzmann (NPB) equation is used for representing the nonlinear electrostatic ef-fect. To speed up, we propose to solve the time-transient NPB equation by using operatorsplitting based alternating direction implicit (ADI) schemes. With an analytical treatmentof nonlinear term, the proposed ADI schemes are found to be unconditionally stable forsolving NPB equation. In solving coupled PDEs for chemical compounds and proteins, theproposed numerical schemes are very efficient, because large time increments are allowed.

28

The 9th Mississippi State – UAB Conference on Differential Equations and Computational

Simulations

Proceedings

Instruction for Authors

The proceedings of the 2012 conference will be published as a special issue of the Electronic Journal of Differential Equations. All submitted manuscripts will be refereed. Manuscripts should be prepared using TEX, LATEX, or AMS-TEX and submitted electronically. Figure files should be in postscript or encapsulated postscript format. Detailed instruction for authors to prepare the manuscripts can be obtained at:

http://ejde.math.txstate.edu

• The deadline for submission is December 31, 2012. • All manuscripts should be submitted to Jerome Goddard II at jgoddard@aum.edu

MISSISSIPPI STATE UNIVERSITY

DEPARTMENT OF MATHEMATICS AND STATISTICS

The Department of Mathematics and Statistics at Mississippi State University is the largest department in the College of Arts & Sciences. It offers a B.A. in Mathematics, B.S. in Mathematics, M.S. in Mathematics, M.S. in Statistics, and Ph.D. in Mathematical Sciences. Undergraduate students may receive a minor in Mathematics or Statistics and graduate students may receive a minor in Statistics. The Department currently has thirty-six faculty members (including twenty-five graduate faculty), approximately eighty majors in the undergraduate mathematics programs, and approximately forty-five full time graduate students. Computing resources include a departmental computer laboratory, two computer classrooms, and personal computers in all offices. All computers are higher-end, networked, and loaded with the latest versions of commonly used software packages in Mathematics and Statistics. Research: The Department of Mathematics and Statistics boasts a very active research program with faculty publishing numerous refereed papers in professional journals and participating in colloquiums and conference talks. In addition, faculty members have published several monographs, served as referees for numerous international journals in mathematics and statistics, and continue to serve on the editorial boards of professional journals. Several faculty members are members of Center for Computational Sciences and Center for Advanced Vehicular Systems at Mississippi State University. The Department has been very successful in obtaining external funding. Several faculty members have been supported through contracts or research grants by the United States Department of Agriculture, the Department of Defense, the Department of Energy, the National Aeronautics and Space Administration, the National Institutes of Health, the National Science Foundation, the National Security Agency, the National Center for Intermodal Transportation, the American Chemistry Council, the Danish Science Research Council, and the Italian National Research Council.

Population Dynamics Graph Theory Computational Math Biology Applied Statistics Graduate Program: The Department of Mathematics and Statistics offers Master's degrees in Mathematics and Statistics, and the Ph.D. degree in Mathematical Sciences. The doctoral program is designed to ensure that the student acquires knowledge in a broad spectrum of the mathematical sciences, in addition to expertise in a chosen field of concentration. Active areas of research include applied and computational mathematics, ordinary and partial differential equations, functional analysis and operator theory, topology, graph theory, functional equations, and statistics. The degree program for the M.S. in Mathematics is flexible enough to allow the student to prepare for employment or further graduate study. The M.S. in Statistics program is a blend of statistical theory and statistical methods, which provides the student with excellent training for professional employment in government or industry. Students in this program obtain sufficient theoretical background to qualify to teach elementary statistics or to enter a doctoral program in statistics. Undergraduate Programs: The Department of Mathematics and Statistics offers degrees that prepare students for a variety of careers in business industry, government, and education. The Bachelor of Science degree is an excellent vehicle for individuals planning to pursue more technical careers or who plan to attend graduate school in mathematics or statistics. The Bachelor of Arts provides a thorough grounding in mathematics along with a broad selection of liberal arts courses. The Bachelor of Science with Teaching Certification is the ideal course for those who wish to teach mathematics at the secondary school level. It is also possible to double major in mathematics and any other discipline. Undergraduate mathematics majors at Mississippi State have opportunities to get involved in research projects in one-on-one collaboration with members of the faculty. Some of these projects have resulted in presentations at conferences and publications in conference proceedings; others have lead to papers in undergraduate research journals and even professional mathematics journals. Anna Meade, our undergraduate math major, was awarded Northeast Mississippi Daily Journal Undergraduate Research Awards from the College of Arts & Sciences in the Fall 2008. MSU mathematics majors have also successfully competed for positions in Research Experiences for Undergraduates (REU) programs sponsored by The National Science Foundation (NSF). Our students have participated in programs at Iowa State University, Texas A&M University, Louisiana State University and our own Mississippi State University. Directed by members of the Department, the Center for Computational Sciences hosted an NSF REU program during the summer of 2010 and 2011. Two of our own MSU mathematics majors were selected to participate in this highly competitive program. The University: Mississippi State University is a Land-Grant Institution with a Carnegie classification of a very high Doctoral/research university. MSU has current enrollment of over 20,000, which includes approximately 4,100 graduate students. The campus is located in northeast Mississippi adjacent to the city of Starkville and the Mississippi Research and Technology Park. The University library is the largest in the State of Mississippi. It has extensive holdings in the mathematical sciences and maintains a subscription list of over three hundred mathematical and statistical journals. The library catalog is available electronically from terminals located in the library or through the campus network. A major expansion and renovation project doubling the size of the library was completed a few years ago. In addition to traditional resources, the expansion makes available a broad variety of electronic information services through a 24-hour computing lab. The University is a participating institution of the Institute for Mathematics and its Applications (IMA).

2012 – 2013 Graduate Faculty Hai Dinh Dang, Ph.D., Ho Chi Minh City University, 1990, Partial Differential Equations Edward T. Dobson, Ph.D., Louisiana State University, 1995, Graph Theory Janice L. Dubien, Ph.D., Oklahoma State University, 1976, Applied Statistics Bruce R. Ebanks, Ph.D., University of Waterloo, (Canada), 1977, Functional Equations Paul Fabel, Ph.D., University of Texas at Austin, 1994, Topology Corlis P. Johnson, Ph.D., Emory University, 1981, Algebra and Combinatorics Seongjai Kim, Ph. D., Purdue University, 1995, Numerical Analysis Hyeona Lim, Ph.D., Michigan State University, 2001, Numerical Analysis and Scientific Computation T. Len Miller, Ph.D., Virginia Polytechnic Institute & State University, 1982, Operator Theory Vivien G. Miller, Ph.D., Mississippi State University, 1994, Operator Theory Michael M. Neumann, Ph.D., University of Saarbrücken (Germany), 1974, Analysis and Operator Theory Seth F. Oppenheimer, Ph.D., University of Texas at Austin, 1987, Modeling and Differential Equations Chuanxi Qian, Ph.D., University of Rhode Island, 1993, Differential and Difference Equations Mohsen Razzaghi, Ph.D., University of Sussex (England), 1972, Optimal Control Mohammad Sepehrifar, Ph.D., University of Central Florida, 2006, Reliability, Nonparametric Life-testing and Life Data Analysis Suzanne Shontz, Ph.D., Cornell University, 2005, Scientific Computing, Numerical Analysis, and Applications Justin Shows, Ph.D., North Carolina State University, 2009, Survival Analysis and Variable Selection Robert Smith, Ph.D., University of Arkansas, 1983, Complex and Functional Analysis Russ Woodroofe, Ph.D., Cornell University, 2005, Geometric Combinatorics Jon Woody, Ph.D., Clemson University, 2009, Statistical Climatology, Time Series, and Extreme Value Theory Xiangsheng Xu, Ph.D., University of Texas at Austin, 1988, Partial Differential Equations Xingzhou Yang, Ph.D., North Carolina State University, 2004, Applied Numerical PDEs and Scientific Computing Shantia Yarahmadian, Ph.D., Indiana University Bloomington, 2008, Partial Differential Equations and Mathematical Biology Haimeng Zhang, Ph.D., University of Southern California, 1998, Biostatistics and Applied Probability Meng Zhao, Ph.D., Clemson University, 2007, Nonparametric Estimation

http://www.uab.edu/engineering Phone: (205) 934-8460 FAX: (205) 975-7217

Mechanical Engineering is the discipline that deals with motion and energy, including the transformation of energy from one form to another, its transmission, and its utilization. Mechanical engineers conceive, plan, design, and direct the manufacture, distribution, and operation of a wide variety of devices, machines, and systems for energy conversion, environmental control, materials processing, biomechanics, biofluid dynamics, automated manufacturing, materials handling, and other purposes. Mechanical engineers are engaged in all the engineering functions, including creative design, applied research, development, multi-disciplinary thinking, and management.

Degree Programs Our department awards Bachelor of Science in Mechanical Engineering (BSME) and Master of Science in Mechanical Engineering (MSME) degrees. We also offer a five-year plan for completion of combined BSME and MSME degrees. Doctoral programs include an Interdisciplinary Engineering PhD with Computational Engineering and Environmental Health & Safety Engineering tracks.

Honors Program This program is designed for outstanding undergraduate students majoring in Mechanical Engineering. Through a mentored research program, Honors students' problem solving, critical thinking, and communication skills are developed to provide excellent preparation for graduate school or for a professional career. Upon completion of the program, students receive a certificate at the UAB Honors Convocation and graduate "With Honors in Mechanical Engineering."

Labs Our undergraduate labs contain experiments in thermal science, heat transfer, fluids, and mechanical systems, including transmissions and gears, flexible drives, vibrations, balancing in machinery, fasteners, Rankine cycle engines, a refrigeration system, and a wind tunnel. Our labs give students invaluable hands-on experience in the design and analysis of their own experiments, as well. Several experiments in the Thermal Fluid Systems lab use the latest data acquisition systems based on LabVIEW interface. Our research labs are being upgraded to include a state-of-the-art High Performance Computing facility - a 2500+ processor Distributed Computing Cluster with 6.5+ TeraFlop performance and a Visualization Laboratory - a nine-tile ultra-high-resolution visualization wall (very large-scale digital data), and a stereoscopic visualization screen for three-dimensional display and virtual reality. This UAB-Shared High Performance Computing platform and visualization equipment is used for modeling and simulation of continuum, molecular, and atomic scale science, engineering, and biomedical research. The new Vehicle and Robotics Engineering Laboratory conducts projects on unmanned ground vehicles, vehicle autonomous systems, and robotics.

Student Projects Baja SAE - Our students and teams from across the country design and build an off-road vehicle to survive the severe punishment of rough terrain and water, participating in regional competitions that simulate real-world engineering design projects and their related challenges. Shell Eco-marathon – Our students participate in this competition to test their energy-efficient car.

The UAB Department of Mechanical Engineering is active in computational, experimental, and design research, all of which enhance our survivability, health, economy, environment, and overall quality of life. Our faculty, staff, and students are involved in multi-disciplinary research with support from industry and government agencies and collaborate with many other departments at UAB, with other universities, and with national laboratories.

Thermal, Energy, and Power Systems Our Thermal, Energy, and Power Systems research includes computational fluid dynamics, chemically reacting multi-phase flows, coal combustion systems, emissions reduction and pollution control for combustion processes, turbomachinery, turbulence modeling, and flow through porous media. Our applied research includes areas such as rocket engine design and performance analysis, power plant support for combustion processes, air pollutant emissions control, land-based and marine gas turbine design and performance analysis, and geologic sequestration of carbon dioxide, building energy modeling, and energy conservation through energy audits and energy efficiency measures. The group is also engaged in experimental investigation of fundamental heat transfer phenomena.

Mechatronics, Vehicle and Robotics Design and Manufacturing Our research and design work goes in the areas of inverse problems in multi-physics domain systems, intelligent mechatronics and innovative mechanical systems, manned and unmanned ground vehicles, robotic systems, component and system design and optimization, energy conversion and utilization in mechatronic systems, vibration protection, and bio-mechatronics. Our applied research includes inverse ground vehicle dynamics for manned/unmanned vehicles, vehicle mobility and fuel/energy efficiency, stability of motion, multi-wheel vehicle driveline systems design and tests (torque vectoring systems, transfer cases, axles, and various differentials), hybrid-electric transmissions and wheel power distribution control, autonomous individual wheel drives. We do mechatronics design and computer modeling of vehicle and robotic systems for industrial and medical applications; vehicle systems design for manufacturing and quality analysis of manufacturing processes; material properties and characterization.

Computational Mechanics and Simulation Our Computational Mechanics and Simulation research includes structural mechanics, fluid dynamics, combustion, multi-scale simulations, and design optimization, as well as enabling technologies such as geometry and mesh generation, visualization, virtual reality, high performance computing, and information technology. Our applied research includes areas such as disaster mitigation, contaminant transport, propulsion, aerothermodynamics, manufacturing processes, fluid-structure interaction, vehicle crashworthiness, bio-flow dynamics, biomechanics, multidisciplinary design optimization framework, reservoir simulations, carbon sequestration, and adaptive, generalized grid generation techniques.

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The High Performance Computing Collaboratory (HPC²) at Mississippi State University is a coalition of member centers and groups that share a common core objective of advancing the state-of-the-art in computational science and engineering using high performance computing; a common approach to research that embraces a multi-disciplinary, team-oriented concept; and a commitment to a full partnership between education, research, and service. The mission of the HPC² is to serve the University, State, and Nation through excellence in computational science and engineering.

The HPC² is comprised of six independent centers/institutes with the common characteristics of a multi-disciplinary, team-oriented effort that is strategically involved in the application and advancement of computational science and engineering using high performance computing.

Center for Advanced Vehicular Systems (CAVS) Center for Battlefield Innovation (CBI)

Center for Computational Sciences (CCS) Geosystems Research Institute (GRI)

Institute for Genomics, Biocomputing and Biotechnology (IGBB) Northern Gulf Institute (NGI)

www.hpc.msstate.edu

Organizing Committee

Main Organizers Hyeona Lim, Department of Mathematics and Statistics, MSU

Roy Koomullil, Department of Mechanical Engineering, UAB

Founding Organizers Ratnasingham Shivaji, W. L. Giles Distinguished Professor Emeritus, Department of Mathematics and Statistics, MSU Bharat Soni, Chair and Professor of Mechanical Engineering, Department of Mechanical Engineering, UAB

Program Chair and Webmaster Jerome Goddard II, Department of Mathematics, AUM

Travel Support Coordinator Hyeona Lim, Department of Mathematics and Statistics, MSU

Administrative & Logistic Support Judith Goodman, Department of Mathematics and Statistics, MSU

Local Organizing Committee Hai Dang, Department of Mathematics and Statistics, MSU Seongjai Kim, Department of Mathematics and Statistics, MSU Debbie McBride, HPC² Publishing Group, MSU Mark Novotny, Department of Physics and Astronomy, MSU Marilda O'Bryant, HPC2, MSU Seth Oppenheimer, Department of Mathematics and Statistics, MSU Suzanne Shontz, Department of Mathematics and Statistics, MSU David Thompson, Department of Aerospace Engineering, MSU Chuanxi Qian, Department of Mathematics and Statistics, MSU Xiangsheng Xu, Department of Mathematics and Statistics, MSU Shantia Yarahmadian, Department of Mathematics and Statistics, MSU

Advisory Group Alfonso Castro, Department of Mathematics, Harvey Mudd College

John Graef, Department of Mathematics, UT Chattanooga Bharat Soni, Department of Mechanical Engineering, UAB Ratnasingham Shivaji, Department of Mathematics and Statistics, UNCG Jianping Zhu, Office of the Provost and College of Graduate Studies, CSU

Conference Proceedings

Main Editors Jerome Goddard II, Department of Mathematics, AUM John Graef, Department of Mathematics, UT Chattanooga Roy Koomullil, Department of Mechanical Engineering, UAB Hyeona Lim, Department of Mathematics and Statistics, MSU Ratnasingham Shivaji, Department of Mathematics and Statistics, UNCG Bharat Soni, Department of Mechanical Engineering, UAB Jianping Zhu, Office of the Provost and College of Graduate Studies, CSU

Associate Editors Alfonso Castro, Harvey Mudd College

Gary Cheng, University of Alabama at Birmingham Maya Chhetri, University of North Carolina at Greensboro Hai Dang, Mississippi State University Zhaosheng Feng, University Of Texas-pan American Seongjai Kim, Mississippi State University Eun Kyoung Lee, Mississippi State University Mark Novotny, Mississippi State University Seth Oppenheimer, Mississippi State University Chuanxi Qian, Mississippi State University Mohsen Razzaghi, Mississippi State University Padmanabhan Seshaiyer, George Mason University Junping Shi, College of William and Mary Alan Shih, Amplicode, Inc. Suzanne Shontz, Mississippi State University Shantia Yarahmadian, Mississippi State University