Proceedings of the Fifth Mississippi State Conference on Difference Equations and Computational Simulations

Foreword

With the rapid advancement in high performance computing and efficient numerical algorithms, mathematical modeling and computational simulations have become the third means, in addition to theory and experimentation, for scientific research. They have fundamentally changed the way the underlying principles of science and engineering are applied to research, design, and development. In many applications, mathematical modeling and computational simulations involve (i) system(s) of differential equations representing the scientific or engineering phenomena to be studied (mathematical model(s)); (ii) numerical methods used to calculate solutions to the mathematical model(s); and (iii) an efficient sequential/parallel/distributed computing environment. Because of the interdisciplinary nature of this process, a successful modeling and simulation effort requires close collaborations among mathematicians, computer scientists, and researchers in various scientific and engineering fields. A truly multidisciplinary conference on Differential Equations and Computational Simulation, biannually organized by the Department of Mathematics and Statistics and the NSF Engineering Research Center (NSF/ERC) at Mississippi State University (MSU), provides a joint forum where mathematicians, scientists, and engineers from industries, federal laboratories, and academia exchange research and development ideas. An overall goal for this series of conferences is to promote research and education in mathematical and computational analyses of differential equations.The first four Mississippi State Conferences on Differential Equations and Computational Simulations were held March 19-20, 1993, April 7-8, 1995, May 16-17, 1997, and May 21 – 22, 1999. Special issues of the Journal of Applied Mathematics and Computation (65:1-3, 1994 and 89:1-3, 1998) and of the Electronic Journal of Differential Equations (Conference-01, 1997 and Conference-03, 1999) were dedicated to the reviewed papers presented at these conferences.

The Fifth Mississippi State Conference on Differential Equations and Computational Simulations took place May 18 - 19, 2001. There were one hundred and thirty-eight participants from Japan, Germany, Brazil, Russia, Saudi Arabia and the United States registered for the conference. Invited principal lectures were

- Peter Bates, Brigham Young University,
*Invariant manifolds for semiflows in Banach space* - Carlos Castillo-Chavez, Cornell University,
*Mathematics models for tuberculosis and connection to data* - Jerome Goldstein, University of Memphis,
*Heat equations with singular potentials* - Anthony Ingraffea, Cornell University,
*Computational fracture mechanics applications in aircfaft structures* - James Keener, University of Utah,
*The Mechanism and dynamics of defibrillation* - David Keyes, Old Dominion University,
*High Performance parallel implicit CFD* - Hiroshi Matano, University of Tokyo,
*Travelling waves in spatially inhomogeneous diffusive media-the non-periodic case* - Suresh Menon, Georgia Institute of Technology,
*Large-Eddy simulation of multiphase reacting flows: current trends and future directions* - Wei-Ming Ni, University of Minnesota,
*Recent progress in a competition system with cross-diffusions* - George Papanicolaou, Stanford University,
*Imaging and time reversal in a noisy environment*

The papers in this special issue represent broad research in the following multidisciplinary areas:

- Mathematical Analysis and Bifurcation theory - Ordinary and partial differential equations involving reaction-diffusion, stability, and existence and uniqueness theories associated with initial and boundary value problems.
- Computational/Numerical Techniques - Computational fluid dynamic involving free surface flows and moving boundaries, grid generation and adaptive methods, and parallel algorithms. Applications pertinent to wind engineering and aerospace, automotive and space vehicle design and analysis were presented.
- Computational Biology - Modeling of tumor growth, toxicity of mixtures of insecticides, and antibiotic penetration in biofilms.

Department of Mathematics

University of Tennessee at Chattanooga

Rathasingham Shivaji

Department of Mathematics and Statistics

Mississippi State University

Bharat Soni

Department of Mechanical Engineering

University of Alabama at Birmingham

Jiangping Zhu

Department of Theoretical and Applied Mathematics

The University of Akron

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