Electronic Journal of Differential Equations, Conference 10, 2003.
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
In addition, 69 contributed papers were presented during the two days of
meetings. The conference also featured an honoring ceremony for Professor
Jack Hale, a special lecture by Dr. Henry Warchall on the Funding
Opportunities in the Mathematical Sciences at the NSF, and a Banquet
Lecture titled "Highway to Space" by Dr. Gary Lyles.
Professors Ratnasingham Shivaji and Bharat Soni served as conference
organizers while Professor Jianping Zhu served as the Program Chair.
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.
We would like to thank the participants and principal speakers for their
valuable contributions to the success of the conference and publication of
the proceedings. We gratefully acknowledge the support provided by the
National Science Foundation and the Institute for Mathematics and its
Applications at University of Minnesota. We also acknowledge the support
from the College of Arts and Sciences, the College of Engineering,
the Office of Research, and the faculty and staff of the Department of
Mathematics and Statistics and the NSF Engineering Research Center at
Mississippi State University. Last but not least, we appreciate very much
the diligence and responsiveness of the reviewers of the manuscripts that
made the publication of this proceedings possible.
Special Issue Editors
John Graef
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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