Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 CongressJames M. Hill, Ross Moore SIAM, 2004/04/01 - 413 ページ Included in this volume are the Invited Talks given at the 5th International Congress of Industrial and Applied Mathematics. The authors of these papers are all acknowledged masters of their fields, having been chosen through a rigorous selection process by a distinguished International Program Committee. This volume presents an overview of contemporary applications of mathematics, with the coverage ranging from the rhythms of the nervous system, to optimal transportation, elasto-plasticity, computational drug design, hydrodynamic and meteorological modeling, and valuation in financial markets. Many papers are direct products of the computer revolution: grid generation, multi-scale modeling, high-dimensional numerical integration, nonlinear optimization, accurate floating-point computations and advanced iterative methods. Other papers demonstrate the close dependence on developments in mathematics itself, and the increasing importance of statistics. Additional topics relate to the study of properties of fluids and fluid-flows, or add to our understanding of Partial Differential Equations. |
目次
O Anderson | 2 |
Preface | 3 |
List of Contributors | 9 |
Grid Generation and Flow Solvers | 25 |
Optimal Transportation Theory and Geometric Partial | 37 |
Peter A Markowich and Department of Mathematics | 49 |
Accurate and Efficient Algorithms for Floating Point | 73 |
Molecular Conformation Dynamics and Computational Drug | 107 |
How Mature is Nonlinear Optimization? | 141 |
O Anderson Nick Gould | 162 |
Aging in Particle Systems by Alice Guionnet | 163 |
Marsha Berger UMPA Ecole Normale Supérieure | 176 |
Multiscale Modelling and Computation of Incompressible Flow | 177 |
Yann Brenier California Institute of Technology | 211 |
Alexander Mielke University of Namur Belgium | 357 |
Helsinki University of Technology The Netherlands | 409 |
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algorithm Anal Appl applications approach approximation asymptotic base functions boundary condition cell problem coarse-grid coefficients computing conformations convergence convex crystalline curvature decomposition denotes derive described discretisation dynamics effect eigenvalues elliptic problems energy error estimate Euler equation evolution example factorisation Figure finite floating point flow geometry Giga global grid Hidden Markov Model homogenized ICIAM initial input integration Kalman Filter level-set linear Markov chain Math matrix measure mesh metastable MsFEM multiscale analysis multiscale bases multiscale finite-element method nonlinear optimization nonlinear programming numerical obtained optimal transportation parameter Partial Differential Equations PDEs Perron cluster polynomial porous media portfolio random Section Sherrington-Kirkpatrick model signal simulation small scales smooth solution solve spin glass stochastic structure temperature theorem theory Toint transfer operator upscaling Vandermonde variable vector velocity field viscosity viscosity solutions Wiener filtering zero