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Home | Seminars and Symposia | Past seminars/symposia: Tuesday, March 22, 2005

DTC Science and Technology Innovators Lecture Series

Multi-Scale Problems: macroscopic behavior from micro-scale models

by

C. William Gear
Princeton University
NEC Research Institute

Tuesday, March 22, 2005
4:30 p.m. Reception
5:00 p.m. Seminar

402 Walter Library

C. William Gear

WE ARE INTERESTED IN PROBLEMS THAT CAN ONLY BE MODELED at the microscopic scale but for which we are interested in the macroscopic-scale behavior. The reasons for the necessity of microscopic-scale modeling are varied. It could be that we are dealing with a legacy code which takes small steps and it is impractical to change it. Or it could be that we have a microscopic-scale model with enormous detail such as might be found in a particle model or KMC model, we wish to find the macroscopic behavior of macroscopic variables (typically moments of the microscopic variables or their distributions), but we don't have the equations that describe the macroscopic behavior. We discuss ways in which the behavior of a macroscopic model can be derived from a microscopic model. The microscopic model is called on-demand to execute a short burst of simulation from initial conditions specified by the macroscopic modeling package. This provides an estimate of the forward time derivative of macroscopic variables as a function of initial conditions. This can then be used in essentially any process that could use a direct evaluation of the macroscopic derivatives. Using appropriate macroscopic packages we can then determine the long-term large-space behavior, steady states (stable and unstable), estimates of the slow manifold, and even, in some cases, integrate backwards in spite of instability of the underlying problem.

 

C. W. Gear is President Emeritus, NEC Research Institute, Princeton, NJ and Professor Emeritus, University of Illinois at Urbana-Champaign. He was President of the NEC Research Institute from 1992 to 2000, and Vice President of its Computer Science Research Division from 1990 to 1992. Prior to joining NEC he was Professor of Computer Science, Applied Mathematics, and Electrical and Computer Engineering at the Computer Science Department of the University of Illinois, serving as Head of the Department from 1985. In 1960-1962 he was an engineer for IBM British Laboratories, participating in the original System 360 design team. He received a B.A. from Cambridge (England) in 1956 and a Ph.D. from the University of Illinois in 1960 while on a Fulbright Fellowship. He has over 100 publications and ten books, one of which has four editions and has been translated into three other languages. His research interests have included numerical problem solving, software, computer architecture, and computer graphics, and since his second retirement has been active in scientific computing. In 1987-1988 he served as President of the Society for Industrial and Applied Mathematics (SIAM) and as Vice President for Publications from 1990 to 1992. He is a Fellow of the IEEE, and the American Association for the Advancement of Science. He has an honorary doctorate from the Royal Institute of Technology, Stockholm, was a recipient of the Forsythe Award of the Special Interest Group for Numerical Mathematics of the ACM, and has been elected to the National Academy of Engineering and the American Academy of Arts and Sciences.