Monday, May 19

10:00 AM-12:00 PM Ballroom III - Level B

Pattern Formation and Singular Perturbations

Many physical systems exhibit dynamics on multiple time scales and/or multiple length scales. Examples arise in nonlinear fiber optics, multi-degree-of-freedom Hamiltonian systems, chemical reactions, fluid dynamics, and neurophysiology. In this minisymposium, the speakers will address important current nonlinear dynamics questions in problems from several of these areas. For systems modeled by reaction diffusion equations, spatial patterns evolving in complex time-dependent ways will be discussed. In addition, a number of speakers will focus on the mathematical theory and applications of the existence and stability of time asymptotic stationary patterns. These states include traveling waves, their concatenations, and spatially periodic states. In those systems modeled by Hamilton's equations, speakers will focus on the existence and stability of a diverse array of multiple pulse orbits and where they arise in applications. Mathematically, the methods used in these studies range from variational techniques and matched asymptotic expansions to analytical and geometrical methods in stability theory and singular perturbation theory. Theoretical tools from complex dynamics and electromagnetism theory also play significant roles.

Organizers: Arjen Doelman, University of Utrecht, The Netherlands; Tasso Kaper, Boston University; and Todd Kapitula, University of New Mexico, Albuquerque

10:00 Singular Limits of Phase Equations for Patterns Far from Threshold
Nicholas M. Ercolani and Robert Indik, University of Arizona; Alan Newell, University of Warwick, England; and Thierry Passot, Observatoire de Nice, France
10:30 Self-Replicating Spots
John Pearson, Los Alamos National Laboratory
11:00 Stability Analysis of Pulse Solutions of the Gray-Scott Model
Robert Gardner, University of Massachusetts, Amherst
11:30 Oscillatory Instabilities of Labyrinthine Fronts
David Muraki, Courant Institute of Mathematical Sciences, New York University

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TMP, 4/3/97