Workshop on Dynamics and Bifurcations of Patterns in Dissipative Systems

Colorado State University, Fort Collins CO

Investigators

Abstract

Progress in nonlinear science achieved during the last decades has brought mathematicians and physicists a better understanding of the variety of structures observed in systems far from equilibrium. The emergence of macroscopic order and the spontaneous breaking of spatiotemporal symmetries are features common to many natural phenomena. Virtually every structure seen in our world can be considered the result of a long sequence of successive symmetry-breaking instabilities of a complex nonlinear system under nonequilibrium conditions. The interdisciplinary field of pattern formation seeks a common understanding of such spontaneous formation of spatial and spatiotemporal patterns in systems from areas as diverse as fluid mechanics, solid state physics, nonlinear optics, chemistry, and biology. While much progress towards understanding pattern formation has been made in recent years, fundamental challenges remain. This award supports participants in the Workshop on Dynamics and Bifurcations of Patterns in Dissipative Systems, held at Colorado State University in the spring of 2003. The goal of the workshop is to bring together theorists and experimentalists from different fields, from applied mathematics to theoretical and experimental physics, unified by their interest in nonlinear phenomena and in search of a deeper understanding of pattern formation and dynamics in complex systems. The workshop will stimulate communication and collaboration between experts, advanced graduate students, and young researchers in identifying key ideas, new advances, and open questions in the mathematical analysis of spatiotemporal patterns in dissipative systems. Topics of interest include stability, bifurcation, and dynamics of patterns, reduction of governing equations, and the role of symmetry. The presentations and roundtable discussions will stimulate further theoretical and applied investigations in pattern formation and analysis. The extremely rapid pace of developments in the science of patterns, identified as one of the six grand challenges for physics in a new era, lends urgency to the goals of the workshop.