Emergence of Spatial Patterns in Physical, Chemical, and Biological Systems

Harry L. Swinney

University of Texas at Austin

Abstract

We consider macroscopic systems driven away from thermodynamic equilibrium by an imposed gradient in temperature, velocity, or concentration. For a sufficiently small imposed gradient, the system will exist in a base state, which has the symmetry of the boundary conditions. However, when the imposed gradient is increased, a critical value is reached at which the base state becomes unstable -- the system spontaneously breaks the symmetry of the boundary conditions and forms a spatial pattern with long range order. With larger imposed gradients, the patterns can become chaotic or turbulent, but often some order persists. The general principles of pattern formation in systems driven away from equilibrium will be discussed and illustrated with examples from physics, chemistry, and biology.