Nonequilibrium Steady States With Spatial Patterns

This talk is intended to provide an introduction to the study of pattern selection and propagation in nonequilibrium systems. For simplicity we shall confine the discussion to systems under steady external conditions. Examples from hydrodynamics are Rayleigh-Bénard convection and Taylor-Couette flow in large aspect-ratio containers, or Faraday crispations; related phenomena appear in flame-front propagation, chemical reactions, plate buckling, and various problems in crystal growth. Questions of interest include: (i) the prediction of steady vs time dependent behavior and of the relevant time scales for reaching this behavior; (ii) an analysis of spatial patterns, both ordered and disordered; (iii) elucidation of the mechanisms for the onset of temporal chaos in systems with many active degrees of freedom (e.g., are the attractors low-dimensional?).