Pattern formation outside of equilibrium

Journal Article · Thu Jul 01 00:00:00 EDT 1993 · Reviews of Modern Physics; (United States)

DOI:https://doi.org/10.1103/RevModPhys.65.851· OSTI ID:6217709

Cross, M C ^[1]; Hohenberg, P C ^[2]

---

1. Department of Physics, California Institute of Technology 114-36, Pasadena, California 91125 (United States)
2. AT T Bell Laboratories, MH 1D-268, Murray Hill, New Jersey 07974 (United States)

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector [ital q][sub 0] and frequency [omega][sub 0] of the instability. Type I[sub s] systems ([omega][sub 0]=0, [ital q][sub 0][ne]0) are stationary in time and periodic in space; type III[sub o] systems ([omega][sub 0][ne]0, [ital q][sub 0]=0) are periodic in time and uniform in space; and type I[sub o] systems ([omega][sub 0][ne]0, [ital q][sub 0][ne]0) are periodic in both space and time.

• OSTI ID: 6217709
• Journal Information: Reviews of Modern Physics; (United States), Vol. 65:3; ISSN 0034-6861
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONVECTIVE INSTABILITIES
STATISTICAL MODELS
COUETTE FLOW
TURBULENCE
CHEMICAL REACTIONS
FLUID MECHANICS
MORPHOLOGICAL CHANGES
NONLINEAR OPTICS
PARAMETRIC INSTABILITIES
PERTURBATION THEORY
SOLIDIFICATION
STOCHASTIC PROCESSES
FLUID FLOW
INSTABILITY
MATHEMATICAL MODELS
MECHANICS
OPTICS
PHASE TRANSFORMATIONS
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
VISCOUS FLOW
661300* - Other Aspects of Physical Science- (1992-)