Spontaneous evolution of spatiotemporal patterns in materials

Abstract

Supersaturated material systems in isolation often exhibit the spontaneous evolution of quasi-steady states that are highly patterned. The commonly associated free-boundary degeneracies invite a search for theoretical constraints that select for pattern mode and wavenumber. Devices such as microscopic solvability, phase fields, cellular automata and dissipation principles, among others, are considered. The author emphasizes the universal and successful role of a minimax principle in the dissipation rate in specifying the mode selection, the scaling relations and universality within the phenomena of Ostwald ripening, free dendrites and Widmanstatten figures, eutectoid(ic)s, forced velocity cells and dendrites, and the various Liesegang patterns. The role of solitons in the construction of patterns, and the effects of deterministic chaos at high supersaturations in the deconstruction of patterns are examined. In the most general context self-organization including life, is the outcome of a process in which a system with many internal degrees of freedom accommodates stochastically to the simultaneous influence of a heat bath and a strong, sustained source of available energy. The optimal degree of organization, patterning and autonomy is achieved at a fluctuating dissipation minimax balance point between the dual influences. If either the sink or source tends to dominate, the patterning trend is towards chaos.