Ordered shapes in nonequilibrium growth

Abstract

Patterns observed during nonequilibrium growth display complex ordering on many length scales. We focus on ordered patterns which reflect the interplay of microscopic and macroscopic dynamics. The fundamental morphologies which result, and which are the building blocks of more complex patterns, include dendritic and tip-splitting growth. The latter gives rise to the two- dimensional dense-branching morphology (DBM). We review the current understanding of how dendritic growth and the DBM arise from the microscopic dynamics of surface tension and surface kinetics. We emphasize the open questions, with particular attention to the question of developing theory for morphology selection and transitions between dendritic and dense-branching growth. In this context, we review our hypotheses of the selection of the fastest growing morphology, and the existence of first- and second-order-like morphology transitions. Theoretical issues are illustrated using the Hele-Shaw and electrodeposition experiments.