Growth oscillations

Abstract

The authors describe an up till now unrecognised phenomenon in kinetic growth models which leads to observable oscillations in such quantities as the density and velocity of growth. These oscillations, which can occur on length scales of many lattice spacings, arise because of an induced incommensuration in the growth mechanism. To illustrate the phenomenon, they present results for a particularly simple model, but the phenomenon is expected to be quite general and appear in a wide range of growth processes. The essential ingredients for the existence of the oscillations are that the growth take place at a reasonably well defined interface and that the growth process be discrete (e.g. that the cluster grows by the addition of discrete particles of finite size). The growth process is related to a functional stochastic iterative map so that the growth oscillations play the role of limit cycles. They suggest that the fixed point of this map is related to critical fractal kinetic growth.