Introduction to Growth Oscillations

Abstract

Recent developments in the study of growth and aggregation have underscored the incredibly rich and varied properties that can be obtained from very simple dynamical algorithms. One such remarkable aspect of non-equilibrium growth is the existence of oscillatory behavior in a variety of physical properties of a growing cluster [1]. These oscillations, which should occur in a wide range of growth models, arise as the result of an induced incommensuration between two length scales. One length scale is a statically defined length corresponding to the size of the accreting particles, or if the model is defined on a lattice, to the lattice spacing. The second length scale is dynamical in origin. In the simplest models, in which growth events occur at discrete times, this second length scale can be thought of as the average distance which the growing interface moves per time step. (Generalizations to growth systems for which time is not discrete will be discussed below.) It is the beating between these two length scales that causes the oscillations.