A one dimensional nearest neighbor model of coarsening

Abstract: "A one dimensional model of coarsening is developed in which the domain boundaries are points on a line, either finite (with periodic boundary conditions) or (doubly) infinite, and a domain is an interval between any two adjacent points. The postulated equation of motion for the length l of a given interval depends only on the two nearest neighbor interval lengths, yields a zero average rate of change of interval lengths and makes the state of equal interval lengths unstable. It is proved that coarsening occurs by the disappearance of intervals. A special power law form of the equation of motion, treated by an approximation which ignores correlations of the lengths of neighboring intervals, shows a self-similar behavior with an asymptotic distribution of reduced interval lengths at long times that is time-independent. Comparison of the approximate results with computer simulations is made."