Nonequilibrium dynamics of the complex Ginzburg-Landau equation: numerical results in two and three dimensions

Abstract

This paper is the second of a two-stage exposition, in which we study the nonequilibrium dynamics of the complex Ginzburg-Landau (CGL) equation. We use spiral defects to characterize the system evolution and morphologies. In the first paper of this exposition [S.K. Das, S. Puri, and M.C. Cross, Phys. Rev E 64, 046206 (2001)], we presented analytical results for the correlation function of a single spiral defect, and its short-distance singular behavior. We had also examined the utility of the Gaussian auxiliary field ansatz for characterizing multispiral morphologies. In this paper, we present results from an extensive numerical study of nonequilibrium dynamics in the CGL equation with dimensionality d=2,3. We discuss the behavior of domain growth laws; real-space correlation functions; and momentum-space structure factors. We also compare numerical results for the correlation functions and structure factors with analytical results presented in our first paper.