Structure Functions and Intermittency for Coarsening Systems

TL;DR

This paper explores the applicability of structure functions and intermittency analysis, traditionally used in turbulence, to domain growth and coarsening phenomena modeled by TDGL and CH equations, revealing anomalous scaling behavior.

Contribution

It introduces the study of structure functions and intermittency in coarsening systems, extending turbulence analysis tools to phase-ordering dynamics.

Findings

Structure functions scale as S_q ∼ r^{ζ_q} with ζ_q = 1 for coarsening models.

Sharp interfaces lead to anomalous scaling in coarsening systems.

Energy transfer analysis in domain growth is reviewed.

Abstract

In studies of turbulence, there has been extensive use of physical quantities such as {\it energy transfers} and {\it structure functions}. We examine whether these quantities can be useful in understanding problems of domain growth or coarsening, as modeled by the {\it time-dependent Ginzburg-Landau} (TDGL) equation and the {\it Cahn-Hilliard} (CH) equation. This paper has two major themes. First, we review our recent papers on energy transfers in domain growth. Second, we study structure functions and intermittency for coarsening systems. As a consequence of sharp interfaces, the structure functions scale as $S_q \sim r^{\zeta_q}$, where $r$ is the distance between two points. For the TDGL and CH models, $\zeta_q = 1$, indicating {\it anomalous scaling}