Curvature autocorrelations in domain growth dynamics

TL;DR

This paper introduces the interface curvature autocorrelation function and structure factor as new tools to analyze domain structures in non-equilibrium pattern formation, providing insights beyond traditional order-parameter analysis.

Contribution

It demonstrates how ICAF and ICSF reveal detailed domain information in model A dynamics, including length-scale identification and scaling behavior, which were not accessible through existing methods.

Findings

ICAF is Gaussian at short distances and shows dynamical scaling.

ICAF exhibits $t^{1/2}$ power-law growth.

Provides a physical interpretation of the typical length-scale in model A.

Abstract

We show how the interface curvature autocorrelation function (ICAF) and associated structure factor (ICSF), of relevance in non-equilibrium pattern-formation problems where sharp interfaces are present, provide new and interesting information on domain structure, as yet not visible via the order-parameter structure factor (OPSF). This is done by discussing numerical simulations of model A (non-conserved relaxational phase-ordering kinetics) in two-dimensional systems. The ICAF is Gaussian over short distances and exhibits dynamical scaling and $t^{1/2}$ power-law growth. We use it to show what the typical length-scale in the model A dynamics corresponds to physically and how it can be obtained uniquely, rather than simply within a multiplicative constant. Experimental methods to measure the ICAF and/or ICSF are still needed at this point.