Multiscaling to Standard Scaling Crossover in the Bray-Humayun Model for Phase Ordering Kinetics

TL;DR

This paper investigates the Bray-Humayun model for phase ordering, revealing a crossover from multiscaling to standard scaling and discovering exponential tails in the scaling functions across different cases.

Contribution

It provides a detailed numerical analysis of the model, identifying the multiscaling to standard scaling crossover and novel exponential tail features in the scaling functions.

Findings

Crossover from multiscaling to standard scaling in conserved case.

Exponential tails observed in scaling functions for both conserved and nonconserved cases.

Numerical solutions in 1D and 2D elucidate scaling properties.

Abstract

The Bray-Humayun model for phase ordering dynamics is solved numerically in one and two space dimensions with conserved and non conserved order parameter. The scaling properties are analysed in detail finding the crossover from multiscaling to standard scaling in the conserved case. Both in the nonconserved case and in the conserved case when standard scaling holds the novel feature of an exponential tail in the scaling function is found.