Stochastic Phase Segregation on Surfaces

TL;DR

This paper models stochastic phase segregation on surfaces using the Cahn-Hilliard-Cook model, analyzing coarsening behavior on different geometries and the effects of noise and mobility, with results fitting a log-normal distribution.

Contribution

It introduces a stochastic surface segregation model with statistical analysis of coarsening, highlighting the influence of noise and mobility on the process.

Findings

Coarsening behavior varies with surface geometry.

Noise level significantly affects segregation dynamics.

Results follow a log-normal distribution.

Abstract

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modeled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analyzed on two sample surfaces: a unit sphere and a dumbbell using a variety and a statistical analysis of the growth rate is performed. The influence of noise level and mobility is also investigated. It is also shown that a log-normal distribution fits the results well.