Deterministic Soluble Model of Coarsening

TL;DR

This paper presents an analytical study of a deterministic 3-phase one-dimensional coarsening model, deriving autocorrelation functions and analyzing domain structures to understand interface dynamics and spatial organization.

Contribution

It introduces an exact analytical approach to compute autocorrelation and domain size distributions in a deterministic coarsening model, advancing understanding of interface dynamics.

Findings

Analytical expression for autocorrelation function A(t)

Distribution of domain sizes characterized

Interfaces move ballistically and annihilate upon collision

Abstract

We investigate a 3-phase deterministic one-dimensional phase ordering model in which interfaces move ballistically and annihilate upon colliding. We determine analytically the autocorrelation function A(t). This is done by computing generalized first-passage type probabilities P_n(t) which measure the fraction of space crossed by exactly n interfaces during the time interval (0,t), and then expressing the autocorrelation function via P_n's. We further reveal the spatial structure of the system by analyzing the domain size distribution.