A Note on Homogenization Effects on Phase Transition Problems

2018/11/18 by Adrian Hagerty, Hagerty, Adrian · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1811.07357

openalex publication_date 2018/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In fluid-fluid phase transitions problems featuring small scale heterogeneity, we see that when the scale heterogeneity is sufficiently small, the periodic potential function W(x,p) can be replaced with a homogenized potential function W_H(p). This allows for a reduction to a problem already studied by Fonseca and Tartar. In particular, we see an isotropic transition potential, in contrast with the case where the scales are roughly comensurate. This note is intended as a prelude to a more complete analysis of the full range of scales.

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• Phase separation in multiply periodic materials with fine microstructures

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