A New Measure of Coarseness for Solutions to Cahn--Hilliard Equations
Analysis of PDEs
2026-01-22 v1
Abstract
We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it remains consistent throughout the evolution, including for solutions with no periodic structure. We use our measure to compare two previous models of coarsening dynamics with numerically generated dynamics, providing the first direct check that we are aware of for the efficacy of these methods.
Keywords
Cite
@article{arxiv.2601.15134,
title = {A New Measure of Coarseness for Solutions to Cahn--Hilliard Equations},
author = {Peter Howard and Adam Larios and Quyuan Lin},
journal= {arXiv preprint arXiv:2601.15134},
year = {2026}
}
Comments
33 pages, 14 figures. arXiv admin note: substantial text overlap with arXiv:2405.11709