2015/01/22 by Alexander Nepomnyashchy, Nepomnyashchy, A. A. · 2 citations
Computer Science · Earth and Planetary Sciences · Materials Science · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #Solidification and crystal growth phenomena #Statistical Mechanics (cond-mat.stat-mech) #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.1501.05514
openalex publication_date 2015/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that similar physical systems can reveal two quite different ways of behavior, either coarsening, which creates a uniform state or a large-scale structure, or formation of ordered or disordered patterns, which are never homogenized. We present a description of coarsening using simple basic models, the Allen-Cahn equation and the Cahn-Hilliard equation, and discuss the factors that may slow down and arrest the process of coarsening. Among them are pinning of domain walls on inhomogeneities, oscillatory tails of domain walls, nonlocal interactions, and others. Coarsening of pattern domains is also discussed.