Horizontal patterns from finite speed directional quenching

TL;DR

This paper investigates how phase separation patterns evolve during directional quenching with finite front speed, focusing on pattern persistence and selection mechanisms as the interface speed varies.

Contribution

It extends previous work by analyzing the persistence of phase separation patterns at finite quenching speeds and clarifies the pattern selection mechanism related to the front speed.

Findings

Patterns persist for finite positive speeds c>0.

Pattern selection depends on the speed c of the quenching front.

The study clarifies the mechanism behind pattern formation during directional quenching.

Abstract

In this paper we study the process of phase separation from directional quenching, considered as an externally triggered variation in parameters that changes the system from monostable to bistable across an interface; in the case presented here the interface moves with speed $c$ in such a way that the bistable region grows, which is the most physically relevant scenario. According to previous results in the literature (Phase separation patterns from directional quenching, Journal of Nonlinear Science, 2017, by Monteiro, R. and Scheel, A.), several patterns exist when $c \gtrsim0$, and here we investigate their persistence for finite $c>0$, clarifying the pattern selection mechanism related to the speed $c$ of the quenching front.