Coalescence in the 1D Cahn-Hilliard model
Simon Villain-Guillot
TL;DR
This paper provides an approximate analytical solution to the 1D Cahn-Hilliard equation, describing coalescence during phase transitions, and introduces a family of ansatz based on soliton lattice properties to model destabilization and period doubling.
Contribution
It introduces a novel analytical approach to model coalescence in the 1D Cahn-Hilliard equation using soliton lattice properties and ansatz construction.
Findings
Identified all intermediate stationary profiles.
Constructed a family of ansatz for destabilization and period doubling.
Linked solutions to Langer's self-similar scenario.
Abstract
We present an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition. We have identified all the intermediate profiles, stationary solutions of the noiseless Cahn-Hilliard equation. Using properties of the soliton lattices, periodic solutions of the Ginzburg-Landau equation, we have construct a family of ansatz describing continuously the processus of destabilization and period doubling predicted in Langer's self similar scenario.
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