Critical holes in undercooled wetting layers

TL;DR

This paper analyzes the formation of critical holes in undercooled wetting layers by mapping the problem onto a dynamical system, revealing different nucleation regimes and thermodynamic behaviors.

Contribution

It introduces a novel dynamical systems approach to study critical holes in wetting layers, providing new insights into their thermodynamics and stability properties.

Findings

Identification of four fixed points with distinct stability in the phase space

Derivation of thermodynamic behavior across three nucleation regimes

Mapping of the saddle-point equation to an autonomous dynamical system

Abstract

The profile of a critical hole in an undercooled wetting layer is determined by the saddle-point equation of a standard interface Hamiltonian supported by convenient boundary conditions. It is shown that this saddle-point equation can be mapped onto an autonomous dynamical system in a three-dimensional phase space. The corresponding flux has a polynomial form and in general displays four fixed points, each with different stability properties. On the basis of this picture we derive the thermodynamic behaviour of critical holes in three different nucleation regimes of the phase diagram.