Phase nucleation in curved space

TL;DR

This paper investigates how curvature of surfaces influences nucleation and growth processes in two-dimensional phase transitions, revealing that positive curvature accelerates nucleation and creates complex energy landscapes with multiple local minima.

Contribution

It introduces the first analysis of nucleation on curved surfaces, showing how curvature affects critical nucleus sizes and pathways, and uncovers geometry-induced stabilization of nuclei.

Findings

Nucleation occurs faster on regions of positive Gaussian curvature.

Curved substrates create complex energy landscapes with multiple local minima.

Nucleation becomes inhomogeneous due to surface curvature.

Abstract

Nucleation and growth is the dominant relaxation mechanism driving first order phase transitions. In two-dimensional at systems nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study nucleation and growth of two-dimensional phases lying on curved surfaces and show that curvature modify both, critical sizes of nuclei and paths towards the equilibrium phase. In curved space nucleation and growth becomes inherently inhomogeneous and critical nuclei form faster on regions of positive Gaussian curvature. Substrates of varying shape display complex energy landscapes with several geometry-induced local minima, where initially propagating nuclei become stabilized and trapped by the underlying curvature.