title: Phase nucleation in curved space.
abstract: Nucleation and growth is the dominant relaxation mechanism driving first-order phase transitions. In two-dimensional flat 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 modifies 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.
authors.affiliation: Department of Physics, Universidad Nacional del Sur-IFISUR-CONICET, 8000 Bahía Blanca, Argentina.
authors.forename: Leopoldo R
authors.initials: LR
authors.lastname: Gómez
authors.affiliation: Department of Physics, Universidad Nacional del Sur-IFISUR-CONICET, 8000 Bahía Blanca, Argentina.
authors.forename: Nicolás A
authors.initials: NA
authors.lastname: García
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands.
authors.forename: Vincenzo
authors.initials: V
authors.lastname: Vitelli
authors.affiliation: 1] Institute for Complex Systems, Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy [2] Physics Department, University of Rome La Sapienza, I-00185 Rome, Italy.
authors.forename: José
authors.initials: J
authors.lastname: Lorenzana
authors.affiliation: Department of Physics, Universidad Nacional del Sur-IFISUR-CONICET, 8000 Bahía Blanca, Argentina.
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Vega