Open AccessStability of facets of crystals growing from vapor
Author(s) -
Yoshikazu Giga,
Piotr Rybka
Publication year - 2006
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2006.14.689
Subject(s) - facet (psychology) , plane (geometry) , cylinder , crystal (programming language) , constant (computer programming) , surface (topology) , upper and lower bounds , phase (matter) , stability (learning theory) , stability criterion , thermodynamics , physics , materials science , mathematical analysis , mathematics , geometry , discrete time and continuous time , computer science , psychology , social psychology , statistics , personality , quantum mechanics , machine learning , big five personality traits , programming language
Consider a Stefan-like problem with Gibbs-Thomson and kinetic effects as a model of crystal growth from vapor. The equilibrium shape is assumed to be a regular circular cylinder. Our main concern is a problem whether or not a surface of cylindrical crystals (called a facet) is stable under evolution in the sense that its normal velocity is constant over the facet. If a facet is unstable, then it breaks or bends. A typical result we establish is that all facets are stable if the evolving crystal is near the equilibrium. The stability criterion we use is a variational principle for selecting the correct Cahn-Hoffman vector. The analysis of the phase plane of an evolving cylinder (identied with points in the plane) near the unique equilibrium provides a bound for ratio of velocities of top and lateral facets of the cylinders. 1
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