Abstract
This paper introduces and studies a mathematical evolution process which models one type of growth of a crystal as it freezes from a cold melt. The crystal freezes (melts) as rapidly as it can anywhere along its interface where the temperature is below (above) the local freezing temperature so that rate of growth is governed by the rate at which latent heat of fusion can diffuse. The model incorporates general Gibbs-Thomson relations between freezing temperatures and interface surface tension and general heat capacities and conductivities.
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Almgren, F., Wang, L. Mathematical existence of crystal growth with Gibbs-Thomson curvature effects. J Geom Anal 10, 1–100 (2000). https://doi.org/10.1007/BF02921806
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DOI: https://doi.org/10.1007/BF02921806