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Abstract: We present a numerical method which computes the motion of complex solid/liquid boundaries in crystal growth. The model we solve includes physical effects such as crystalline anisotropy, surface tension, molecular kinetics and undercooling. The method is based on two ideas. First, the equations of motion are recast as a single history-dependent boundary integral equation on the solid/liquid boundary. A fast algorithm is used to solve the integral equation efficiently. Second, the boundary is... (Update)
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BibTeX entry: (Update)
@misc{ mathematics-james,
author = "Department Of Mathematics",
title = "James A. Sethian",
url = "citeseer.ist.psu.edu/755919.html" }
Citations (may not include all citations):567 Fronts Propagating with Curvature-Dependent Speed: Algorithm.. - Sethian - 1988
141 Motion of Level Sets by Mean Curvature (context) - Spruck
49 Fourier Series and Integrals (context) - McKean - 1972
16 Dynamics of Layered Interfaces Arising from Phase Boundaries (context) - Fife - 1988
13 Pure and Appl (context) - Comm - 1957
13 Stability of a Planar Interface During Solidification (context) - Sekerka - 1964
6 Communications of Mathematical Physics (context) - Curvature, of - 1985
5 A Non-linear Stability Analysis of the Solidification of a P.. (context) - Notestine - 1981
4 Capillarity-Limited Steady-State Dendritic Growth (context) - Glicksman - 1974
4 Capillarity-Limited Steady-State Dendritic Growth-II (context) - Glicksman - 1974
3 A Numerical Study of Two-Dimensional Crystal Growth Forms in.. (context) - Sekerka
3 Finite Element Simulation of Planar Instabilities (context) - Lynch, O'Neill - 1987
2 Stability and Instability in Crystal Growth: Symmetric (context) - Taylor - 1985
2 Steady and Oscillatory Cellular Morphologies (context) - Ungar - 1986
2 Computing Interface Motion: The Rayleigh-Taylor and Kelvin-H.. (context) - Osher, Sethian - 1991
2 Stability of Dendritic Crystals (context) - Levine - 1986
2 Morphological Stability of a Particle Growing by (context) - Sekerka - 1963
2 Singularity Formation and Minimal Surfaces (context) - Chopp
2 Theory of Dendritic Growth in a Weakly Undercooled Melt (context) - Amar, Pomeau - 1986
2 The Stabilizing Effect of Surface Tension on the Development (context) - Ortoleva - 1983
2 Numerical Simulation of Complex Crystal Growth (context) - Strain
2 A Fast Algorithm for Heat Potentials (context) - Strain - 1990
2 Problem with Supercooling and Superheating (context) - Visintin, Numerical et al. - 1987
2 Three-Dimensional Crystal Growth (context) - Strain
2 the Two-Phase Stefan Problem with Interfacial (context) - On - 1986
2 Theories and Models (context) - Dendritic, of - 1985
2 Evolution d'une Interface par Capillarite (context) - Robert - 1984
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