Displaying similar documents to “Diffuse-interface treatment of the anisotropic mean-curvature flow”

Computational studies of non-local anisotropic Allen-Cahn equation

Michal Beneš, Shigetoshi Yazaki, Masato Kimura (2011)

Mathematica Bohemica

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The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.

Computational studies of conserved mean-curvature flow

Miroslav Kolář, Michal Beneš, Daniel Ševčovič (2014)

Mathematica Bohemica

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The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational...

Two examples of fattening for the curvature flow with a driving force

Giovanni Bellettini, Maurizio Paolini (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We provide two examples of a regular curve evolving by curvature with a forcing term, which degenerates in a set having an interior part after a finite time.