Displaying similar documents to “Dynamical morphology of the brain's ventricular cavities in hydrocephalus.”

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.

Direct approach to mean-curvature flow with topological changes

Petr Pauš, Michal Beneš (2009)

Kybernetika

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This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves Γ ( t ) : S → ℝ 2 , t ≧ 0 . The curves are driven by the normal velocity v which is the function of curvature κ and the position. The evolution law reads as: v = - κ + F . The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability...

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...