In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it is specified for the case of evolving plane curves, and is characterized by using the intrinsic heat equation.
Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex:...
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.
The Special Issue of Kybernetika is devoted to the publication of selected peer-reviewed articles submitted by the participants of the Czech-Japanese Seminar in Applied Mathematics 2008 which took place on September 1-7, 2008 in Takachi-ho and Miyazaki, Japan. The Czech-Japanese Seminar in Applied Mathematics 2008 was organized by the Department of Applied Physics, Faculty of Engineering, University of Miyazaki. It was the fourth meeting in the series of the Czech-Japanese Seminars in Applied Mathematics....
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