Journal Article10.1239/aap/1033662162
A two-dimensional random crystalline algorithm for Gauss curvature flow
Hitoshi Ishii,Toshio Mikami +1 more
1
TL;DR: A discrete approximation of Gauss curvature flow for closed curves in ℝ2.
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Abstract: We propose and study a random crystalline algorithm (a discrete approximation) of the Gauss curvature flow of smooth simple closed convex curves in ℝ2 as a stepping stone to the full understanding of such phenomena as the wearing process of stones on a beach.
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Citations
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Motion of a graph by R-curvature
Hitoshi Ishii,Toshio Mikami +1 more
- 01 Jan 2001
TL;DR: In this paper, the authors show that weak solutions of the PDE are viscosity solutions, and give the uniqueness result on both weak and visco-coalesity solutions.
References
Flow by mean curvature of convex surfaces into spheres
TL;DR: In this paper, the authors consider a compact, uniformly convex w-dimensional surface M = Mo without boundary, which is smoothly imbedded in R. They show that the behavior of grain boundaries in annealing pure metal can be modeled by a diffeomorphism.