平均曲率流への不規則外乱の影響と運動の一意性

概要

論文の詳細を見る
Phase boundaries are defined as a surface separating different physical states such as a water-ice interface. The mean curvature flow is motion that the phase boundary moves with a normal velocity equals the mean curvature at each point on the phase boundary. We formulate the mean curvature flow by a stochastic level set equation and study the influence of the random noise on motion of the phase boundary by a numerical simulation. In numerical simulations, sample behaviors of the stochastic mean curvature flows of two types of torus shapes are studied. And we numerically show that sample behaviors of the torus shape in stochastic mean curvature flows have a possibility of remarkably changing by the random noise without any fattening phenomena. And in the case where fattening occurs, we show that the random noise plays a role of selecting a unique solution among the set of possible solutions. From simulation results, we have conjectured that the unique solution selected by the random noise is the maximum solution in the sense defined in this paper.
日本シミュレーション学会の論文
2005-12-15