Bifurcations of stationary solutions with triple junctions in phase separation problems — A new view of bifurcation analysis

Investigated here are bifurcations of stationary solutions with triple junctions to the curvature-driven motion of curves, which arises in phase separation problems. We demonstrate that, when seen from a new perspective, typical bifurcations under perturbations of domain shape can be analyzed using only elementary geometry.     

Identification of geometrical models of interface evolution for dendritic crystal growth

This Letter introduces a method for identifying geometrical models of interface evolution, directly from experimental imaging data. These local growth models relate normal growth velocity to curvature and its derivatives estimated along the growing interface. Such models can reproduce many qualitative features of dendritic crystal growth as well as predict quantitatively its early stages of evolution. Numerical simulations and experimental crystal growth data are used to demonstrate the applicability of this approach.     

曲率驱动与边缘停止相结合的非线性扩散及其在图像去噪中的应用

根据等照度线曲率在图像表征中的重要意义,将曲率作为一个控制传导率的因素引入非线性扩散方程,提出了一个新的曲率驱动与边缘停止相结合的非线性扩散模型,实验结果表明这一模型在图像去噪方面较经典的P-M方程具有更好的性能.