Motion by Mean Curvature from Glauber-Kawasaki Dynamics
Motion by Mean Curvature from Glauber-Kawasaki Dynamics
复制标题
Glauber-Kawasaki Dynamics 的平均曲率运动
DOI：
10.1007/s10955-019-02364-7
复制
发表时间：
2019
影响因子：
1.6
通讯作者：
K.
中科院分区：
文献类型：
--
作者：
Funaki;T.;Tsunoda;K.
我们研究格劳伯-川崎动力学的流体动力学标度极限。众所周知，如果将川崎部分在扩散时空尺度上加速，就可以推导出艾伦-卡恩方程，这是一种极限反应扩散方程。本文涉及的缩放比例是，控制粒子产生和湮灭的格劳伯部分也加速但比川崎部分慢。在这种尺度下，我们直接从粒子系统中推导出分离稀疏和密集粒子区域的界面的平均曲率运动，作为流体动力学和尖锐界面限制的组合。
We study the hydrodynamic scaling limit for the Glauber–Kawasaki dynamics. It is known that, if the Kawasaki part is speeded up in a diffusive space-time scaling, one can derive the Allen–Cahn equation which is a kind of the reaction–diffusion equation in the limit. This paper concerns the scaling that the Glauber part, which governs the creation and annihilation of particles, is also speeded up but slower than the Kawasaki part. Under such scaling, we derive directly from the particle system the motion by mean curvature for the interfaces separating sparse and dense regions of particles as a combination of the hydrodynamic and sharp interface limits.