论文标题
通过速度变化的Glauber-Kawasaki动力学从平均曲率进行运动
Motion by mean curvature from Glauber-Kawasaki dynamics with speed change
论文作者
论文摘要
我们将连续的均值曲流流传为Glauber-Kawasaki动力学的一定水动力缩放限制，并随速度变化。川崎部分描述了颗粒通过颗粒相互作用的运动。它以扩散的时空缩放速度加速。 Glauber部分控制着颗粒的创造和歼灭。 Glauber部分设置为有利于两个粒子密度的水平。它也随着时间的推移加速，但比川崎部分的速度要少。在此缩放下，均值曲率界面流出现，具有反映显微镜速率的“表面张力型”参数。界面将两个粒子密度的两个级别分开。 最近的两篇论文也得出了类似的流体动力限制。川崎部分描述了简单最近的邻居相互作用的地方，其中川崎部分被零范围的过程代替。我们将这两篇论文的主要结果扩展到了最近的邻居互动之外。我们证明的主要新颖性是涵盖一类局部粒子相互作用的“ Boltzmann-Gibbs”原理的推导。
We derive a continuum mean-curvature flow as a certain hydrodynamic scaling limit of Glauber-Kawasaki dynamics with speed change. The Kawasaki part describes the movement of particles through particle interactions. It is speeded up in a diffusive space-time scaling. The Glauber part governs the creation and annihilation of particles. The Glauber part is set to favor two levels of particle density. It is also speeded up in time, but at a lesser rate than the Kawasaki part. Under this scaling, a mean-curvature interface flow emerges, with a homogenized `surface tension-mobility' parameter reflecting microscopic rates. The interface separates the two levels of particle density. Similar hydrodynamic limits have been derived in two recent papers; one where the Kawasaki part describes simple nearest neighbor interactions, and one where the Kawasaki part is replaced by a zero-range process. We extend the main results of these two papers beyond nearest-neighbor interactions. The main novelty of our proof is the derivation of a `Boltzmann-Gibbs' principle which covers a class of local particle interactions.
