论文标题

不平衡的Glauber-Kawasaki动力学的恒定接口流

Constant-speed interface flow from unbalanced Glauber-Kawasaki dynamics

论文作者

Funaki, Tadahisa, van Meurs, Patrick, Sethuraman, Sunder, Tsunoda, Kenkichi

论文摘要

我们得出了Glauber-Kawasaki动力学的流体动力极限。川崎部分很简单,并描述了具有硬核独家相互作用的粒子的独立运动。它以扩散的时空缩放速度加速。 Glauber部分描述了颗粒的出生和死亡。它设定为两个级别的粒子密度,偏爱两者之一。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,限制粒子密度立即采用两个有利的密度值之一。分隔这两个值的界面以恒定速度(Huygens的原理)演变。 在最近的四篇论文中也得出了类似的流体动力限制。与这些论文的关键差异在于,我们考虑了Glauber动力学,该动力具有对两个有利密度值之一的偏好。结果,我们观察到较短的时间尺度上的限制动力学,并且演变与前四篇论文中获得的平均曲率流不同。尽管我们的证据中的几个步骤可以从这些论文中采用,但界面传播的证据是新的。

We derive the hydrodynamic limit of Glauber-Kawasaki dynamics. The Kawasaki part is simple and describes independent movement of the particles with hard core exclusive interactions. It is speeded up in a diffusive space-time scaling. The Glauber part describes the birth and death of particles. It is set to favor two levels of particle density with a preference for one of the two. It is also speeded up in time, but at a lesser rate than the Kawasaki part. Under this scaling, the limiting particle density instantly takes either of the two favored density values. The interface which separates these two values evolves with constant speed (Huygens' principle). Similar hydrodynamic limits have been derived in four recent papers. The crucial difference with these papers is that we consider Glauber dynamics which has a preferences for one of the two favored density values. As a result, we observe limiting dynamics on a shorter time scale, and the evolution is different from the mean curvature flow obtained in the four previous papers. While several steps in our proof can be adopted from these papers, the proof for the propagation of the interface is new.

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