Motion by Mean Curvature from Glauber-Kawasaki Dynamics with Speed Change
Motion by Mean Curvature from Glauber-Kawasaki Dynamics with Speed Change
复制标题
速度变化的格劳伯-川崎动力学中的平均曲率运动
DOI：
10.1007/s10955-022-03044-9
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发表时间：
2023
影响因子：
1.6
通讯作者：
Tsunoda Kenkichi
中科院分区：
文献类型：
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作者：
Funaki Tadahisa;van Meurs Patrick;Sethuraman Sunder;Tsunoda Kenkichi
我们得到了具有速度变化的Glauber-Kawasaki动力学的一个流体动力学标度极限的连续平均曲率流。川崎部分描述了粒子通过粒子相互作用的运动。它在扩散的时空尺度中加速。Glauber部分掌管着粒子的产生和湮灭。Glauber部分设置为支持两个级别的粒子密度。它也在时间上加快了速度，但速度低于川崎部分。在这种标度下，出现了平均曲率界面流，具有反映微观速率的均化的表面张力-迁移率参数。该界面将两个级别的粒子密度分开。最近的两篇论文也得出了类似的流体力学极限；其中一篇是川崎部分描述了简单的近邻相互作用，另一篇是川崎部分被零程过程所取代。我们将这两篇论文的主要结果推广到最近邻相互作用之外。我们证明的主要新奇之处在于推导出了涵盖一类局部粒子相互作用的“Boltzmann-Gibbs”原理。
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.