论文标题
Glauber+零范围相互作用粒子的平均曲率界面极限
Mean curvature interface limit from Glauber+Zero-range interacting particles
论文作者
论文摘要
我们得出连续均值曲流流，作为一类Glauber+零范围粒子系统的一定水动力缩放限制。零范围的部分在保留颗粒数的同时移动颗粒，而Glauber部分控制着颗粒的产生和an灭，并设置为有利于两个层次的粒子密度。当两个部分在某些不同的时间尺度中同时看到两个部分时，零范围的部分将扩散地缩放，而Glauber部分以较小的速率加速，均值曲线界面流出，出现了均质的“表面张力 - 运动型”参数，反映了微观的粒子密度之间的显微镜速率。我们使用相对的熵方法以及合适的“玻尔兹曼·吉布斯”原理，以表明随机微观系统可以通过具有非线性扩散的“离散” allen-cahn PDE近似。反过来，我们显示了这种“离散” PDE的行为，尤其是界面属性的生成和传播。
We derive a continuum mean-curvature flow as a certain hydrodynamic scaling limit of a class of Glauber+Zero-range particle systems. The Zero-range part moves particles while preserving particle numbers, and the Glauber part governs the creation and annihilation of particles and is set to favor two levels of particle density. When the two parts are simultaneously seen in certain different time-scales, the Zero-range part being diffusively scaled while the Glauber part is speeded up at a lesser rate, a mean-curvature interface flow emerges, with a homogenized `surface tension-mobility' parameter reflecting microscopic rates, between the two levels of particle density. We use relative entropy methods, along with a suitable `Boltzmann-Gibbs' principle, to show that the random microscopic system may be approximated by a `discretized' Allen-Cahn PDE with nonlinear diffusion. In turn, we show the behavior, especially generation and propagation of interface properties, of this `discretized' PDE.
