多相格点随机游动的均匀化方法
Homogenization Approaches to Multiphase Lattice Random Walks
摘要：
本文分析了几种不同的均匀化方法的长期性能的多相晶格随机游动，最近介绍了由Giona和Cocco，其特征在于不同的值的跳跃时间和相邻站点之间的距离在每个晶格相位。抛物线和双曲线模型被认为是。虽然所有的抛物线模型从微观朗之万方程驱动的维纳过程未能预测长期的流体动力学行为观察到的晶格模型，不连续的抛物线模型，其中相分配系数是先验强加的，提供了正确的答案。这一结果的影响方面的平衡约束和非平衡输运性质之间的连接是彻底解决。
英文摘要：
This article analyzes several different homogenization approaches to the long-term properties of multiphase lattice random walks, recently introduced by Giona and Cocco, and characterized by different values of the hopping times and of the distance between neighboring sites in each lattice phase. Both parabolic and hyperbolic models are considered. While all the parabolic models deriving from microscopic Langevin equations driven by Wiener processes fail to predict the long-term hydrodynamic behavior observed in lattice models, the discontinuous parabolic model, in which the phase partition coefficient is a-priori imposed, provides the correct answer. The implications of this result as regards the connection between equilibrium constraints and non-equilibrium transport properties is thoroughly addressed.
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