Guérin T, Dean D S
Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS, UMR 5798/Université de Bordeaux, F-33400 Talence, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062103. doi: 10.1103/PhysRevE.92.062103. Epub 2015 Dec 2.
We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.
我们考虑了示踪粒子在非平衡非均匀周期介质中运动的扩散特性。示踪粒子的运动由一个福克 - 普朗克方程描述，该方程具有任意空间周期性（但时间上恒定）的局部扩散张量和漂移项，最终还存在障碍物。我们推导了一个在任何维度都有效的随时间变化的有效扩散张量的类似久保公式。从这个通用公式出发，我们得出了这些系统中晚期有效扩散张量和漂移的表达式。此外，我们找到了这些输运系数晚期有限时间修正的显式公式。在一维情况下，我们给出了输运系数的封闭解析公式。这里推导的公式非常通用，为计算任意非平衡周期平流 - 扩散系统中的扩散特性提供了一种直接的方法。
