论文标题
由不同媒体和界面组成的区域内的晶格随机行走动力学
Dynamics of lattice random walk within regions composed of different media and interfaces
论文作者
论文摘要
我们研究了两个介质的异质空间中的晶格随机步行动力学，这些介质被界面分离，并且具有不同的扩散率和偏见。根据接口的位置，存在两种独家方法来建模动力学：（1）键入A动力学，将接口放置在两个晶格点之间，以及（2）B型动力学，将接口放置在晶格上。对于这两种类型，我们都会为无界域以及与反射，吸收和混合边界所构成的复合系统的绿色函数或传播器的一维生成函数的确切结果。对于在没有偏见的情况下反射限制的情况，稳态概率显示了A型动力学的阶梯状行为，而B型动力学对于B型动力学均匀。我们还针对第一页的概率和平均第一通道时间得出了明确的表达式，并将击球时间依赖性与单个目标进行比较。最后，考虑到传播器的连续空间连续时间极限，我们在界面处获得边界条件。在界面处，虽然通量相同，但A型A型概率密度是不连续的，并且对于B型。对于后者，我们在适当的极限下得出了所谓的皮革边界条件的广义版本。
We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity and bias. Depending on the position of the interface, there exist two exclusive ways to model the dynamics: (1) Type A dynamics whereby the interface is placed between two lattice points, and (2) Type B dynamics whereby the interface is placed on a lattice point. For both types, we obtain exact results for the one-dimensional generating function of the Green's function or propagator for the composite system in unbounded domain as well as domains confined with reflecting, absorbing, and mixed boundaries. For the case with reflecting confinement in the absence of bias, the steady-state probability shows a step-like behavior for the Type A dynamics, while it is uniform for the Type B dynamics. We also derive explicit expressions for the first-passage probability and the mean first-passage time, and compare the hitting time dependence to a single target. Finally, considering the continuous-space continuous-time limit of the propagator, we obtain the boundary conditions at the interface. At the interface, while the flux is the same, the probability density is discontinuous for Type A and is continuous for Type B. For the latter we derive a generalized version of the so-called leather boundary condition in the appropriate limit.
