We extend the step-balanced random walk [Y. Maruyama, Phys. Rev. E 96, 032135 (2017)], which was proposed for diffusion phenomena in three-dimensional discontinuous media, to systems that contain anisotropic phase zones with nonplane interfaces. What is key is threefold: For each interstep transition at discontinuous interfaces to be equilibrated by its reverse transition, incident and penetration steps are in one-to-one correspondence; at each incidence, penetration probability is determined by the normal components of an incident step and the corresponding penetration step with respect to an incident tangential plane, and for reflection, the reverse of an incident step, which satisfies the conditions for time reversibility at any interface, is used as a reflection step.

中文翻译：

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随机游走描述三维不连续介质中的扩散现象：扩展到各向异性相和非平面界面

我们扩展了步长均衡的随机游走[Y. 丸山物理 启ë 96，032135（2017）]，它提出了扩散现象在三维非连续媒体，对包含与非平面界面各向异性相区的系统。关键是三个方面：对于要通过其反向过渡来平衡不连续界面处的每个步间过渡，入射和穿透步骤是一对一的对应关系。在每次入射时，穿透概率由入射步骤的法向分量和相对于入射切线平面的相应穿透步骤确定，对于反射而言，入射概率由入射步骤的反方向确定，这满足了任何界面上时间可逆的条件用作反射步骤。