Conduction in disordered media has been the subject of interest in applications and basic research. Percolation theory is used to study conduction, and mean-field theory has been used to describe macroscopic conduction. However, such an approximation theory cannot provide specific insights into the local limiting factors of conduction. In this study, a finite element simulation based on the site percolation model is used to investigate the effect of microstructural defects in materials on transport current. Statistical analysis of the local current obtained by the simulation experiment shows that the meandering of the transport current because of the disturbance of the current path increases as the concentration of defects increases, thus observing a dimensional crossover of the transport current from 1D to 3D. Λ, which represents the degree of current meandering, has a value of 5.3 in the vicinity of the singularity of the percolation threshold ( P c ). The gove...

中文翻译：

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渗流建模定量分析3D无序介质中传导路径的弯曲和尺寸交叉。

无序介质中的传导一直是应用程序和基础研究的主题。渗流理论用于研究传导，均场理论用于描述宏观传导。但是，这种近似理论无法提供对传导的局部限制因素的具体见解。在这项研究中，基于站点渗流模型的有限元模拟被用来研究材料中的微结构缺陷对传输电流的影响。通过模拟实验获得的局部电流的统计分析表明，由于电流路径的干扰而引起的传输电流的曲折随着缺陷浓度的增加而增加，从而观察到了传输电流从1D到3D的尺寸跨度。Λ，代表电流蜿蜒的程度，在渗透阈值（P c）的奇异性附近具有5.3的值。哥...