发表机构
Technion—Israel Institute of Technology; Macedonian Academy of Sciences and Arts; Ss. Cyril and Methodius University; Korea University（以色列理工学院; 马其顿科学院与艺术院; 圣西里尔和圣美多德大学; 韩国大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出了基于康托尔集直积的分形海绵扩散模型，其对应一维扩散由带幂律记忆核和位置依赖扩散系数的广义福克-普朗克方程支配，可用于描述多孔分形介质的反常热输运。
AI 中文摘要
我们提出了一种分形海绵结构内部的扩散过程模型，该模型是梳状结构和分形网格结构上扩散过程的推广。此海绵模型被视为康托尔集的直积。研究表明，对应的一维扩散过程由具有幂律记忆核和位置依赖扩散系数的广义福克-普朗克方程支配，即介质的分形结构会在输运系统中诱导出记忆效应和异质性。所考虑的模型可能对描述多孔分形介质中的反常热输运具有重要意义。
英文摘要
We suggest a model of a diffusive process inside a fractal sponge structure, which is a generalization of the diffusion processes on a comb and fractal mesh structure. The sponge model is considered as the direct product of Cantor sets. It is shown that the corresponding one-dimensional diffusion process is governed by a generalized Fokker-Planck equation with a power-law memory kernel and a position-dependent diffusion coefficient. That is, the fractal structure of the medium induces memory effects and heterogeneity in the transport system. The considered model may be of interest to describe anomalous heat transport in porous fractal media.
