分形多孔介质中的奇异扩散

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基金项目: 石油大学自然科学研究基金资助项目

Anomalous Diffusion in Fractal Porous Medium

Department of Applied Mathematics, University of Petroleum, Dongying, Shandong 257062, P. R. China

摘要: 分形多孔介质和均质多孔介质相比具有许多特殊的性质,它在各个不同的尺度上有相互钳套的自相似结构.孔隙分形中的粒子扩散和经典的Fick扩散不同,其均方位移服从分形幂律关系.据此对孔隙分形中的粒子扩散利用随机过程的统计方法建立了奇异扩散的理论模型,讨论了奇异扩散的非马尔可夫性质和分形性质.
- 分形 /
- 奇异扩散 /
- 多孔介质
Abstract: Fractal media has many characteristics different from those of homogeneous media, it has a correlated self-similar structure. The particle diffusion in pore fractal is different from Ficks diffusion, and its mean-squared displacement follows fractal scaling law. The model of particle diffusion in pore fractal by means of the statistics method of stochastic process is structured and some fractal characteristics and non-Markov property are proved.
- fractal /
- anomalous diffusion /
- porous media

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