[1]张东晖,杨浩,施明恒.多孔介质分形模型的难点与探索[J].东南大学学报(自然科学版),2002,32(5):692-697.[doi:10.3969/j.issn.1001-0505.2002.05.003]
 Zhang Donghui,Yang Hao,Shi Mingheng.Important problems of fractal model in porous media[J].Journal of Southeast University (Natural Science Edition),2002,32(5):692-697.[doi:10.3969/j.issn.1001-0505.2002.05.003]
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多孔介质分形模型的难点与探索()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
32
期数:
2002年第5期
页码:
692-697
栏目:
能源与动力工程
出版日期:
2002-09-20

文章信息/Info

Title:
Important problems of fractal model in porous media
作者:
张东晖12 杨浩2 施明恒1
1 东南大学动力工程系, 南京 210096; 2 中国科学院南京土壤研究所,南京 210008
Author(s):
Zhang Donghui12 Yang Hao2 Shi Mingheng1
1 Department of Power Engineering,Southeast University, Nanjing 210096, China
2 Institute of Soil Science, Chinese Academy of Science, Nanjing 210008, China
关键词:
分形维数 随机行走 分形布朗运动 密度分布函数
Keywords:
fractal dimension random walk fractional Brownian motion probability density function
分类号:
TK121
DOI:
10.3969/j.issn.1001-0505.2002.05.003
摘要:
对分形理论的一些关键而又复杂的概念,如谱维数、Hurst数、稳定分布进行了讨论,谱维数是联系分形介质中静态结构参数和动程的桥梁,而Hurst数的大小划分各种类型的分形布朗运动,这也同时决定了分形介质中扩散过程的快慢; 物质在分形结构中的扩散密度分布函数属于稳定分布.并对应用于分形介质扩散动力学各种方法的实质进行了分析,分数微分扩散方程可以得到扩散密度分布函数,但目前仍然是一种近似解; 随机模拟方法比较直观,但决定过程的扩散密度分布函数目前只能采用预估的方法; 而传统的差分方法比较实用,却难以给出对分形介质网格之间的扩散系数.因此.将分形理论应用于实际的多孔介质仍然有很多难点,有待未来更深入的研究.
Abstract:
Fractal theory would offer promise for new sight on heat and mass transfer in porous media. Some confused conceptions in fractal percolation theory, spectral dimension, Hurst number and stable distribution are discussed. Spectral dimension links static structure exponents with dynamic processes in fractals. Hurst number corresponds to different kind of fractional Brownian motion, which means the different mode of the particle diffusion. Diffusion probability density function in fractals is described by stable distribution.Three general dynamic methods, fractional fractal equation, random walk model and a finite-difference theory, are analysed. Diffusion probability density function can be solved by fractional fractal equation,but it only provides an approximate solution. Random walk model is easily understood, but the important probability density function must be estimated through other methods. The classic finite-difference approach is widely used, which is limited by ambiguity of diffusion coefficient between the grids or pores. Therefore, these are still many difficulties and complexities for the fractal model in porous media,and further study is needed in the future.

参考文献/References:

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备注/Memo

备注/Memo:
基金项目: 国家重点基础研究发展规划资助项目(G2000026303).
作者简介: 张东晖(1970—),男,博士生; 施明恒(联系人),男,教授,博士生导师.
更新日期/Last Update: 2002-09-20