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复杂介质中扩散和耗散行为的分数阶导数唯象建模

庞国飞 陈文 张晓棣 孙洪广

庞国飞, 陈文, 张晓棣, 孙洪广. 复杂介质中扩散和耗散行为的分数阶导数唯象建模[J]. 应用数学和力学, 2015, 36(11): 1117-1134. doi: 10.3879/j.issn.1000-0887.2015.11.001
引用本文: 庞国飞, 陈文, 张晓棣, 孙洪广. 复杂介质中扩散和耗散行为的分数阶导数唯象建模[J]. 应用数学和力学, 2015, 36(11): 1117-1134. doi: 10.3879/j.issn.1000-0887.2015.11.001
PANG Guo-fei, CHEN Wen, ZHANG Xiao-di, SUN Hong-guang. Fractional Differential Phenomenological Modeling for Diffusion and Dissipation Behaviors of Complex Media[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1117-1134. doi: 10.3879/j.issn.1000-0887.2015.11.001
Citation: PANG Guo-fei, CHEN Wen, ZHANG Xiao-di, SUN Hong-guang. Fractional Differential Phenomenological Modeling for Diffusion and Dissipation Behaviors of Complex Media[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1117-1134. doi: 10.3879/j.issn.1000-0887.2015.11.001

复杂介质中扩散和耗散行为的分数阶导数唯象建模

doi: 10.3879/j.issn.1000-0887.2015.11.001
基金项目: 国家自然科学基金(面上项目)(11372097);国家杰出青年科学基金(11125208);111引智计划(B12032)
详细信息
    作者简介:

    庞国飞(1987—),男,四川南充人,博士生(E-mail: guofeipang_1987@hhu.edu.cn);陈文(1967—),男,福州人,教授,博士,博士生导师 (通讯作者. E-mail: chenwen@hhu.edu.cn);张晓棣(1985—),男,山东青岛人,工程师,博士;孙洪广(1982—),男,山东聊城人,教授,博士,博士生导师.

  • 中图分类号: O39;O352;O371;O175.2

Fractional Differential Phenomenological Modeling for Diffusion and Dissipation Behaviors of Complex Media

Funds: The National Natural Science Foundation of China(General Program)(11372097);The National Science Fund for Distinguished Young Scholars of China(11125208)
  • 摘要: 复杂介质一般是多相混合物.与普通固体、液体和气体相比,其力学行为具有明显的记忆、路径依赖性特征,难以用一般的经典力学模型来描述,因而显得反常.从数学力学建模上看,整数阶导数的局部极限定义不适合描述这样的非局部力学行为.分数阶导数实质上是微分-积分算子,能精确地刻画力学行为的全局相关特征.而且分数阶模型具有明确的统计物理解释.20世纪末至今,复杂介质反常力学行为的分数阶导数模型由于具有参数少,且参数的物理意义明确等突出优点,开始引起广泛关注.该文从唯象建模的角度,综述了分数阶导数和分形导数在复杂介质的反常扩散和频率依赖能量耗散建模中的应用与发展.
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  • 收稿日期:  2015-08-26
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