力学与实践 ›› 2018, Vol. 40 ›› Issue (2): 161-166.DOI: 10.6052/1000-0879-17-383

• 应用研究 • 上一篇    下一篇

豪斯道夫导数扩散模型的谱熵与累积谱熵1)

秦雅楠*,†,2), 梁英杰*,3), 陈文*,4)   

  1. *河海大学,软物质力学研究所,力学与材料学院,南京 211100;
    河海大学理学院,南京 211100;
  • 收稿日期:2017-11-08 修回日期:2017-11-30 出版日期:2018-04-15 发布日期:2018-05-18
  • 通讯作者: 2) 秦雅楠,在读研究生,主要从事熵相关的研究工作. E-mail:Qyn18705156728@163.com;3) 梁英杰,讲师,主要从事裂隙介质中溶质运移的工作. E-mail:liangyj@hhu.edu.cn;4) 陈文,教授,主要从事计算力学和仿真、软物质力学行为建模方面的工作. E-mail: chenwen@hhu.edu.cn;
  • 基金资助:
    1) 111 引智计划(B12032), 国家自然科学基金(11702085) 资助项目.

SPECTRAL ENTROPY AND CUMULATIVE SPECTRAL ENTROPY OF HAUSDORFF DERIVATIVE DIFFUSION MODEL1)

QIN Yanan*,†,2), LIANG Yingjie*,3), CHEN Wen*,4)   

  1. *Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 211100, China;
    College of Science, Hohai University, Nanjing 211100, China;
  • Received:2017-11-08 Revised:2017-11-30 Online:2018-04-15 Published:2018-05-18

摘要: 基于豪斯道夫导数扩散模型的空间谱熵推导 描述反常扩散过程时空复杂程度的空间累积谱熵,并考察 个体谱熵、谱熵、累积谱熵随时 空豪斯道夫导数、扩散系数和扩散时间的变化情况. 计算结果表明,谱熵与累积谱熵随时间豪斯道夫导数α或空间豪斯道夫导数β的减小而增大,且具有拖尾特征. 此外,随着扩散时间t或扩散系数Dα,β的减小,正常扩散对应的个体谱熵衰减的速率比反常扩散快,且对应的谱密度更窄. 因此,豪斯道夫导数扩散模型的谱熵和累积谱熵均能够反映复杂介质的非均质特征和内部扩散过程的不确定性.

关键词: 谱熵|累积谱熵|豪斯道夫导数|反常扩散|空间频率

Abstract: The cumulative spectral entropy in space is derived based on the spectral entropy of the Hausdorff derivative diffusion model for describing the spatial and temporal complexity of the anomalous diffusion process. The individual, the total spectral and the cumulative spectral entropies are investigated by varying the diffusion coefficient and the diffusion time. It is shown that the spectral and the cumulative spectral entropies increase with the decrease of the order of the time Hausdorff derivative α or the space Hausdorff derivative β and are characterized by a heavy tail. With the decrease of the diffusion time or the diffusion coefficient, the normal diffusion ( α = 1,β = 1) sees a faster decay of the individual spectral entropy than the anomalous diffusion, and the corresponding spectral density becomes narrower. Thus, the spectral and the cumulative spectral entropies of the Hausdorff derivative diffusion model can reflect the heterogeneous structure of complex media and the uncertainty of the underlying diffusion process.

Key words: spectral entropy|cumulative spectral entropy|Hausdorff derivative|anomalous diffusion|spatial frequency

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