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Chin. Phys. B, 2016, Vol. 25(11): 110504    DOI: 10.1088/1674-1056/25/11/110504
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Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Hong Zhang(张红), Guo-Hua Li(李国华)
Department of Mathematics Teaching, Chengdu University of Technology, Chengdu 610059, China
Abstract  Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation.
Keywords:  non-Fickian transport      continuous time random walk      advection-dispersion equation  
Received:  04 June 2016      Revised:  16 July 2016      Accepted manuscript online: 
PACS:  05.60.-k (Transport processes)  
  02.50.-r (Probability theory, stochastic processes, and statistics)  
  47.10.A- (Mathematical formulations)  
Fund: Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).
Corresponding Authors:  Hong Zhang, Guo-Hua Li     E-mail:  math_126@126.com;ligh_0906@126.com

Cite this article: 

Hong Zhang(张红), Guo-Hua Li(李国华) Anomalous transport in fluid field with random waiting time depending on the preceding jump length 2016 Chin. Phys. B 25 110504

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