Anomalous transport in fluid field with random waiting time depending on the preceding jump length

doi:10.1088/1674-1056/25/11/110504

中国物理B ›› 2016, Vol. 25 ›› Issue (11): 110504-110504.doi: 10.1088/1674-1056/25/11/110504

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

收稿日期:2016-06-04 修回日期:2016-07-16 出版日期:2016-11-05 发布日期:2016-11-05
通讯作者: Hong Zhang, Guo-Hua Li E-mail:math_126@126.com;ligh_0906@126.com
基金资助:
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).

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

Received:2016-06-04 Revised:2016-07-16 Online:2016-11-05 Published:2016-11-05
Contact: Hong Zhang, Guo-Hua Li E-mail:math_126@126.com;ligh_0906@126.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: non-Fickian transport, continuous time random walk, advection-dispersion equation

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.

Key words: non-Fickian transport, continuous time random walk, advection-dispersion equation

中图分类号: (Transport processes)

05.60.-k

02.50.-r (Probability theory, stochastic processes, and statistics) 47.10.A- (Mathematical formulations)

张红, 李国华. Anomalous transport in fluid field with random waiting time depending on the preceding jump length[J]. 中国物理B, 2016, 25(11): 110504-110504.

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[J]. Chin. Phys. B, 2016, 25(11): 110504-110504.

参考文献 27

[1]	Bradley D N, Tucker G E and Benson D A 2010 J. Geophys. Res. 115 F00A09
[2]	Schumer R, Meerschaert M M and Baeumer B 2009 J. Geophys. Res. 114 F00A07
[3]	Benson D A, Wheatcraft S W and Meerschaert M M 2000 Water Resour. Res. 36 1403
[4]	Liu G J, Guo Z L and Shi B C 2016 Acta Phys. Sin. 65 014702(in Chinese)
[5]	Berkowitz B, Cortis A, Dentz M and Scher H 2006 Rev. Geophys. 44 RG2003
[6]	Chang F X, Chen J and Huang W 2005 Acta Phys. Sin. 54 1113(in Chinese)
[7]	Zhang Y, Martin R L, Chen D, Baeumer B, Sun H G and Li C 2014 J. Geophys. Res. Earth Surf. 119 2711
[8]	Baeumer B, Benson D A, Meerschaert M M and Wheatcraft S W 2001 Water Resour. Res. 37 1543
[9]	Addison P S, Qu B, Ndumu A S and Pyrah I C 1998 Math. Geol. 30 695
[10]	Atangana A 2014 J. Earth Syst. Sci. 123 101
[11]	Fourar M and Radilla G 2009 Transp. Porous. Med. 80 561
[12]	Wang J, Zhou J, Lv L J, Qiu W Y and Ren F Y 2014 J. Stat. Phys. 156 1111
[13]	Zhang H, Li G H and Luo M K 2013 J. Stat. Phys. 152 1194
[14]	Shahmohammadi-Kalalagh S and Beyrami H 2015 Geotech. Geol. Eng. 33 1511
[15]	Lü Y and Bao J D 2011 Phys. Rev. E 84 051108
[16]	Zhang H, Li G H and Luo M K 2012 Chin. Phys. B 21 060201
[17]	Metzler R and Klafter J 2000 Phys. Rep. 339 1
[18]	Baeumer B, Benson D A and Meerschaert M M 2005 Physica A 350 245
[19]	Zaburdaev V Y 2006 J. Stat. Phys. 123 871
[20]	Compte A 1997 Phys. Rev. E 55 6821
[21]	Liu J, Yang B, Chen X S and Bao J D 2015 Eur. Phys. J. B 88 88
[22]	Emmanuel S and Berkowitz B 2007 Transp. Porous. Med. 67 413
[23]	Bakunin O G 2008 Turbulence and Diffusion:Scaling Versus Equations (Berlin:Springer-Verlag) pp. 223-226
[24]	Klafter J and Silbey R 1980 Phys. Rev. Lett. 44 55
[25]	Gorenflo R, Vivoli A and Mainardi F 2004 Nonlinear Dyn. 38 101
[26]	Podlubny I 1999 Fractional Differential Equations (San Diego:Academic Press) pp. 62-77
[27]	Li G H, Zhang H and Luo M K 2012 Chin. Phys. B 21 128901

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

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