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

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

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

[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

[1]	Environment-dependent continuous time random walk Lin Fang(林方) and Bao Jing-Dong(包景东). Chin. Phys. B, 2011, 20(4): 040502.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention