Advection and dispersion in time and space

被引：57

作者：

Baeumer, B ^{[1
]}

Benson, DA

Meerschaert, MM

机构：

[1] Univ Nevada, Dept Math & Stat, Grad Program Hydrol Sci, Reno, NV 89557 USA

[2] Desert Res Inst, Reno, NV 89512 USA

[3] Univ Nevada, Dept Phys, Reno, NV 89557 USA

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2005年 / 350卷 / 2-4期

关键词：

anomalous diffusion; continuous time random walks; first passage time; fractional calculus; subdiffusion; power laws;

D O I：

10.1016/j.physa.2004.11.008

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection-dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection-dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions to the equation are obtained by subordination. The form of the time derivative is related to the probability distribution of particle waiting times and the subordinator is given as the first passage time density of the waiting time process which is computed explicitly. (c) 2004 Elsevier B.V. All rights reserved.

引用

页码：245 / 262

页数：18

共 29 条

[1]

AHIFORS L, 1978, INTRO THEORY ANAL FU

[2]

[Anonymous], 1999, STABLE DISTRIBUTIONS

[3]

Arendt W., 2001, VECTOR VALUED LAPLAC, DOI DOI 10.1007/978-3-0348-5075-9

[4]

Baeumer B., 2001, FRACT CALCU APPL ANA, V4, P481

[5]

Baxter Glen, 1957, T AM MATH SOC, V85, P73

[6] Limit theorem for continuous-time random walks with two time scales [J].

Becker-Kern, P ;

Meerschaert, MM ;

Scheffler, HP .

JOURNAL OF APPLIED PROBABILITY, 2004, 41 (02) :455-466

[7] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2 [J].

CAPUTO, M .

GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05) :529-&

[8] Stochastic foundations of fractional dynamics [J].

Compte, A .

PHYSICAL REVIEW E, 1996, 53 (04) :4191-4193

[9] On the late-time behavior of tracer test breakthrough curves [J].

Haggerty, R ;

McKenna, SA ;

Meigs, LC .

WATER RESOURCES RESEARCH, 2000, 36 (12) :3467-3479

[10] Fractional relaxation-oscillation and fractional diffusion-wave phenomena [J].

Mainardi, F .

CHAOS SOLITONS & FRACTALS, 1996, 7 (09) :1461-1477

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