Continuous-time random walks with internal dynamics and subdiffusive reaction-diffusion equations

被引：18

作者：

Eule, S. ^{[1
]}

Friedrich, R. ^{[1
]}

Jenko, F. ^{[1
,2
]}

Sokolov, I. M. ^{[1
,3
]}

机构：

[1] Univ Munster, Inst Theoret Phys, D-48149 Munster, Germany

[2] Max Planck Inst Plasma Phys, D-85748 Garching, Germany

[3] Humboldt Univ, D-12489 Berlin, Germany

来源：

PHYSICAL REVIEW E | 2008年 / 78卷 / 06期

关键词：

master equation; random processes; reaction-diffusion systems;

D O I：

10.1103/PhysRevE.78.060102

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We formulate the generalized master equation for a class of continuous-time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean-field approximation.

引用

页数：4

共 23 条

[1] From continuous time random walks to the fractional Fokker-Planck equation [J].

Barkai, E ;

Metzler, R ;

Klafter, J .

PHYSICAL REVIEW E, 2000, 61 (01) :132-138

[2] Non-linear shot noise: Levy, Noah, & Joseph [J].

Eliazar, I ;

Klafter, J .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2006, 360 (02) :227-260

[3] The wave of advance of advantageous genes [J].

Fisher, RA .

ANNALS OF EUGENICS, 1937, 7 :355-369

[4] LANGEVIN-EQUATIONS FOR CONTINUOUS-TIME LEVY FLIGHTS [J].

FOGEDBY, HC .

PHYSICAL REVIEW E, 1994, 50 (02) :1657-1660

[5] Anomalous diffusion of inertial, weakly damped particles [J].

Friedrich, R. ;

Jenko, F. ;

Baule, A. ;

Eule, S. .

PHYSICAL REVIEW LETTERS, 2006, 96 (23)

[6] Exact solution of a generalized Kramers-Fokker-Planck equation retaining retardation effects [J].

Friedrich, R. ;

Jenko, F. ;

Baule, A. ;

Eule, S. .

PHYSICAL REVIEW E, 2006, 74 (04)

[7] Front propagation in A+B→2A reaction under subdiffusion [J].

Froemberg, D. ;

Schmidt-Martens, H. ;

Sokolov, I. M. ;

Sagues, F. .

PHYSICAL REVIEW E, 2008, 78 (01)

[8] Random time-scale invariant diffusion and transport coefficients [J].

He, Y. ;

Burov, S. ;

Metzler, R. ;

Barkai, E. .

PHYSICAL REVIEW LETTERS, 2008, 101 (05)

[9]

Kolmogorov A., 1937, Bull. Moscow State Univ. Ser. A: Math. Mech, V1, P1

[10] Nonergodicity mimics inhomogeneity in single particle tracking [J].

Lubelski, Ariel ;

Sokolov, Igor M. ;

Klafter, Joseph .

PHYSICAL REVIEW LETTERS, 2008, 100 (25)

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