Telegraphic Transport Processes and Their Fractional Generalization: A Review and Some Extensions

被引：18

作者：

Masoliver, Jaume ^{[1
,2
]}

机构：

[1] Univ Barcelona, Dept Condensed Matter Phys, Barcelona 08007, Catalonia, Spain

[2] Univ Barcelona, Complex Syst Inst UBICS, Barcelona 08007, Catalonia, Spain

来源：

ENTROPY | 2021年 / 23卷 / 03期

关键词：

telegrapher’ s equations; fractional telegrapher’ s equation; continuous time random walk; transport problems; 1ST PASSAGE TIMES; PERSISTENT RANDOM-WALK; ANOMALOUS DIFFUSION; RANDOM MOTION; EQUATIONS; DIMENSIONS; FLIGHTS; LIGHT; LIMIT;

D O I：

10.3390/e23030364

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher's equations-as well as their fractional generalizations-from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations.

引用

页数：32

共 78 条

[1]

[Anonymous], 1994, Aspects and Applications of the Random Walk

[2] V-Langevin equations, continuous time random walks and fractional diffusion [J].

Balescu, R. .

CHAOS SOLITONS & FRACTALS, 2007, 34 (01) :62-80

[3]

Balescu R, 2005, SER PLASMA PHYS

[4]

Ben-Avraham D., 2000, DIFFUSION REACTIONS

[5] Generalization of the persistent random walk to dimensions greater than 1 [J].

Boguñá, M ;

Porrà, JM ;

Masoliver, J .

PHYSICAL REVIEW E, 1998, 58 (06) :6992-6998

[6] ANOMALOUS DIFFUSION IN DISORDERED MEDIA - STATISTICAL MECHANISMS, MODELS AND PHYSICAL APPLICATIONS [J].

BOUCHAUD, JP ;

GEORGES, A .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1990, 195 (4-5) :127-293

[7] RESPONSE OF A 2-LEVEL SYSTEM TO A RANDOM MODULATION OF THE RESONANCE WITH AN ARBITRARY STRONG EXTERNAL-FIELD [J].

BURSHTEIN, AI ;

ZHARIKOV, AA ;

TEMKIN, SI .

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS, 1988, 21 (10) :1907-1931

[8] On strong anomalous diffusion [J].

Castiglione, P ;

Mazzino, A ;

Muratore-Ginanneschi, P ;

Vulpiani, A .

PHYSICA D-NONLINEAR PHENOMENA, 1999, 134 (01) :75-93

[9] RANDOM-WALK WITH PERSISTENCE [J].

CLAES, I ;

VANDENBROECK, C .

JOURNAL OF STATISTICAL PHYSICS, 1987, 49 (1-2) :383-392

[10] Time-Changed Processes Governed by Space-Time Fractional Telegraph Equations [J].

D'ovidio, Mirko ;

Orsingher, Enzo ;

Toaldo, Bruno .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2014, 32 (06) :1009-1045

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