Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

Description:

Article discussing research on anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation.

Creator(s):
Creation Date: August 2000
Partner(s):
UNT College of Arts and Sciences
Collection(s):
UNT Scholarly Works
Usage:
Total Uses: 217
Past 30 days: 15
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Creator (Author):
Bologna, Mauro

University of North Texas

Creator (Author):
Tsallis, Constantino

University of North Texas; Centro Brasileiro de Pesquisas Físicas

Creator (Author):
Grigolini, Paolo

University of North Texas; Istituto di Biofisica CNR; Universitá di Pisa

Publisher Info:
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
Date(s):
  • Creation: August 2000
Description:

Article discussing research on anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation.

Degree:
Department: Physics
Note:

Copyright 2000 American Physical Society. The following article appeared in Physical Review E, 62:2, pp. 2213-2218; http://pre.aps.org/abstract/PRE/v62/i2/p2213_1

Note:

Abstract: We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives (∂/∂t)P(x,t) = D(∂ƴ/∂xƴ)[P(x,t]v. Exact time-dependent solutions are found for v = (2 - y)/(1 + y)(-∞ < y ⩽ 2). By considering the long-distance asymptotic behavior of these solutions, a connection is established, namely, q = (y + 3)/(Y + 1)(0 < y ⩽ 2), with the solutions optimizing the nonextensive entropy characterized by index q. Interestingly enough, this relation coincides with the only already known for Lévy-like superdiffusion (i.e., v = 1 and 0 < y ⩽ 2). Finally, for (y,v) = (2,0) the authors obtain q=5/3, which differs from the value q = 2 corresponding to the y = 2 solutions available in the literature (v < 1 porous medium equation), thus exhibiting nonuniform convergence.

Physical Description:

6 p.

Language(s):
Subject(s):
Keyword(s): anomalous diffusion | fractional derivatives
Source: Physical Review E, 2000, College Park: American Physical Society, pp. 2213-2218
Partner:
UNT College of Arts and Sciences
Collection:
UNT Scholarly Works
Identifier:
  • DOI: 10.1103/PhysRevE.62.2213
  • ARK: ark:/67531/metadc77162
Resource Type: Article
Format: Text
Rights:
Access: Public
Citation:
Publication Title: Physical Review E
Volume: 62
Issue: 2
Page Start: 2213
Page End: 2218
Pages: 6
Peer Reviewed: Yes