Noise-induced transition from anomalous to ordinary diffusion: The crossover time as a function of noise intensity

Description:

This article discusses noise-induced transition from anomalous to ordinary diffusion and the crossover time as a function of noise intensity.

Creator(s):
Creation Date: December 1995
Partner(s):
UNT College of Arts and Sciences
Collection(s):
UNT Scholarly Works
Usage:
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Creator (Author):
Floriani, Elena

Università di Pisa

Creator (Author):
Grigolini, Paolo

University of North Texas; Università di Pisa

Creator (Author):
Mannella, Riccardo

Università di Pisa

Publisher Info:
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
Date(s):
  • Creation: December 1995
Description:

This article discusses noise-induced transition from anomalous to ordinary diffusion and the crossover time as a function of noise intensity.

Degree:
Department: Physics
Note:

Copyright 1995 American Physical Society. The following article appeared in Physical Review E, 52:6, pp. 5910-5917, http://link.aps.org/doi/10.1103/PhysRevE.52.5910

Note:

Abstract: We study the interplay between a deterministic process of weak chaos, responsible for the anomalous diffusion of a variable x, and a white noise of intensity ≡. The deterministic process of anomalous diffusion results from the correlated fluctuations of a statistical variable ξ between two distinct values +1 and -1, each of them characterized by the same waiting time distribution ψ(t), given by ψ(t)≃ t(-μ) with 2 < μ < 3, in the long-time limit. We prove that under the influence of a weak white noise of intensity ≡, the process of anomalous diffusion becomes normal at a time t(c) given by t(c) ~ 1/≡(β)(μ). Here β(μ) is a function of μ which depends on the dynamical generator of the waiting-time distribution ψ(t). We derive an explicit expression for β(μ) in the case of two dynamical systems, a one-dimensional superdiffusive map and the standard map in the accelerating state. The theoretical prediction is supported by numerical calculations.

Physical Description:

8 p.

Language(s):
Subject(s):
Keyword(s): anomalous diffusion | Brownian motion | dynamical model
Source: Physical Review E, 1995, College Park: American Physical Society
Partner:
UNT College of Arts and Sciences
Collection:
UNT Scholarly Works
Identifier:
  • DOI: 10.1103/PhysRevE.52.5910
  • ARK: ark:/67531/metadc139501
Resource Type: Article
Format: Text
Rights:
Access: Public
Citation:
Publication Title: Physical Review E
Volume: 52
Issue: 6
Page Start: 5910
Page End: 5917
Peer Reviewed: Yes