| Description: | In this article, the authors 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. The authors 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). The authors 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. |
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| Creator(s): | |
| Creation Date: | December 1995 |
| Partner(s): |
UNT College of Arts and Sciences
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| Collection(s): |
UNT Scholarly Works
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| Usage: |
Total Uses: 4
Past 30 days: 1
Yesterday: 0
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| Creator (Author): |
Floriani, Elena
Universitá di Pisa |
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| Creator (Author): |
Mannella, Riccardo
Universitá di Pisa |
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| Creator (Author): |
Grigolini, Paolo
University of North Texas; Universitá di Pisa |
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| Publisher Info: |
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
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| Original Creation Date: | December 1995 | |
| Description: | In this article, the authors 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. The authors 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). The authors 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. |
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| Degree: |
Department:
Physics
Department:
Center for Nonlinear Science
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| 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 |
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| Physical Description: |
8 p. |
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| 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
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| Collection: |
UNT Scholarly Works
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| Identifier: |
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| Resource Type: | Article | |
| Format: | Text | |
| Rights: |
Access:
Public
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| Citation: |
Publication Title: Physical Review E
Volume: 52
Issue: 6
Page Start: 5910
Page End: 5917
Peer Reviewed: Yes
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