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

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

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8 p.

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Floriani, Elena; Grigolini, Paolo & Mannella, Riccardo December 1995.

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

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8 p.

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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

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.

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  • Physical Review E, 1995, College Park: American Physical Society

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  • Publication Title: Physical Review E
  • Volume: 52
  • Issue: 6
  • Page Start: 5910
  • Page End: 5917
  • Peer Reviewed: Yes

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  • December 1995

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  • Feb. 1, 2013, 9:58 a.m.

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  • April 2, 2014, 4:17 p.m.

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Floriani, Elena; Grigolini, Paolo & Mannella, Riccardo. Noise-induced transition from anomalous to ordinary diffusion: The crossover time as a function of noise intensity, article, December 1995; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc139501/: accessed September 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.