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Random diffusivity scenarios behind anomalous non-Gaussian diffusion

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  • dos Santos, M.A.F.
  • Colombo, E.H.
  • Anteneodo, C.

Abstract

The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we consider the spread of a population of fractional (long-time correlated) Brownian walkers, with time-dependent and heterogeneous diffusivity. We aim to obtain the possible scenarios related to these individual-level features from the observation of the temporal evolution of the population spatial distribution. We develop and discuss the possibility and limitations of this connection for the broad class of self-similar diffusion processes. Our results are presented in terms of a general framework, which is then used to address well-known processes, such as Laplace diffusion, nonlinear diffusion, and their extensions.

Suggested Citation

  • dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007761
    DOI: 10.1016/j.chaos.2021.111422
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    References listed on IDEAS

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    1. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    2. dos Santos, Maike A.F. & Junior, Luiz Menon, 2021. "Random diffusivity models for scaled Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
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    5. Celia Anteneodo & Silvio M. Duarte Queiros, 2009. "Statistical mixing and aggregation in Feller diffusion," Papers 0910.1394, arXiv.org.
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    8. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    9. dos Santos, Maike A.F., 2020. "Mittag-Leffler functions in superstatistics," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    Cited by:

    1. dos Santos, M.A.F. & Menon, L. & Cius, D., 2022. "Superstatistical approach of the anomalous exponent for scaled Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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