IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921007761.html
   My bibliography  Save this article

Random diffusivity scenarios behind anomalous non-Gaussian diffusion

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921007761
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111422?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    4. Celia Anteneodo & Silvio M. Duarte Queiros, 2009. "Statistical mixing and aggregation in Feller diffusion," Papers 0910.1394, arXiv.org.
    5. Anteneodo, C., 2005. "Non-extensive random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(2), pages 289-298.
    6. dos Santos, Maike A.F., 2020. "Mittag-Leffler functions in superstatistics," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    7. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    8. R. S. Mendes & L. C. Malacarne & C. Anteneodo, 2007. "Statistics of football dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(3), pages 357-363, June.
    9. Wang, Xudong & Chen, Yao, 2021. "Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    10. Plastino, A.R. & Plastino, A., 1995. "Non-extensive statistical mechanics and generalized Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 222(1), pages 347-354.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shi, Hong-Da & Du, Lu-Chun & Huang, Fei-Jie & Guo, Wei, 2022. "Collective topological active particles: Non-ergodic superdiffusion and ageing in complex environments," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. 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).
    3. Pereira, A.P.P. & Fernandes, J.P. & Atman, A.P.F. & Acebal, J.L., 2018. "Parameter calibration between models and simulations: Connecting linear and non-linear descriptions of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 369-382.
    4. Carlota Torrents & Angel Ric & Robert Hristovski & Lorena Torres-Ronda & Emili Vicente & Jaime Sampaio, 2016. "Emergence of Exploratory, Technical and Tactical Behavior in Small-Sided Soccer Games when Manipulating the Number of Teammates and Opponents," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-15, December.
    5. Tawfik, Ashraf M. & Abdelhamid, Hamdi M., 2021. "Generalized fractional diffusion equation with arbitrary time varying diffusivity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    6. Ván, P, 2004. "One- and two-component fluids: restrictions from the Second Law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 418-426.
    7. Akıllı, Mahmut & Yılmaz, Nazmi & Akdeniz, K. Gediz, 2021. "The ‘wavelet’ entropic index q of non-extensive statistical mechanics and superstatistics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Janczura, Joanna & Burnecki, Krzysztof & Muszkieta, Monika & Stanislavsky, Aleksander & Weron, Aleksander, 2022. "Classification of random trajectories based on the fractional Lévy stable motion," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    9. Ván, P., 2006. "Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 28-33.
    10. Maike A. F. dos Santos, 2019. "Mittag–Leffler Memory Kernel in Lévy Flights," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    11. Leon Chen, L. & Beck, Christian, 2008. "A superstatistical model of metastasis and cancer survival," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3162-3172.
    12. Guo, Wei & Liu, Ying-Zhou & Huang, Fei-Jie & Shi, Hong-Da & Du, Lu-Chun, 2023. "Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    13. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Wang, Xiaolong & Feng, Jing & Liu, Qi & Li, Yongge & Xu, Yong, 2022. "Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    15. Lenzi, E.K. & Ribeiro, M.A. & Fuziki, M.E.K. & Lenzi, M.K. & Ribeiro, H.V., 2018. "Nonlinear diffusion equation with reaction terms: Analytical and numerical results," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 254-265.
    16. Qiao, Le & Ilow, Nicholas & Ignacio, Maxime & Slater, Gary W., 2022. "An empirical method to characterize displacement distribution functions for anomalous and transient diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    17. Moretto, Enrico & Pasquali, Sara & Trivellato, Barbara, 2016. "Option pricing under deformed Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 246-263.
    18. Kelty-Stephen, Damian G. & Mangalam, Madhur, 2023. "Multifractal descriptors ergodically characterize non-ergodic multiplicative cascade processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    19. Aranda, Orestes Tumbarell & Penna, André L.A. & Oliveira, Fernando A., 2021. "Nonlocal pattern formation effects in evolutionary population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    20. Eliazar, Iddo, 2023. "Spectral design of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007761. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.