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Spectral design of anomalous diffusion

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  • Eliazar, Iddo

Abstract

This paper poses and addresses the following goal: design a random motion that displays one type of anomalous diffusion in real space, and another type of anomalous diffusion in Fourier space. The two prominent Gaussian and selfsimilar anomalous-diffusion models – scaled Brownian motion (SBM), and fractional Brownian motion (FBM) – are not up to the task. This paper establishes a class of random motions that are up to the task. As a ‘bonus’, the random-motions’ velocities are also up to an additional task: generating flicker noise (1/f noise) behaviors. In general, the random motions are neither Gaussian nor selfsimilar. When both Gaussian and selfsimilar then the resulting random motion is a ‘hybrid’ Brownian model: it generalizes SBM on the one hand, and it generalizes the Riemann–Liouville FBM on the other hand.

Suggested Citation

  • Eliazar, Iddo, 2023. "Spectral design of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    • Handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123006210
    DOI: 10.1016/j.physa.2023.129066
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    References listed on IDEAS

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    1. Denis S Grebenkov & Vittoria Sposini & Ralf Metzler & Gleb Oshanin & Flavio Seno, 2021. "Exact distributions of the maximum and range of random diffusivity processes," Post-Print hal-03137323, HAL.
    2. Aleksejus Kononovicius & Bronislovas Kaulakys, 2022. "$1/f$ noise from the sequence of nonoverlapping rectangular pulses," Papers 2210.11792, arXiv.org, revised Mar 2023.
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    4. Zachary R. Fox & Eli Barkai & Diego Krapf, 2021. "Aging power spectrum of membrane protein transport and other subordinated random walks," Nature Communications, Nature, vol. 12(1), pages 1-9, December.
    5. Nava Leibovich & Eli Barkai, 2017. "1∕ f β noise for scale-invariant processes: how long you wait matters," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(11), pages 1-8, November.
    6. 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).
    7. Aleksejus Kononovicius & Rytis Kazakeviv{c}ius & Bronislovas Kaulakys, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Papers 2205.07563, arXiv.org, revised Jul 2022.
    8. Kononovicius, Aleksejus & Kazakevičius, Rytis & Kaulakys, Bronislovas, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    9. Rytis Kazakeviv{c}ius & Aleksejus Kononovicius, 2023. "Anomalous diffusion and long-range memory in the scaled voter model," Papers 2301.08088, arXiv.org, revised Feb 2023.
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