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Universal spectral features of different classes of random-diffusivity processes

  • Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential,Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.show moreshow less

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Metadaten
Author details:Vittoria SposiniORCiD, Denis S. GrebenkovORCiD, Ralf MetzlerORCiDGND, Gleb OshaninORCiDGND, Flavio SenoORCiD
URN:urn:nbn:de:kobv:517-opus4-476960
DOI:https://doi.org/10.25932/publishup-47696
ISSN:1866-8372
Title of parent work (German):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
Publication series (Volume number):Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (999)
Publication type:Postprint
Language:English
Date of first publication:2020/09/22
Publication year:2020
Publishing institution:Universität Potsdam
Release date:2020/09/22
Tag:diffusion; power spectrum; random diffusivity; single trajectories
Issue:999
Number of pages:27
Source:New Journal of Physics 22 (2020) 6, 063056 DOI: 10.1088/1367-2630/ab9200
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert
Publishing method:Open Access / Green Open-Access
License (German):License LogoCC-BY - Namensnennung 4.0 International
External remark:Bibliographieeintrag der Originalveröffentlichung/Quelle
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