The search result changed since you submitted your search request. Documents might be displayed in a different sort order.
  • search hit 6 of 16
Back to Result List

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

Download full text files

  • pmnr999.pdfeng
    (13761KB)

    SHA-1: 3fc71378f5c7d312c8b469262020c710a3b4a323

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics
Metadaten
Author: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
Parent Title (German):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (999)
Document Type:Postprint
Language:English
Date of first Publication:2020/09/22
Year of Completion:2020
Publishing Institution:Universität Potsdam
Release Date:2020/09/22
Tag:diffusion; power spectrum; random diffusivity; single trajectories
Issue:999
Page Number: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
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Publication Way:Open Access / Green Open-Access
Licence (German):License LogoCreative Commons - Namensnennung, 4.0 International
Notes extern:Bibliographieeintrag der Originalveröffentlichung/Quelle