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.…
Verfasserangaben: | Vittoria SposiniORCiD, Denis S. GrebenkovORCiD, Ralf MetzlerORCiDGND, Gleb OshaninORCiDGND, Flavio SenoORCiD |
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DOI: | https://doi.org/10.1088/1367-2630/ab9200 |
ISSN: | 1367-2630 |
Titel des übergeordneten Werks (Englisch): | New Journal of Physics |
Verlag: | Dt. Physikalische Ges. |
Verlagsort: | Bad Honnef |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 26.06.2020 |
Erscheinungsjahr: | 2020 |
Datum der Freischaltung: | 22.09.2020 |
Freies Schlagwort / Tag: | diffusion; power spectrum; random diffusivity; single trajectories |
Band: | 22 |
Ausgabe: | 6 |
Seitenanzahl: | 26 |
Fördernde Institution: | Universität Potsdam |
Fördernummer: | PA 2020_052 |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer Review: | Referiert |
Fördermittelquelle: | Publikationsfonds der Universität Potsdam |
Publikationsweg: | Open Access / Gold Open-Access |
Lizenz (Deutsch): | CC-BY - Namensnennung 4.0 International |
Externe Anmerkung: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 999 |