47695
2020
2020
eng
26
6
22
article
Dt. Physikalische Ges.
Bad Honnef
1
2020-06-26
2020-06-26
--
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, 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.
New Journal of Physics
10.1088/1367-2630/ab9200
1367-2630
063056
<a href="https://doi.org/10.25932/publishup-47696">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 999</a>
Universität Potsdam
PA 2020_052
1357.79
false
false
CC-BY - Namensnennung 4.0 International
Vittoria Sposini
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Flavio Seno
eng
uncontrolled
diffusion
eng
uncontrolled
power spectrum
eng
uncontrolled
random diffusivity
eng
uncontrolled
single trajectories
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
47696
2020
2020
eng
27
999
postprint
1
2020-09-22
2020-09-22
--
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, 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.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-47696
urn:nbn:de:kobv:517-opus4-476960
1866-8372
063056
<a href="http://publishup.uni-potsdam.de/47695">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
New Journal of Physics 22 (2020) 6, 063056 DOI: 10.1088/1367-2630/ab9200
false
true
CC-BY - Namensnennung 4.0 International
Vittoria Sposini
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Flavio Seno
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
999
eng
uncontrolled
diffusion
eng
uncontrolled
power spectrum
eng
uncontrolled
random diffusivity
eng
uncontrolled
single trajectories
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/47696/pmnr999.pdf