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 d...

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Detalles Bibliográficos
Autores: Sposini, V., Grebenkov, D.S., Metzler, R., Oshanin, G., Seno, F.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1192
Acceso en línea:http://hdl.handle.net/20.500.11824/1192
Access Level:acceso embargado
Palabra clave:Anomalous diffusion
Random diffusivity
Spectral features
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spelling Universal spectral features of different classes of random diffusivity processesSposini, V.Grebenkov, D.S.Metzler, R.Oshanin, G.Seno, F.Anomalous diffusionRandom diffusivitySpectral featuresStochastic 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 $1/f^2$-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.Severo Ochoa.SEV-2017-0718 BERC.2018-2021202020202020info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1192reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://iopscience.iop.org/article/10.1088/1367-2630/ab9200/pdfinfo:eu-repo/grantAgreement/MINECO//SEV-2017-0718Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/embargoedAccessoai:bird.bcamath.org:20.500.11824/11922026-06-19T12:47:47Z
dc.title.none.fl_str_mv Universal spectral features of different classes of random diffusivity processes
title Universal spectral features of different classes of random diffusivity processes
spellingShingle Universal spectral features of different classes of random diffusivity processes
Sposini, V.
Anomalous diffusion
Random diffusivity
Spectral features
title_short Universal spectral features of different classes of random diffusivity processes
title_full Universal spectral features of different classes of random diffusivity processes
title_fullStr Universal spectral features of different classes of random diffusivity processes
title_full_unstemmed Universal spectral features of different classes of random diffusivity processes
title_sort Universal spectral features of different classes of random diffusivity processes
dc.creator.none.fl_str_mv Sposini, V.
Grebenkov, D.S.
Metzler, R.
Oshanin, G.
Seno, F.
author Sposini, V.
author_facet Sposini, V.
Grebenkov, D.S.
Metzler, R.
Oshanin, G.
Seno, F.
author_role author
author2 Grebenkov, D.S.
Metzler, R.
Oshanin, G.
Seno, F.
author2_role author
author
author
author
dc.subject.none.fl_str_mv Anomalous diffusion
Random diffusivity
Spectral features
topic Anomalous diffusion
Random diffusivity
Spectral features
description 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 $1/f^2$-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.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1192
url http://hdl.handle.net/20.500.11824/1192
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://iopscience.iop.org/article/10.1088/1367-2630/ab9200/pdf
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/embargoedAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv embargoedAccess
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