Quantifying non-ergodicity of anomalous diffusion with higher order moments

Abstract Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the in...

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Autores principales:	Maria Schwarzl, Aljaž Godec, Ralf Metzler
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/c5b5a642e8074a58b75d073239cd1234
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spelling	oai:doaj.org-article:c5b5a642e8074a58b75d073239cd12342021-12-02T11:51:13ZQuantifying non-ergodicity of anomalous diffusion with higher order moments10.1038/s41598-017-03712-x2045-2322https://doaj.org/article/c5b5a642e8074a58b75d073239cd12342017-06-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-03712-xhttps://doaj.org/toc/2045-2322Abstract Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.Maria SchwarzlAljaž GodecRalf MetzlerNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-18 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Maria Schwarzl Aljaž Godec Ralf Metzler Quantifying non-ergodicity of anomalous diffusion with higher order moments
description	Abstract Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.
format	article
author	Maria Schwarzl Aljaž Godec Ralf Metzler
author_facet	Maria Schwarzl Aljaž Godec Ralf Metzler
author_sort	Maria Schwarzl
title	Quantifying non-ergodicity of anomalous diffusion with higher order moments
title_short	Quantifying non-ergodicity of anomalous diffusion with higher order moments
title_full	Quantifying non-ergodicity of anomalous diffusion with higher order moments
title_fullStr	Quantifying non-ergodicity of anomalous diffusion with higher order moments
title_full_unstemmed	Quantifying non-ergodicity of anomalous diffusion with higher order moments
title_sort	quantifying non-ergodicity of anomalous diffusion with higher order moments
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/c5b5a642e8074a58b75d073239cd1234
work_keys_str_mv	AT mariaschwarzl quantifyingnonergodicityofanomalousdiffusionwithhigherordermoments AT aljazgodec quantifyingnonergodicityofanomalousdiffusionwithhigherordermoments AT ralfmetzler quantifyingnonergodicityofanomalousdiffusionwithhigherordermoments
_version_	1718395189082456064

Quantifying non-ergodicity of anomalous diffusion with higher order moments

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