Show simple item record

dc.contributor.authorDi Tullio F.en_US
dc.contributor.authorParadisi P.en_US
dc.contributor.authorSpigler R.en_US
dc.contributor.authorPagnini G.en_US
dc.description.abstractNormal or Brownian diffusion is historically identified by the linear growth in time of the variance and by a Gaussian shape of the displacement distribution. Processes departing from the at least one of the above conditions defines anomalous diffusion, thus a nonlinear growth in time of the variance and/or a non-Gaussian displacement distribution. Motivated by the idea that anomalous diffusion emerges from standard diffusion when it occurs in a complex medium, we discuss a number of anomalous diffusion models for strongly heterogeneous systems. These models are based on Gaussian processes and characterized by a population of scales, population that takes into account the medium heterogeneity. In particular, we discuss diffusion processes whose probability density function solves space- and time-fractional diffusion equations through a proper population of time-scales or a proper population of length-scales. The considered modeling approaches are: the continuous time random walk, the generalized gray Brownian motion, and the time-subordinated process. The results show that the same fractional diffusion follows from different populations when different Gaussian processes are considered. The different populations have the common feature of a large spreading in the scale values, related to power-law decay in the distribution of population itself. This suggests the key role of medium properties, embodied in the population of scales, in the determination of the proper stochastic process underlying the given heterogeneous medium.en_US
dc.description.sponsorshipThis research was supported by the Basque Government through the BERC 2014–2017 and BERC 2018–2021 programs, and by the Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditations SEV- 2013-0323 and SEV-2017-0718 and through project MTM2016- 76016-R MIPen_US
dc.publisherFront. Phys.en_US
dc.subjectanomalous diffusionen_US
dc.subjectfractional diffusionen_US
dc.subjectcomplex mediumen_US
dc.subjectGaussian processen_US
dc.subjectcontinuous time random walken_US
dc.subjectgeneralized gray Brownian motionen_US
dc.subjecttime-subordinated processen_US
dc.titleGaussian processes in complex media: new vistas on anomalous diffusionen_US

Files in this item


This item appears in the following Collection(s)

Show simple item record

Except where otherwise noted, this item's license is described as info:eu-repo/semantics/openAccess