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dc.contributor.authorSliusarenko, O. 
dc.contributor.authorVitali, S. 
dc.contributor.authorSposini, V.
dc.contributor.authorParadisi, P. 
dc.contributor.authorChechkin, A.V.
dc.contributor.authorCastellani, G.
dc.contributor.authorPagnini, G.
dc.description.abstractComplex systems are known to display anomalous diffusion, whose signature is a space/time scaling $x \sim t^\delta$ with $\delta \neq 1/2$ in the probability density function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g. fractional Brownian motion, and power-law decaying distributions, e.g. Lévy Flights or Lévy Walks (LWs). Lévy flights get anomalous scaling, but, being jumps of any size allowed even at short times, have infinite position variance, infinite energy and discontinuous paths. LWs, which are based on random trapping events, overcome these limitations: they resemble a Lévy-type power-law distribution that is truncated in the large displacement range and have finite moments, finite energy and, even with discontinuous velocity, they are continuous. However, LWs do not take into account the role of strong heterogeneity in many complex systems, such as biological transport in the crowded cell environment. In this work we propose and discuss a model describing a heterogeneous ensemble of Brownian particles (HEBP). Velocity of each single particle obeys a standard underdamped Langevin equation for the velocity, with linear friction term and additive Gaussian noise. Each particle is characterized by its own relaxation time and velocity diffusivity. We show that, for proper distributions of relaxation time and velocity diffusivity, the HEBP resembles some LW statistical features, in particular power-law decaying PDF, long-range correlations and anomalous diffusion, at the same time keeping finite position moments and finite energy. The main differences between the HEBP model and two different LWs are investigated, finding that, even when both velocity and position PDFs are similar, they differ in four main aspects: (i) LWs are biscaling, while HEBP is monoscaling; (ii) a transition from anomalous ($\delta \neq 1/2$) to normal ($\delta = 1/2$) diffusion in the long-time regime is seen in the HEBP and not in LWs; (iii) the power-law index of the position PDF and the space/time diffusion scaling are independent in the HEBP, while they both depend on the scaling of the inter-event time PDF in LWs; (iv) at variance with LWs, our HEBP model obeys a fluctuation--dissipation theorem.en_US
dc.description.sponsorshipBERC 2014–2017 SEV-2013-0323 Marco Polo Programme AYD-000-252 ME 1535/6-1 (DFG)en_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectanomalous diffusionen_US
dc.subjectheterogeneous ensemble of Brownian particlesen_US
dc.subjectbiological transporten_US
dc.subjectLangevin equationen_US
dc.subjectGaussian processesen_US
dc.subjectfractional diffusionen_US
dc.subjectLévy walken_US
dc.titleFinite-energy Lévy-type motion through heterogeneous ensemble of Brownian particlesen_US
dc.journal.titleJournal of Physics A: Mathematical and Theoreticalen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España