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We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
This document outlines the development of numerous new theoretical approaches to model associating fluids. For a detailed abstract please see page ii.
The incomplete version of the Macdonald function has various appellations in literature and earns a well-deserved reputation of being a computational challenge. This paper ties together the previously disjoint literature and presents the…
We comment on a recent paper by Li and Wang [Phys. Rev. Lett. 91, 044301 (2003)], and argue that their results violate the non-existence of a characteristic time scale in subdiffusive systems.
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
Subcritical transition of an inhomogeneous plasma where turbulences with different characteristic space-time scales coexist is analyzed with methods of statistical physics of turbulences. We derived the development equations of the…
We consider diffusion processes in media with pockets of large diffusivity. The asymptotic behavior of such processes is described when the diffusion coefficients in the pockets tend to infinity. The limiting process is identified as a…
This is a survey article written for the Springer's Intelligencer, in the occasion of the 2018 International Congress of Mathematicians.
Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms…
We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong…
Anomalous diffusion phenomena are ubiquitous in complex media, such as biological tissues. A wide class of sub-diffusive phenomena phenomena is described by the time-fractional diffusion equation. The paper investigates the case of…
Fluid flow through bimodal porous media, characterized by a distinct separation in pore size distribution, is critical in various scientific and engineering applications, including groundwater management, oil and gas production, and carbon…
Anomalous diffusion and non-Gaussian statistics are detected experimentally in a two-dimensional driven-dissipative system. A single-layer dusty plasma suspension with a Yukawa interaction and frictional dissipation is heated with laser…
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are…
In this paper we investigate the behavior of particles crossing a neat interface between two media. A Monte Carlo and analytical model, based on fractional derivatives, are presented and discussed in detail, together with a comparison.…
The article is devoted to new mathematical methods for psychophysical filtering of experimental data and their processing.
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
We propose a model of sub-diffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the…