Related papers: Spatio-temporal anomalous diffusion in heterogeneo…
The position $x(t)$ of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray $x=v_0 t$, where $v_0$ is the average drift. However,…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
The fractional diffusion equation is derived from the master equation of continuous-time random walks (CTRWs) via a straightforward application of the Gnedenko-Kolmogorov limit theorem. The Cauchy problem for the fractional diffusion…
Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian…
We show that the dynamics of supercooled liquids, analyzed from computer simulations of the binary mixture Lennard-Jones system, can be described in terms of a continuous time random walk (CTRW). The required discretization comes from…
Two models are first presented, of one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with…
The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects,…
The diffusing-diffusivity mechanism proposed by Chubynsky and Slater [PRL 113, 098302, 2014] predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the…
Systems living in complex non equilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
Background: This study is mainly motivated by the need of understanding how the diffusion behaviour of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell,…
Traditional concepts for flow in porous media assume that the heterogeneous distribution of hydraulic conductivity is the source for the contaminant temporal and spatial heavy tail, a process known as anomalous or non-Fickian transport;…
We demonstrate that the diffusion coefficient, $D$, for ultrasound propagating in a multiple scattering medium, such as a dense granular suspension, can be measured using a time reversal experiment. This requires an unprecedented…
Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder famously explains the origin of non-Arrhenius $\exp[-\sigma^2/(k_BT^2)]$ temperature-dependence in disordered systems. Here we show that unbiased…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…
In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the…
Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…
Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a…
The Continuous Time Random Walk (CTRW) formalism is used to model the non-Poisson relaxation of a system response to perturbation. Two mechanisms to perturb the system are analyzed: a first in which the perturbation, seen as a potential…