Related papers: Subdiffusive random walk in a membrane system. The…
We consider the transmission of massless Dirac fermions through an array of short range scatterers which are modeled as randomly positioned $\delta$- function like potentials along the x-axis. We particularly discuss the interplay between…
We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity and bias. Depending on the position of the interface, there exist two exclusive ways to model the…
In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report ''anomalous diffusion'', where mean-squared displacements scale as a power law of time with exponent $\alpha< 1$ (subdiffusion). While…
Molecular transport in living systems regulates numerous processes underlying biological function. Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive motion been associated with nonergodic…
We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the…
Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction…
The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, $P_l$, and waiting-time, $P_t$,…
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $\Omega \subset \R^d$ containing a set of small subdomains or interior…
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation, -the resolvent formula-, Green's…
We develop a non-perturbative formulation based on the Green-function quantization method, that can describe spontaneous parametric down-conversion in the high-gain regime in nonlinear optical structures with arbitrary amount of loss and…
We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies…
The sluggish and heterogeneous dynamics of glass forming liquids is frequently associated to the transient coexistence of two phases of particles, respectively with an high and low mobility. In the absence of a dynamical order parameter…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
The dynamics of a tracer molecule near a fluid membrane is investigated, with particular emphasis given to the interplay between the instantaneous position of the particle and membrane fluctuations. It is found that hydrodynamic…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
Diffusive random walks feature the surprising property that the average length of all possible random trajectories that enter and exit a finite domain is determined solely by the domain boundary. Changes in the diffusion constant or the…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…