Related papers: From continuous-time random walks to controlled-di…
Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
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…
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of the walker grows non-linearly with time in contrast to the diffusive motion described by simple random walks…
We study diffusion-reaction processes on periodic square planar lattices and simple cubic (sc) lattices. Considered first is a single diffusing reactant undergoing an irreversible reaction upon first encounter with a stationary co-reactant…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We show through intensive simulations that the paradigmatic features of anomalous diffusion are indeed the features of a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms. If $p \in (0,1/2)$ and $1-p$…
We present two complementary simulations that lead to an exploration of Anderson localization, a phenomenon in which wave diffusion is suppressed in disordered media by interference from multiple scattering. To build intuition, the first…
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,…
Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $< x^2(t) >\propto t$, while anomalous behavior is expected to show a different time dependence, $ < x^2(t) > \propto…
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…
Using exact expressions for the persistence probability and for the leading eigenvalue of the Focker-Planck operator of a random walk in a random environment we establish a fundamental relation between the statistical properties of…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard…
The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is…