Related papers: On log--normal distribution on a comb structure

A random walk scheme, consisting of alternating phases of regular Brownian motion and L\'evy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and…

The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far…

A generalization of the Drude model is studied. On the one hand, the free motion of the particles is allowed to be sub- or superdiffusive; on the other hand, the distribution of the time delay between collisions is allowed to have a long…

We consider transport properties for a non-homogeneous persistent random walk, that may be viewed as a mean-field version of the L\'evy-Lorentz gas, namely a 1-d model characterized by a fat polynomial tail of the distribution of…

This article considers the statistical properties of L\'evy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply.…

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…

Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology,…

Diffusion in complex heterogeneous media such as biological tissues or porous materials typically involves constrained displacements in tortuous structures and {\em sticky} environments. Therefore, diffusing particles experience both…

We have established in a pilot study, that the spreading of liquids in sandy porous materials at low levels of saturation, typically less than ten percent of the available void space, has very distinctive features in comparison to that at…

We investigate multiple scattering of near-resonant light in a Doppler-broadened atomic vapor. We experimentally characterize the length distribution of the steps between successive scattering events. The obtained power law is…

We introduce a new exactly solvable model in quantum mechanics that describes the propagation of particles through a potential field created by regularly spaced $\delta'$-type point interactions, which model the localized dipoles often…

From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…

We study the diffusive motion of a test particle in a two-dimensional comb structure consisting of a main backbone channel with continuously distributed side branches, in the presence of stochastic Markovian resetting to the initial…

In this paper we deal with high-order corrections for the Fractional Derivative approach to anomalous diffusion, in super-diffusive regime, which become relevand whenever one attempts to describe the behavior of particles close to normal…

Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…

Non-equilibrium transport of particles embedded in a liquid crystal host can, by cooling through a phase transition, be exploited to create a remarkable variety of structures including shells, foams, and gels. Due to the complexity of the…

In this paper we study the motion of two particles diffusing on low-dimensional discrete structures in presence of a hard-core repulsive interaction. We show that the problem can be mapped in two decoupled problems of single particles…

Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…

Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…

We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…