Related papers: Anomalous diffusion in random dynamical systems
Diffusion rates through a membrane can be asymmetric, if the diffusing particles are spatially extended and the pores in the membrane have asymmetric structure. This phenomenon is demonstrated here via a deterministic simulation of a…
The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…
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…
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 $1-p$…
The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy,…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view,…
Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively…
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…
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between…
We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescing Brownian motions. The main difference is that…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
Active particles (i.e., self-propelled particles or called microswimmers), different from passive Brownian particles, possess more complicated translational and angular dynamics, which can generate a series of anomalous transport phenomena.…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motion and create offspring at constant rate. Particles of type…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
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…
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
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…