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Motion of an ensemble of particles in a space-periodic potential well with a weak wave-like perturbation imposed is considered. We found that slow oscillations of wavenumber of the perturbation lead to occurrence of directed particle…
The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this paper. Multiscale techniques are used to derive general formulae for the steady…
The Brownian motion of a particle in a one-dimensional periodic potential subjected to a uniform external force F is studied. Using the formula for the diffusion coefficient D obtained by other authors and an alternative one derived from…
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of…
The paper studies the overdamped motion of Brownian particles in a tilted sawtooth potential. The dependencies of the diffusion coefficient and coherence level of Brownian transport on temperature, tilting force, and the shape of the…
We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e. a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force which takes the system…
We study the response of one dimensional diffusive systems, consisting of particles interacting via symmetric or asymmetric exclusion, to time-periodic driving from two reservoirs coupled to the ends. The dynamical response of the system…
Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject…
Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the…
Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their…
Typically, in the description of active Brownian particles, a constant effective propulsion force is assumed, which is then subjected to fluctuations in orientation and translation leading to a persistent random walk with an enlarged…
We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely,…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
The transport properties of a spherical active Brownian particle in a periodic potential under heavy damping are considered. The self-propelled particle is subjected to the asymmetric potential, detailed balance is lost and the particles…
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…
Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite - an "anomaleous diffusion process" where initially diffusive motion…
It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on "intermediate" time scales before diffusion sets in.…
We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states presenting super-diffusion of rotor…
We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous…