Related papers: Diffusion and escape times in the open-leaky stand…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which…
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…
The dynamics of particle transport under the influence of localised high energy anomalies (explosions) is a complicated phenomena dependent on many physical parameters of both the particle and the medium it resides in. Here we present a…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We perform an extensive and detailed analysis of the generalized diffusion processes in deterministic area preserving maps with noncompact phase space, exemplified by the standard map, with the special emphasis on understanding the…
This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as…
The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of processes the parameter $K$ is chosen at random from a Gaussian…
The escape mechanism of the four hill potential is explored. A thorough numerical investigation takes place in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional phase space in…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
Particles confined to a single file, in a narrow quasi-one dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles can begin to pass each other. The…
Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For…
The escape probability $\xi_{x}$ from a site $x$ of a one-dimensional disordered lattice with trapping is treated as a discrete dynamical evolution by random iterations over nonlinear maps parametrized by the right and left jump…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
We provide escape rates formulae for piecewise expanding interval maps with `random holes'. Then we obtain rigorous approximations of invariant densities of randomly perturbed metabstable interval maps. We show that our escape rates…
This paper summarises an investigation of the statistical properties of orbits escaping from three different two-degree-of-freedom Hamiltonian systems which exhibit global stochasticity. Each H=H_{0}+eH', with H_{0} integrable and eH' a…