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We employ renewal processes to characterize the spatiotemporal dynamics of an active Brownian particle under stochastic orientational resetting. By computing the experimentally accessible intermediate scattering function (ISF) and…
We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different noise intensities, or temperatures,…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with…
We present a model for variations in atmospheric temperature from time scales of one day to one million years based on a stochastic diffusion (random walk) model of the turbulent transport of heat energy vertically in a coupled…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
We consider an open model possessing a Markovian quantum stochastic limit and derive the limit stochastic Schrodinger equations for the wave function conditioned on indirect observations using only the von Neumann projection postulate. We…
We propose a new stochastic model involving state-dependent variable exponent $p(\cdot)$ which allows modeling of systems where noise intensity adapts to the current state. This new flexible theoretical framework generalizes both the…
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective…
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…
A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress…
We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between the…
We study the Brownian motion of a charged colloid, confined between two charged walls, for small separation between the colloid and the walls. The system is embedded in an ionic solution. The combined effect of electrostatic repulsion and…
We investigate out of equilibrium stationary distributions induced by a stochastic dichotomous noise on double and multi-well models for ion channels. Ion-channel dynamics is analyzed both through over-damped Langevin equations and master…
We investigate the dynamics of an overdamped Brownian particle moving in a washboard potential with space dependent friction coefficient. Analytical expressions have been obtained for current and diffusion coefficient. We show that the…
Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the…
The Bass diffusion equation is a well-known and established modeling approach for describing new product adoption in a competitive market. This model also describes diffusion phenomena in various contexts: infectious disease spread modeling…
The equilibrium-dispersive model of the linear GC (gas chromatography) was derived using both assumptions and the method of its derivation different from the known in literature. It was concluded that this model is a specific case of the…
The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…