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In this paper the distribution of charged particles is constructed under the approximation of ambipolar diffusion. The results of mathematical modelling in two-dimensional case taking into account the velocities of the system are presented.
The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…
We study the problem of stationarity and ergodicity for autoregressive multinomial logistic time series models which possibly include a latent process and are defined by a GARCH-type recursive equation. We improve considerably upon the…
We propose a numerical method to simulate electrohydrodynamic phenomena in charged colloidal dispersions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton,…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
In order to control aggregation phenomena in suspensions of nanoparticles, one often charges the particles electrically, e.g. by triboelectric charging. Stabilization of suspensions against aggregation of particles is an important issue,…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
In this paper we study the bicausal optimal transport problem for Markov chains, an optimal transport formulation suitable for stochastic processes which takes into consideration the accumulation of information as time evolves. Our analysis…
An analytical study of the charged particle dynamics in the presence of an elliptically polarized electromagnetic wave and a uniform axial magnetic field, is presented. It is found that for $g\omega_{0}/ \omega' = \pm 1$, maximum energy…
In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…
Partial atomic charges are a useful and intuitive concept for understanding molecular properties and chemical reaction mechanisms, showing how changes in molecular geometry can affect the flow of electronic charge within a molecule.…
We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients $A=B=C=1$ are chaotic, and we show that the motion…
We consider an $N$-body system of charged particle coupled to gravitational, electromagnetic, and scalar fields. The metric on moduli space for the system can be considered if a relation among the charges and mass is satisfied, which…
We present an approach to electronic polarization in molecular solids treated as a set of quantum systems interacting classically. Individual molecules are dealt with rigorously as quantum-mechanical systems subject to classical external…
Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…
This article describes Monte-Carlo algorithms for charged systems using constrained updates for the electric field. The method is generalized to treat inhomogeneous dielectric media, electrolytes via the Poisson-Boltzmann equation and…
We consider a stationary Markov process that models certain queues with a bulk service of a fixed number $m$ of admitted customers. We find an integral expression of its transition probability function in terms of certain multi-orthogonal…
The combination of electric vehicles (EVs) and renewable energy is taking shape as a potential driver for a future free of fossil fuels. However, the efficient management of the EV fleet is not exempt from challenges. It calls for the…
Intracellular transport is mediated by molecular motors that pull cargos along cytoskeletal filaments. Many cargos move bidirectionally and are transported by two teams of motors which move into opposite directions along the filament. We…
The behaviour and stability of soft and biological matter depend significantly on electrostatic interactions, as particles such as proteins and colloids acquire a charge when dispersed in an electrolytic solution. A typical simplification…