Related papers: A Nonlinear Transform for the Diagonalization of t…
This work proposes a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method is based on simple numerical rules between two matrices. One of the matrix represent the identification of all…
We discuss a class of hyperbolic reaction-diffusion equations and apply the modified method of simplest equation in order to obtain an exact solution of an equation of this class (namely the equation that contains polynomial nonlinearity of…
We consider a generalized coagulation-decoagulation system on a one-dimensional discrete lattice with reflecting boundaries. It is known that a Bernoulli shock measure with two shock fronts might have a simple random-walk dynamics, provided…
Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…
In the present paper we consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the…
This paper considers the $(n,k)$-Bernoulli--Laplace model in the case when there are two urns, the total number of red and white balls is the same, and the number of selections $k$ at each step is on the same asymptotic order as the number…
The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete…
We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This is a system of two convection-diffusion equations, one in…
A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator)…
We analyze and simulate a two dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the two dimensional box, whose boundaries…
An approximative method for solving the Bloch-Torrey equation in general porous media is presented. The method expand the boundaries defining the porous media using electrostatic charges. As a result the eigenvalue problem of the Laplace…
We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the X and the Y directions. In the…
Given a non-hermitean matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note will explain how to determine the minimal polynomial of a matrix without going through its characteristic…
We investigate a reaction-diffusion problem in a two-component porous medium with a nonlinear interface condition between the different components. One component is connected and the other one is disconnected. The ratio between the…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases,…
Maxwell-Bloch system describing the resonant propagation of electromagnetic pulses in both two-level media with degeneracy in angle moment projection and three-level media with equal oscillator forces is considered. The inhomogeneous…
A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with…
In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination…
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…