Related papers: On the "Matrix Approach" to interacting particle s…
The Lagrange-mesh $R$-matrix method is generalized to inhomogeneous equations. This method is numerically stable and efficient. It can be directly used for transfer reactions with the formalism discussed by Ascuitto and Glendenning [Phys.…
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines…
For the system with inhomogeneous distribution of macroscopic parameters we obtain thermodynamic relation which depends on the spatial point (coordinate). In our approach, to obtain such a relation we use the basic ideas of the method of…
We study a substitute for the matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the ``singular case'' $\alpha\beta=q^N\gamma\delta$, when the standard form of the matrix product ansatz of Derrida, Evans,…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
The asymmetric simple inclusion process (ASIP) --- a lattice-gas model for unidirectional transport with irreversible aggregation --- has been proposed as an inclusion counterpart of the asymmetric simple exclusion process and as a batch…
We study the one dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida, Evans,…
Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of…
Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large random interaction matrix. Under some known conditions, a global equilibrium exists and is unique. In this article, we…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product {\it ansatz}. Due to the similarity of the master equation and the Schr\"odinger equation at imaginary times the…
We introduce a process algebra that concerns the timed behaviour of distributed systems with a known spatial distribution. This process algebra provides a communication mechanism that deals with the fact that a datum sent at one point in…
We employ the Unitary Correlation Operator Method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models.…
In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The…
It is shown that the Schr\"{o}dinger equation for a system of interacting particles whose Compton wavelengths are of the same order of magnitude as the system size is contradictory and is not strictly nonrelativistic, because it is based on…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…