Related papers: Zubarev nonequilibrium statistical operator method…
In this work, we present an extensive computational study on the Ziff-Gulari-Barshad (ZGB) model extended in order to include the spatial diffusion of oxygen atoms and carbon monoxide molecules, both adsorbed on the surface. In our…
In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used…
In this paper, we propose and analyze a positivity-preserving, energy stable numerical scheme for certain type reaction-diffusion systems involving the Law of Mass Action with the detailed balance condition. The numerical scheme is…
In this article, we first review the connection between L\'evy processes and infinitely divisible random variables, and the classification of infinitely divisible distributions. Using this connection and the L\'evy-Khinchine representation…
In this paper we study pseudo-processes related to odd-order heat-type equations composed with L\'evy stable subordinators. The aim of the article is twofold. We first show that the pseudo-density of the subordinated pseudo-process can be…
In the present follow-up article of a previous one [1] we illustrate the use of the Unconventional Statistical Mechanics described and discussed in the latter. This is done via the analysis, resorting to Renyi approach, of experimental…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of corre- lation functions are closed, are considered. A transfer matrix method is used to find the…
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
Diffusion models have recently demonstrated notable success in solving inverse problems. However, current diffusion model-based solutions typically require a large number of function evaluations (NFEs) to generate high-quality images…
We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex…
This article presents a mathematical study of the problem of identifying a time-dependent source term in transport processes described by a timefractional parabolic equation, based on noisy time-dependent measurements taken at an arbitrary…
The LASSO is a widely used statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. We introduce and study the adaptive…
The question of existence and properties of stationary solutions to Langevin equations driven by noise processes with stationary increments is discussed, with particular focus on noise processes of pseudo-moving-average type. On account of…
A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type…
Diffusion models are typically trained using score matching, a learning objective agnostic to the underlying noising process that guides the model. This paper argues that Markov noising processes enjoy an advantage over alternatives, as the…
Nonequilibrium Green's functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and…