Related papers: Reaction-drift-diffusion models from master equati…
The charging of insulating samples degrades the quality and complicates the interpretation of images in scanning electron microscopy and is important in other applications, such as particle detectors. In this paper we analyze this…
Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the response of nonequilibrium steady state…
Kinetic descriptions of runaway electrons (RE) are usually based on Fokker-Planck models that determine the probability distribution function (PDF) of RE in 2-dimensional momentum space. Despite of the simplification involved, the…
We study a minimal model to understand the formation of clusters on surfaces in the presence of surface defects. We consider reaction diffusion model in which atoms undergoes reactions at the defect centers to form clusters. Volume…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the…
This paper deals with a complete bipartite matching problem with the objective of finding an optimal matching that maximizes a certain generic predefined utility function on the set of all matchings. After proving the NP-hardness of the…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the…
This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment…
We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations and entropy type Lyapunov functionals, we study their gradient flows formulations…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…
To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction-diffusion master equations or deterministic, macroscopic reaction-diffusion system. The connection between these two models is not…
Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…
We have developed a Monte Carlo technique for self-consistently calculating the hydrodynamic structure of oblique, steady-state shocks, together with the first-order Fermi acceleration process and associated non-thermal particle…
Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…
A central challenge in materials science is characterizing chemical processes that are elusive to direct measurement, particularly in functional materials operating under realistic conditions. Here, we demonstrate that mechanical strain…
Diffusive acceleration at collisionless shock waves remains one of the most promising acceleration mechanisms for the description of the origin of cosmic rays at all energies. A crucial ingredient to be taken into account is the reaction of…
The "standard" Brownian motion master equation, used to describe thermal damping, is not completely positive, and does not admit a Monte Carlo method, important in numerical simulations. To eliminate both these problems one must add a term…