相关论文: An integration scheme for reaction-diffusion model…

We present the analysis of the phase space geometry of 2 $\rightarrow$ 3 reaction for the general case of nonzero and unequal particle masses. Its purpose is to elaborate an alternative approach to the problem of integration over phase…

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

We study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear filtering of jump-diffusion processes. We show…

Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…

A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic…

We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…

A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the…

We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…

We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This…

We introduce a novel particle-based algorithm for end-to-end training of latent diffusion models. We reformulate the training task as minimizing a free energy functional and obtain a gradient flow that does so. By approximating the latter…

We construct, analyse and assess various schemes of second order of accuracy in space and time for model advection-diffusion-reaction differential equations. The constructed schemes are meant to be of practical use in solving industrial…

We study an autocatalytic reaction-diffusion scheme, the Gray-Scott model, when the mixing processes do not homogenize the reactants. Starting from the master equation, we derive the resulting coupled, nonlinear, stochastic partial…

The aim of this work is to propose a provably convergent finite volume scheme for the so-called Stefan-Maxwell model, which describes the evolution of the composition of a multi-component mixture and reads as a cross-diffusion system. The…

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…

A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…

Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…

In recent years, several fast solvers for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by penetrable inhomogeneous obstacles, have been proposed. While…

A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and…

In the bistable regime of the FitzHugh-Nagumo model of reaction-diffusion systems, spatially homogeneous patterns may be nonlinearly unstable to the formation of compact ``localized states." The formation of space-filling patterns from…

The convergence to equilibrium of renormalized solutions to reaction-cross-diffusion systems in a bounded domain under no-flux boundary conditions is studied. The reactions model complex balanced chemical reaction networks coming from…