相关论文: An Unstructured Mesh Convergent Reaction-Diffusion…
We present a general method to produce well-conditioned continuum reaction-drift-diffusion equations directly from master equations on a discrete, periodic state space. We assume the underlying data to be kinetic Monte Carlo models (i.e.,…
In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD…
The ring polymer molecular dynamics (RPMD) rate theory is an efficient and accurate method for estimating rate coefficients of chemical reactions affected by nuclear quantum effects. The commonly used RPMD treatment of gas-phase bimolecular…
Reaction-diffusion PDEs and particle-based stochastic reaction-diffusion (PBSRD) models are commonly-used approaches for modeling the spatial dynamics of chemical and biological systems. Standard reaction-diffusion PDE models ignore the…
The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We propose a probabilistic derivation of the so-called chemical diffusion master equation (CDME) and describe an infinite dimensional moment generating function method for finding its analytical solution. CDMEs model by means of an infinite…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles…
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and…
Biochemical reactions inside living cells often occur in the presence of crowders -- molecules that do not participate in the reactions but influence the reaction rates through excluded volume effects. However the standard approach to…
We present a fully adaptive multiresolution scheme for spatially two-dimensional, possibly degenerate reaction-diffusion systems, focusing on combustion models and models of pattern formation and chemotaxis in mathematical biology.…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving…
A multi-relaxation-time central-moment discrete Boltzmann method (CDBM) is developed for compressible reactive flows, incorporating the effects of chemical reactions. The Chapman--Enskog multiscale analysis demonstrates that the model…
The motivation of this work is to produce an integrated formulation for material response due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we are interested to capture miscible and…
In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…
Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good…
We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…