Related papers: Computing macroscopic reaction rates in reaction-d…
The interplay between stochastic chemical reactions and diffusion can generate rich spatiotemporal patterns. While the timescale for individual reaction or diffusion events may be very fast, the timescales for organization can be much…
We provide an overview of Monte Carlo algorithms based on Markovian stochastic dynamics of interacting and reacting many-particle systems not in thermal equilibrium. These agent-based simulations are an effective way of introducing students…
Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for…
Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Stochastic modeling of reaction networks is a framework used to describe the time evolution of many natural and artificial systems, including, biochemical reactive systems at the molecular level, viral kinetics, the spread of epidemic…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
The past decade has seen a revived interest in the unavoidable or intrinsic noise in biochemical and genetic networks arising from the finite copy number of the participating species. That is, rather than modeling regulatory networks in…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
We show that reaction-diffusion processes in three dimensions can be efficiently handled by event-driven numerical simulations, based on statistical waiting times (Gillespie's Monte-Carlo method). The algorithm is efficient for dilute…
Rate-equation models are a widely-used and inexpensive tool for the simulation of interstellar chemistry under a range of physical conditions. However, their application to grain-surface chemical systems necessitates a number of simplifying…
Recently, hybrid models have emerged that combine microscopic and mesoscopic regimes in a single stochastic reaction-diffusion simulation. Microscopic simulations track every individual molecule and are generally more accurate. Mesoscopic…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
We present a method which extends Monte Carlo studies to situations that require a large dynamic range in particle number. The underlying idea is that, in order to calculate the collisional evolution of a system, some particle interactions…
Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
Rigorous statistical methods for estimating thermonuclear reaction rates and nucleosynthesis are becoming increasingly established in nuclear astrophysics. The main challenge being faced is that experimental reaction rates are highly…