Related papers: Two-scale large deviations for chemical reaction k…
Techniques for coherent multidimensional optical spectroscopy have been developed and utilised to understand many different processes, including energy transfer in photosynthesis and many-body effects in semiconductor nanostructures.…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
We consider a diffusion equation in $\mathbb{R}^d$ with drift equal to the gradient of a homogeneous potential of degree $1+\gamma$, with $0<\gamma<1$, and local variance equal to $\varepsilon^2$ with $\varepsilon\to 0$. The associated…
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
We study random velocity effects on a two-species reaction-diffusion system consisting of three reaction processes $A + A \rightarrow (\varnothing, A),A+B \rightarrow A$. Using the field-theoretic perturbative renormalization group we…
The Adaptive Multilevel Splitting (AMS) algorithm is a powerful and versatile method for the simulation of rare events. It is based on an interacting (via a mutation-selection procedure) system of replicas, and depends on two integer…
Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle…
Physical kinetic roughening processes are well known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available…
A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…
We investigate the multi-chain version of the Chemical Master Equation, when there are transitions between different states inside the long chains, as well as transitions between (a few) different chains. In the discrete version, such a…
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the inclusion of spatial coordinates in their analysis. Stochastic…
A standard model for the study of scalar dispersion through advection and molecular diffusion is a two-dimensional periodic flow with closed streamlines inside periodic cells. Over long time scales, the dispersion of a scalar in this flow…
We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic…
We establish large deviation principles for the couple of the maximum likelihood estimators of dimensional and drift coefficients in the generalised squared radial Ornstein-Uhlenbeck process. We focus our attention to the most tractable…
We study a stochastic system of $N$ interacting particles which models bimolecular chemical reaction-diffusion. In this model, each particle $i$ carries two attributes: the spatial location $X_t^i\in \mathbb{T}^d$, and the type $\Xi_t^i\in…