Related papers: Stochastic Analysis of Dimerization Systems
We investigate analytically and numerically a system of clusters evolving via collisions with clusters of minimal mass (monomers). Each collision either leads to the addition of the monomer to the cluster or the chipping of a monomer from…
We introduce a simple zero-range process with constant rates and one fast rate for a particular occupation number, which diverges with the system size. Surprisingly, this minor modification induces a condensation transition in the…
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…
The phase separation of a simple binary mixture of incompatible linear polymers in solution is investigated using an extension of the sedimentation equilibrium method, whereby the osmotic pressure of the mixture is extracted from the…
In the past one hundred years, deterministic rate equations have been successfully used to infer enzyme-catalysed reaction mechanisms and to estimate rate constants from reaction kinetics experiments conducted in vitro. In recent years,…
The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is…
A numerical method is presented to obtain approximate solutions to problems arising from sedimentation models. These processes are widely utilized in minery for recovering water from suspensions coming out of flotation processes. The main…
Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of…
We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modelling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit,…
The effects of a stochastic reset, to its initial configuration, is studied in the exactly solvable one-dimensional coagulation-diffusion process. A finite resetting rate leads to a modified non-equilibrium stationary state. If in addition…
By combining the nonconserved spin-flip dynamics driving ferromagnetic ordering with the conserved Kawasaki-exchange dynamics driving phase segregation, we perform Monte Carlo simulations of the nearest neighbor Ising model. Such a set up…
The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…
In this paper, we propose a data-driven method to discover multiscale chemical reactions governed by the law of mass action. First, we use a single matrix to represent the stoichiometric coefficients for both the reactants and products in a…
The stochastic limit approximation method for ``rapid'' decay is presented, where the damping rate \gamma is comparable to the system frequency \Omega, i.e., \gamma \sim \Omega, whereas the usual stochastic limit approximation is applied…
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…
Model distillation has been a popular method for producing interpretable machine learning. It uses an interpretable "student" model to mimic the predictions made by the black box "teacher" model. However, when the student model is sensitive…
Molecular process of polymer collapse was reproduced by isothermal molecular dynamics simulation. The initial polymer chains were obtained by mean of random walks in continuum space. Two potential models were considered to represent short…
In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of…
We introduce a model with diffusive and evaporation/condensation processes, depending on 3 parameters obeying some inequalities. The model can be solved in the sense that all correlation functions can be computed exactly without the use of…
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically-reacting species is built on the stochastic trajectories of reaction events obtained from the Chemical Master Equation. However, when the molecular populations…