Related papers: Statistical product distributions for ultracold re…
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…
This paper studies the dynamics of scalar particle production, focusing on the presence of multiple fields and couplings in the medium. The interplay of various fields and couplings can influence the production rate, potentially…
The yield of a chemical reaction quantifies the percentage of the target product formed in relation to the reactants consumed during the chemical reaction. Accurate yield prediction can guide chemists toward selecting high-yield reactions…
It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently…
Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform…
Gibbs and Boltzmann definitions of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite sized `small' system exchanging energy with a bath is usually understood as a…
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…
Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction…
Machine learning-based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based…
Dynamic properties of chemical reactions and appropriate relationships for open chemical equilibrium are discussed in approach of the chemical dynamics. New way to calculate composition of chemical systems in open equilibrium, based on the…
Nuclear reaction rates are one of the most important ingredients in describing how stars evolve. The study of the nuclear reactions involved in different astrophysical sites is thus mandatory to address most questions in nuclear…
We describe and contrast two distinct problem areas for statistical causality: studying the likely effects of an intervention ("effects of causes"), and studying whether there is a causal link between the observed exposure and outcome in an…
We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
We examine theoretically a new idea for spatial and temporal control of chemical reactions. When chemical reactions take place in a mixture of solvents, an external electric field can alter the local mixture composition thereby accelerating…
Singular limit problems of reaction-diffusion systems have been studied in cases where the effects of the reaction terms are very large compared with those of the other terms. Such problems appear in literature in various fields such as…
We study reaction diffusion equations with a deterministic reaction term as well as two random reaction terms, one that acts on the interior of the domain, and another that acts only on the boundary of the domain. We are interested in the…
The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
An ion in a radiofrequency ion trap interacting with a buffer gas of ultracold neutral atoms is a driven dynamical system which has been found to develop a non-thermal energy distribution with a power law tail. The exact analytical form of…