Related papers: Stochastic Chemical Kinetics with Energy Parameter…
Mathematical problems with mean field and local type interaction related to stochastic chemical kinetics,are considered. Our main concern various definitions of reversibility, their corollaries (Boltzmann type equations, fluctuations,…
We introduce an infinite particle system dynamics, which includes stochastic chemical kinetics models, the classical Kac model and free space movement. We study energy redistribution between two energy types (kinetic and chemical) in…
In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics. We consider deterministic (i.e., a priori averaged) and…
A new tool for modeling electrochemical kinetics is presented. An extension of the Stochastic Simulation Algorithm framework to electrochemical systems is proposed. The physical justifications and constraints for the derivation of a…
The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Since molecular energy transformations are responsible for chemical reaction rates at the most fundamental level, chemical kinetics should provide some information about molecular energies. This is the premise and objective of this note. We…
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…
In this article, we propose a generalized non-equilibrium chemical kinetics model from \textit{ab initio} simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air…
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 recombination reaction model for high-temperature chemical kinetics is derived from ab initio simulations data. A kinetic recombination rate model is derived using a recently developed ab initio state-specific dissociation model and the…
Mathematical models of physical systems are subject to many uncertainties such as measurement errors and uncertain initial and boundary conditions. After accounting for these uncertainties, it is often revealed that discrepancies between…
We propose a general stochastic formalism for describing the evolution of chemical reactions involving a finite number of molecules. This approach is consistent with the statistical analysis based on the Chemical Master Equation, and…
We consider a one-dimensional "gas" of inelastically colliding particles where kinetic energy is dissipated by the excitation of vibrational degrees of freedom. In our model the coefficient of restitution is a stochastic quantity whose…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the…