Related papers: Chemical kinetics and stochastic differential equa…
The study of chemical reactions in environments under nonequilibrium conditions has been of interest recently in a variety of contexts, including current-induced reactions in molecular junctions and scanning tunneling microscopy…
Drastic change in dynamics and statistics in a chemical reaction system, induced by smallness in the molecule number, is reported. Through stochastic simulations for random catalytic reaction networks, transition to a novel state is…
The theory of chemical kinetics form the basis to describe the dynamics of chemical systems. Owing to physical and thermodynamic constraints, chemical reaction systems possess various structures, which can be utilized to characterize…
Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie…
These are lecture notes of a course that I gave to people doing research for their Ph.D. thesis in theoretical chemistry or spectroscopy. The course was given on December 9-13, 2002, in Han-sur-Lesse, Belgium. The lecture notes start with…
This manuscript contains nothing new, but synthesizes known results: For the theoretical population geneticist with a probabilistic background, we provide a summary of some key results on stochastic differential equations. For the…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
We consider a biochemical model that consists of a system of partial differential equations based on reaction terms and subject to non--homogeneous Dirichlet boundary conditions. The model is discretised using the gradient discretisation…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
In this paper, we propose a novel sequential data-driven method for dealing with equilibrium based chemical simulations, which can be seen as a specific machine learning approach called active learning. The underlying idea of our approach…
For the investigation of chemical reaction networks, the identification of all relevant intermediates and elementary reactions is mandatory. Many algorithmic approaches exist that perform explorations efficiently and automatedly. These…
Classical chemical kinetics use rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, or in other…
In a stochastic reaction network setting we consider the problem of tracking the fate of individual molecules. We show that using the classical large volume limit results, we may approximate the dynamics of a single tracked molecule in a…
The canonical-ensemble description of reactive quantum gas mixtures is reformulated by incorporating a single global particle-number-conservation constraint over the combined spectra of inter-converting species. This constraint replaces the…
Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations.…
The reinterpretation of quantum mechanical formalism in terms of a classical model with a continuous material "$\Psi$-field" acting upon a point-like particle which is subjected to large friction and random forces is proposed. This model…
We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can…
We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis-Menten mechanism, which exemplifies an…
Starting from a microscopic approach, we develop a covariant formalism to describe a set of interacting gases. For that purpose, we model the collision term entering the Boltzmann equation for a class of interactions and then integrate this…
Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…