The difficulties with and controversies surrounding the interpretation of electrophysiological data were highlighted in the recent Perspectives on Ion Permeation through membrane-spanning channels. The main issue was whether such data are more appropriately analyzed within the framework of chemical kinetics (Eyring’s Transition State Theory; Eyring, 1935) or the continuum electrodiffusional app...

We present a three-dimensional, time-dependent simulation of a laboratory-scale rod-stabilized premixed turbulent V-flame. The experimental parameters correspond to a turbulent Reynolds number, Re(t) = 40, and to a Damköhler number, D(a) = 6. The simulations are performed using an adaptive time-dependent low-Mach-number model with detailed chemical kinetics and a mixture model for differential ...

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no g...

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original ...

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particu...

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population dynamics and genetics, where it originated. Here we demonstrate that the GFE can also be useful in other fields, specifically in chemistry, with models of two chemical reaction systems for ...

Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here, we numerically study the conditions under whi...

Characterizing the sensitivity to infinitesimally small perturbations in parameters is a powerful tool for the analysis, modeling, and design of chemical reaction networks. Sensitivity analysis of networks modeled using stochastic chemical kinetics, in which a probabilistic description is used to characterize the inherent randomness of the system, is commonly performed using Monte Carlo methods...

The dynamics of one-dimensional laminar premixed combustion in reactive mixtures described by a 1) simple one-species model, 2) simple two-species model, and 3) detailed chemical kinetics model with multicomponent transport in hydrogen–air is investigated. For each model 1) spatially homogeneous results are first obtained, followed by 2) timeindependent, spatially inhomogeneous results, and end...

In this paper, we numerically investigate local properties of dynamical systems close to a Hopf bifurcation instability. We focus on chemical systems and present an approach based on the theory of normal forms for determining numerical estimates of the limit cycle that branches off at the Hopf bifurcation point. For several numerically ill-conditioned examples taken from chemical kinetics, we c...