Homogeneous ignition for a three-step chain-branching reaction model

Homogeneous ignition for a three-step chain-branching reaction model

Spatially homogeneous thermal explosions governed by a three-step chain-branching kinetic model are described in the asymptotic limit of large activation energy for a range of chain-branching cross-over temperatures. The model consists of a sequence of chain-initiation, chain-branching and chain-termination steps. Temperaturesensitive Arrhenius kinetics is employed for the initiation and branch...

Linear Stability of a Detonation Wave with a Model Three-Step Chain-Branching Reaction

The linear stability of a planar detonation wave with a three-step chain-branching reaction is studied by a normal mode approsch. The reaction model consists of a chain-initiation step and a chain-branching step governed by Arrhenius kinetics, with a chain-termination step which is independent of temperature. It mimics the essential reaction dynamics of a real chain-branching chemical system. T...

The Polymerase Chain Reaction and Branching Processes

We construct a mathematical model for the polymerase chain reaction and its mutations using the theory of branching processes. Under this model we study the number of mutations in a randomly chosen sequence after n PCR cycles. A method for estimating the mutation is proposed and the variance of this estimator is studied. We also study the distribution of the Hamming distance between two randoml...

Ignition Process in a Non-Homogeneous Mixture

Pulsating Instabilities of Combustion Waves in a Chain-Branching Reaction Model

In this paper we investigate the properties and linear stability of travelling premixed combustion waves and the formation of pulsating combustion waves in a model with two-step chain-branching reaction mechanism. These calculations are undertaken in the adiabatic limit, in one spatial dimension and for the case of arbitrary Lewis numbers for fuel and radicals. It is shown that the Lewis number...