Thermal explosion near bifurcation: stochastic features of ignition

We study stochastic effects in a thermochemical explosive system exchanging heat with a thermostat. We use a mesoscopic description based on the master equation for temperature which includes a transition rate for the Newtonian thermal transfer process. This master equation for a continuous variable has a complicated integro-differential form and to solve it we resort to Monte Carlo simulations. The results of the master equation approach are compared with those of direct simulations of the microscopic particle dynamics in a dilute gas system. We study the Semenov model in the vicinity of the bifurcation related to the emergence of bistability. The probability distributions of ignition time are calculated below and above the bifurcation point. An approximate analytical prediction for the main statistical properties of ignition time is deduced from the Fokker–Planck equation derived from the master equation. The theoretical results are compared with the experimental data obtained for cool flames of a hydrocarbon in the explosive regime.