Microscopic simulations of supersonic and subsonic exothermic chemical wave fronts and transition to detonation

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

Front propagation in a bistable system: how the energy is released

In this Rapid Communication we consider a front of transition between metastable and stable states in a conservative system. Due to the difference of energies between initial and finite states, such transition front can propagate only while radiating energy. A simulation of such a process in a one-dimensional nonlinear lattice shows an essential imbalance between the energy released in each act of transition, and the density of energy of oscillations behind the front. It means that the stationary front propagation must be accompanied by an essentially nonstationary radiative process. We reveal the origin of this phenomenon and show that the characteristics of the front propagation critically depend on boundary conditions. In the framework of a simple model of a bistable system we propose analytic evaluation of all important features of the transition process, such as front velocity, radiation frequency, and oscillation amplitude. All calculated values are in good agreement with numerical simulation data.

Temperature-driven coherence resonance and stochastic resonance in a thermochemical system

We perform the stochastic analysis of a thermochemical system using a master equation which describes a chemical reaction and includes discrete and continuous temperature jumps. We study the time evolution of the system selecting the temperature of the thermostat as an easily tunable control parameter. Depending on the thermostat temperature, the system can be in an excitable, oscillatory, or stationary regime. Stochastic time series for the system temperature are generated and the distributions of interspike intervals are analyzed in the three dynamical regimes separated by a homoclinic bifurcation and a Hopf bifurcation. Different constructive roles of internal fluctuations are exhibited. A noise-induced transition is observed in the vicinity of the Hopf bifurcation. Coherence resonance and stochastic resonance are found in the oscillatory regime. In a range of thermostat temperatures, a nontrivial behavior of the highly nonlinear system is revealed by the existence of both a minimum and a maximum in the scaled standard deviation of interspike intervals as a function of particle number. This high sensitivity to system size illustrates that controlling dynamics in nanoreactors may remain a difficult task.