STOCHASTIC-MODEL FOR A WAVE-LIKE EXOTHERMAL REACTION IN CONDENSED HETEROGENEOUS SYSTEMS

The relationship between the stochastic and deterministic approaches t o the description of the dynamic behavior for a nonlinear reacting sys tem is studied. A self-propagating exothermal reaction in a heterogene ous medium has been chosen as an example. A stochastic model for this phenomenon is developed. The system is composed of cells characterized by temperature and degree of conversion, their transformation probabi lity being dependent on temperature. Computer simulation showed that s tochasticity reveals itself in the generation of disturbances that are absent in the deterministic model. For a well-developed steady-state regime, the distributions of the mean temperature and degree of conver sion are close to those given by the deterministic model. Under the co nditions of planar-wave-front instability, the stochastic model posses ses a mechanism for spontaneous transfer to a stable regime from arbit rary initial conditions (temperature distribution, etc.) due to origin ation, propagation, and disintegration of disturbances. Such behavior agrees with experimental data and is not predicted by the deterministi c model.