Experiments indicate that small-scale inhomogeneities have a prominent role in accelerating the global heat-release rate in a variety of condensed-phase liquid and solid materials. In this paper, simplified asymptotic, equations are studied that incorporate small-scale inhomogeneities, their interaction with each other, and the interaction of the microstructure with the global reaction scale. A variety of chemical-acoustic resonant mechanisms with the microstructure are developed and documented for both temperature-sensitive and pressure-sensitive reaction rates. It is demonstrated that these specific resonant mechanisms lead to dramatic shortening of the local induction time for regimes of equations of state and chemical reactions appropriate for condensed phases. These mechanisms are completely different than the conventional mechanism of simple thermal explosion of hot spots.
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