Asymptotic Analysis of Reacting Materials with Saturated Explosion. II. High-Frequency Waves

Robert F. Almgren, Andrew Majda, Rodolfo R. Rosales

Research output: Contribution to journalArticlepeer-review


The interaction of small-scale material inhomogeneities with high-frequency acoustic waves is known to have a prominent role in accelerating the heat-release rate in liquid and solid explosive materials. In the present paper, simplified asymptotic equations are studied which incorporate the above interaction, and which include reactant depletion at leading order. Because fuel may be completely exhausted, singularities do not always form in the model equations; it is conjectured that when a singularity does form, the material has initiated. The detailed mechanisms by which shock formation and resonant wave interaction can either enhance or retard reaction are explored. In a realistic model for inhomogeneous condensed-phase reaction, with pressure-dependent reaction rate and nonconstant initial fuel concentration, initiation of the material depends on correct placement of the fuel relative to the acoustic waves.

Original languageEnglish (US)
Pages (from-to)315-360
Number of pages46
JournalStudies in Applied Mathematics
Issue number4
StatePublished - May 1 1991

ASJC Scopus subject areas

  • Applied Mathematics


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