# Mathematical Modelling of Possible Mechanisms for The Formation of Hot Spots

F.G. Magazov, E.S. ShestakovskayaThis paper is devoted to the study of the consequences of an initiating shock propagating through a condensed substance on a free surface. To close the laws of conservation of mass, momentum and internal energy, the equation of state of a condensed substance was constructed. The form of this equation of state corresponded to the form of the equation of state of Mie-Gruneisen with the separation of pressure and internal energy into thermal and cold parts. The ratio of the thermal part of the pressure to the thermal part of the internal energy is determine by the Gruneisen coefficient, which in this work is a constant. The cold part of the pressure was described by potential in Theta form. The analysis of the results presented in the work shows that after the shock reaches the free surface, a strong rarefaction wave begins to propagate into the condensed matter, which causes the pressure to drop in the condensed matter and the stress greatly increases, which can lead to a discontinuity of the material and appearance of a separate microparticle. This confirmed the assumption that hot spots could appear as a result of the warming up and burning of the smallest droplets of condensed explosive during the collapse of a gas bubble.Full text

- Keywords
- mathematical model; equation of state; continuity; hot spot; shock.
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