Dynamic Picture of Shock Excitation

With slow up-pumping only a time-dependent thermodynamic temperature T(t) is needed to describe the state. In a nonequilibrium system where phonons and vibrations are pumped at different rates, a much larger number of parameters are needed to specify the state. Dlott and Fayer simplified 

If all the energy Ej - Eo is initially input to the phonons only, then the initial phonon quasitemperature (0) = Ej - Eo)IC, ph will be much greater than the final temperature T/, because the phonon heat capacity Qp/, in Eq. (9) is much smaller than the total heat capacity of phonons plus vibrations, C T) [50]. For instance with a shock that heats naphthalene by 400K, the initial phonon quasitemperature dph(0) is nearly 2400K [51]. 

The up-pumping model says that instead of the molecule s vibrations becoming activated right at the shock front, there is a brief delay before vibrational activation occurs. This might be a trivial and unimportant feature of shock excitation—just an irrelevant brief delay-unless the nonequilibrium conditions that persist during this brief time play a significant role in shock initiation. Several possible ways that up-pumping can affect explosive sensitivity are discussed in the next section. 

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