Shock wave profile in a crystalline solid

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Abstract
The results of Paskin, Gohar and Dienes (1977) obtained from their molecular dynamical simulation of shock wave propagation in a solid are analysed. Their kinetic 'temperature' profiles T1 and T3 behind the shock front are found to be in error, because these are defined with respect to a reference frame that experiences acceleration, instead of one that moves at a uniform velocity with the compressed lattice as a whole. The basic difficulty with their definition is that with respect to non-Galilean transformation the Newtonian equations of motion are not invariant and the kinetic energy is not conserved. The error incurred is precisely equal to the kinetic energy associated with the oscillatory motion of the atomic planes relative to the compressed lattice. This error is very large in the region immediately behind the shock front, and it is not zero even in the tail region of the shock profile, where the interplaner oscillations are expected to disappear.

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