Two Shock Wave Physics Problems: The Macro-Micro Coupling Term and Shock Amplification in Piezoelectric Media.

Problem 1 The transfer of momentum from internal microscopic to center of mass macroscopic coordinates is considered for a system of nonuniform mass density and typical internal coordinates. First order averaging over the mass density is shown to lead to an internal variable contribution to the center of mass velocity proportional to time to the fourth power in the t goes to 0 limit and proportional to the square of the nonuniformity i.e., the mass density disturbance amplitude. Problem 2 The gain is calculated for a boundary value problem with a strain function of the modulated exponential form in an active piezoelectric semiconductor. The boundary, via the electric field gradient, is seen to make a contribution to the gain and the allowed frequencies for the linearized problem in a way which does not appear in the acoustoelectric ultrasonic amplification problem. A formulism is set up which allows for the rapid calculation of gain even for the highly nonlinear problem.