Shock profiles caused by different end conditions in one-dimensional quiescent lattices

Abstract

Shock propagation in a one-dimensional discrete lattice is generated by accelerating the end-most particle from zero to its final velocity in a finite rise time after which the end particle is maintained at that velocity. The wave profiles for various rise times are compared to the zero-time case in a quiescent lattice. For the anharmonic lattice the classical equations of motion of the atoms are solved numerically on the computer. A Morse-type potential is assumed. For a finite rise time the amplitude of the wave passing through the surface atoms is diminished when compared with he zero-time case. For the anharmonic lattice the head of the wave develops into a solitary wave train with an oscillatory tail, and for certain rise times and anharmonicity parameters an apparent envelope soliton forms behind the shock front. This envelope soliton travels much slower than the shock wave.