Shock propagation in the onedimensional lattice
Abstract
Shock propagation in a onedimensional, discrete lattice is studied in some detail both by reviewing existing treatments of the problem and by providing a number of extensions to those treatments. Although some analytic work is presented, most of the study is in the form of a computer simulation. The purpose of the simulation is to solve numerically the classical equations of motion of the atoms of the lattice as they respond to the shock wave. Various forms of interatomic potential are considered and the resulting differences are noted and discussed. The effect of the initial state of the lattice upon the shock profile is studied by considering two sets of initial conditions. In the first, the atoms are at rest in their equilibrium positions prior to compression by the shock wave; in the second, the lattice is initially in thermal equilibrium at approximately room temperature. All anharmonic potentials studied are found to support the propagation of welldefined, stable pulses (solitons) and the physical implications of these rather unusual pulses are examined. Specific future investigations are recommended and their relevance to Armyrelated problems is explained.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 August 1977
 Bibcode:
 1977STIN...7812378P
 Keywords:

 Crystal Lattices;
 Shock Waves;
 Wave Propagation;
 Computerized Simulation;
 NavierStokes Equation;
 Nonequilibrium Flow;
 Numerical Analysis;
 Fluid Mechanics and Heat Transfer