Computer simulation study on propagation of nonlinear waves through heavily defective crystals

Abstract

A molecular dynamics computer simulation has been performed for a monatomic, anharmonic, and twodimensional hexagonal crystal. Central forces between the nearest neighbor atoms and anharmonic forces up to the third order are considered. Pulse displacements are applied to the line of atoms at the left end of a rectangular model crystal, in the right half of which a number of light or heavy mass defects are randomly placed. Phonons or solitons propagating in the crystal and scattered by the defects are observed.

Computer Experiments on Collisions of Linear and Nonlinear Waves with Defects in Two-Dimensional Square Lattice with Nearest Neighbor and Next Nearest Neighbor Interactions

“…The method of numerical calculation is the fourth-order Runge-Kutta method. The details of the calculation are the same as those of the previous works, [1][2][3][4][5][6][7] where MD units are used, i.e., the atomic mass m ¼ 1, the lattice spacing L ¼ 1000, the time T ¼ 1, and force constant C ð1Þ ¼ 1. In the present computation, the second-and third-order force constants are chosen as C ð2Þ ¼ À0:1 and C ð3Þ ¼ 0:01 in the MD units.…”

“…In the present paper, we call the former waves ''phonon'' and the latter waves ''soliton''. In most previous computer experiments, [1][2][3][4][5][6][7] only the nearest neighbor (NN) interatomic interactions were considered. In the present study, the next nearest neighbor (NNN) interactions are also taken into account in addition to the NN interactions because the NNN interactions seem to be essential for the 2D behavior of waves in the square lattice system.…”