Computer Experiments on Solitons in Three-Dimensional Crystals with Nearest-Neighbor and Next-Nearest-Neighbor Atomic Interactions

Abstract

Molecular dynamics simulation was performed for three-dimensional (3D) cubic mass-spring model crystals. Anharmonic potential up to the fourth order was taken into account, and central forces between the nearest neighbor (nn) and the next nearest neighbor (nnn) atoms were considered. The ratio of the potential between the nnn atoms to the potential between the nn atoms was varied. An input pulse displacement was given to central atomic planes in the crystal or to the end atomic plane of the crystal, and induced displacements and velocities of all atoms were computed. As the nnn interaction was enhanced, the soliton velocity increased and the soliton energy decreased. The results were compared with those of 1D and 2D crystals obtained previously. The increase of soliton velocity due to the enhanced nnn interaction was largest for 1D crystals, and the decrease of soliton energy was smallest for 2D crystals. Discussions and remarks were presented for these results.

Lattice Model with Nearest-Neighbor and Next-Nearest-Neighbor Interactions for Gradient Elasticity

“…For example, equations for an electromagnetic line with the second-order couplings can be used to describe the bound solitons with oscillating tails in this line [45]. The approach suggested in this paper can be generalized in order to consider continuum models that correspond to discrete model of a dynamical lattice with the on-site nonlinearity and both nearest-neighbor and next-nearest-neighbor interactions between lattice sites [46,47,48]. We also assume that the unbounded lattice models suggested in this paper can be extended to describe bounded lattices and correspondent continuum models analogous to electromagnetic line described in [45].…”