Global spectrum model of discrete dislocation equation

The fully discrete dislocation equation can be rationally derived from the spectrum model. In this paper, the previous spectrum model is reinterpreted to cover the global feature of the spectrum. Instead of the local behavior around the origin of the Brilouin zone, the global spectrum model focuses the maximum at the boundary of the Brillouin as well as the slope at the origin of the Brilouin zone. The strength of the point-contact interaction that effectively describes the discreteness effect becomes larger because the whole lattice effect is included in the global spectrum model. The validness and signification of the new model are illustrated by a solvable lattice dynamical model of the cubic lattice.