Dynamics of Dense Discrete Systems: High Order Effects

The quasi-continuous formalism introduced in previous works to treat discrete systems in close to continuous conditions, is extended to include higher order discrete effects. These effects not only provide a more faithful description of the discrete problem, but for some systems are shown to be crucial for a proper description of their dynamics. Concrete examples of such systems are provided. Their dynamics is governed by new equations of motion. Typically; Ut =+ [u + u 2Jx + Ux=xt =0 and the last term models the high order discrete effect.