Quasicontinuum modelling of short-wave instabilities in crystal lattices

Abstract

We propose a hybrid quasicontinuum model which captures both long and short-wave instabilities of crystal lattices and combines the advantages of weakly non-local (higher gradient) and strongly non-local (integral) continuum models. To illustrate the idea, we study the simplest one-dimensional lattice exhibiting commensurate and incommensurate short-wave instabilities. We explicitly compute stability limits of the homogeneous states using both discrete and quasicontinuum models. The new quasicontinuum approximation is shown to be capable of reproducing a detailed structure of the discrete stability diagram.

Acknowledgements

This work was supported by the NSF grants DMS-0102841 (L.T.) and DMS-0137634 (A.V.).