Atomistic formulation of a multiscale field theory for nano/micro solids

Abstract

This paper aims to formulate a field theory for the solution of classical N-body problem. In this paper, multi-length and time scale material behaviour is addressed from the viewpoint of lattice dynamics. A multiscale field theory that can work as an alternative to molecular dynamics simulation in studying statistical and finite temperature properties of materials is proposed. Atomistic definitions and the corresponding field representations of fundamental physical quantities are obtained. Time evolutions of conserved physical quantities are derived in terms of atomic variables and are expressed in terms of field quantities. The mathematical representation of conservation laws for a multiscale field theory is formulated.

Acknowledgement

The support to this work by National Science Foundation under Awards Numbers CMS-0301539 and CMS-0428419 is gratefully acknowledged.