Quasiatomistic Method of Solids

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

The main objective of the present proposal is to develop a new model for multiscale analysis of solids, the quasi-atomistic model, which plays a transitional role between the atomistic and continuum models. In addition, the PIs propose to develop an energy-based procedure to couple fully atomistic descriptions and continuum descriptions in a seamless way, which allows for systematic coarse-graining with controllable error. A second objective is the analysis of the proposed methodology, including consistency, stability and convergence. Inconsistency, known as ghost force in this context, can be systematically removed even in the case of interfaces with corners. Another component of the project is to combine the principles of the multigrid method and multi-resolution analysis for the efficient implementation. This will be done by constructing multilevel grids by multi-resolution analysis and solving nonlinear minimization problems with multigrid methods. Molecular mechanics is a common approach to modeling the behavior of matter, where atoms are treated as the essential degrees of freedom and a potential function is used to describe the interactive effects between atoms. Equilibrium structures can be computed by minimizing the potential energy with respect to the position of the atoms. Other information about the system, such as the vibrational spectrum, thermodynamic properties, equations of state, and reaction rates, can also be computed. Extensive applications of molecular mechanics modeling can be found in materials science, chemistry and biology. The proposed work will mainly focus on solids, with generalizations to soft matter and biological systems, and conduct mathematical, numerical and applicative studies of the proposed methodology.