Regularity and Locality of Point Defects in Multilattices

TL;DR

This paper develops a mathematical model for point defects in multilattice crystals, providing decay estimates of elastic fields that are crucial for improving numerical simulations and coarse-grained models.

Contribution

It introduces a new formulation for point defects in multilattices and quantifies the decay of elastic fields under stability assumptions, aiding computational methods.

Findings

Decay estimates of elastic fields around defects

Quantification of approximation errors in models

Guidance for numerical method development

Abstract

We formulate a model for a point defect embedded in a homogeneous multilattice crystal with an empirical interatomic potential interaction. Under a natural, phonon stability assumption we quantify the decay of the long-range elastic fields with increasing distance from the defect. These decay estimates are an essential ingredient in quantifying approximation errors in coarse-grained models and in the construction of optimal numerical methods for approximating crystalline defects.