Regularity and Locality of Point Defects in Multilattices

2016/08/31 by Olson, Derek, Ortner, Christoph
#35Q74 #74E15 #74G40 #74G65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.08930

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.

Related

• Theoretical Study of Elastic Far-Field Decay from Dislocations in Multilattices
• Stacking faults in the limit of a discrete model for partial edge dislocations
• Sharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect
• Geometry Equilibration of Crystalline Defects in Quantum and Atomistic Descriptions
• Ballistic properties of crystalline defects