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Geometry equilibration of crystalline defects in quantum and atomistic descriptions

Huajie Chen

School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

E-mail Address: chen.huajie@bnu.edu.cn

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Faizan Q. Nazar

CNRS and CEREMADE, University of Paris-Dauphine, Paris 75775, France

E-mail Address: nazar@ceremade.dauphine.fr

Corresponding author

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, and

Christoph Ortner

Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK

E-mail Address: christoph.ortner@warwick.ac.uk

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https://doi.org/10.1142/S0218202519500131Cited by:15 (Source: Crossref)

Abstract

We develop a rigorous framework for modeling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problem on a discrete energy space and establish qualitatively sharp far-field decay estimates for the equilibrium configuration. This work extends [V. Ehrlacher, C. Ortner and A. Shapeev, Analysis of boundary conditions for crystal defect atomistic simulations, Arch. Ration. Mech. Anal.222 (2016) 1217–1268] by admitting infinite-range interaction which in particular includes some quantum chemistry based interatomic interactions.

Communicated by I. Fonseca

Keywords:

AMSC: 65L20, 65L70, 70C20, 74G40, 74G65

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