Convergence from Atomistic Model to Peierls-Nabarro Model for Dislocations in Bilayer System with Complex Lattice

2021/03/17 by Yahong Yang, T. Luo, Yang, Yahong +3 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #35Q70 #35Q74 #74A50 #74G10 #Analysis of PDEs (math.AP) #Block Copolymer Self-Assembly #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2103.09412

openalex publication_date 2021/03/17 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the convergence from the atomistic model to the Peierls--Nabarro (PN) model of two-dimensional bilayer system with complex lattice. We show that the displacement field of the dislocation solution of the PN model converges to the dislocation solution of the atomistic model with second-order accuracy. The consistency of PN model and the stability of atomistic model are essential in our proof. The main idea of our approach is to use several low-degree polynomials to approximate the energy due to atomistic interactions of different groups of atoms of the complex lattice.

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