Harnack inequalities and discrete-continuous error estimates for a chain of atoms with two-body interactions
type: Item
instance of: scholarly article
title: Harnack inequalities and discrete-continuous error estimates for a chain of atoms with two-body interactions
zbMATH Open document ID: 1174.82007
author: Jean Dolbeault
author: Régis Monneau
author: Rafael D. Benguria
published in: Journal of Statistical Physics
publication date: 2009-04-22T00:00:00Z
review text: From the authors' abstract: We consider deformations in \(\mathbb R^3\) of an infinite linear chain of atoms where each atom interacts with all others through a two-body potential. We compute the effect of an external force applied to the chain. At equilibrium, the positions of the particles satisfy an Euler-Lagrange equation. For large classes of potentials, we prove that every solution is well approximated by the solution of a continuous model when applied forces and displacements of the atoms are small. We establish an error estimate between the discrete and the continuous solution based on a Harnack lemma of independent interest. Finally we apply our results to some Lennard-Jones potentials.
reviewed by: Achim Klenke
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 81V70
Mathematics Subject Classification ID: 74H25
zbMATH DE Number: 5545961
zbMATH Keywords: two-body interactions
zbMATH Keywords: nonlinear elasticity
zbMATH Keywords: discrete-continuous
zbMATH Keywords: error estimates
zbMATH Keywords: Cauchy-Born rule
zbMATH Keywords: Harnack inequality
zbMATH Keywords: thermodynamic limit
Wikidata QID: Q59158106
MaRDI profile type: Publication
full work available at URL: s10955-008-9662-4
OpenAlex ID: W2036533098
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DOI: 10.1007/S10955-008-9662-4
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description: scientific article; zbMATH DE number 5545961