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On assessing the accuracy of defect free energy computations

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Dobson, Matthew, Duong, Manh Hong and Ortner, Christoph (2018) On assessing the accuracy of defect free energy computations. ESAIM: Mathematical Modelling and Numerical Analysis, 52 (4). pp. 1315-1352. doi:10.1051/m2an/2017052

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Official URL: https://doi.org/10.1051/m2an/2017052

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Abstract

We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the same rate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Harmonic analysis -- Simulation methods, Thermodynamics
Journal or Publication Title: ESAIM: Mathematical Modelling and Numerical Analysis
Publisher: EDP Sciences
ISSN: 0764-583X
Official Date: July 2018
Dates:
DateEvent
July 2018Published
28 September 2017Available
28 September 2017Accepted
Date of first compliant deposit: 2 October 2017
Volume: 52
Number: 4
Page Range: pp. 1315-1352
DOI: 10.1051/m2an/2017052
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: The material cannot be used for any other purpose without further permission of the publisher, and is for private use only.
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
335120European Research Councilhttp://viaf.org/viaf/130022607
W911NF1520122Defense Advanced Research Projects Agencyhttp://dx.doi.org/10.13039/100000185
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