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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 ISSN 0764-583X.
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WRAP-on-assessing-accuracy-defect-free-energy-computations-Ortner-2017.pdf - Accepted Version - Requires a PDF viewer. Download (808Kb) | Preview |
Official URL: https://doi.org/10.1051/m2an/2017052
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 | |||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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Volume: | 52 | |||||||||
Number: | 4 | |||||||||
Page Range: | pp. 1315-1352 | |||||||||
DOI: | 10.1051/m2an/2017052 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Reuse Statement (publisher, data, author rights): | 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 | |||||||||
Date of first compliant deposit: | 2 October 2017 | |||||||||
Date of first compliant Open Access: | 9 November 2018 | |||||||||
RIOXX Funder/Project Grant: |
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