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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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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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