| Issue |
ESAIM: M2AN
Volume 52, Number 4, July-August 2018
|
|
|---|---|---|
| Page(s) | 1315 - 1352 | |
| DOI | https://doi.org/10.1051/m2an/2017052 | |
| Published online | 28 September 2018 | |
On assessing the accuracy of defect free energy computations
1
Department of Mathematics and Statistics, UMass Amherst, 710 N Pleasant Street, Amherst, MA 01003, USA
2
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
* Corresponding author: m.h.duong@warwick.ac.uk
Received:
3
April
2016
Accepted:
28
September
2017
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.
Mathematics Subject Classification: 65G99 / 74E15 / 74S60
Key words: Defect formation free energy / finite temperature / material defects / Cauchy–Born rule
© EDP Sciences, SMAI 2018
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