Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model

J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.

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Abstract
In the computation of the material properties of random alloys, the method of 'special quasirandom structures' attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach is based on a recent analysis of a related variance reduction method in stochastic homogenization of linear elliptic PDEs and the locality properties of the TFW model. Concerning the latter, we extend an exponential locality result by Nazar and Ortner to include point charges, a result that may be of independent interest.
Publishing Year
Date Published
2020-11-01
Journal Title
Nonlinearity
Volume
33
Issue
11
Page
5733-5772
ISSN
eISSN
IST-REx-ID

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Fischer JL, Kniely M. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772. doi:10.1088/1361-6544/ab9728
Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity, 33(11), 5733–5772. https://doi.org/10.1088/1361-6544/ab9728
Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity 33, no. 11 (2020): 5733–72. https://doi.org/10.1088/1361-6544/ab9728.
J. L. Fischer and M. Kniely, “Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity, vol. 33, no. 11, pp. 5733–5772, 2020.
Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772.
Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity, vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728.
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