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

article Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model published yes Julian L Fischer author 2C12A0B0-F248-11E8-B48F-1D18A9856A870000-0002-0479-558X Michael Kniely author 2CA2C08C-F248-11E8-B48F-1D18A9856A870000-0001-5645-4333 JuFi department 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. https://research-explorer.ista.ac.at/download/8697/8710/2020_Nonlinearity_Fischer.pdf application/pdfno IOP Publishing2020 eng Nonlinearity 0951-7715 1361-6544 1906.12245 00057649270000110.1088/1361-6544/ab9728 33115733-5772 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:<a href="https://doi.org/10.1088/1361-6544/ab9728">10.1088/1361-6544/ab9728</a>. 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 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:<a href="https://doi.org/10.1088/1361-6544/ab9728">10.1088/1361-6544/ab9728</a> Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity. IOP Publishing, 2020. <a href="https://doi.org/10.1088/1361-6544/ab9728">https://doi.org/10.1088/1361-6544/ab9728</a>. J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772. Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. IOP Publishing. <a href="https://doi.org/10.1088/1361-6544/ab9728">https://doi.org/10.1088/1361-6544/ab9728</a> 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. IOP Publishing, pp. 5733–5772, 2020. 86972020-10-25T23:01:16Z2026-04-02T14:31:34Z