[{"oa":1,"publication_status":"published","tmp":{"short":"CC BY (3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","image":"/images/cc_by.png"},"volume":33,"file_date_updated":"2020-10-27T12:09:57Z","article_processing_charge":"Yes (via OA deal)","issue":"11","arxiv":1,"date_published":"2020-11-01T00:00:00Z","_id":"8697","abstract":[{"text":"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.","lang":"eng"}],"file":[{"relation":"main_file","file_id":"8710","content_type":"application/pdf","success":1,"date_created":"2020-10-27T12:09:57Z","file_size":1223899,"creator":"cziletti","file_name":"2020_Nonlinearity_Fischer.pdf","access_level":"open_access","date_updated":"2020-10-27T12:09:57Z","checksum":"ed90bc6eb5f32ee6157fef7f3aabc057"}],"publication_identifier":{"issn":["09517715"],"eissn":["13616544"]},"scopus_import":"1","external_id":{"arxiv":["1906.12245"],"isi":["000576492700001"]},"date_updated":"2023-08-22T10:38:38Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","has_accepted_license":"1","year":"2020","oa_version":"Published Version","article_type":"original","isi":1,"publisher":"IOP Publishing","status":"public","intvolume":"        33","publication":"Nonlinearity","quality_controlled":"1","department":[{"_id":"JuFi"}],"page":"5733-5772","date_created":"2020-10-25T23:01:16Z","month":"11","doi":"10.1088/1361-6544/ab9728","ddc":["510"],"language":[{"iso":"eng"}],"title":"Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model","citation":{"chicago":"Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” <i>Nonlinearity</i>. IOP Publishing, 2020. <a href=\"https://doi.org/10.1088/1361-6544/ab9728\">https://doi.org/10.1088/1361-6544/ab9728</a>.","ieee":"J. L. Fischer and M. Kniely, “Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,” <i>Nonlinearity</i>, vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020.","ista":"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.","mla":"Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” <i>Nonlinearity</i>, 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>.","short":"J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.","ama":"Fischer JL, Kniely M. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. <i>Nonlinearity</i>. 2020;33(11):5733-5772. doi:<a href=\"https://doi.org/10.1088/1361-6544/ab9728\">10.1088/1361-6544/ab9728</a>","apa":"Fischer, J. L., &#38; Kniely, M. (2020). Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/ab9728\">https://doi.org/10.1088/1361-6544/ab9728</a>"},"author":[{"last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X"},{"orcid":"0000-0001-5645-4333","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","last_name":"Kniely","first_name":"Michael","full_name":"Kniely, Michael"}],"type":"journal_article","day":"01"},{"publication_identifier":{"eissn":["13616544"],"issn":["09517715"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2023-08-18T10:26:07Z","scopus_import":"1","external_id":{"isi":["000508175400001"],"arxiv":["1811.06448"]},"oa_version":"Preprint","year":"2020","article_type":"original","volume":33,"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.06448"}],"publication_status":"published","abstract":[{"text":"The evolution of finitely many particles obeying Langevin dynamics is described by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki model based on second order Langevin dynamics by analysing a system of particles interacting via a pairwise potential. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise stochastic perturbation of the undamped McKean–Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model.","lang":"eng"}],"_id":"7637","date_published":"2020-01-10T00:00:00Z","issue":"2","article_processing_charge":"No","arxiv":1,"doi":"10.1088/1361-6544/ab5174","language":[{"iso":"eng"}],"type":"journal_article","author":[{"full_name":"Cornalba, Federico","first_name":"Federico","last_name":"Cornalba","id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149"},{"last_name":"Shardlow","full_name":"Shardlow, Tony","first_name":"Tony"},{"first_name":"Johannes","full_name":"Zimmer, Johannes","last_name":"Zimmer"}],"day":"10","title":"From weakly interacting particles to a regularised Dean-Kawasaki model","citation":{"mla":"Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” <i>Nonlinearity</i>, vol. 33, no. 2, IOP Publishing, 2020, pp. 864–91, doi:<a href=\"https://doi.org/10.1088/1361-6544/ab5174\">10.1088/1361-6544/ab5174</a>.","chicago":"Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” <i>Nonlinearity</i>. IOP Publishing, 2020. <a href=\"https://doi.org/10.1088/1361-6544/ab5174\">https://doi.org/10.1088/1361-6544/ab5174</a>.","ieee":"F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles to a regularised Dean-Kawasaki model,” <i>Nonlinearity</i>, vol. 33, no. 2. IOP Publishing, pp. 864–891, 2020.","ista":"Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891.","ama":"Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised Dean-Kawasaki model. <i>Nonlinearity</i>. 2020;33(2):864-891. doi:<a href=\"https://doi.org/10.1088/1361-6544/ab5174\">10.1088/1361-6544/ab5174</a>","apa":"Cornalba, F., Shardlow, T., &#38; Zimmer, J. (2020). From weakly interacting particles to a regularised Dean-Kawasaki model. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/ab5174\">https://doi.org/10.1088/1361-6544/ab5174</a>","short":"F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891."},"intvolume":"        33","status":"public","quality_controlled":"1","department":[{"_id":"JuFi"}],"publication":"Nonlinearity","isi":1,"publisher":"IOP Publishing","date_created":"2020-04-05T22:00:49Z","month":"01","page":"864-891"}]