---
_id: '8697'
abstract:
- lang: eng
  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.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
  full_name: Fischer, Julian L
  id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
  last_name: Fischer
  orcid: 0000-0002-0479-558X
- first_name: Michael
  full_name: Kniely, Michael
  id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
  last_name: Kniely
  orcid: 0000-0001-5645-4333
citation:
  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>
  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.
date_created: 2020-10-25T23:01:16Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-08-22T10:38:38Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab9728
external_id:
  arxiv:
  - '1906.12245'
  isi:
  - '000576492700001'
file:
- access_level: open_access
  checksum: ed90bc6eb5f32ee6157fef7f3aabc057
  content_type: application/pdf
  creator: cziletti
  date_created: 2020-10-27T12:09:57Z
  date_updated: 2020-10-27T12:09:57Z
  file_id: '8710'
  file_name: 2020_Nonlinearity_Fischer.pdf
  file_size: 1223899
  relation: main_file
  success: 1
file_date_updated: 2020-10-27T12:09:57Z
has_accepted_license: '1'
intvolume: '        33'
isi: 1
issue: '11'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '11'
oa: 1
oa_version: Published Version
page: 5733-5772
publication: Nonlinearity
publication_identifier:
  eissn:
  - '13616544'
  issn:
  - '09517715'
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Variance reduction for effective energies of random lattices in the Thomas-Fermi-von
  Weizsäcker model
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
  name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
  short: CC BY (3.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2020'
...
---
_id: '7637'
abstract:
- lang: eng
  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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Federico
  full_name: Cornalba, Federico
  id: 2CEB641C-A400-11E9-A717-D712E6697425
  last_name: Cornalba
  orcid: 0000-0002-6269-5149
- first_name: Tony
  full_name: Shardlow, Tony
  last_name: Shardlow
- first_name: Johannes
  full_name: Zimmer, Johannes
  last_name: Zimmer
citation:
  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>
  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.
  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>.
  short: F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.
date_created: 2020-04-05T22:00:49Z
date_published: 2020-01-10T00:00:00Z
date_updated: 2023-08-18T10:26:07Z
day: '10'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab5174
external_id:
  arxiv:
  - '1811.06448'
  isi:
  - '000508175400001'
intvolume: '        33'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1811.06448
month: '01'
oa: 1
oa_version: Preprint
page: 864-891
publication: Nonlinearity
publication_identifier:
  eissn:
  - '13616544'
  issn:
  - '09517715'
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: From weakly interacting particles to a regularised Dean-Kawasaki model
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2020'
...