---
_id: '14884'
abstract:
- lang: eng
  text: We perform a stochastic homogenization analysis for composite materials exhibiting
    a random microstructure. Under the assumptions of stationarity and ergodicity,
    we characterize the Gamma-limit of a micromagnetic energy functional defined on
    magnetizations taking value in the unit sphere and including both symmetric and
    antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic
    energy functional with homogeneous coefficients. We provide explicit formulas
    for the effective magnetic properties of the composite material in terms of homogenization
    correctors. Additionally, the variational analysis of the two exchange energy
    terms is performed in the more general setting of functionals defined on manifold-valued
    maps with Sobolev regularity, in the case in which the target manifold is a bounded,
    orientable smooth surface with tubular neighborhood of uniform thickness. Eventually,
    we present an explicit characterization of minimizers of the effective exchange
    in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s
    predictions on the emergence of helical structures in composite ferromagnetic
    materials with stochastic microstructure.
acknowledgement: All authors acknowledge support of the Austrian Science Fund (FWF)
  through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally
  been supported by the FWF through grants V662, Y1292, and P35359, as well as from
  OeAD through the WTZ grant CZ09/2023.
article_number: '30'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Elisa
  full_name: Davoli, Elisa
  last_name: Davoli
- first_name: Lorenza
  full_name: D’Elia, Lorenza
  last_name: D’Elia
- first_name: Jonas
  full_name: Ingmanns, Jonas
  id: 71523d30-15b2-11ec-abd3-f80aa909d6b0
  last_name: Ingmanns
citation:
  ama: Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic
    energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear Science</i>.
    2024;34(2). doi:<a href="https://doi.org/10.1007/s00332-023-10005-3">10.1007/s00332-023-10005-3</a>
  apa: Davoli, E., D’Elia, L., &#38; Ingmanns, J. (2024). Stochastic homogenization
    of micromagnetic energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear
    Science</i>. Springer Nature. <a href="https://doi.org/10.1007/s00332-023-10005-3">https://doi.org/10.1007/s00332-023-10005-3</a>
  chicago: Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization
    of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” <i>Journal of
    Nonlinear Science</i>. Springer Nature, 2024. <a href="https://doi.org/10.1007/s00332-023-10005-3">https://doi.org/10.1007/s00332-023-10005-3</a>.
  ieee: E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic
    energies and emergence of magnetic skyrmions,” <i>Journal of Nonlinear Science</i>,
    vol. 34, no. 2. Springer Nature, 2024.
  ista: Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic
    energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2),
    30.
  mla: Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies
    and Emergence of Magnetic Skyrmions.” <i>Journal of Nonlinear Science</i>, vol.
    34, no. 2, 30, Springer Nature, 2024, doi:<a href="https://doi.org/10.1007/s00332-023-10005-3">10.1007/s00332-023-10005-3</a>.
  short: E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).
date_created: 2024-01-28T23:01:42Z
date_published: 2024-01-23T00:00:00Z
date_updated: 2024-02-05T08:54:44Z
day: '23'
department:
- _id: JuFi
doi: 10.1007/s00332-023-10005-3
external_id:
  arxiv:
  - '2306.05151'
intvolume: '        34'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2306.05151
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
publication: Journal of Nonlinear Science
publication_identifier:
  eissn:
  - 1432-1467
  issn:
  - 0938-8974
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stochastic homogenization of micromagnetic energies and emergence of magnetic
  skyrmions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2024'
...
---
_id: '10550'
abstract:
- lang: eng
  text: The global existence of renormalised solutions and convergence to equilibrium
    for reaction-diffusion systems with non-linear diffusion are investigated. The
    system is assumed to have quasi-positive non-linearities and to satisfy an entropy
    inequality. The difficulties in establishing global renormalised solutions caused
    by possibly degenerate diffusion are overcome by introducing a new class of weighted
    truncation functions. By means of the obtained global renormalised solutions,
    we study the large-time behaviour of complex balanced systems arising from chemical
    reaction network theory with non-linear diffusion. When the reaction network does
    not admit boundary equilibria, the complex balanced equilibrium is shown, by using
    the entropy method, to exponentially attract all renormalised solutions in the
    same compatibility class. This convergence extends even to a range of non-linear
    diffusion, where global existence is an open problem, yet we are able to show
    that solutions to approximate systems converge exponentially to equilibrium uniformly
    in the regularisation parameter.
acknowledgement: "We thank the referees for their valuable comments and suggestions.
  A major part of this work was carried out when B. Q. Tang visited the Institute
  of Science and Technology Austria (ISTA). The hospitality of ISTA is greatly acknowledged.
  This work was partially supported by NAWI Graz.\r\nOpen access funding provided
  by University of Graz."
article_number: '66'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Klemens
  full_name: Fellner, Klemens
  last_name: Fellner
- 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
- first_name: Bao Quoc
  full_name: Tang, Bao Quoc
  last_name: Tang
citation:
  ama: Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and
    equilibration of reaction-diffusion systems with non-linear diffusion. <i>Journal
    of Nonlinear Science</i>. 2023;33. doi:<a href="https://doi.org/10.1007/s00332-023-09926-w">10.1007/s00332-023-09926-w</a>
  apa: Fellner, K., Fischer, J. L., Kniely, M., &#38; Tang, B. Q. (2023). Global renormalised
    solutions and equilibration of reaction-diffusion systems with non-linear diffusion.
    <i>Journal of Nonlinear Science</i>. Springer Nature. <a href="https://doi.org/10.1007/s00332-023-09926-w">https://doi.org/10.1007/s00332-023-09926-w</a>
  chicago: Fellner, Klemens, Julian L Fischer, Michael Kniely, and Bao Quoc Tang.
    “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems
    with Non-Linear Diffusion.” <i>Journal of Nonlinear Science</i>. Springer Nature,
    2023. <a href="https://doi.org/10.1007/s00332-023-09926-w">https://doi.org/10.1007/s00332-023-09926-w</a>.
  ieee: K. Fellner, J. L. Fischer, M. Kniely, and B. Q. Tang, “Global renormalised
    solutions and equilibration of reaction-diffusion systems with non-linear diffusion,”
    <i>Journal of Nonlinear Science</i>, vol. 33. Springer Nature, 2023.
  ista: Fellner K, Fischer JL, Kniely M, Tang BQ. 2023. Global renormalised solutions
    and equilibration of reaction-diffusion systems with non-linear diffusion. Journal
    of Nonlinear Science. 33, 66.
  mla: Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of
    Reaction-Diffusion Systems with Non-Linear Diffusion.” <i>Journal of Nonlinear
    Science</i>, vol. 33, 66, Springer Nature, 2023, doi:<a href="https://doi.org/10.1007/s00332-023-09926-w">10.1007/s00332-023-09926-w</a>.
  short: K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science
    33 (2023).
date_created: 2021-12-16T12:15:35Z
date_published: 2023-06-07T00:00:00Z
date_updated: 2023-08-01T14:40:33Z
day: '07'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00332-023-09926-w
external_id:
  arxiv:
  - '2109.12019'
  isi:
  - '001002343400002'
file:
- access_level: open_access
  checksum: f3f0f0886098e31c81116cff8183750b
  content_type: application/pdf
  creator: dernst
  date_created: 2023-06-19T07:33:53Z
  date_updated: 2023-06-19T07:33:53Z
  file_id: '13149'
  file_name: 2023_JourNonlinearScience_Fellner.pdf
  file_size: 742315
  relation: main_file
  success: 1
file_date_updated: 2023-06-19T07:33:53Z
has_accepted_license: '1'
intvolume: '        33'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Nonlinear Science
publication_identifier:
  eissn:
  - 1432-1467
  issn:
  - 0938-8974
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global renormalised solutions and equilibration of reaction-diffusion systems
  with non-linear diffusion
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2023'
...