[{"article_number":"30","arxiv":1,"title":"Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions","author":[{"full_name":"Davoli, Elisa","last_name":"Davoli","first_name":"Elisa"},{"full_name":"D’Elia, Lorenza","last_name":"D’Elia","first_name":"Lorenza"},{"id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","full_name":"Ingmanns, Jonas","last_name":"Ingmanns","first_name":"Jonas"}],"day":"23","publication":"Journal of Nonlinear Science","article_type":"original","article_processing_charge":"No","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","department":[{"_id":"JuFi"}],"doi":"10.1007/s00332-023-10005-3","quality_controlled":"1","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"issue":"2","language":[{"iso":"eng"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"volume":34,"date_created":"2024-01-28T23:01:42Z","oa_version":"Preprint","type":"journal_article","month":"01","abstract":[{"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.","lang":"eng"}],"date_updated":"2024-02-05T08:54:44Z","_id":"14884","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.","year":"2024","date_published":"2024-01-23T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.05151"}],"publication_status":"epub_ahead","oa":1,"intvolume":"        34","citation":{"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.","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>.","short":"E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).","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>","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>.","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.","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>"},"external_id":{"arxiv":["2306.05151"]},"status":"public"},{"status":"public","external_id":{"isi":["001002343400002"],"arxiv":["2109.12019"]},"citation":{"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.","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>.","short":"K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (2023).","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>","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>.","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.","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>"},"intvolume":"        33","has_accepted_license":"1","publication_status":"published","oa":1,"date_published":"2023-06-07T00:00:00Z","ddc":["510"],"year":"2023","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.","_id":"10550","month":"06","type":"journal_article","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"date_updated":"2023-08-01T14:40:33Z","date_created":"2021-12-16T12:15:35Z","file_date_updated":"2023-06-19T07:33:53Z","volume":33,"language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"issn":["0938-8974"],"eissn":["1432-1467"]},"quality_controlled":"1","doi":"10.1007/s00332-023-09926-w","department":[{"_id":"JuFi"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","scopus_import":"1","article_processing_charge":"No","publication":"Journal of Nonlinear Science","day":"07","file":[{"access_level":"open_access","date_created":"2023-06-19T07:33:53Z","checksum":"f3f0f0886098e31c81116cff8183750b","file_id":"13149","date_updated":"2023-06-19T07:33:53Z","creator":"dernst","file_size":742315,"content_type":"application/pdf","relation":"main_file","file_name":"2023_JourNonlinearScience_Fellner.pdf","success":1}],"author":[{"first_name":"Klemens","last_name":"Fellner","full_name":"Fellner, Klemens"},{"full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L"},{"full_name":"Kniely, Michael","orcid":"0000-0001-5645-4333","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","last_name":"Kniely","first_name":"Michael"},{"full_name":"Tang, Bao Quoc","last_name":"Tang","first_name":"Bao Quoc"}],"article_number":"66","arxiv":1,"title":"Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion"}]