[{"license":"https://creativecommons.org/licenses/by/4.0/","file":[{"checksum":"760de2631b6fd7d57bcd5115ed36c0a2","date_created":"2026-04-28T09:55:32Z","file_id":"21770","success":1,"file_name":"2026_JourNonlinearScience_Bauer.pdf","file_size":1108518,"creator":"dernst","access_level":"open_access","date_updated":"2026-04-28T09:55:32Z","content_type":"application/pdf","relation":"main_file"}],"day":"15","language":[{"iso":"eng"}],"oa":1,"date_updated":"2026-04-28T09:59:01Z","oa_version":"Published Version","issue":"2","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s00332-026-10266-8","month":"04","OA_type":"hybrid","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2026-04-15T00:00:00Z","status":"public","ddc":["510"],"publication_status":"published","abstract":[{"text":"We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden–Weinstein structure. Our method integrates the Liouville 1-form of the Marsden–Weinstein structure with Riemannian structures that have been introduced in mathematical shape analysis. We also derive Hamiltonian vector fields for several classical Hamiltonian functions with respect to these new symplectic structures.","lang":"eng"}],"type":"journal_article","intvolume":"        36","publisher":"Springer Nature","PlanS_conform":"1","_id":"21743","file_date_updated":"2026-04-28T09:55:32Z","author":[{"first_name":"Martin","last_name":"Bauer","full_name":"Bauer, Martin"},{"full_name":"Ishida, Sadashige","first_name":"Sadashige","orcid":"0000-0002-3121-3100","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","last_name":"Ishida"},{"full_name":"Michor, Peter W.","first_name":"Peter W.","last_name":"Michor"}],"quality_controlled":"1","scopus_import":"1","article_number":"45","has_accepted_license":"1","citation":{"short":"M. Bauer, S. Ishida, P.W. Michor, Journal of Nonlinear Science 36 (2026).","apa":"Bauer, M., Ishida, S., &#38; Michor, P. W. (2026). Symplectic structures on the space of space curves. <i>Journal of Nonlinear Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00332-026-10266-8\">https://doi.org/10.1007/s00332-026-10266-8</a>","chicago":"Bauer, Martin, Sadashige Ishida, and Peter W. Michor. “Symplectic Structures on the Space of Space Curves.” <i>Journal of Nonlinear Science</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00332-026-10266-8\">https://doi.org/10.1007/s00332-026-10266-8</a>.","ista":"Bauer M, Ishida S, Michor PW. 2026. Symplectic structures on the space of space curves. Journal of Nonlinear Science. 36(2), 45.","ieee":"M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space of space curves,” <i>Journal of Nonlinear Science</i>, vol. 36, no. 2. Springer Nature, 2026.","mla":"Bauer, Martin, et al. “Symplectic Structures on the Space of Space Curves.” <i>Journal of Nonlinear Science</i>, vol. 36, no. 2, 45, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s00332-026-10266-8\">10.1007/s00332-026-10266-8</a>.","ama":"Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves. <i>Journal of Nonlinear Science</i>. 2026;36(2). doi:<a href=\"https://doi.org/10.1007/s00332-026-10266-8\">10.1007/s00332-026-10266-8</a>"},"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2026-04-16T07:29:17Z","acknowledgement":"The authors are grateful to Boris Khesin for valuable comments on the MW symplectic structure and S. Ishida thanks Albert Chern for insightful discussions on space curves and Chris Wojtan for his continuous support. M. Bauer was partially supported by NSF grant DMS-1953244 and by the Binational Science Foundation (BSF). S. Ishida was partially supported by ERC Consolidator Grant 101045083 “CoDiNA” funded by the European Research Council. Some figures were generated by the software Houdini and its education license was provided by SideFX. Open access funding provided by University of Vienna.","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"volume":36,"title":"Symplectic structures on the space of space curves","external_id":{"arxiv":["2407.19908"]},"article_type":"original","project":[{"grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"publication":"Journal of Nonlinear Science","year":"2026","OA_place":"publisher","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"17361"}]}},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.05151"}],"month":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1007/s00332-023-10005-3","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."}],"publication_status":"published","status":"public","date_published":"2024-01-23T00:00:00Z","day":"23","arxiv":1,"oa_version":"Preprint","date_updated":"2025-09-04T11:54:01Z","issue":"2","oa":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"article_processing_charge":"No","date_created":"2024-01-28T23:01:42Z","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.","department":[{"_id":"JuFi"}],"publication":"Journal of Nonlinear Science","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"year":"2024","volume":34,"external_id":{"arxiv":["2306.05151"],"isi":["001147480200001"]},"article_type":"original","title":"Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions","publisher":"Springer Nature","intvolume":"        34","isi":1,"type":"journal_article","citation":{"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.","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.","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>","short":"E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (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>."},"article_number":"30","quality_controlled":"1","scopus_import":"1","_id":"14884","author":[{"full_name":"Davoli, Elisa","last_name":"Davoli","first_name":"Elisa"},{"full_name":"D’Elia, Lorenza","last_name":"D’Elia","first_name":"Lorenza"},{"full_name":"Ingmanns, Jonas","id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","last_name":"Ingmanns","first_name":"Jonas"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s00332-023-09926-w","month":"06","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2023-06-07T00:00:00Z","status":"public","ddc":["510"],"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."}],"publication_status":"published","file":[{"creator":"dernst","access_level":"open_access","date_updated":"2023-06-19T07:33:53Z","content_type":"application/pdf","relation":"main_file","checksum":"f3f0f0886098e31c81116cff8183750b","date_created":"2023-06-19T07:33:53Z","file_id":"13149","success":1,"file_size":742315,"file_name":"2023_JourNonlinearScience_Fellner.pdf"}],"day":"07","language":[{"iso":"eng"}],"oa":1,"date_updated":"2023-08-01T14:40:33Z","oa_version":"Published Version","arxiv":1,"department":[{"_id":"JuFi"}],"article_processing_charge":"No","date_created":"2021-12-16T12:15:35Z","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.","publication_identifier":{"issn":["0938-8974"],"eissn":["1432-1467"]},"volume":33,"article_type":"original","title":"Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion","external_id":{"arxiv":["2109.12019"],"isi":["001002343400002"]},"publication":"Journal of Nonlinear Science","year":"2023","isi":1,"type":"journal_article","intvolume":"        33","publisher":"Springer Nature","file_date_updated":"2023-06-19T07:33:53Z","_id":"10550","author":[{"full_name":"Fellner, Klemens","last_name":"Fellner","first_name":"Klemens"},{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L"},{"first_name":"Michael","last_name":"Kniely","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5645-4333","full_name":"Kniely, Michael"},{"full_name":"Tang, Bao Quoc","first_name":"Bao Quoc","last_name":"Tang"}],"scopus_import":"1","article_number":"66","quality_controlled":"1","has_accepted_license":"1","citation":{"short":"K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (2023).","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.","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.","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>"}}]