[{"type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-023-01254-0"}],"oa_version":"Published Version","day":"04","month":"01","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"arxiv":1,"author":[{"last_name":"Clozeau","id":"fea1b376-906f-11eb-847d-b2c0cf46455b","full_name":"Clozeau, Nicolas","first_name":"Nicolas"},{"last_name":"Mattesini","full_name":"Mattesini, Francesco","first_name":"Francesco"}],"publication":"Probability Theory and Related Fields","language":[{"iso":"eng"}],"has_accepted_license":"1","scopus_import":"1","title":"Annealed quantitative estimates for the quadratic 2D-discrete random matching problem","article_processing_charge":"Yes (in subscription journal)","date_updated":"2025-08-12T12:22:41Z","oa":1,"quality_controlled":"1","department":[{"_id":"JuFi"}],"date_published":"2024-01-04T00:00:00Z","publisher":"Springer Nature","project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"abstract":[{"text":"We study a random matching problem on closed compact 2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity, the optimal transport plan between the two empirical measures μn and νm is quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure.","lang":"eng"}],"external_id":{"arxiv":["2303.00353"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"publication_status":"epub_ahead","doi":"10.1007/s00440-023-01254-0","_id":"14797","article_type":"original","ec_funded":1,"keyword":["Troll","Norway","Fjell"],"date_created":"2024-01-14T23:00:57Z","citation":{"mla":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory and Related Fields, Springer Nature, 2024, doi:10.1007/s00440-023-01254-0.","chicago":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01254-0.","ista":"Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields.","ama":"Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. 2024. doi:10.1007/s00440-023-01254-0","ieee":"N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic 2D-discrete random matching problem,” Probability Theory and Related Fields. Springer Nature, 2024.","short":"N. Clozeau, F. Mattesini, Probability Theory and Related Fields (2024).","apa":"Clozeau, N., & Mattesini, F. (2024). Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01254-0"},"year":"2024","acknowledgement":"NC has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems. FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute for Mathematics in the Sciences."},{"publication_status":"epub_ahead","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"}],"external_id":{"arxiv":["2306.05151"]},"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"quality_controlled":"1","volume":34,"department":[{"_id":"JuFi"}],"date_published":"2024-01-23T00:00:00Z","publisher":"Springer Nature","citation":{"ama":"Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 2024;34(2). doi:10.1007/s00332-023-10005-3","ieee":"E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions,” Journal of Nonlinear Science, vol. 34, no. 2. Springer Nature, 2024.","short":"E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).","mla":"Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science, vol. 34, no. 2, 30, Springer Nature, 2024, doi:10.1007/s00332-023-10005-3.","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.","chicago":"Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science. Springer Nature, 2024. https://doi.org/10.1007/s00332-023-10005-3.","apa":"Davoli, E., D’Elia, L., & Ingmanns, J. (2024). Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-10005-3"},"date_created":"2024-01-28T23:01:42Z","year":"2024","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_type":"original","_id":"14884","doi":"10.1007/s00332-023-10005-3","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"},{"full_name":"Ingmanns, Jonas","first_name":"Jonas","id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","last_name":"Ingmanns"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"23","oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.05151","open_access":"1"}],"month":"01","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"status":"public","type":"journal_article","title":"Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions","article_processing_charge":"No","issue":"2","date_updated":"2024-02-05T08:54:44Z","oa":1,"scopus_import":"1","intvolume":" 34","language":[{"iso":"eng"}],"publication":"Journal of Nonlinear Science"},{"arxiv":1,"author":[{"full_name":"Agresti, Antonio","first_name":"Antonio","last_name":"Agresti","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962"},{"last_name":"Lindemulder","full_name":"Lindemulder, Nick","first_name":"Nick"},{"last_name":"Veraar","first_name":"Mark","full_name":"Veraar, Mark"}],"file":[{"relation":"main_file","file_size":449280,"access_level":"open_access","content_type":"application/pdf","creator":"dernst","date_updated":"2023-08-16T11:40:02Z","date_created":"2023-08-16T11:40:02Z","file_name":"2023_MathNachrichten_Agresti.pdf","checksum":"6f099f1d064173784d1a27716a2cc795","file_id":"14067","success":1}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","day":"01","month":"04","publication_identifier":{"issn":["0025-584X"],"eissn":["1522-2616"]},"type":"journal_article","status":"public","title":"On the trace embedding and its applications to evolution equations","issue":"4","article_processing_charge":"No","oa":1,"date_updated":"2023-08-16T11:41:42Z","scopus_import":"1","has_accepted_license":"1","intvolume":" 296","isi":1,"language":[{"iso":"eng"}],"publication":"Mathematische Nachrichten","publication_status":"published","abstract":[{"text":"In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equations, where uniform trace estimates on the half-line are shown.","lang":"eng"}],"external_id":{"arxiv":["2104.05063"],"isi":["000914134900001"]},"tmp":{"short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png"},"ddc":["510"],"volume":296,"quality_controlled":"1","page":"1319-1350","department":[{"_id":"JuFi"}],"date_published":"2023-04-01T00:00:00Z","license":"https://creativecommons.org/licenses/by-nc/4.0/","publisher":"Wiley","citation":{"short":"A. Agresti, N. Lindemulder, M. Veraar, Mathematische Nachrichten 296 (2023) 1319–1350.","ama":"Agresti A, Lindemulder N, Veraar M. On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. 2023;296(4):1319-1350. doi:10.1002/mana.202100192","ieee":"A. Agresti, N. Lindemulder, and M. Veraar, “On the trace embedding and its applications to evolution equations,” Mathematische Nachrichten, vol. 296, no. 4. Wiley, pp. 1319–1350, 2023.","ista":"Agresti A, Lindemulder N, Veraar M. 2023. On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. 296(4), 1319–1350.","mla":"Agresti, Antonio, et al. “On the Trace Embedding and Its Applications to Evolution Equations.” Mathematische Nachrichten, vol. 296, no. 4, Wiley, 2023, pp. 1319–50, doi:10.1002/mana.202100192.","chicago":"Agresti, Antonio, Nick Lindemulder, and Mark Veraar. “On the Trace Embedding and Its Applications to Evolution Equations.” Mathematische Nachrichten. Wiley, 2023. https://doi.org/10.1002/mana.202100192.","apa":"Agresti, A., Lindemulder, N., & Veraar, M. (2023). On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. Wiley. https://doi.org/10.1002/mana.202100192"},"date_created":"2023-01-29T23:00:59Z","year":"2023","acknowledgement":"The first author has been partially supported by the Nachwuchsring—Network for the promotion of young scientists—at TU Kaiserslautern. The second and third authors were supported by the Vidi subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).","article_type":"original","_id":"12429","file_date_updated":"2023-08-16T11:40:02Z","doi":"10.1002/mana.202100192"},{"date_published":"2023-11-28T00:00:00Z","publisher":"Springer Nature","department":[{"_id":"JuFi"}],"project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"abstract":[{"lang":"eng","text":"This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between the two areas."}],"external_id":{"arxiv":["2207.08293"]},"publication_status":"epub_ahead","doi":"10.1007/s40072-023-00319-4","_id":"12486","article_type":"original","ec_funded":1,"year":"2023","acknowledgement":"The author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948819).\r\nThe author thanks Lorenzo Dello Schiavo, Lucio Galeati and Mark Veraar for helpful comments. The author acknowledges Caterina Balzotti for her support in creating the picture. The author\r\nthanks the anonymous referee for helpful comments. ","citation":{"apa":"Agresti, A. (2023). Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-023-00319-4","ista":"Agresti A. 2023. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations.","mla":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential Equations: Analysis and Computations, Springer Nature, 2023, doi:10.1007/s40072-023-00319-4.","chicago":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023. https://doi.org/10.1007/s40072-023-00319-4.","short":"A. Agresti, Stochastics and Partial Differential Equations: Analysis and Computations (2023).","ama":"Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. 2023. doi:10.1007/s40072-023-00319-4","ieee":"A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations,” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023."},"date_created":"2023-02-02T10:45:47Z","type":"journal_article","status":"public","month":"11","publication_identifier":{"issn":["2194-0401"],"eissn":["2194-041X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"28","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s40072-023-00319-4"}],"oa_version":"Submitted Version","arxiv":1,"author":[{"orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","first_name":"Antonio","full_name":"Agresti, Antonio"}],"publication":"Stochastics and Partial Differential Equations: Analysis and Computations","language":[{"iso":"eng"}],"has_accepted_license":"1","scopus_import":"1","article_processing_charge":"No","oa":1,"date_updated":"2023-12-18T07:53:45Z","title":"Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations"},{"project":[{"grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","name":"Bridging Scales in Random Materials"}],"volume":25,"quality_controlled":"1","page":"37-107","department":[{"_id":"JuFi"}],"date_published":"2023-04-20T00:00:00Z","publisher":"EMS Press","publication_status":"published","abstract":[{"text":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction\r\nof a gradient flow calibration in the sense of the recent work of Fischer et al. (2020) for any such\r\ncluster. This extends the two-dimensional construction to the three-dimensional case of surfaces\r\nmeeting along triple junctions.","lang":"eng"}],"external_id":{"arxiv":["2108.01733"],"isi":["000975817300002"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"article_type":"original","_id":"13043","file_date_updated":"2023-05-22T07:24:13Z","doi":"10.4171/IFB/484","citation":{"apa":"Hensel, S., & Laux, T. (2023). Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. EMS Press. https://doi.org/10.4171/IFB/484","chicago":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” Interfaces and Free Boundaries. EMS Press, 2023. https://doi.org/10.4171/IFB/484.","mla":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” Interfaces and Free Boundaries, vol. 25, no. 1, EMS Press, 2023, pp. 37–107, doi:10.4171/IFB/484.","ista":"Hensel S, Laux T. 2023. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 25(1), 37–107.","ieee":"S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” Interfaces and Free Boundaries, vol. 25, no. 1. EMS Press, pp. 37–107, 2023.","ama":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 2023;25(1):37-107. doi:10.4171/IFB/484","short":"S. Hensel, T. Laux, Interfaces and Free Boundaries 25 (2023) 37–107."},"date_created":"2023-05-21T22:01:06Z","year":"2023","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10013"}]},"ec_funded":1,"status":"public","type":"journal_article","arxiv":1,"author":[{"first_name":"Sebastian","full_name":"Hensel, Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","orcid":"0000-0001-7252-8072"},{"full_name":"Laux, Tim","first_name":"Tim","last_name":"Laux"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"file_id":"13045","file_name":"2023_Interfaces_Hensel.pdf","checksum":"622422484810441e48f613e968c7e7a4","success":1,"date_updated":"2023-05-22T07:24:13Z","date_created":"2023-05-22T07:24:13Z","creator":"dernst","file_size":867876,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"day":"20","oa_version":"Published Version","month":"04","publication_identifier":{"issn":["1463-9963"],"eissn":["1463-9971"]},"language":[{"iso":"eng"}],"publication":"Interfaces and Free Boundaries","title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","article_processing_charge":"No","issue":"1","date_updated":"2023-08-01T14:43:29Z","oa":1,"scopus_import":"1","intvolume":" 25","has_accepted_license":"1","isi":1},{"citation":{"apa":"Clozeau, N., Josien, M., Otto, F., & Xu, Q. (2023). Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-023-09613-y","ista":"Clozeau N, Josien M, Otto F, Xu Q. 2023. Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics.","chicago":"Clozeau, Nicolas, Marc Josien, Felix Otto, and Qiang Xu. “Bias in the Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational Mathematics. Springer Nature, 2023. https://doi.org/10.1007/s10208-023-09613-y.","mla":"Clozeau, Nicolas, et al. “Bias in the Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational Mathematics, Springer Nature, 2023, doi:10.1007/s10208-023-09613-y.","ama":"Clozeau N, Josien M, Otto F, Xu Q. Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. 2023. doi:10.1007/s10208-023-09613-y","ieee":"N. Clozeau, M. Josien, F. Otto, and Q. Xu, “Bias in the representative volume element method: Periodize the ensemble instead of its realizations,” Foundations of Computational Mathematics. Springer Nature, 2023.","short":"N. Clozeau, M. Josien, F. Otto, Q. Xu, Foundations of Computational Mathematics (2023)."},"date_created":"2023-06-11T22:00:40Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","year":"2023","doi":"10.1007/s10208-023-09613-y","article_type":"original","_id":"13129","external_id":{"isi":["000999623100001"]},"abstract":[{"lang":"eng","text":"We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior ahom of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory of homogenization, the method proceeds by computing d=3 correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩. We make this point by investigating the bias (or systematic error), i.e., the difference between ahom and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O(L−1). In case of a suitable periodization of ⟨⋅⟩\r\n, we rigorously show that it is O(L−d). In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩\r\n of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function."}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"epub_ahead","department":[{"_id":"JuFi"}],"quality_controlled":"1","publisher":"Springer Nature","date_published":"2023-05-30T00:00:00Z","scopus_import":"1","has_accepted_license":"1","isi":1,"title":"Bias in the representative volume element method: Periodize the ensemble instead of its realizations","date_updated":"2023-08-02T06:12:39Z","oa":1,"article_processing_charge":"Yes (via OA deal)","publication":"Foundations of Computational Mathematics","language":[{"iso":"eng"}],"day":"30","oa_version":"Published Version","main_file_link":[{"url":"https://doi.org/10.1007/s10208-023-09613-y","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]},"month":"05","author":[{"first_name":"Nicolas","full_name":"Clozeau, Nicolas","last_name":"Clozeau","id":"fea1b376-906f-11eb-847d-b2c0cf46455b"},{"full_name":"Josien, Marc","first_name":"Marc","last_name":"Josien"},{"full_name":"Otto, Felix","first_name":"Felix","last_name":"Otto"},{"last_name":"Xu","full_name":"Xu, Qiang","first_name":"Qiang"}],"type":"journal_article","status":"public"},{"doi":"10.1016/j.jde.2023.05.038","file_date_updated":"2024-01-29T11:03:09Z","article_type":"original","_id":"13135","ec_funded":1,"acknowledgement":"The first author has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 948819) Image 1. The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).","year":"2023","citation":{"chicago":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” Journal of Differential Equations. Elsevier, 2023. https://doi.org/10.1016/j.jde.2023.05.038.","ista":"Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 368(9), 247–300.","mla":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” Journal of Differential Equations, vol. 368, no. 9, Elsevier, 2023, pp. 247–300, doi:10.1016/j.jde.2023.05.038.","ieee":"A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity,” Journal of Differential Equations, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.","ama":"Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 2023;368(9):247-300. doi:10.1016/j.jde.2023.05.038","short":"A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300.","apa":"Agresti, A., & Veraar, M. (2023). Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2023.05.038"},"date_created":"2023-06-18T22:00:45Z","publisher":"Elsevier","date_published":"2023-09-25T00:00:00Z","department":[{"_id":"JuFi"}],"page":"247-300","quality_controlled":"1","volume":368,"project":[{"grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","call_identifier":"H2020"}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"isi":["001019018700001"]},"abstract":[{"lang":"eng","text":"In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model."}],"publication_status":"published","publication":"Journal of Differential Equations","language":[{"iso":"eng"}],"isi":1,"has_accepted_license":"1","scopus_import":"1","intvolume":" 368","oa":1,"date_updated":"2024-01-29T11:04:41Z","article_processing_charge":"Yes (in subscription journal)","issue":"9","title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity","status":"public","type":"journal_article","publication_identifier":{"eissn":["1090-2732"],"issn":["0022-0396"]},"month":"09","day":"25","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","file_size":834638,"content_type":"application/pdf","access_level":"open_access","creator":"dernst","date_updated":"2024-01-29T11:03:09Z","date_created":"2024-01-29T11:03:09Z","file_id":"14895","file_name":"2023_JourDifferentialEquations_Agresti.pdf","checksum":"246b703b091dfe047bfc79abf0891a63","success":1}],"author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","orcid":"0000-0002-9573-2962","full_name":"Agresti, Antonio","first_name":"Antonio"},{"first_name":"Mark","full_name":"Veraar, Mark","last_name":"Veraar"}]},{"language":[{"iso":"eng"}],"publication":"Journal of Mathematical Fluid Mechanics","date_updated":"2023-12-13T12:08:08Z","oa":1,"article_processing_charge":"Yes (via OA deal)","issue":"3","title":"On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary","isi":1,"scopus_import":"1","has_accepted_license":"1","intvolume":" 25","status":"public","type":"journal_article","author":[{"last_name":"Bulíček","first_name":"Miroslav","full_name":"Bulíček, Miroslav"},{"last_name":"Málek","first_name":"Josef","full_name":"Málek, Josef"},{"id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","full_name":"Maringová, Erika","first_name":"Erika"}],"arxiv":1,"month":"08","publication_identifier":{"issn":["1422-6928"],"eissn":["1422-6952"]},"oa_version":"Published Version","day":"01","file":[{"creator":"dernst","content_type":"application/pdf","access_level":"open_access","file_size":845748,"relation":"main_file","success":1,"checksum":"c549cd8f0dd02ed60477a05ca045f481","file_id":"14046","file_name":"2023_JourMathFluidMech_Bulicek.pdf","date_created":"2023-08-14T07:24:17Z","date_updated":"2023-08-14T07:24:17Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2023-08-14T07:24:17Z","_id":"14042","article_type":"original","doi":"10.1007/s00021-023-00803-w","acknowledgement":"M. Bulíček and J. Málek acknowledge the support of the project No. 20-11027X financed by the Czech Science foundation (GAČR). M. Bulíček and J. Málek are members of the Nečas Center for Mathematical Modelling.\r\nOpen access publishing supported by the National Technical Library in Prague.","year":"2023","date_created":"2023-08-13T22:01:13Z","citation":{"apa":"Bulíček, M., Málek, J., & Maringová, E. (2023). On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-023-00803-w","ama":"Bulíček M, Málek J, Maringová E. On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. 2023;25(3). doi:10.1007/s00021-023-00803-w","ieee":"M. Bulíček, J. Málek, and E. Maringová, “On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary,” Journal of Mathematical Fluid Mechanics, vol. 25, no. 3. Springer Nature, 2023.","short":"M. Bulíček, J. Málek, E. Maringová, Journal of Mathematical Fluid Mechanics 25 (2023).","chicago":"Bulíček, Miroslav, Josef Málek, and Erika Maringová. “On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.” Journal of Mathematical Fluid Mechanics. Springer Nature, 2023. https://doi.org/10.1007/s00021-023-00803-w.","ista":"Bulíček M, Málek J, Maringová E. 2023. On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. 25(3), 72.","mla":"Bulíček, Miroslav, et al. “On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.” Journal of Mathematical Fluid Mechanics, vol. 25, no. 3, 72, Springer Nature, 2023, doi:10.1007/s00021-023-00803-w."},"article_number":"72","publisher":"Springer Nature","date_published":"2023-08-01T00:00:00Z","department":[{"_id":"JuFi"}],"quality_controlled":"1","volume":25,"publication_status":"published","ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"isi":["001040354900001"],"arxiv":["2301.12834"]},"abstract":[{"text":"Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of incompressible fluids is nowadays available not only for Navier–Stokes fluids but also for various fluid models where the relation between the Cauchy stress tensor and the symmetric part of the velocity gradient is nonlinear. The majority of such studies however concerns models where such a dependence is explicit (the stress is a function of the velocity gradient), which makes the class of studied models unduly restrictive. The same concerns boundary conditions, or more precisely the slipping mechanisms on the boundary, where the no-slip is still the most preferred condition considered in the literature. Our main objective is to develop a robust mathematical theory for unsteady internal flows of implicitly constituted incompressible fluids with implicit relations between the tangential projections of the velocity and the normal traction on the boundary. The theory covers numerous rheological models used in chemistry, biorheology, polymer and food industry as well as in geomechanics. It also includes, as special cases, nonlinear slip as well as stick–slip boundary conditions. Unlike earlier studies, the conditions characterizing admissible classes of constitutive equations are expressed by means of tools of elementary calculus. In addition, a fully constructive proof (approximation scheme) is incorporated. Finally, we focus on the question of uniqueness of such weak solutions.","lang":"eng"}]},{"doi":"10.1007/s00521-023-09033-7","_id":"14451","article_type":"original","ec_funded":1,"date_created":"2023-10-22T22:01:16Z","citation":{"chicago":"Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” Neural Computing and Applications. Springer Nature, 2023. https://doi.org/10.1007/s00521-023-09033-7.","mla":"Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” Neural Computing and Applications, Springer Nature, 2023, doi:10.1007/s00521-023-09033-7.","ista":"Cornalba F, Disselkamp C, Scassola D, Helf C. 2023. Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications.","short":"F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications (2023).","ieee":"F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading,” Neural Computing and Applications. Springer Nature, 2023.","ama":"Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. 2023. doi:10.1007/s00521-023-09033-7","apa":"Cornalba, F., Disselkamp, C., Scassola, D., & Helf, C. (2023). Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. Springer Nature. https://doi.org/10.1007/s00521-023-09033-7"},"acknowledgement":"Open access funding provided by Università degli Studi di Trieste within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft.","year":"2023","department":[{"_id":"JuFi"}],"quality_controlled":"1","publisher":"Springer Nature","date_published":"2023-10-05T00:00:00Z","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":["2203.04579"]},"abstract":[{"lang":"eng","text":"We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format."}],"publication_status":"epub_ahead","publication":"Neural Computing and Applications","language":[{"iso":"eng"}],"scopus_import":"1","title":"Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading","oa":1,"date_updated":"2023-10-31T10:58:28Z","article_processing_charge":"Yes (via OA deal)","type":"journal_article","status":"public","main_file_link":[{"url":"https://doi.org/10.1007/s00521-023-09033-7","open_access":"1"}],"day":"05","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0941-0643"],"eissn":["1433-3058"]},"month":"10","author":[{"full_name":"Cornalba, Federico","first_name":"Federico","last_name":"Cornalba","id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149"},{"full_name":"Disselkamp, Constantin","first_name":"Constantin","last_name":"Disselkamp"},{"last_name":"Scassola","full_name":"Scassola, Davide","first_name":"Davide"},{"first_name":"Christopher","full_name":"Helf, Christopher","last_name":"Helf"}],"arxiv":1},{"doi":"10.1051/m2an/2023077","file_date_updated":"2023-11-20T08:34:57Z","article_type":"original","_id":"14554","ec_funded":1,"related_material":{"link":[{"url":"https://github.com/tonyshardlow/RIDK-FD","relation":"software"}]},"acknowledgement":"The authors thank the anonymous referees for their careful reading of the manuscript and their\r\nvaluable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 754411 (the latter funding source covered the first part of this project).","year":"2023","date_created":"2023-11-19T23:00:55Z","citation":{"mla":"Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 5, EDP Sciences, 2023, pp. 3061–90, doi:10.1051/m2an/2023077.","ista":"Cornalba F, Shardlow T. 2023. The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. 57(5), 3061–3090.","chicago":"Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.” ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences, 2023. https://doi.org/10.1051/m2an/2023077.","ama":"Cornalba F, Shardlow T. The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. 2023;57(5):3061-3090. doi:10.1051/m2an/2023077","ieee":"F. Cornalba and T. Shardlow, “The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime,” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 5. EDP Sciences, pp. 3061–3090, 2023.","short":"F. Cornalba, T. Shardlow, ESAIM: Mathematical Modelling and Numerical Analysis 57 (2023) 3061–3090.","apa":"Cornalba, F., & Shardlow, T. (2023). The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences. https://doi.org/10.1051/m2an/2023077"},"publisher":"EDP Sciences","date_published":"2023-09-01T00:00:00Z","page":"3061-3090","department":[{"_id":"JuFi"}],"volume":57,"quality_controlled":"1","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"abstract":[{"lang":"eng","text":"The Regularised Inertial Dean–Kawasaki model (RIDK) – introduced by the authors and J. Zimmer in earlier works – is a nonlinear stochastic PDE capturing fluctuations around the meanfield limit for large-scale particle systems in both particle density and momentum density. We focus on the following two aspects. Firstly, we set up a Discontinuous Galerkin (DG) discretisation scheme for the RIDK model: we provide suitable definitions of numerical fluxes at the interface of the mesh elements which are consistent with the wave-type nature of the RIDK model and grant stability of the simulations, and we quantify the rate of convergence in mean square to the continuous RIDK model. Secondly, we introduce modifications of the RIDK model in order to preserve positivity of the density (such a feature only holds in a “high-probability sense” for the original RIDK model). By means of numerical simulations, we show that the modifications lead to physically realistic and positive density profiles. In one case, subject to additional regularity constraints, we also prove positivity. Finally, we present an application of our methodology to a system of diffusing and reacting particles. Our Python code is available in open-source format."}],"publication_status":"published","publication":"ESAIM: Mathematical Modelling and Numerical Analysis","language":[{"iso":"eng"}],"has_accepted_license":"1","intvolume":" 57","scopus_import":"1","oa":1,"date_updated":"2023-11-20T08:38:47Z","article_processing_charge":"Yes (in subscription journal)","issue":"5","title":"The regularised inertial Dean' Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime","status":"public","type":"journal_article","month":"09","publication_identifier":{"eissn":["2804-7214"],"issn":["2822-7840"]},"day":"01","oa_version":"Published Version","file":[{"file_name":"2023_ESAIM_Cornalba.pdf","checksum":"3aef1475b1882c8dec112df9a5167c39","file_id":"14560","success":1,"date_updated":"2023-11-20T08:34:57Z","date_created":"2023-11-20T08:34:57Z","creator":"dernst","content_type":"application/pdf","access_level":"open_access","file_size":1508534,"relation":"main_file"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"2CEB641C-A400-11E9-A717-D712E6697425","last_name":"Cornalba","orcid":"0000-0002-6269-5149","first_name":"Federico","full_name":"Cornalba, Federico"},{"full_name":"Shardlow, Tony","first_name":"Tony","last_name":"Shardlow"}]},{"ec_funded":1,"related_material":{"record":[{"status":"public","id":"11842","relation":"part_of_dissertation"},{"id":"14597","relation":"part_of_dissertation","status":"public"}]},"degree_awarded":"PhD","acknowledgement":"The research projects contained in this thesis have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819).","year":"2023","date_created":"2023-11-21T11:41:05Z","citation":{"apa":"Marveggio, A. (2023). Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14587","ieee":"A. Marveggio, “Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences,” Institute of Science and Technology Austria, 2023.","ama":"Marveggio A. Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. 2023. doi:10.15479/at:ista:14587","short":"A. Marveggio, Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences, Institute of Science and Technology Austria, 2023.","mla":"Marveggio, Alice. Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14587.","chicago":"Marveggio, Alice. “Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14587.","ista":"Marveggio A. 2023. Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. Institute of Science and Technology Austria."},"doi":"10.15479/at:ista:14587","file_date_updated":"2023-11-29T09:28:30Z","_id":"14587","ddc":["515"],"tmp":{"image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)"},"abstract":[{"text":"This thesis concerns the application of variational methods to the study of evolution problems arising in fluid mechanics and in material sciences. The main focus is on weak-strong stability properties of some curvature driven interface evolution problems, such as the two-phase Navier–Stokes flow with surface tension and multiphase mean curvature flow, and on the phase-field approximation of the latter. Furthermore, we discuss a variational approach to the study of a class of doubly nonlinear wave equations.\r\nFirst, we consider the two-phase Navier–Stokes flow with surface tension within a bounded domain. The two fluids are immiscible and separated by a sharp interface, which intersects the boundary of the domain at a constant contact angle of ninety degree. We devise a suitable concept of varifolds solutions for the associated interface evolution problem and we establish a weak-strong uniqueness principle in case of a two dimensional ambient space. In order to focus on the boundary effects and on the singular geometry of the evolving domains, we work for simplicity in the regime of same viscosities for the two fluids.\r\nThe core of the thesis consists in the rigorous proof of the convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow for a suitable class of multi- well potentials and for well-prepared initial data. We even establish a rate of convergence. Our relative energy approach relies on the concept of gradient-flow calibration for branching singularities in multiphase mean curvature flow and thus enables us to overcome the limitations of other approaches. To the best of the author’s knowledge, our result is the first quantitative and unconditional one available in the literature for the vectorial/multiphase setting.\r\nThis thesis also contains a first study of weak-strong stability for planar multiphase mean curvature flow beyond the singularity resulting from a topology change. Previous weak-strong results are indeed limited to time horizons before the first topology change of the strong solution. We consider circular topology changes and we prove weak-strong stability for BV solutions to planar multiphase mean curvature flow beyond the associated singular times by dynamically adapting the strong solutions to the weak one by means of a space-time shift.\r\nIn the context of interface evolution problems, our proofs for the main results of this thesis are based on the relative energy technique, relying on novel suitable notions of relative energy functionals, which in particular measure the interface error. Our statements follow from the resulting stability estimates for the relative energy associated to the problem.\r\nAt last, we introduce a variational approach to the study of nonlinear evolution problems. This approach hinges on the minimization of a parameter dependent family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy (WIDE) functionals. We consider a class of doubly nonlinear wave equations and establish the convergence, up to subsequences, of the associated WIDE minimizers to a solution of the target problem as the parameter goes to zero.","lang":"eng"}],"publication_status":"published","publisher":"Institute of Science and Technology Austria","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","date_published":"2023-11-21T00:00:00Z","supervisor":[{"first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer"}],"department":[{"_id":"GradSch"},{"_id":"JuFi"}],"page":"228","project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"has_accepted_license":"1","date_updated":"2023-11-30T13:25:03Z","oa":1,"article_processing_charge":"No","title":"Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences","language":[{"iso":"eng"}],"month":"11","publication_identifier":{"issn":["2663 - 337X"]},"day":"21","oa_version":"Published Version","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_size":2881100,"creator":"amarvegg","date_created":"2023-11-29T09:09:31Z","date_updated":"2023-11-29T09:09:31Z","success":1,"file_name":"thesis_Marveggio.pdf","checksum":"6c7db4cc86da6cdc79f7f358dc7755d4","file_id":"14626"},{"checksum":"52f28bdf95ec82cff39f3685f9c48e7d","file_id":"14627","file_name":"Thesis_Marveggio.zip","date_created":"2023-11-29T09:10:19Z","date_updated":"2023-11-29T09:28:30Z","creator":"amarvegg","content_type":"application/zip","access_level":"open_access","file_size":10189696,"relation":"source_file"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"full_name":"Marveggio, Alice","first_name":"Alice","last_name":"Marveggio","id":"25647992-AA84-11E9-9D75-8427E6697425"}],"alternative_title":["ISTA Thesis"],"type":"dissertation","status":"public"},{"_id":"14661","article_type":"original","citation":{"chicago":"Carioni, Marcello, Julian L Fischer, and Anja Schlömerkemper. “External Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.” Journal of Convex Analysis. Heldermann Verlag, 2023.","mla":"Carioni, Marcello, et al. “External Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.” Journal of Convex Analysis, vol. 30, no. 1, Heldermann Verlag, 2023, pp. 217–47.","ista":"Carioni M, Fischer JL, Schlömerkemper A. 2023. External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. 30(1), 217–247.","short":"M. Carioni, J.L. Fischer, A. Schlömerkemper, Journal of Convex Analysis 30 (2023) 217–247.","ieee":"M. Carioni, J. L. Fischer, and A. Schlömerkemper, “External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development,” Journal of Convex Analysis, vol. 30, no. 1. Heldermann Verlag, pp. 217–247, 2023.","ama":"Carioni M, Fischer JL, Schlömerkemper A. External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. 2023;30(1):217-247.","apa":"Carioni, M., Fischer, J. L., & Schlömerkemper, A. (2023). External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. Heldermann Verlag."},"date_created":"2023-12-10T23:00:59Z","year":"2023","department":[{"_id":"JuFi"}],"page":"217-247","volume":30,"quality_controlled":"1","publisher":"Heldermann Verlag","date_published":"2023-01-01T00:00:00Z","publication_status":"published","external_id":{"arxiv":["1811.09857"],"isi":["001115503400013"]},"abstract":[{"text":"This paper is concerned with equilibrium configurations of one-dimensional particle systems with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness results for a Γ-development of the energy with the novelty that external forces are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates and thus may model dead as well as live loads. Our result is based on a new technique for deriving compactness results which are required for calculating the first-order Γ-limit in the presence of external forces: instead of comparing a configuration of n atoms to a global minimizer of the Γ-limit, we compare the configuration to a minimizer in some subclass of functions which in some sense are \"close to\" the configuration. The paper is complemented with the study of the minimizers of the Γ-limit.","lang":"eng"}],"language":[{"iso":"eng"}],"publication":"Journal of Convex Analysis","title":"External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development","date_updated":"2024-01-16T12:03:05Z","oa":1,"article_processing_charge":"No","issue":"1","scopus_import":"1","intvolume":" 30","isi":1,"type":"journal_article","status":"public","author":[{"full_name":"Carioni, Marcello","first_name":"Marcello","last_name":"Carioni"},{"full_name":"Fischer, Julian L","first_name":"Julian L","orcid":"0000-0002-0479-558X","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schlömerkemper","first_name":"Anja","full_name":"Schlömerkemper, Anja"}],"arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.09857"}],"oa_version":"Preprint","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"01","publication_identifier":{"eissn":["2363-6394"],"issn":["0944-6532"]}},{"title":"Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result","article_processing_charge":"No","issue":"3-4","oa":1,"date_updated":"2024-01-09T09:22:16Z","intvolume":" 131","scopus_import":"1","language":[{"iso":"eng"}],"publication":"Asymptotic Analysis","arxiv":1,"author":[{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser","full_name":"Moser, Maximilian","first_name":"Maximilian"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.07100","open_access":"1"}],"day":"02","oa_version":"Preprint","publication_identifier":{"issn":["0921-7134"],"eissn":["1875-8576"]},"month":"02","status":"public","type":"journal_article","keyword":["General Mathematics"],"citation":{"ista":"Moser M. 2023. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 131(3–4), 297–383.","mla":"Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” Asymptotic Analysis, vol. 131, no. 3–4, IOS Press, 2023, pp. 297–383, doi:10.3233/asy-221775.","chicago":"Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” Asymptotic Analysis. IOS Press, 2023. https://doi.org/10.3233/asy-221775.","short":"M. Moser, Asymptotic Analysis 131 (2023) 297–383.","ieee":"M. Moser, “Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result,” Asymptotic Analysis, vol. 131, no. 3–4. IOS Press, pp. 297–383, 2023.","ama":"Moser M. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 2023;131(3-4):297-383. doi:10.3233/asy-221775","apa":"Moser, M. (2023). Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. IOS Press. https://doi.org/10.3233/asy-221775"},"date_created":"2024-01-08T13:13:28Z","year":"2023","acknowledgement":"The author gratefully acknowledges support through DFG, GRK 1692 “Curvature,\r\nCycles and Cohomology” during parts of the work.","article_type":"original","_id":"14755","doi":"10.3233/asy-221775","publication_status":"published","abstract":[{"text":"We consider the sharp interface limit for the scalar-valued and vector-valued Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse interface has developed and intersects the boundary ∂ Ω. The limit problem is mean curvature flow with 90°-contact angle and we show convergence in strong norms for well-prepared initial data as long as a smooth solution to the limit problem exists. To this end we assume that the limit problem has a smooth solution on [ 0 , T ] for some time T > 0. Based on the latter we construct suitable curvilinear coordinates and set up an asymptotic expansion for the scalar-valued and the vector-valued Allen–Cahn equation. In order to estimate the difference of the exact and approximate solutions with a Gronwall-type argument, a spectral estimate for the linearized Allen–Cahn operator in both cases is required. The latter will be shown in a separate paper, cf. (Moser (2021)).","lang":"eng"}],"external_id":{"arxiv":["2105.07100"]},"volume":131,"quality_controlled":"1","page":"297-383","department":[{"_id":"JuFi"}],"date_published":"2023-02-02T00:00:00Z","publisher":"IOS Press"},{"publication_status":"published","ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["2108.01962"],"isi":["001081809000001"]},"abstract":[{"text":"Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.","lang":"eng"}],"publisher":"Elsevier","date_published":"2023-12-01T00:00:00Z","department":[{"_id":"JuFi"}],"volume":285,"quality_controlled":"1","acknowledgement":"We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for valuable discussions. We also thank the anonymous referees for their helpful comments and suggestions, and for the very accurate reading of the manuscript.\r\nThe first author has been supported partially by the Nachwuchsring – Network for the promotion of young scientists – at TU Kaiserslautern. Both authors have been supported by MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative of the Federal State of Rhineland-Palatinate, Germany.","year":"2023","date_created":"2024-01-10T09:15:18Z","citation":{"mla":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” Journal of Functional Analysis, vol. 285, no. 11, 110146, Elsevier, 2023, doi:10.1016/j.jfa.2023.110146.","ista":"Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 285(11), 110146.","chicago":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110146.","short":"A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).","ieee":"A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block operator matrices and applications,” Journal of Functional Analysis, vol. 285, no. 11. Elsevier, 2023.","ama":"Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 2023;285(11). doi:10.1016/j.jfa.2023.110146","apa":"Agresti, A., & Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.110146"},"keyword":["Analysis"],"article_number":"110146","file_date_updated":"2024-01-10T11:23:57Z","_id":"14772","article_type":"original","doi":"10.1016/j.jfa.2023.110146","author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","orcid":"0000-0002-9573-2962","first_name":"Antonio","full_name":"Agresti, Antonio"},{"full_name":"Hussein, Amru","first_name":"Amru","last_name":"Hussein"}],"arxiv":1,"month":"12","publication_identifier":{"issn":["0022-1236"]},"day":"01","oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":1120592,"relation":"main_file","access_level":"open_access","creator":"dernst","date_created":"2024-01-10T11:23:57Z","date_updated":"2024-01-10T11:23:57Z","success":1,"file_id":"14789","checksum":"eda98ca2aa73da91bd074baed34c2b3c","file_name":"2023_JourFunctionalAnalysis_Agresti.pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","type":"journal_article","oa":1,"date_updated":"2024-01-10T11:24:56Z","article_processing_charge":"Yes (in subscription journal)","issue":"11","title":"Maximal Lp-regularity and H∞-calculus for block operator matrices and applications","isi":1,"scopus_import":"1","has_accepted_license":"1","intvolume":" 285","language":[{"iso":"eng"}],"publication":"Journal of Functional Analysis"},{"language":[{"iso":"eng"}],"publication":"Stochastics and Partial Differential Equations: Analysis and Computations","title":"Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields","article_processing_charge":"Yes (via OA deal)","date_updated":"2023-08-14T11:51:47Z","oa":1,"scopus_import":"1","has_accepted_license":"1","intvolume":" 11","isi":1,"type":"journal_article","status":"public","arxiv":1,"author":[{"id":"fea1b376-906f-11eb-847d-b2c0cf46455b","last_name":"Clozeau","full_name":"Clozeau, Nicolas","first_name":"Nicolas"}],"file":[{"date_created":"2023-08-14T11:51:04Z","date_updated":"2023-08-14T11:51:04Z","success":1,"file_name":"2023_StochPartialDiffEquations_Clozeau.pdf","checksum":"f83dcaecdbd3ace862c4ed97a20e8501","file_id":"14052","content_type":"application/pdf","relation":"main_file","file_size":1635193,"access_level":"open_access","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","day":"01","publication_identifier":{"issn":["2194-0401"]},"month":"09","article_type":"original","_id":"10173","file_date_updated":"2023-08-14T11:51:04Z","doi":"10.1007/s40072-022-00254-w","date_created":"2021-10-23T10:50:22Z","citation":{"apa":"Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-022-00254-w","ieee":"N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 11. Springer Nature, pp. 1254–1378, 2023.","ama":"Clozeau N. Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 2023;11:1254–1378. doi:10.1007/s40072-022-00254-w","short":"N. Clozeau, Stochastics and Partial Differential Equations: Analysis and Computations 11 (2023) 1254–1378.","ista":"Clozeau N. 2023. Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 11, 1254–1378.","chicago":"Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization for Correlated Coefficient Fields.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023. https://doi.org/10.1007/s40072-022-00254-w.","mla":"Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization for Correlated Coefficient Fields.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 11, Springer Nature, 2023, pp. 1254–1378, doi:10.1007/s40072-022-00254-w."},"year":"2023","acknowledgement":"I would like to thank my advisor Antoine Gloria for suggesting this problem to me, as well for many interesting discussions and suggestions.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","quality_controlled":"1","volume":11,"department":[{"_id":"JuFi"}],"page":"1254–1378","date_published":"2023-09-01T00:00:00Z","publisher":"Springer Nature","publication_status":"published","abstract":[{"lang":"eng","text":"We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we analyze the so-called corrector equation, a degenerate elliptic equation posed in the probability space. In this contribution, we use a parabolic approach and optimally quantify the time decay of the semigroup. For the theoretical point of view, we prove an optimal decay estimate of the gradient and flux of the corrector when spatially averaged over a scale R larger than 1. For the numerical point of view, our results provide convenient tools for the analysis of various numerical methods."}],"external_id":{"arxiv":["2102.07452"],"isi":["000799715600001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"]},{"day":"07","oa_version":"Published Version","file":[{"creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_size":742315,"success":1,"file_name":"2023_JourNonlinearScience_Fellner.pdf","checksum":"f3f0f0886098e31c81116cff8183750b","file_id":"13149","date_created":"2023-06-19T07:33:53Z","date_updated":"2023-06-19T07:33:53Z"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"06","publication_identifier":{"issn":["0938-8974"],"eissn":["1432-1467"]},"author":[{"full_name":"Fellner, Klemens","first_name":"Klemens","last_name":"Fellner"},{"first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Michael","full_name":"Kniely, Michael","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","last_name":"Kniely","orcid":"0000-0001-5645-4333"},{"last_name":"Tang","full_name":"Tang, Bao Quoc","first_name":"Bao Quoc"}],"arxiv":1,"status":"public","type":"journal_article","scopus_import":"1","has_accepted_license":"1","intvolume":" 33","isi":1,"title":"Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion","oa":1,"date_updated":"2023-08-01T14:40:33Z","article_processing_charge":"No","publication":"Journal of Nonlinear Science","language":[{"iso":"eng"}],"external_id":{"isi":["001002343400002"],"arxiv":["2109.12019"]},"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"}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","department":[{"_id":"JuFi"}],"quality_controlled":"1","volume":33,"publisher":"Springer Nature","date_published":"2023-06-07T00:00:00Z","article_number":"66","date_created":"2021-12-16T12:15:35Z","citation":{"apa":"Fellner, K., Fischer, J. L., Kniely, M., & Tang, B. Q. (2023). Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-09926-w","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,” Journal of Nonlinear Science, vol. 33. Springer Nature, 2023.","ama":"Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-023-09926-w","short":"K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (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.","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.” Journal of Nonlinear Science. Springer Nature, 2023. https://doi.org/10.1007/s00332-023-09926-w.","mla":"Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science, vol. 33, 66, Springer Nature, 2023, doi:10.1007/s00332-023-09926-w."},"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.","year":"2023","doi":"10.1007/s00332-023-09926-w","file_date_updated":"2023-06-19T07:33:53Z","_id":"10550","article_type":"original"},{"scopus_import":"1","has_accepted_license":"1","intvolume":" 247","isi":1,"title":"The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles","oa":1,"date_updated":"2024-01-30T12:10:10Z","article_processing_charge":"Yes (via OA deal)","issue":"5","publication":"Archive for Rational Mechanics and Analysis","language":[{"iso":"eng"}],"oa_version":"Published Version","day":"04","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_id":"14904","checksum":"4529eeff170b6745a461d397ee611b5a","file_name":"2023_ArchiveRationalMech_Cornalba.pdf","success":1,"date_updated":"2024-01-30T12:09:34Z","date_created":"2024-01-30T12:09:34Z","creator":"dernst","file_size":1851185,"content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"month":"08","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"author":[{"full_name":"Cornalba, Federico","first_name":"Federico","last_name":"Cornalba","id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149"},{"full_name":"Fischer, Julian L","first_name":"Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","orcid":"0000-0002-0479-558X"}],"arxiv":1,"status":"public","type":"journal_article","ec_funded":1,"article_number":"76","date_created":"2021-12-16T12:16:03Z","citation":{"ista":"Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 247(5), 76.","mla":"Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive for Rational Mechanics and Analysis, vol. 247, no. 5, 76, Springer Nature, 2023, doi:10.1007/s00205-023-01903-7.","chicago":"Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01903-7.","ieee":"F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles,” Archive for Rational Mechanics and Analysis, vol. 247, no. 5. Springer Nature, 2023.","ama":"Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 2023;247(5). doi:10.1007/s00205-023-01903-7","short":"F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247 (2023).","apa":"Cornalba, F., & Fischer, J. L. (2023). The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01903-7"},"acknowledgement":"We thank the anonymous referee for his/her careful reading of the manuscript and valuable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science Fund (FWF).","year":"2023","doi":"10.1007/s00205-023-01903-7","file_date_updated":"2024-01-30T12:09:34Z","article_type":"original","_id":"10551","external_id":{"isi":["001043086800001"],"arxiv":["2109.06500"]},"abstract":[{"lang":"eng","text":"The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the regime of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation presents a substantial challenge for both its analysis and its rigorous mathematical justification. Besides being non-renormalisable by the theory of regularity structures by Hairer et al., it has recently been shown to not even admit nontrivial martingale solutions. In the present work, we give a rigorous and fully quantitative justification of the Dean–Kawasaki equation by considering the natural regularisation provided by standard numerical discretisations: We show that structure-preserving discretisations of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting diffusing particles to arbitrary order in N−1 (in suitable weak metrics). In other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate and efficient numerical simulations of the density fluctuations of independent diffusing particles."}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","department":[{"_id":"JuFi"}],"volume":247,"quality_controlled":"1","publisher":"Springer Nature","date_published":"2023-08-04T00:00:00Z","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}]},{"author":[{"first_name":"Antonio","full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti"},{"first_name":"Matthias","full_name":"Hieber, Matthias","last_name":"Hieber"},{"full_name":"Hussein, Amru","first_name":"Amru","last_name":"Hussein"},{"last_name":"Saal","first_name":"Martin","full_name":"Saal, Martin"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://doi.org/10.1007/s40072-022-00277-3","open_access":"1"}],"day":"27","oa_version":"Published Version","publication_identifier":{"eissn":["2194-041X"],"issn":["2194-0401"]},"month":"10","type":"journal_article","status":"public","title":"The stochastic primitive equations with transport noise and turbulent pressure","article_processing_charge":"Yes (via OA deal)","date_updated":"2023-08-16T09:11:38Z","oa":1,"scopus_import":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Stochastics and Partial Differential Equations: Analysis and Computations","publication_status":"epub_ahead","abstract":[{"text":"In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L² regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well.","lang":"eng"}],"external_id":{"isi":["000874389000001"]},"quality_controlled":"1","department":[{"_id":"JuFi"}],"date_published":"2022-10-27T00:00:00Z","publisher":"Springer Nature","keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"citation":{"apa":"Agresti, A., Hieber, M., Hussein, A., & Saal, M. (2022). The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-022-00277-3","ieee":"A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive equations with transport noise and turbulent pressure,” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2022.","ama":"Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations. 2022. doi:10.1007/s40072-022-00277-3","short":"A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential Equations: Analysis and Computations (2022).","ista":"Agresti A, Hieber M, Hussein A, Saal M. 2022. The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations.","mla":"Agresti, Antonio, et al. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” Stochastics and Partial Differential Equations: Analysis and Computations, Springer Nature, 2022, doi:10.1007/s40072-022-00277-3.","chicago":"Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2022. https://doi.org/10.1007/s40072-022-00277-3."},"date_created":"2023-01-12T12:12:29Z","year":"2022","acknowledgement":"The authors thank the anonymous referees for their helpful comments and suggestions. Open Access funding enabled and organized by Projekt DEAL.","article_type":"original","_id":"12178","doi":"10.1007/s40072-022-00277-3"},{"issue":"7","article_processing_charge":"No","oa":1,"date_updated":"2023-08-04T10:34:31Z","title":"Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation","isi":1,"scopus_import":"1","intvolume":" 47","language":[{"iso":"eng"}],"publication":"Communications in Partial Differential Equations","arxiv":1,"author":[{"first_name":"Nicola","full_name":"De Nitti, Nicola","last_name":"De Nitti"},{"first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"}],"publication_identifier":{"eissn":["1532-4133"],"issn":["0360-5302"]},"month":"07","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","day":"01","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1907.05342"}],"type":"journal_article","status":"public","year":"2022","acknowledgement":"N. De Nitti acknowledges the kind hospitality of IST Austria within the framework of the ISTernship Summer Program 2018, during which most of the present article was written. N. DeNitti has received funding by The Austrian Agency for International Cooperation in Education &Research (OeAD-GmbH) via its financial support of the ISTernship Summer Program 2018. N.De Nitti would also like to thank Giuseppe Coclite, Giuseppe Devillanova, Giuseppe Florio, Sebastian Hensel, and Francesco Maddalena for several helpful conversations on topics related to this work.","keyword":["Applied Mathematics","Analysis"],"citation":{"mla":"De Nitti, Nicola, and Julian L. Fischer. “Sharp Criteria for the Waiting Time Phenomenon in Solutions to the Thin-Film Equation.” Communications in Partial Differential Equations, vol. 47, no. 7, Taylor & Francis, 2022, pp. 1394–434, doi:10.1080/03605302.2022.2056702.","ista":"De Nitti N, Fischer JL. 2022. Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. Communications in Partial Differential Equations. 47(7), 1394–1434.","chicago":"De Nitti, Nicola, and Julian L Fischer. “Sharp Criteria for the Waiting Time Phenomenon in Solutions to the Thin-Film Equation.” Communications in Partial Differential Equations. Taylor & Francis, 2022. https://doi.org/10.1080/03605302.2022.2056702.","short":"N. De Nitti, J.L. Fischer, Communications in Partial Differential Equations 47 (2022) 1394–1434.","ieee":"N. De Nitti and J. L. Fischer, “Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation,” Communications in Partial Differential Equations, vol. 47, no. 7. Taylor & Francis, pp. 1394–1434, 2022.","ama":"De Nitti N, Fischer JL. Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. Communications in Partial Differential Equations. 2022;47(7):1394-1434. doi:10.1080/03605302.2022.2056702","apa":"De Nitti, N., & Fischer, J. L. (2022). Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. Communications in Partial Differential Equations. Taylor & Francis. https://doi.org/10.1080/03605302.2022.2056702"},"date_created":"2023-01-16T10:06:50Z","article_type":"original","_id":"12304","doi":"10.1080/03605302.2022.2056702","publication_status":"published","abstract":[{"lang":"eng","text":"We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass (as opposed to previous almost-optimal results), reflecting the fact that mass is a locally conserved quantity for the thin-film equation. In the regime of weak slippage, our criteria are at the same time necessary and sufficient. The proof of our upper bounds on free boundary propagation is based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial scales: We combine estimates on the local mass and estimates on energies to show that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially smaller space-time cylinder with the same time horizon. The derivation of our lower bounds on free boundary propagation is based on a combination of a monotone quantity and almost optimal estimates established previously by the second author with a new estimate connecting motion of mass to entropy production."}],"external_id":{"arxiv":["1907.05342"],"isi":["000805689800001"]},"date_published":"2022-07-01T00:00:00Z","publisher":"Taylor & Francis","volume":47,"quality_controlled":"1","page":"1394-1434","department":[{"_id":"JuFi"}]},{"article_processing_charge":"No","issue":"1","oa":1,"date_updated":"2023-08-04T10:34:56Z","title":"Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°","isi":1,"intvolume":" 54","scopus_import":"1","language":[{"iso":"eng"}],"publication":"SIAM Journal on Mathematical Analysis","arxiv":1,"author":[{"last_name":"Abels","full_name":"Abels, Helmut","first_name":"Helmut"},{"full_name":"Moser, Maximilian","first_name":"Maximilian","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser"}],"publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"month":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2105.08434","open_access":"1"}],"day":"04","status":"public","type":"journal_article","year":"2022","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"date_created":"2023-01-16T10:07:00Z","citation":{"apa":"Abels, H., & Moser, M. (2022). Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424925","mla":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” SIAM Journal on Mathematical Analysis, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:10.1137/21m1424925.","chicago":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424925.","ista":"Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. SIAM Journal on Mathematical Analysis. 54(1), 114–172.","short":"H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172.","ama":"Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. SIAM Journal on Mathematical Analysis. 2022;54(1):114-172. doi:10.1137/21m1424925","ieee":"H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°,” SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 114–172, 2022."},"article_type":"original","_id":"12305","doi":"10.1137/21m1424925","publication_status":"published","abstract":[{"text":"This paper is concerned with the sharp interface limit for the Allen--Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain Ω⊂\\R2. We assume that a diffuse interface already has developed and that it is in contact with the boundary ∂Ω. The boundary condition is designed in such a way that the limit problem is given by the mean curvature flow with constant α-contact angle. For α close to 90° we prove a local in time convergence result for well-prepared initial data for times when a smooth solution to the limit problem exists. Based on the latter we construct a suitable curvilinear coordinate system and carry out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear Robin boundary condition. Moreover, we show a spectral estimate for the corresponding linearized Allen--Cahn operator and with its aid we derive strong norm estimates for the difference of the exact and approximate solutions using a Gronwall-type argument.","lang":"eng"}],"external_id":{"arxiv":["2105.08434"],"isi":["000762768000004"]},"date_published":"2022-01-04T00:00:00Z","publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","volume":54,"page":"114-172","department":[{"_id":"JuFi"}]}]