[{"type":"journal_article","abstract":[{"lang":"eng","text":"The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy inequality. The difficulties in establishing global renormalised solutions caused by possibly degenerate diffusion are overcome by introducing a new class of weighted truncation functions. By means of the obtained global renormalised solutions, we study the large-time behaviour of complex balanced systems arising from chemical reaction network theory with non-linear diffusion. When the reaction network does not admit boundary equilibria, the complex balanced equilibrium is shown, by using the entropy method, to exponentially attract all renormalised solutions in the same compatibility class. This convergence extends even to a range of non-linear diffusion, where global existence is an open problem, yet we are able to show that solutions to approximate systems converge exponentially to equilibrium uniformly in the regularisation parameter."}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10550","intvolume":" 33","ddc":["510"],"status":"public","title":"Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion","file":[{"checksum":"f3f0f0886098e31c81116cff8183750b","success":1,"date_updated":"2023-06-19T07:33:53Z","date_created":"2023-06-19T07:33:53Z","relation":"main_file","file_id":"13149","file_size":742315,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2023_JourNonlinearScience_Fellner.pdf"}],"oa_version":"Published Version","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"07","citation":{"short":"K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (2023).","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.","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.","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","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.","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","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."},"publication":"Journal of Nonlinear Science","article_type":"original","date_published":"2023-06-07T00:00:00Z","article_number":"66","file_date_updated":"2023-06-19T07:33:53Z","license":"https://creativecommons.org/licenses/by/4.0/","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","publisher":"Springer Nature","department":[{"_id":"JuFi"}],"publication_status":"published","author":[{"full_name":"Fellner, Klemens","last_name":"Fellner","first_name":"Klemens"},{"full_name":"Fischer, Julian L","last_name":"Fischer","first_name":"Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kniely, Michael","last_name":"Kniely","first_name":"Michael","orcid":"0000-0001-5645-4333","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Tang","first_name":"Bao Quoc","full_name":"Tang, Bao Quoc"}],"volume":33,"date_updated":"2023-08-01T14:40:33Z","date_created":"2021-12-16T12:15:35Z","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"month":"06","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["001002343400002"],"arxiv":["2109.12019"]},"oa":1,"quality_controlled":"1","isi":1,"doi":"10.1007/s00332-023-09926-w","language":[{"iso":"eng"}]},{"publisher":"Society for Industrial and Applied Mathematics","department":[{"_id":"JuFi"}],"publication_status":"published","year":"2022","acknowledgement":"M.K. gratefully acknowledges the hospitality of WIAS Berlin, where a major part of the project was carried out. The research stay of M.K. at WIAS Berlin was funded by the Austrian Federal Ministry of Education, Science and Research through a research fellowship for graduates of a promotio sub auspiciis. The research of A.M. has been partially supported by Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center SFB 1114 “Scaling Cascades in Complex Systems” (Project no. 235221301), Subproject C05 “Effective models for materials and interfaces with multiple scales”. J.F. and A.M. are grateful for the hospitality of the Erwin Schrödinger Institute in Vienna, where some ideas for this work have been developed. The authors are grateful to two anonymous referees for several helpful comments, in particular for the short proof of estimate (2.7).","volume":54,"date_created":"2021-12-16T12:08:56Z","date_updated":"2023-08-02T13:37:03Z","author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","first_name":"Julian L","last_name":"Fischer","full_name":"Fischer, Julian L"},{"first_name":"Katharina","last_name":"Hopf","full_name":"Hopf, Katharina"},{"full_name":"Kniely, Michael","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5645-4333","first_name":"Michael","last_name":"Kniely"},{"full_name":"Mielke, Alexander","last_name":"Mielke","first_name":"Alexander"}],"publication_identifier":{"issn":["0036-1410"]},"month":"01","quality_controlled":"1","isi":1,"oa":1,"external_id":{"isi":["000762768000006"],"arxiv":["2012.03792 "]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2012.03792"}],"language":[{"iso":"eng"}],"doi":"10.1137/20M1387237","type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities,\r\nwhile at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear."}],"intvolume":" 54","title":"Global existence analysis of energy-reaction-diffusion systems","status":"public","_id":"10547","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","keyword":["Energy-Reaction-Diffusion Systems","Cross Diffusion","Global-In-Time Existence of Weak/Renormalised Solutions","Entropy Method","Onsager System","Soret/Dufour Effect"],"scopus_import":"1","article_processing_charge":"No","day":"04","page":"220-267","article_type":"original","citation":{"short":"J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical Analysis 54 (2022) 220–267.","mla":"Fischer, Julian L., et al. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal on Mathematical Analysis, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 220–67, doi:10.1137/20M1387237.","chicago":"Fischer, Julian L, Katharina Hopf, Michael Kniely, and Alexander Mielke. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/20M1387237.","ama":"Fischer JL, Hopf K, Kniely M, Mielke A. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 2022;54(1):220-267. doi:10.1137/20M1387237","apa":"Fischer, J. L., Hopf, K., Kniely, M., & Mielke, A. (2022). Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1387237","ieee":"J. L. Fischer, K. Hopf, M. Kniely, and A. Mielke, “Global existence analysis of energy-reaction-diffusion systems,” SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 220–267, 2022.","ista":"Fischer JL, Hopf K, Kniely M, Mielke A. 2022. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 54(1), 220–267."},"publication":"SIAM Journal on Mathematical Analysis","date_published":"2022-01-04T00:00:00Z"},{"abstract":[{"lang":"eng","text":"In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy–entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation."}],"type":"journal_article","file":[{"access_level":"open_access","file_name":"2020_JourEllipticParabEquat_Fellner.pdf","file_size":8408694,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"8802","checksum":"6bc6832caacddceee1471291e93dcf1d","success":1,"date_updated":"2020-11-25T08:59:59Z","date_created":"2020-11-25T08:59:59Z"}],"oa_version":"Published Version","intvolume":" 6","status":"public","title":"Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model","ddc":["510"],"_id":"7866","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2020-12-01T00:00:00Z","page":"529-598","article_type":"original","citation":{"ista":"Fellner K, Kniely M. 2020. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 6, 529–598.","ieee":"K. Fellner and M. Kniely, “Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model,” Journal of Elliptic and Parabolic Equations, vol. 6. Springer Nature, pp. 529–598, 2020.","apa":"Fellner, K., & Kniely, M. (2020). Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. Springer Nature. https://doi.org/10.1007/s41808-020-00068-8","ama":"Fellner K, Kniely M. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 2020;6:529-598. doi:10.1007/s41808-020-00068-8","chicago":"Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations. Springer Nature, 2020. https://doi.org/10.1007/s41808-020-00068-8.","mla":"Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations, vol. 6, Springer Nature, 2020, pp. 529–98, doi:10.1007/s41808-020-00068-8.","short":"K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations 6 (2020) 529–598."},"publication":"Journal of Elliptic and Parabolic Equations","file_date_updated":"2020-11-25T08:59:59Z","volume":6,"date_created":"2020-05-17T22:00:45Z","date_updated":"2021-01-12T08:15:47Z","author":[{"full_name":"Fellner, Klemens","last_name":"Fellner","first_name":"Klemens"},{"full_name":"Kniely, Michael","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5645-4333","first_name":"Michael","last_name":"Kniely"}],"department":[{"_id":"JuFi"}],"publisher":"Springer Nature","publication_status":"published","acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). The second author has been supported by the International Research Training Group IGDK 1754 “Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures”, funded by the German Research Council (DFG) and the Austrian Science Fund (FWF) under grant number [W 1244-N18].","year":"2020","publication_identifier":{"issn":["22969020"],"eissn":["22969039"]},"month":"12","language":[{"iso":"eng"}],"doi":"10.1007/s41808-020-00068-8","project":[{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund","call_identifier":"FWF"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"}},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"8697","title":"Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model","ddc":["510"],"status":"public","intvolume":" 33","file":[{"access_level":"open_access","file_name":"2020_Nonlinearity_Fischer.pdf","file_size":1223899,"content_type":"application/pdf","creator":"cziletti","relation":"main_file","file_id":"8710","checksum":"ed90bc6eb5f32ee6157fef7f3aabc057","success":1,"date_created":"2020-10-27T12:09:57Z","date_updated":"2020-10-27T12:09:57Z"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"text":"In the computation of the material properties of random alloys, the method of 'special quasirandom structures' attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach is based on a recent analysis of a related variance reduction method in stochastic homogenization of linear elliptic PDEs and the locality properties of the TFW model. Concerning the latter, we extend an exponential locality result by Nazar and Ortner to include point charges, a result that may be of independent interest.","lang":"eng"}],"issue":"11","publication":"Nonlinearity","citation":{"chicago":"Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity. IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab9728.","mla":"Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity, vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728.","short":"J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.","ista":"Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772.","apa":"Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ab9728","ieee":"J. L. Fischer and M. Kniely, “Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity, vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020.","ama":"Fischer JL, Kniely M. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772. doi:10.1088/1361-6544/ab9728"},"article_type":"original","page":"5733-5772","date_published":"2020-11-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","year":"2020","publication_status":"published","department":[{"_id":"JuFi"}],"publisher":"IOP Publishing","author":[{"first_name":"Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"},{"full_name":"Kniely, Michael","last_name":"Kniely","first_name":"Michael","orcid":"0000-0001-5645-4333","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-08-22T10:38:38Z","date_created":"2020-10-25T23:01:16Z","volume":33,"file_date_updated":"2020-10-27T12:09:57Z","license":"https://creativecommons.org/licenses/by/3.0/","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000576492700001"],"arxiv":["1906.12245"]},"isi":1,"quality_controlled":"1","doi":"10.1088/1361-6544/ab9728","language":[{"iso":"eng"}],"month":"11","publication_identifier":{"eissn":["13616544"],"issn":["09517715"]}},{"oa_version":"Preprint","status":"public","title":"New optimal control problems in density functional theory motivated by photovoltaics","intvolume":" 17","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"6762","abstract":[{"lang":"eng","text":"We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate various desirable properties of the excitations as mathematical control goals at the Kohn-Sham-DFT level\r\nof theory, with the control being given by the nuclear charge distribution. We prove that nuclear distributions exist which give rise to optimal HOMO-LUMO excitations, and present illustrative numerical simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features such as large electron-hole separation, and a hierarchy of length scales: internal HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the doping profiles < system size."}],"issue":"3","type":"journal_article","date_published":"2019-07-16T00:00:00Z","page":"926-947","publication":"Multiscale Modeling and Simulation","citation":{"ista":"Friesecke G, Kniely M. 2019. New optimal control problems in density functional theory motivated by photovoltaics. Multiscale Modeling and Simulation. 17(3), 926–947.","ieee":"G. Friesecke and M. Kniely, “New optimal control problems in density functional theory motivated by photovoltaics,” Multiscale Modeling and Simulation, vol. 17, no. 3. SIAM, pp. 926–947, 2019.","apa":"Friesecke, G., & Kniely, M. (2019). New optimal control problems in density functional theory motivated by photovoltaics. Multiscale Modeling and Simulation. SIAM. https://doi.org/10.1137/18M1207272","ama":"Friesecke G, Kniely M. New optimal control problems in density functional theory motivated by photovoltaics. Multiscale Modeling and Simulation. 2019;17(3):926-947. doi:10.1137/18M1207272","chicago":"Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density Functional Theory Motivated by Photovoltaics.” Multiscale Modeling and Simulation. SIAM, 2019. https://doi.org/10.1137/18M1207272.","mla":"Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density Functional Theory Motivated by Photovoltaics.” Multiscale Modeling and Simulation, vol. 17, no. 3, SIAM, 2019, pp. 926–47, doi:10.1137/18M1207272.","short":"G. Friesecke, M. Kniely, Multiscale Modeling and Simulation 17 (2019) 926–947."},"day":"16","article_processing_charge":"No","scopus_import":"1","date_created":"2019-08-04T21:59:21Z","date_updated":"2023-09-05T15:05:45Z","volume":17,"author":[{"first_name":"Gero","last_name":"Friesecke","full_name":"Friesecke, Gero"},{"full_name":"Kniely, Michael","first_name":"Michael","last_name":"Kniely","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5645-4333"}],"publication_status":"published","department":[{"_id":"JuFi"}],"publisher":"SIAM","year":"2019","language":[{"iso":"eng"}],"doi":"10.1137/18M1207272","quality_controlled":"1","isi":1,"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1808.04200","open_access":"1"}],"external_id":{"arxiv":["1808.04200"],"isi":["000487931800002"]},"month":"07","publication_identifier":{"issn":["15403459"],"eissn":["15403467"]}}]