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An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>, <i>109</i>(3). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>","bibtex":"@article{Wang_Winkler_2024, title={An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>}, number={3}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }","mla":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, Wiley, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).","ama":"Wang Y, Winkler M. An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>. 2024;109(3). doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>","chicago":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i> 109, no. 3 (2024). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>.","ieee":"Y. Wang and M. Winkler, “An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, 2024, doi: <a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>."},"publication_identifier":{"issn":["0024-6107","1469-7750"]},"publication_status":"published","issue":"3","title":"An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system","doi":"10.1112/jlms.12885","publisher":"Wiley","date_updated":"2024-04-07T12:36:25Z","volume":109,"author":[{"first_name":"Yulan","full_name":"Wang, Yulan","last_name":"Wang"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-04-07T12:27:28Z","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional domain  and for a given nondecreasing positive unbounded , for each  and  the inequality\r\n<jats:disp-formula />is shown to hold for any positive  fulfilling\r\n<jats:disp-formula />This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over  near its explosion time.</jats:p>","lang":"eng"}],"status":"public","publication":"Journal of the London Mathematical Society","type":"journal_article","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"53315","user_id":"31496"},{"type":"journal_article","publication":"Mitteilungen des Instituts für Europäische Kulturgeschichte","status":"public","user_id":"42693","_id":"53375","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Voß_2024, title={Rezension zu Anna-Victoria Bognár: Der Architekt in der Frühen Neuzeit. 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Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, Applied and Computational Harmonic Analysis  71 (2024).","apa":"Philipp, F., Schaller, M., Worthmann, K., Peitz, S., &#38; Nüske, F. (2024). Error bounds for kernel-based approximations of the Koopman operator. <i>Applied and Computational Harmonic Analysis </i>, <i>71</i>, Article 101657. <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">https://doi.org/10.1016/j.acha.2024.101657</a>","ama":"Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error bounds for kernel-based approximations of the Koopman operator. <i>Applied and Computational Harmonic Analysis </i>. 2024;71. doi:<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>","ieee":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error bounds for kernel-based approximations of the Koopman operator,” <i>Applied and Computational Harmonic Analysis </i>, vol. 71, Art. no. 101657, 2024, doi: <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>.","chicago":"Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and Feliks Nüske. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>Applied and Computational Harmonic Analysis </i> 71 (2024). <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">https://doi.org/10.1016/j.acha.2024.101657</a>."},"publication_status":"published","doi":"10.1016/j.acha.2024.101657","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2301.08637"}],"volume":71,"author":[{"first_name":"Friedrich","last_name":"Philipp","full_name":"Philipp, Friedrich"},{"last_name":"Schaller","full_name":"Schaller, Manuel","first_name":"Manuel"},{"last_name":"Worthmann","full_name":"Worthmann, Karl","first_name":"Karl"},{"id":"47427","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"last_name":"Nüske","full_name":"Nüske, Feliks","first_name":"Feliks"}],"date_updated":"2024-04-11T12:41:13Z","oa":"1","status":"public","type":"journal_article","article_number":"101657","department":[{"_id":"655"}],"user_id":"47427","_id":"38031","year":"2024","title":"Error bounds for kernel-based approximations of the Koopman operator","date_created":"2023-01-23T07:03:39Z","publisher":"Springer ","abstract":[{"text":"We consider the data-driven approximation of the Koopman operator for\r\nstochastic differential equations on reproducing kernel Hilbert spaces (RKHS).\r\nOur focus is on the estimation error if the data are collected from long-term\r\nergodic simulations. We derive both an exact expression for the variance of the\r\nkernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and\r\nprobabilistic bounds for the finite-data estimation error. Moreover, we derive\r\na bound on the prediction error of observables in the RKHS using a finite\r\nMercer series expansion. Further, assuming Koopman-invariance of the RKHS, we\r\nprovide bounds on the full approximation error. Numerical experiments using the\r\nOrnstein-Uhlenbeck process illustrate our results.","lang":"eng"}],"publication":"Applied and Computational Harmonic Analysis ","language":[{"iso":"eng"}],"external_id":{"arxiv":["2301.08637"]}},{"doi":"10.1080/08856257.2023.2195075","title":"Measuring collective efficacy for inclusion in a global context","author":[{"last_name":"Sharma ","full_name":"Sharma ,  Umesh ","first_name":" Umesh "},{"full_name":"Loreman ,  Tim ","last_name":"Loreman ","first_name":" Tim "},{"first_name":" Fiona ","full_name":"May ,  Fiona ","last_name":"May "},{"first_name":" Alessandra ","last_name":"Romano ","full_name":"Romano ,  Alessandra "},{"full_name":"Lozano , Caroline Sahli","last_name":"Lozano ","first_name":"Caroline Sahli"},{"first_name":" Elias ","last_name":"Avramidis ","full_name":"Avramidis ,  Elias "},{"first_name":" Stuart ","full_name":"Woodcock ,  Stuart ","last_name":"Woodcock "},{"first_name":" Pearl ","last_name":"Subban ","full_name":"Subban ,  Pearl "},{"id":"77972","full_name":"Kullmann, Harry","last_name":"Kullmann","first_name":"Harry"}],"date_created":"2023-03-28T13:01:09Z","volume":39,"date_updated":"2024-04-11T13:17:29Z","citation":{"mla":"Sharma ,  Umesh , et al. “Measuring Collective Efficacy for Inclusion in a Global Context.” <i>European Journal of Special Needs Education</i>, vol. 39, no. 2, 2024, pp. 167–184, doi:<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>.","short":"Umesh  Sharma ,  Tim  Loreman ,  Fiona  May ,  Alessandra  Romano , C.S. Lozano ,  Elias  Avramidis ,  Stuart  Woodcock ,  Pearl  Subban , H. Kullmann, European Journal of Special Needs Education 39 (2024) 167–184.","bibtex":"@article{Sharma _Loreman _May _Romano _Lozano _Avramidis _Woodcock _Subban _Kullmann_2024, title={Measuring collective efficacy for inclusion in a global context}, volume={39}, DOI={<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>}, number={2}, journal={European Journal of Special Needs Education}, author={Sharma ,  Umesh  and Loreman ,  Tim  and May ,  Fiona  and Romano ,  Alessandra  and Lozano , Caroline Sahli and Avramidis ,  Elias  and Woodcock ,  Stuart  and Subban ,  Pearl  and Kullmann, Harry}, year={2024}, pages={167–184} }","apa":"Sharma ,  Umesh , Loreman ,  Tim , May ,  Fiona , Romano ,  Alessandra , Lozano , C. S., Avramidis ,  Elias , Woodcock ,  Stuart , Subban ,  Pearl , &#38; Kullmann, H. (2024). Measuring collective efficacy for inclusion in a global context. <i>European Journal of Special Needs Education</i>, <i>39</i>(2), 167–184. <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">https://doi.org/10.1080/08856257.2023.2195075</a>","ieee":"Umesh  Sharma  <i>et al.</i>, “Measuring collective efficacy for inclusion in a global context,” <i>European Journal of Special Needs Education</i>, vol. 39, no. 2, pp. 167–184, 2024, doi: <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>.","chicago":"Sharma ,  Umesh ,  Tim  Loreman ,  Fiona  May ,  Alessandra  Romano , Caroline Sahli Lozano ,  Elias  Avramidis ,  Stuart  Woodcock ,  Pearl  Subban , and Harry Kullmann. “Measuring Collective Efficacy for Inclusion in a Global Context.” <i>European Journal of Special Needs Education</i> 39, no. 2 (2024): 167–184. <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">https://doi.org/10.1080/08856257.2023.2195075</a>.","ama":"Sharma   Umesh , Loreman   Tim , May   Fiona , et al. Measuring collective efficacy for inclusion in a global context. <i>European Journal of Special Needs Education</i>. 2024;39(2):167–184. doi:<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>"},"intvolume":"        39","page":"167–184","year":"2024","issue":"2","language":[{"iso":"eng"}],"user_id":"65969","department":[{"_id":"556"}],"_id":"43135","status":"public","type":"journal_article","publication":"European Journal of Special Needs Education"},{"author":[{"last_name":"Pritom","full_name":"Pritom, Touhid Hossain","first_name":"Touhid Hossain"},{"last_name":"Welzel","full_name":"Welzel, Simon","first_name":"Simon"},{"first_name":"Florian","full_name":"Klingler, Florian","last_name":"Klingler"}],"date_created":"2024-04-11T18:26:09Z","date_updated":"2024-04-11T18:29:47Z","title":"Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks","citation":{"ama":"Pritom TH, Welzel S, Klingler F. Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks. In: <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>. ; 2024.","ieee":"T. H. Pritom, S. Welzel, and F. Klingler, “Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks,” 2024.","chicago":"Pritom, Touhid Hossain, Simon Welzel, and Florian Klingler. “Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks.” In <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>. Big Island, HI, 2024.","apa":"Pritom, T. H., Welzel, S., &#38; Klingler, F. (2024). Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks. <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>.","bibtex":"@inproceedings{Pritom_Welzel_Klingler_2024, place={Big Island, HI}, title={Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks}, booktitle={11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)}, author={Pritom, Touhid Hossain and Welzel, Simon and Klingler, Florian}, year={2024} }","short":"T.H. Pritom, S. Welzel, F. Klingler, in: 11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024), Big Island, HI, 2024.","mla":"Pritom, Touhid Hossain, et al. “Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks.” <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>, 2024."},"year":"2024","place":"Big Island, HI","user_id":"49153","_id":"53437","language":[{"iso":"eng"}],"publication":"11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)","type":"conference","status":"public"},{"status":"public","type":"journal_article","article_number":"012011","user_id":"94328","_id":"53417","intvolume":"      2727","citation":{"apa":"Gschwind, S., Hohmann, S., Müller, A., Nordine, J., &#38; Riesen, T.-E. (2024). The Stellarium Gornergrat: Astrophysics with your own Data. <i>Journal of Physics: Conference Series</i>, <i>2727</i>(1), Article 012011. <a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">https://doi.org/10.1088/1742-6596/2727/1/012011</a>","short":"S. Gschwind, S. Hohmann, A. Müller, J. Nordine, T.-E. Riesen, Journal of Physics: Conference Series 2727 (2024).","mla":"Gschwind, Stéphane, et al. “The Stellarium Gornergrat: Astrophysics with Your Own Data.” <i>Journal of Physics: Conference Series</i>, vol. 2727, no. 1, 012011, IOP Publishing, 2024, doi:<a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">10.1088/1742-6596/2727/1/012011</a>.","bibtex":"@article{Gschwind_Hohmann_Müller_Nordine_Riesen_2024, title={The Stellarium Gornergrat: Astrophysics with your own Data}, volume={2727}, DOI={<a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">10.1088/1742-6596/2727/1/012011</a>}, number={1012011}, journal={Journal of Physics: Conference Series}, publisher={IOP Publishing}, author={Gschwind, Stéphane and Hohmann, Sascha and Müller, Andreas and Nordine, Jeffrey and Riesen, Timm-Emanuel}, year={2024} }","chicago":"Gschwind, Stéphane, Sascha Hohmann, Andreas Müller, Jeffrey Nordine, and Timm-Emanuel Riesen. “The Stellarium Gornergrat: Astrophysics with Your Own Data.” <i>Journal of Physics: Conference Series</i> 2727, no. 1 (2024). <a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">https://doi.org/10.1088/1742-6596/2727/1/012011</a>.","ieee":"S. Gschwind, S. Hohmann, A. Müller, J. Nordine, and T.-E. Riesen, “The Stellarium Gornergrat: Astrophysics with your own Data,” <i>Journal of Physics: Conference Series</i>, vol. 2727, no. 1, Art. no. 012011, 2024, doi: <a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">10.1088/1742-6596/2727/1/012011</a>.","ama":"Gschwind S, Hohmann S, Müller A, Nordine J, Riesen T-E. The Stellarium Gornergrat: Astrophysics with your own Data. <i>Journal of Physics: Conference Series</i>. 2024;2727(1). doi:<a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">10.1088/1742-6596/2727/1/012011</a>"},"publication_identifier":{"issn":["1742-6588","1742-6596"]},"publication_status":"published","doi":"10.1088/1742-6596/2727/1/012011","conference":{"name":"3rd World Conference on Physics Education","start_date":"2021-12-13","end_date":"2021-12-16","location":"Hanoi"},"main_file_link":[{"url":"https://iopscience.iop.org/article/10.1088/1742-6596/2727/1/012011/pdf","open_access":"1"}],"volume":2727,"author":[{"first_name":"Stéphane","full_name":"Gschwind, Stéphane","last_name":"Gschwind"},{"first_name":"Sascha","full_name":"Hohmann, Sascha","id":"94328","orcid":"0000-0001-6145-3466","last_name":"Hohmann"},{"last_name":"Müller","full_name":"Müller, Andreas","first_name":"Andreas"},{"first_name":"Jeffrey","full_name":"Nordine, Jeffrey","last_name":"Nordine"},{"first_name":"Timm-Emanuel","full_name":"Riesen, Timm-Emanuel","last_name":"Riesen"}],"date_updated":"2024-04-12T11:34:19Z","oa":"1","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>Remote-controlled telescopes in education provide the opportunity to obtain high quality astronomy images for a broad variety of users. The Stellarium Gornergrat is such a telescope. In addition to pure observation, it offers a user-friendly interface and teaching modules so that astronomical and astrophysical projects can be integrated into everyday school life without any special prior knowledge and without requiring a lot of time. This contribution presents the Stellarium project and a provides an overview of several teaching activities.</jats:p>","lang":"eng"}],"publication":"Journal of Physics: Conference Series","language":[{"iso":"eng"}],"keyword":["Computer Science Applications","History","Education"],"year":"2024","issue":"1","quality_controlled":"1","title":"The Stellarium Gornergrat: Astrophysics with your own Data","date_created":"2024-04-11T12:37:49Z","publisher":"IOP Publishing"},{"language":[{"iso":"ger"}],"user_id":"105","series_title":"Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller","department":[{"_id":"465"},{"_id":"5"}],"_id":"53473","status":"public","editor":[{"full_name":"Elit, Stefan","last_name":"Elit","first_name":"Stefan"},{"first_name":"Norbert Otto","full_name":"Eke, Norbert Otto","last_name":"Eke"}],"type":"book_chapter","publication":"‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023","title":"‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“","date_created":"2024-04-12T16:05:19Z","author":[{"first_name":"Stefan","orcid":"0000-0002-4719-1073","last_name":"Elit","id":"105","full_name":"Elit, Stefan"}],"volume":"41.","publisher":"Aisthesis","date_updated":"2024-04-12T16:06:59Z","citation":{"apa":"Elit, S. (2024). ‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“. In S. Elit &#38; N. O. Eke (Eds.), <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023: Vol. 41.</i> (pp. 137–154). Aisthesis.","short":"S. Elit, in: S. Elit, N.O. Eke (Eds.), ‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023, Aisthesis, Bielefeld, 2024, pp. 137–154.","bibtex":"@inbook{Elit_2024, place={Bielefeld}, series={Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller}, title={‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“}, volume={41.}, booktitle={‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023}, publisher={Aisthesis}, author={Elit, Stefan}, editor={Elit, Stefan and Eke, Norbert Otto}, year={2024}, pages={137–154}, collection={Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller} }","mla":"Elit, Stefan. “‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“.” <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023</i>, edited by Stefan Elit and Norbert Otto Eke, vol. 41., Aisthesis, 2024, pp. 137–54.","ieee":"S. Elit, “‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“,” in <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023</i>, vol. 41., S. Elit and N. O. Eke, Eds. Bielefeld: Aisthesis, 2024, pp. 137–154.","chicago":"Elit, Stefan. “‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“.” In <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023</i>, edited by Stefan Elit and Norbert Otto Eke, 41.:137–54. Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller. Bielefeld: Aisthesis, 2024.","ama":"Elit S. ‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“. In: Elit S, Eke NO, eds. <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023</i>. Vol 41. Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller. Aisthesis; 2024:137-154."},"page":"137-154","year":"2024","place":"Bielefeld","publication_status":"published","publication_identifier":{"eisbn":["978-3-8498-1958-3"],"isbn":["978-3-8498-1957-6"]}},{"year":"2024","quality_controlled":"1","issue":"9","title":"Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator","publisher":"IOP Publishing","date_created":"2024-03-22T08:44:39Z","abstract":[{"text":"Miller's rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller's rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller's rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller's rule, and we illustrate this point by means of a numerical example.","lang":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","creator":"schindlm","date_created":"2024-04-04T09:24:22Z","date_updated":"2024-04-04T09:24:22Z","file_name":"Meyer_2024_J._Phys._B _At._Mol._Opt._Phys._57_095001.pdf","access_level":"open_access","file_id":"53204","title":"Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator","description":"Creative Commons Attribution 4.0 International Public License (CC BY 4.0)","file_size":358155}],"publication":"Journal of Physics B: Atomic, Molecular and Optical Physics","ddc":["530"],"language":[{"iso":"eng"}],"external_id":{"isi":["001196678300001"]},"citation":{"ieee":"M. T. Meyer and A. Schindlmayr, “Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator,” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, vol. 57, no. 9, Art. no. 095001, 2024, doi: <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>.","chicago":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Derivation of Miller’s Rule for the Nonlinear Optical Susceptibility of a Quantum Anharmonic Oscillator.” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i> 57, no. 9 (2024). <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">https://doi.org/10.1088/1361-6455/ad369c</a>.","ama":"Meyer MT, Schindlmayr A. Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator. <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>. 2024;57(9). doi:<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>","apa":"Meyer, M. T., &#38; Schindlmayr, A. (2024). Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator. <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, <i>57</i>(9), Article 095001. <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">https://doi.org/10.1088/1361-6455/ad369c</a>","short":"M.T. Meyer, A. Schindlmayr, Journal of Physics B: Atomic, Molecular and Optical Physics 57 (2024).","mla":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Derivation of Miller’s Rule for the Nonlinear Optical Susceptibility of a Quantum Anharmonic Oscillator.” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, vol. 57, no. 9, 095001, IOP Publishing, 2024, doi:<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>.","bibtex":"@article{Meyer_Schindlmayr_2024, title={Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator}, volume={57}, DOI={<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>}, number={9095001}, journal={Journal of Physics B: Atomic, Molecular and Optical Physics}, publisher={IOP Publishing}, author={Meyer, Maximilian Tim and Schindlmayr, Arno}, year={2024} }"},"intvolume":"        57","publication_status":"published","has_accepted_license":"1","publication_identifier":{"eissn":["1361-6455"],"issn":["0953-4075"]},"doi":"10.1088/1361-6455/ad369c","date_updated":"2024-04-13T11:20:56Z","oa":"1","author":[{"orcid":"0009-0003-4899-0920","last_name":"Meyer","full_name":"Meyer, Maximilian Tim","id":"77895","first_name":"Maximilian Tim"},{"first_name":"Arno","id":"458","full_name":"Schindlmayr, Arno","orcid":"0000-0002-4855-071X","last_name":"Schindlmayr"}],"volume":57,"status":"public","type":"journal_article","article_number":"095001","article_type":"original","isi":"1","file_date_updated":"2024-04-04T09:24:22Z","_id":"52723","user_id":"458","department":[{"_id":"296"},{"_id":"230"},{"_id":"15"},{"_id":"170"},{"_id":"35"}]},{"year":"2024","citation":{"short":"M. Lass, T. Kenter, C. Plessl, M. Brehm, Entropy 26 (2024).","mla":"Lass, Michael, et al. “Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations.” <i>Entropy</i>, vol. 26, no. 4, 322, MDPI AG, 2024, doi:<a href=\"https://doi.org/10.3390/e26040322\">10.3390/e26040322</a>.","bibtex":"@article{Lass_Kenter_Plessl_Brehm_2024, title={Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations}, volume={26}, DOI={<a href=\"https://doi.org/10.3390/e26040322\">10.3390/e26040322</a>}, number={4322}, journal={Entropy}, publisher={MDPI AG}, author={Lass, Michael and Kenter, Tobias and Plessl, Christian and Brehm, Martin}, year={2024} }","apa":"Lass, M., Kenter, T., Plessl, C., &#38; Brehm, M. (2024). Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations. <i>Entropy</i>, <i>26</i>(4), Article 322. <a href=\"https://doi.org/10.3390/e26040322\">https://doi.org/10.3390/e26040322</a>","ieee":"M. Lass, T. Kenter, C. Plessl, and M. Brehm, “Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations,” <i>Entropy</i>, vol. 26, no. 4, Art. no. 322, 2024, doi: <a href=\"https://doi.org/10.3390/e26040322\">10.3390/e26040322</a>.","chicago":"Lass, Michael, Tobias Kenter, Christian Plessl, and Martin Brehm. “Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations.” <i>Entropy</i> 26, no. 4 (2024). <a href=\"https://doi.org/10.3390/e26040322\">https://doi.org/10.3390/e26040322</a>.","ama":"Lass M, Kenter T, Plessl C, Brehm M. Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations. <i>Entropy</i>. 2024;26(4). doi:<a href=\"https://doi.org/10.3390/e26040322\">10.3390/e26040322</a>"},"intvolume":"        26","publication_status":"published","publication_identifier":{"issn":["1099-4300"]},"issue":"4","title":"Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations","doi":"10.3390/e26040322","date_updated":"2024-04-12T18:34:32Z","publisher":"MDPI AG","date_created":"2024-04-12T18:31:39Z","author":[{"orcid":"0000-0002-5708-7632","last_name":"Lass","full_name":"Lass, Michael","id":"24135","first_name":"Michael"},{"first_name":"Tobias","full_name":"Kenter, Tobias","id":"3145","last_name":"Kenter"},{"first_name":"Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl","id":"16153","full_name":"Plessl, Christian"},{"first_name":"Martin","id":"100167","full_name":"Brehm, Martin","last_name":"Brehm"}],"volume":26,"abstract":[{"text":"We present a novel approach to characterize and quantify microheterogeneity and microphase separation in computer simulations of complex liquid mixtures. Our post-processing method is based on local density fluctuations of the different constituents in sampling spheres of varying size. It can be easily applied to both molecular dynamics (MD) and Monte Carlo (MC) simulations, including periodic boundary conditions. Multidimensional correlation of the density distributions yields a clear picture of the domain formation due to the subtle balance of different interactions. We apply our approach to the example of force field molecular dynamics simulations of imidazolium-based ionic liquids with different side chain lengths at different temperatures, namely 1-ethyl-3-methylimidazolium chloride, 1-hexyl-3-methylimidazolium chloride, and 1-decyl-3-methylimidazolium chloride, which are known to form distinct liquid domains. We put the results into the context of existing microheterogeneity analyses and demonstrate the advantages and sensitivity of our novel method. Furthermore, we show how to estimate the configuration entropy from our analysis, and we investigate voids in the system. The analysis has been implemented into our program package TRAVIS and is thus available as free software.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Entropy","article_number":"322","language":[{"iso":"eng"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"53474","user_id":"24135","department":[{"_id":"27"},{"_id":"518"},{"_id":"803"}]},{"date_created":"2024-04-12T15:56:15Z","volume":"41.","publisher":"Aisthesis","date_updated":"2024-04-12T16:19:16Z","title":"'Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23","publication_status":"published","publication_identifier":{"isbn":["978-3-8498-1957-6"],"eisbn":["978-3-8498-1958-3"]},"citation":{"chicago":"Eke, Norbert, and Stefan Elit, eds. <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23</i>. Vol. 41. Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller. Bielefeld: Aisthesis, 2024.","ieee":"N. Eke and S. Elit, Eds., <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23</i>, vol. 41. Bielefeld: Aisthesis, 2024.","ama":"Eke N, Elit S, eds. <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23</i>. Vol 41. Aisthesis; 2024.","short":"N. Eke, S. Elit, eds., ’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23, Aisthesis, Bielefeld, 2024.","mla":"Eke, Norbert, and Stefan Elit, editors. <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23</i>. Aisthesis, 2024.","bibtex":"@book{Eke_Elit_2024, place={Bielefeld}, series={Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller}, title={’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23}, volume={41.}, publisher={Aisthesis}, year={2024}, collection={Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller} }","apa":"Eke, N., &#38; Elit, S. (Eds.). (2024). <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23: Vol. 41.</i> Aisthesis."},"page":"178","year":"2024","place":"Bielefeld","series_title":"Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller","user_id":"105","department":[{"_id":"465"},{"_id":"5"}],"_id":"53472","language":[{"iso":"ger"}],"type":"book_editor","status":"public","editor":[{"last_name":"Eke","id":"104","full_name":"Eke, Norbert","first_name":"Norbert"},{"first_name":"Stefan","full_name":"Elit, Stefan","id":"105","orcid":"0000-0002-4719-1073","last_name":"Elit"}]},{"date_updated":"2024-04-15T05:49:13Z","publisher":"Aisthesis","date_created":"2024-04-10T10:03:47Z","author":[{"first_name":"Norbert","last_name":"Eke","id":"104","full_name":"Eke, Norbert"}],"title":"‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.","publication_status":"published","publication_identifier":{"isbn":["978-3-8498-1957-6"]},"place":"Bielefeld","year":"2024","citation":{"apa":"Eke, N. (2024). ‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung. In N. O. Eke &#38; E. Stefan (Eds.), <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i> (pp. 7-10 (mit Stefan Elit)). Aisthesis.","bibtex":"@inbook{Eke_2024, place={Bielefeld}, title={‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.}, booktitle={‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23}, publisher={Aisthesis}, author={Eke, Norbert}, editor={Eke, Norbert Otto and Stefan, Elit}, year={2024}, pages={7-10 (mit Stefan Elit)} }","short":"N. Eke, in: N.O. Eke, E. Stefan (Eds.), ‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23, Aisthesis, Bielefeld, 2024, pp. 7-10 (mit Stefan Elit).","mla":"Eke, Norbert. “‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.” <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, edited by Norbert Otto Eke and Elit Stefan, Aisthesis, 2024, pp. 7-10 (mit Stefan Elit).","ama":"Eke N. ‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung. In: Eke NO, Stefan E, eds. <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>. Aisthesis; 2024:7-10 (mit Stefan Elit).","ieee":"N. Eke, “‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.,” in <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, N. O. Eke and E. Stefan, Eds. Bielefeld: Aisthesis, 2024, pp. 7-10 (mit Stefan Elit).","chicago":"Eke, Norbert. “‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.” In <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, edited by Norbert Otto Eke and Elit Stefan, 7-10 (mit Stefan Elit). Bielefeld: Aisthesis, 2024."},"page":"7-10 (mit Stefan Elit)","_id":"53396","user_id":"104","language":[{"iso":"ger"}],"type":"book_chapter","publication":"‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23","editor":[{"full_name":"Eke, Norbert Otto","last_name":"Eke","first_name":"Norbert Otto"},{"last_name":"Stefan","full_name":"Stefan, Elit","first_name":"Elit"}],"status":"public"},{"publication":"‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23","type":"book_chapter","status":"public","editor":[{"full_name":"Eke, Norbert Otto","last_name":"Eke","first_name":"Norbert Otto"},{"first_name":"Stefan","last_name":"Elit","full_name":"Elit, Stefan"}],"user_id":"104","_id":"53399","language":[{"iso":"ger"}],"publication_identifier":{"isbn":["978-3-8498-1957-6"]},"publication_status":"published","page":"105-119","citation":{"mla":"Eke, Norbert. “Sich selbst erzählen. Lea Streisands autofiktionales Erzählen. .” <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, edited by Norbert Otto Eke and Stefan Elit, Aisthesis, 2024, pp. 105–19.","short":"N. Eke, in: N.O. Eke, S. Elit (Eds.), ‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23, Aisthesis, Bielefeld, 2024, pp. 105–119.","bibtex":"@inbook{Eke_2024, place={Bielefeld}, title={Sich selbst erzählen. Lea Streisands autofiktionales Erzählen. }, booktitle={‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23}, publisher={Aisthesis}, author={Eke, Norbert}, editor={Eke, Norbert Otto and Elit, Stefan}, year={2024}, pages={105–119} }","apa":"Eke, N. (2024). Sich selbst erzählen. Lea Streisands autofiktionales Erzählen. . In N. O. Eke &#38; S. Elit (Eds.), <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i> (pp. 105–119). Aisthesis.","ama":"Eke N. Sich selbst erzählen. Lea Streisands autofiktionales Erzählen. . In: Eke NO, Elit S, eds. <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>. Aisthesis; 2024:105-119.","chicago":"Eke, Norbert. “Sich selbst erzählen. Lea Streisands autofiktionales Erzählen. .” In <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, edited by Norbert Otto Eke and Stefan Elit, 105–19. Bielefeld: Aisthesis, 2024.","ieee":"N. Eke, “Sich selbst erzählen. Lea Streisands autofiktionales Erzählen. ,” in <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, N. O. Eke and S. Elit, Eds. Bielefeld: Aisthesis, 2024, pp. 105–119."},"year":"2024","place":"Bielefeld","author":[{"last_name":"Eke","full_name":"Eke, Norbert","id":"104","first_name":"Norbert"}],"date_created":"2024-04-10T10:05:54Z","publisher":"Aisthesis","date_updated":"2024-04-15T05:43:09Z","title":"Sich selbst erzählen. Lea Streisands autofiktionales Erzählen. "},{"publication_identifier":{"isbn":["978-0-907311-47-8"]},"publication_status":"published","citation":{"mla":"Langer, Svenja. <i>Lines in the Sand</i>. Bolton Print, 2024.","bibtex":"@book{Langer_2024, place={Bolton}, title={Lines in the Sand}, publisher={Bolton Print}, author={Langer, Svenja}, year={2024} }","short":"S. Langer, Lines in the Sand, Bolton Print, Bolton, 2024.","apa":"Langer, S. (2024). <i>Lines in the Sand</i>. Bolton Print.","ama":"Langer S. <i>Lines in the Sand</i>. Bolton Print; 2024.","chicago":"Langer, Svenja. <i>Lines in the Sand</i>. Bolton: Bolton Print, 2024.","ieee":"S. Langer, <i>Lines in the Sand</i>. 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