[{"citation":{"ieee":"S. De, V. Ansari, J. Sperling, S. Barkhofen, B. Brecht, and C. Silberhorn, “Realization of high-fidelity unitary operations on up to 64 frequency bins,” Physical Review Research, vol. 6, no. 2, Art. no. L022040, 2024, doi: 10.1103/physrevresearch.6.l022040.","chicago":"De, Syamsundar, Vahid Ansari, Jan Sperling, Sonja Barkhofen, Benjamin Brecht, and Christine Silberhorn. “Realization of High-Fidelity Unitary Operations on up to 64 Frequency Bins.” Physical Review Research 6, no. 2 (2024). https://doi.org/10.1103/physrevresearch.6.l022040.","ama":"De S, Ansari V, Sperling J, Barkhofen S, Brecht B, Silberhorn C. Realization of high-fidelity unitary operations on up to 64 frequency bins. Physical Review Research. 2024;6(2). doi:10.1103/physrevresearch.6.l022040","apa":"De, S., Ansari, V., Sperling, J., Barkhofen, S., Brecht, B., & Silberhorn, C. (2024). Realization of high-fidelity unitary operations on up to 64 frequency bins. Physical Review Research, 6(2), Article L022040. https://doi.org/10.1103/physrevresearch.6.l022040","mla":"De, Syamsundar, et al. “Realization of High-Fidelity Unitary Operations on up to 64 Frequency Bins.” Physical Review Research, vol. 6, no. 2, L022040, American Physical Society (APS), 2024, doi:10.1103/physrevresearch.6.l022040.","short":"S. De, V. Ansari, J. Sperling, S. Barkhofen, B. Brecht, C. Silberhorn, Physical Review Research 6 (2024).","bibtex":"@article{De_Ansari_Sperling_Barkhofen_Brecht_Silberhorn_2024, title={Realization of high-fidelity unitary operations on up to 64 frequency bins}, volume={6}, DOI={10.1103/physrevresearch.6.l022040}, number={2L022040}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={De, Syamsundar and Ansari, Vahid and Sperling, Jan and Barkhofen, Sonja and Brecht, Benjamin and Silberhorn, Christine}, year={2024} }"},"intvolume":" 6","publication_status":"published","publication_identifier":{"issn":["2643-1564"]},"doi":"10.1103/physrevresearch.6.l022040","author":[{"first_name":"Syamsundar","last_name":"De","full_name":"De, Syamsundar"},{"first_name":"Vahid","last_name":"Ansari","full_name":"Ansari, Vahid"},{"first_name":"Jan","id":"75127","full_name":"Sperling, Jan","orcid":"0000-0002-5844-3205","last_name":"Sperling"},{"first_name":"Sonja","full_name":"Barkhofen, Sonja","id":"48188","last_name":"Barkhofen"},{"full_name":"Brecht, Benjamin","id":"27150","last_name":"Brecht","orcid":"0000-0003-4140-0556 ","first_name":"Benjamin"},{"last_name":"Silberhorn","full_name":"Silberhorn, Christine","id":"26263","first_name":"Christine"}],"volume":6,"date_updated":"2025-12-18T16:14:39Z","status":"public","type":"journal_article","article_number":"L022040","user_id":"27150","department":[{"_id":"623"},{"_id":"288"},{"_id":"15"}],"project":[{"name":"QuPoPCoRN: QUPOPCORN: Quantum Particles on Programmable Complex Reconfigurable Networks","_id":"216"}],"_id":"54288","year":"2024","issue":"2","title":"Realization of high-fidelity unitary operations on up to 64 frequency bins","date_created":"2024-05-14T12:40:48Z","publisher":"American Physical Society (APS)","abstract":[{"text":"The ability to apply user-chosen large-scale unitary operations with high fidelity to a quantum state is key to realizing future photonic quantum technologies. Here, we realize the implementation of programmable unitary operations on up to 64 frequency-bin modes. To benchmark the performance of our system, we probe different quantum walk unitary operations, in particular, Grover walks on four-dimensional hypercubes with similarities exceeding 95% and quantum walks with 400 steps on circles and finite lines with similarities of 98%. Our results open a path toward implementing high-quality unitary operations, which can form the basis for applications in complex tasks, such as Gaussian boson sampling.\r\n \r\n \r\n \r\n \r\n Published by the American Physical Society\r\n 2024\r\n \r\n \r\n ","lang":"eng"}],"publication":"Physical Review Research","language":[{"iso":"eng"}]},{"status":"public","abstract":[{"lang":"eng","text":"Linear optical quantum networks, consisting of a quantum input state and a multiport interferometer, are an important building block for many quantum technological concepts, e.g., Gaussian boson sampling. Here, we propose the implementation of such networks based on frequency conversion by utilizing a so-called multioutput quantum pulse gate (MQPG). This approach allows the resource-efficient and therefore scalable implementation of frequency-bin-based, fully programmable interferometers in a single spatial and polarization mode. Quantum input states for this network can be provided by utilizing the strong frequency entanglement of a type-0 parametric down-conversion (PDC) source. Here, we develop a theoretical framework to describe linear networks based on an MQPG and PDC and utilize it to investigate the limits and scalabilty of our approach.\r\n \r\n \r\n \r\n \r\n Published by the American Physical Society\r\n 2024\r\n \r\n \r\n "}],"publication":"PRX Quantum","type":"journal_article","language":[{"iso":"eng"}],"article_number":"040329","department":[{"_id":"15"},{"_id":"623"}],"user_id":"27150","_id":"63218","intvolume":" 5","citation":{"ieee":"P. F. Folge, M. Stefszky, B. Brecht, and C. Silberhorn, “A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates,” PRX Quantum, vol. 5, no. 4, Art. no. 040329, 2024, doi: 10.1103/prxquantum.5.040329.","chicago":"Folge, Patrick Fabian, Michael Stefszky, Benjamin Brecht, and Christine Silberhorn. “A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates.” PRX Quantum 5, no. 4 (2024). https://doi.org/10.1103/prxquantum.5.040329.","ama":"Folge PF, Stefszky M, Brecht B, Silberhorn C. A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates. PRX Quantum. 2024;5(4). doi:10.1103/prxquantum.5.040329","apa":"Folge, P. F., Stefszky, M., Brecht, B., & Silberhorn, C. (2024). A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates. PRX Quantum, 5(4), Article 040329. https://doi.org/10.1103/prxquantum.5.040329","short":"P.F. Folge, M. Stefszky, B. Brecht, C. Silberhorn, PRX Quantum 5 (2024).","bibtex":"@article{Folge_Stefszky_Brecht_Silberhorn_2024, title={A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates}, volume={5}, DOI={10.1103/prxquantum.5.040329}, number={4040329}, journal={PRX Quantum}, publisher={American Physical Society (APS)}, author={Folge, Patrick Fabian and Stefszky, Michael and Brecht, Benjamin and Silberhorn, Christine}, year={2024} }","mla":"Folge, Patrick Fabian, et al. “A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates.” PRX Quantum, vol. 5, no. 4, 040329, American Physical Society (APS), 2024, doi:10.1103/prxquantum.5.040329."},"year":"2024","issue":"4","publication_identifier":{"issn":["2691-3399"]},"publication_status":"published","doi":"10.1103/prxquantum.5.040329","title":"A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates","volume":5,"author":[{"first_name":"Patrick Fabian","last_name":"Folge","id":"88605","full_name":"Folge, Patrick Fabian"},{"full_name":"Stefszky, Michael","id":"42777","last_name":"Stefszky","first_name":"Michael"},{"first_name":"Benjamin","full_name":"Brecht, Benjamin","id":"27150","orcid":"0000-0003-4140-0556 ","last_name":"Brecht"},{"first_name":"Christine","last_name":"Silberhorn","full_name":"Silberhorn, Christine","id":"26263"}],"date_created":"2025-12-18T16:10:37Z","publisher":"American Physical Society (APS)","date_updated":"2025-12-18T16:10:55Z"},{"year":"2024","intvolume":" 33","citation":{"ama":"Serino LM, Eigner C, Brecht B, Silberhorn C. Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate. Optics Express. 2024;33(3). doi:10.1364/oe.544206","ieee":"L. M. Serino, C. Eigner, B. Brecht, and C. Silberhorn, “Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate,” Optics Express, vol. 33, no. 3, Art. no. 5577, 2024, doi: 10.1364/oe.544206.","chicago":"Serino, Laura Maria, Christof Eigner, Benjamin Brecht, and Christine Silberhorn. “Programmable Time-Frequency Mode-Sorting of Single Photons with a Multi-Output Quantum Pulse Gate.” Optics Express 33, no. 3 (2024). https://doi.org/10.1364/oe.544206.","apa":"Serino, L. M., Eigner, C., Brecht, B., & Silberhorn, C. (2024). Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate. Optics Express, 33(3), Article 5577. https://doi.org/10.1364/oe.544206","bibtex":"@article{Serino_Eigner_Brecht_Silberhorn_2024, title={Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate}, volume={33}, DOI={10.1364/oe.544206}, number={35577}, journal={Optics Express}, publisher={Optica Publishing Group}, author={Serino, Laura Maria and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}, year={2024} }","short":"L.M. Serino, C. Eigner, B. Brecht, C. Silberhorn, Optics Express 33 (2024).","mla":"Serino, Laura Maria, et al. “Programmable Time-Frequency Mode-Sorting of Single Photons with a Multi-Output Quantum Pulse Gate.” Optics Express, vol. 33, no. 3, 5577, Optica Publishing Group, 2024, doi:10.1364/oe.544206."},"publication_identifier":{"issn":["1094-4087"]},"publication_status":"published","issue":"3","title":"Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate","doi":"10.1364/oe.544206","publisher":"Optica Publishing Group","date_updated":"2025-12-18T16:09:44Z","volume":33,"author":[{"first_name":"Laura Maria","last_name":"Serino","id":"88242","full_name":"Serino, Laura Maria"},{"first_name":"Christof","last_name":"Eigner","orcid":"https://orcid.org/0000-0002-5693-3083","id":"13244","full_name":"Eigner, Christof"},{"full_name":"Brecht, Benjamin","id":"27150","last_name":"Brecht","orcid":"0000-0003-4140-0556 ","first_name":"Benjamin"},{"full_name":"Silberhorn, Christine","id":"26263","last_name":"Silberhorn","first_name":"Christine"}],"date_created":"2025-12-18T16:09:22Z","abstract":[{"text":"We demonstrate a high-dimensional mode-sorter for single photons based on a multi-output quantum pulse gate, which we can program to switch between different temporal-mode encodings including pulse modes, frequency bins, time bins, and their superpositions. This device can facilitate practical realizations of quantum information applications such as high-dimensional quantum key distribution and thus enables secure communication with enhanced information capacity. We characterize the mode-sorter through a detector tomography in 3 and 5 dimensions and find a fidelity up to 0.958 ± 0.030 at the single-photon level.","lang":"eng"}],"status":"public","publication":"Optics Express","type":"journal_article","article_number":"5577","language":[{"iso":"eng"}],"_id":"63217","department":[{"_id":"15"},{"_id":"623"}],"user_id":"27150"},{"user_id":"55629","department":[{"_id":"15"},{"_id":"623"}],"project":[{"name":"PhoQuant: Photonische Quantencomputer - Quantencomputing Testplattform","_id":"191"},{"_id":"239","name":"ERC-Grant: QuESADILLA: Quantum Engineering Superconducting Array Detectors in Low-Light Applications"},{"name":"ISOQC: Quantenkommunikation mit integrierter Optik im Zusammenhang mit supraleitender Elektronik","_id":"209"}],"_id":"50840","language":[{"iso":"eng"}],"article_number":"1","type":"journal_article","publication":"Optica Quantum","status":"public","abstract":[{"text":"Superconducting nanowire single-photon detectors (SNSPDs) have been widely used to study the discrete nature of quantum states of light in the form of photon-counting experiments. We show that SNSPDs can also be used to study continuous variables of optical quantum states by performing homodyne detection at a bandwidth of 400 kHz. By measuring the interference of a continuous-wave field of a local oscillator with the field of the vacuum state using two SNSPDs, we show that the variance of the difference in count rates is linearly proportional to the photon flux of the local oscillator over almost five orders of magnitude. The resulting shot-noise clearance of (46.0 ± 1.1) dB is the highest reported clearance for a balanced optical homodyne detector, demonstrating their potential for measuring highly squeezed states in the continuous-wave regime. In addition, we measured a CMRR = 22.4 dB. From the joint click counting statistics, we also measure the phase-dependent quadrature of a weak coherent state to demonstrate our device’s functionality as a homodyne detector.","lang":"eng"}],"author":[{"id":"46170","full_name":"Protte, Maximilian","last_name":"Protte","first_name":"Maximilian"},{"first_name":"Timon","orcid":"0000-0001-7652-1716","last_name":"Schapeler","id":"55629","full_name":"Schapeler, Timon"},{"full_name":"Sperling, Jan","id":"75127","orcid":"0000-0002-5844-3205","last_name":"Sperling","first_name":"Jan"},{"full_name":"Bartley, Tim","id":"49683","last_name":"Bartley","first_name":"Tim"}],"date_created":"2024-01-25T11:48:02Z","volume":2,"oa":"1","publisher":"Optica Publishing Group","date_updated":"2025-12-18T17:06:27Z","main_file_link":[{"open_access":"1"}],"doi":"10.1364/opticaq.502201","title":"Low-noise balanced homodyne detection with superconducting nanowire single-photon detectors","issue":"1","publication_status":"published","publication_identifier":{"issn":["2837-6714"]},"citation":{"ama":"Protte M, Schapeler T, Sperling J, Bartley T. Low-noise balanced homodyne detection with superconducting nanowire single-photon detectors. Optica Quantum. 2024;2(1). doi:10.1364/opticaq.502201","chicago":"Protte, Maximilian, Timon Schapeler, Jan Sperling, and Tim Bartley. “Low-Noise Balanced Homodyne Detection with Superconducting Nanowire Single-Photon Detectors.” Optica Quantum 2, no. 1 (2024). https://doi.org/10.1364/opticaq.502201.","ieee":"M. Protte, T. Schapeler, J. Sperling, and T. Bartley, “Low-noise balanced homodyne detection with superconducting nanowire single-photon detectors,” Optica Quantum, vol. 2, no. 1, Art. no. 1, 2024, doi: 10.1364/opticaq.502201.","apa":"Protte, M., Schapeler, T., Sperling, J., & Bartley, T. (2024). Low-noise balanced homodyne detection with superconducting nanowire single-photon detectors. Optica Quantum, 2(1), Article 1. https://doi.org/10.1364/opticaq.502201","bibtex":"@article{Protte_Schapeler_Sperling_Bartley_2024, title={Low-noise balanced homodyne detection with superconducting nanowire single-photon detectors}, volume={2}, DOI={10.1364/opticaq.502201}, number={11}, journal={Optica Quantum}, publisher={Optica Publishing Group}, author={Protte, Maximilian and Schapeler, Timon and Sperling, Jan and Bartley, Tim}, year={2024} }","mla":"Protte, Maximilian, et al. “Low-Noise Balanced Homodyne Detection with Superconducting Nanowire Single-Photon Detectors.” Optica Quantum, vol. 2, no. 1, 1, Optica Publishing Group, 2024, doi:10.1364/opticaq.502201.","short":"M. Protte, T. Schapeler, J. Sperling, T. Bartley, Optica Quantum 2 (2024)."},"intvolume":" 2","year":"2024"},{"doi":"10.1039/d3an02210b","date_updated":"2025-12-18T17:42:48Z","volume":149,"author":[{"last_name":"Biermann","full_name":"Biermann, Michael","first_name":"Michael"},{"first_name":"Christian","last_name":"Leppin","full_name":"Leppin, Christian","id":"117722"},{"full_name":"Langhoff, Arne","last_name":"Langhoff","first_name":"Arne"},{"full_name":"Ziemer, Thorben","last_name":"Ziemer","first_name":"Thorben"},{"full_name":"Rembe, Christian","last_name":"Rembe","first_name":"Christian"},{"first_name":"Diethelm","full_name":"Johannsmann, Diethelm","last_name":"Johannsmann"}],"intvolume":" 149","page":"2138-2146","citation":{"ama":"Biermann M, Leppin C, Langhoff A, Ziemer T, Rembe C, Johannsmann D. An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition. The Analyst. 2024;149(7):2138-2146. doi:10.1039/d3an02210b","chicago":"Biermann, Michael, Christian Leppin, Arne Langhoff, Thorben Ziemer, Christian Rembe, and Diethelm Johannsmann. “An Electrochemical Quartz Crystal Microbalance (EQCM) Based on Microelectrode Arrays Allows to Distinguish between Adsorption and Electrodeposition.” The Analyst 149, no. 7 (2024): 2138–46. https://doi.org/10.1039/d3an02210b.","ieee":"M. Biermann, C. Leppin, A. Langhoff, T. Ziemer, C. Rembe, and D. Johannsmann, “An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition,” The Analyst, vol. 149, no. 7, pp. 2138–2146, 2024, doi: 10.1039/d3an02210b.","apa":"Biermann, M., Leppin, C., Langhoff, A., Ziemer, T., Rembe, C., & Johannsmann, D. (2024). An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition. The Analyst, 149(7), 2138–2146. https://doi.org/10.1039/d3an02210b","mla":"Biermann, Michael, et al. “An Electrochemical Quartz Crystal Microbalance (EQCM) Based on Microelectrode Arrays Allows to Distinguish between Adsorption and Electrodeposition.” The Analyst, vol. 149, no. 7, Royal Society of Chemistry (RSC), 2024, pp. 2138–46, doi:10.1039/d3an02210b.","short":"M. Biermann, C. Leppin, A. Langhoff, T. Ziemer, C. Rembe, D. Johannsmann, The Analyst 149 (2024) 2138–2146.","bibtex":"@article{Biermann_Leppin_Langhoff_Ziemer_Rembe_Johannsmann_2024, title={An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition}, volume={149}, DOI={10.1039/d3an02210b}, number={7}, journal={The Analyst}, publisher={Royal Society of Chemistry (RSC)}, author={Biermann, Michael and Leppin, Christian and Langhoff, Arne and Ziemer, Thorben and Rembe, Christian and Johannsmann, Diethelm}, year={2024}, pages={2138–2146} }"},"publication_identifier":{"issn":["0003-2654","1364-5528"]},"publication_status":"published","article_type":"original","extern":"1","_id":"63227","user_id":"117722","status":"public","type":"journal_article","title":"An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition","publisher":"Royal Society of Chemistry (RSC)","date_created":"2025-12-18T17:01:44Z","year":"2024","quality_controlled":"1","issue":"7","language":[{"iso":"eng"}],"abstract":[{"text":"Using a precise electrochemical quartz crystal microbalance (EQCM), it was shown that electrogravimetry can be carried out with microelectrode arrays (MEAs). Significant differences between the potential dependent adsorption of a redox-active molecule and electroplating were presented.","lang":"eng"}],"publication":"The Analyst"},{"_id":"63264","user_id":"31496","language":[{"iso":"eng"}],"publication":"Advanced Nonlinear Studies","type":"journal_article","abstract":[{"text":"Abstract\r\n In a smoothly bounded convex domain \r\n \r\n \r\n Ω\r\n ⊂\r\n \r\n \r\n R\r\n \r\n \r\n n\r\n \r\n \r\n \r\n \r\n${\\Omega}\\subset {\\mathbb{R}}^{n}$\r\n\r\n \r\n \r\n with n ≥ 1, a no-flux initial-boundary value problem for\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n \r\n \r\n t\r\n \r\n \r\n =\r\n Δ\r\n \r\n \r\n u\r\n ϕ\r\n \r\n (\r\n \r\n v\r\n \r\n )\r\n \r\n \r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n v\r\n \r\n \r\n t\r\n \r\n \r\n =\r\n Δ\r\n v\r\n −\r\n u\r\n v\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n$$\\begin{cases}_{t}={\\Delta}\\left(u\\phi \\left(v\\right)\\right),\\quad \\hfill \\\\ {v}_{t}={\\Delta}v-uv,\\quad \\hfill \\end{cases}$$\r\n\r\n \r\n \r\n is considered under the assumption that near the origin, the function ϕ suitably generalizes the prototype given by\r\n \r\n \r\n ϕ\r\n \r\n (\r\n \r\n ξ\r\n \r\n )\r\n \r\n =\r\n \r\n \r\n ξ\r\n \r\n \r\n α\r\n \r\n \r\n ,\r\n \r\n ξ\r\n ∈\r\n \r\n [\r\n \r\n 0\r\n ,\r\n \r\n \r\n ξ\r\n \r\n \r\n 0\r\n \r\n \r\n \r\n ]\r\n \r\n .\r\n \r\n \r\n$$\\phi \\left(\\xi \\right)={\\xi }^{\\alpha },\\qquad \\xi \\in \\left[0,{\\xi }_{0}\\right].$$\r\n\r\n \r\n \r\n By means of separate approaches, it is shown that in both cases α ∈ (0, 1) and α ∈ [1, 2] some global weak solutions exist which, inter alia, satisfy\r\n \r\n \r\n C\r\n \r\n (\r\n \r\n T\r\n \r\n )\r\n \r\n ≔\r\n \r\n \r\n ess sup\r\n \r\n \r\n t\r\n ∈\r\n \r\n (\r\n \r\n 0\r\n ,\r\n T\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n \r\n \r\n Ω\r\n \r\n \r\n u\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n ln\r\n \r\n u\r\n \r\n (\r\n \r\n ⋅\r\n ,\r\n t\r\n \r\n )\r\n \r\n <\r\n ∞\r\n \r\n for all \r\n T\r\n >\r\n 0\r\n ,\r\n \r\n \r\n$$C\\left(T\\right){:=}\\underset{t\\in \\left(0,T\\right)}{\\text{ess\\,sup}}{\\int }_{{\\Omega}}u\\left(\\cdot ,t\\right)\\mathrm{ln}u\\left(\\cdot ,t\\right){< }\\infty \\qquad \\text{for\\,all\\,}T{ >}0,$$\r\n\r\n \r\n \r\n with sup\r\n T>0\r\n C(T) < ∞ if α ∈ [1, 2].","lang":"eng"}],"status":"public","date_updated":"2025-12-18T20:10:00Z","publisher":"Walter de Gruyter GmbH","volume":24,"date_created":"2025-12-18T19:09:41Z","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"title":"A degenerate migration-consumption model in domains of arbitrary dimension","doi":"10.1515/ans-2023-0131","publication_identifier":{"issn":["2169-0375"]},"publication_status":"published","issue":"3","year":"2024","page":"592-615","intvolume":" 24","citation":{"ama":"Winkler M. A degenerate migration-consumption model in domains of arbitrary dimension. Advanced Nonlinear Studies. 2024;24(3):592-615. doi:10.1515/ans-2023-0131","ieee":"M. Winkler, “A degenerate migration-consumption model in domains of arbitrary dimension,” Advanced Nonlinear Studies, vol. 24, no. 3, pp. 592–615, 2024, doi: 10.1515/ans-2023-0131.","chicago":"Winkler, Michael. “A Degenerate Migration-Consumption Model in Domains of Arbitrary Dimension.” Advanced Nonlinear Studies 24, no. 3 (2024): 592–615. https://doi.org/10.1515/ans-2023-0131.","apa":"Winkler, M. (2024). A degenerate migration-consumption model in domains of arbitrary dimension. Advanced Nonlinear Studies, 24(3), 592–615. https://doi.org/10.1515/ans-2023-0131","short":"M. Winkler, Advanced Nonlinear Studies 24 (2024) 592–615.","bibtex":"@article{Winkler_2024, title={A degenerate migration-consumption model in domains of arbitrary dimension}, volume={24}, DOI={10.1515/ans-2023-0131}, number={3}, journal={Advanced Nonlinear Studies}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2024}, pages={592–615} }","mla":"Winkler, Michael. “A Degenerate Migration-Consumption Model in Domains of Arbitrary Dimension.” Advanced Nonlinear Studies, vol. 24, no. 3, Walter de Gruyter GmbH, 2024, pp. 592–615, doi:10.1515/ans-2023-0131."}},{"language":[{"iso":"eng"}],"user_id":"31496","_id":"63248","status":"public","abstract":[{"lang":"eng","text":"Abstract\r\n The Navier–Stokes system \r\n \r\n $$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t + (u\\cdot \\nabla ) u =\\Delta u+\\nabla P + f(x,t), \\\\ \\nabla \\cdot u=0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n +\r\n \r\n (\r\n u\r\n ·\r\n ∇\r\n )\r\n \r\n u\r\n =\r\n Δ\r\n u\r\n +\r\n ∇\r\n P\r\n +\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ∇\r\n ·\r\n u\r\n =\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered along with homogeneous Dirichlet boundary conditions in a smoothly bounded planar domain \r\n \r\n $$\\Omega $$\r\n \r\n Ω\r\n \r\n \r\n . It is firstly, inter alia, observed that if \r\n \r\n $$T>0$$\r\n \r\n \r\n T\r\n >\r\n 0\r\n \r\n \r\n \r\n and \r\n \r\n $$\\begin{aligned} \\int _0^T \\bigg \\{ \\int _\\Omega |f(x,t)| \\cdot \\ln ^\\frac{1}{2} \\big (|f(x,t)|+1\\big ) dx \\bigg \\}^2 dt <\\infty , \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n 0\r\n T\r\n \r\n \r\n {\r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n |\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n ·\r\n \r\n ln\r\n \r\n 1\r\n 2\r\n \r\n \r\n \r\n (\r\n \r\n \r\n |\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n +\r\n 1\r\n \r\n )\r\n \r\n d\r\n x\r\n \r\n \r\n }\r\n \r\n 2\r\n \r\n d\r\n t\r\n <\r\n ∞\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n then for all divergence-free \r\n \r\n $$u_0\\in L^2(\\Omega ;{\\mathbb {R}}^2)$$\r\n \r\n \r\n \r\n u\r\n 0\r\n \r\n ∈\r\n \r\n L\r\n 2\r\n \r\n \r\n (\r\n Ω\r\n ;\r\n \r\n \r\n R\r\n \r\n 2\r\n \r\n )\r\n \r\n \r\n \r\n \r\n , a corresponding initial-boundary value problem admits a weak solution u with \r\n \r\n $$u|_{t=0}=u_0$$\r\n \r\n \r\n \r\n \r\n u\r\n |\r\n \r\n \r\n t\r\n =\r\n 0\r\n \r\n \r\n =\r\n \r\n u\r\n 0\r\n \r\n \r\n \r\n \r\n . For any positive and nondecreasing \r\n \r\n $$L\\in C^0([0,\\infty ))$$\r\n \r\n \r\n L\r\n ∈\r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n such that \r\n \r\n $$\\begin{aligned} \\frac{L(\\xi )}{\\ln ^\\frac{1}{2} \\xi } \\rightarrow 0 \\qquad \\text{ as } \\xi \\rightarrow \\infty , \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n L\r\n (\r\n ξ\r\n )\r\n \r\n \r\n \r\n ln\r\n \r\n 1\r\n 2\r\n \r\n \r\n ξ\r\n \r\n \r\n →\r\n 0\r\n \r\n \r\n as\r\n \r\n ξ\r\n →\r\n ∞\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n this is complemented by a statement on nonexistence of such a solution in the presence of smooth initial data and a suitably constructed \r\n \r\n $$f:\\Omega \\times (0,T)\\rightarrow {\\mathbb {R}}^2$$\r\n \r\n \r\n f\r\n :\r\n Ω\r\n ×\r\n \r\n (\r\n 0\r\n ,\r\n T\r\n )\r\n \r\n →\r\n \r\n \r\n R\r\n \r\n 2\r\n \r\n \r\n \r\n \r\n fulfilling \r\n \r\n $$\\begin{aligned} \\int _0^T \\bigg \\{ \\int _\\Omega |f(x,t)| \\cdot L\\big (|f(x,t)|\\big ) dx \\bigg \\}^2 dt < \\infty . \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n 0\r\n T\r\n \r\n \r\n {\r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n |\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n ·\r\n \r\n L\r\n \r\n (\r\n \r\n |\r\n f\r\n \r\n (\r\n x\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n )\r\n \r\n d\r\n x\r\n \r\n \r\n \r\n }\r\n \r\n 2\r\n \r\n d\r\n t\r\n <\r\n ∞\r\n .\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n This resolves a fine structure in the borderline case \r\n \r\n $$p=1$$\r\n \r\n \r\n p\r\n =\r\n 1\r\n \r\n \r\n \r\n and \r\n \r\n $$q=2$$\r\n \r\n \r\n q\r\n =\r\n 2\r\n \r\n \r\n \r\n appearing in results on existence of weak solutions for sources in \r\n \r\n $$L^q((0,T);L^p(\\Omega ;{\\mathbb {R}}^2))$$\r\n \r\n \r\n \r\n L\r\n q\r\n \r\n \r\n (\r\n \r\n (\r\n 0\r\n ,\r\n T\r\n )\r\n \r\n ;\r\n \r\n L\r\n p\r\n \r\n \r\n (\r\n Ω\r\n ;\r\n \r\n \r\n R\r\n \r\n 2\r\n \r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n when \r\n \r\n $$p\\in (1,\\infty ]$$\r\n \r\n \r\n p\r\n ∈\r\n (\r\n 1\r\n ,\r\n ∞\r\n ]\r\n \r\n \r\n \r\n and \r\n \r\n $$q\\in [1,\\infty ]$$\r\n \r\n \r\n q\r\n ∈\r\n [\r\n 1\r\n ,\r\n ∞\r\n ]\r\n \r\n \r\n \r\n satisfy \r\n \r\n $$\\frac{1}{p}+\\frac{1}{q}\\le \\frac{3}{2}$$\r\n \r\n \r\n \r\n 1\r\n p\r\n \r\n +\r\n \r\n 1\r\n q\r\n \r\n ≤\r\n \r\n 3\r\n 2\r\n \r\n \r\n \r\n \r\n , and on nonexistence if here \r\n \r\n $$p\\in [1,\\infty )$$\r\n \r\n \r\n p\r\n ∈\r\n [\r\n 1\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n \r\n and \r\n \r\n $$q\\in [1,\\infty )$$\r\n \r\n \r\n q\r\n ∈\r\n [\r\n 1\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n \r\n are such that \r\n \r\n $$\\frac{1}{p}+\\frac{1}{q}>\\frac{3}{2}$$\r\n \r\n \r\n \r\n 1\r\n p\r\n \r\n +\r\n \r\n 1\r\n q\r\n \r\n >\r\n \r\n 3\r\n 2\r\n \r\n \r\n \r\n \r\n ."}],"publication":"Mathematische Annalen","type":"journal_article","doi":"10.1007/s00208-024-02987-6","title":"Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system","volume":391,"author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:02:09Z","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:13:05Z","page":"3023-3054","intvolume":" 391","citation":{"ama":"Winkler M. Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system. Mathematische Annalen. 2024;391(2):3023-3054. doi:10.1007/s00208-024-02987-6","chicago":"Winkler, Michael. “Externally Forced Blow-up and Optimal Spaces for Source Regularity in the Two-Dimensional Navier–Stokes System.” Mathematische Annalen 391, no. 2 (2024): 3023–54. https://doi.org/10.1007/s00208-024-02987-6.","ieee":"M. Winkler, “Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system,” Mathematische Annalen, vol. 391, no. 2, pp. 3023–3054, 2024, doi: 10.1007/s00208-024-02987-6.","mla":"Winkler, Michael. “Externally Forced Blow-up and Optimal Spaces for Source Regularity in the Two-Dimensional Navier–Stokes System.” Mathematische Annalen, vol. 391, no. 2, Springer Science and Business Media LLC, 2024, pp. 3023–54, doi:10.1007/s00208-024-02987-6.","short":"M. Winkler, Mathematische Annalen 391 (2024) 3023–3054.","bibtex":"@article{Winkler_2024, title={Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system}, volume={391}, DOI={10.1007/s00208-024-02987-6}, number={2}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2024}, pages={3023–3054} }","apa":"Winkler, M. (2024). Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system. Mathematische Annalen, 391(2), 3023–3054. https://doi.org/10.1007/s00208-024-02987-6"},"year":"2024","issue":"2","publication_identifier":{"issn":["0025-5831","1432-1807"]},"publication_status":"published"},{"year":"2024","page":"1601-1630","intvolume":" 42","citation":{"mla":"Winkler, Michael. “Logarithmically Refined Gagliardo–Nirenberg Interpolation and Application to Blow-up Exclusion in a Singular Chemotaxis–Consumption System.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, vol. 42, no. 6, European Mathematical Society - EMS - Publishing House GmbH, 2024, pp. 1601–30, doi:10.4171/aihpc/141.","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 42 (2024) 1601–1630.","bibtex":"@article{Winkler_2024, title={Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system}, volume={42}, DOI={10.4171/aihpc/141}, number={6}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2024}, pages={1601–1630} }","apa":"Winkler, M. (2024). Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 42(6), 1601–1630. https://doi.org/10.4171/aihpc/141","chicago":"Winkler, Michael. “Logarithmically Refined Gagliardo–Nirenberg Interpolation and Application to Blow-up Exclusion in a Singular Chemotaxis–Consumption System.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 42, no. 6 (2024): 1601–30. https://doi.org/10.4171/aihpc/141.","ieee":"M. Winkler, “Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 42, no. 6, pp. 1601–1630, 2024, doi: 10.4171/aihpc/141.","ama":"Winkler M. Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 2024;42(6):1601-1630. doi:10.4171/aihpc/141"},"publication_identifier":{"issn":["0294-1449","1873-1430"]},"publication_status":"published","issue":"6","title":"Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system","doi":"10.4171/aihpc/141","publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_updated":"2025-12-18T20:12:43Z","volume":42,"author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2025-12-18T19:00:24Z","abstract":[{"lang":"eng","text":"\r\n A family of interpolation inequalities is derived, which differ from estimates of classical Gagliardo–Nirenberg type through the appearance of certain logarithmic deviations from standard Lebesgue norms in zero-order expressions. Optimality of the obtained inequalities is shown. A subsequent application reveals that when posed under homogeneous Neumann boundary conditions in smoothly bounded planar domains and with suitably regular initial data, for any choice of \r\n \r\n \\alpha>0\r\n \r\n the Keller–Segel-type migration–consumption system \r\n \r\n u_{t} = \\Delta (uv^{-\\alpha})\r\n \r\n , \r\n \r\n v_{t} = \\Delta v-uv\r\n \r\n , admits a global classical solution.\r\n "}],"status":"public","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","type":"journal_article","language":[{"iso":"eng"}],"_id":"63245","user_id":"31496"},{"title":"A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects","doi":"10.1007/s00028-024-00954-x","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:14:21Z","date_created":"2025-12-18T19:06:36Z","author":[{"full_name":"Stinner, Christian","last_name":"Stinner","first_name":"Christian"},{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"volume":24,"year":"2024","citation":{"mla":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” Journal of Evolution Equations, vol. 24, no. 2, 26, Springer Science and Business Media LLC, 2024, doi:10.1007/s00028-024-00954-x.","bibtex":"@article{Stinner_Winkler_2024, title={A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects}, volume={24}, DOI={10.1007/s00028-024-00954-x}, number={226}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Stinner, Christian and Winkler, Michael}, year={2024} }","short":"C. Stinner, M. Winkler, Journal of Evolution Equations 24 (2024).","apa":"Stinner, C., & Winkler, M. (2024). A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. Journal of Evolution Equations, 24(2), Article 26. https://doi.org/10.1007/s00028-024-00954-x","chicago":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” Journal of Evolution Equations 24, no. 2 (2024). https://doi.org/10.1007/s00028-024-00954-x.","ieee":"C. Stinner and M. Winkler, “A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects,” Journal of Evolution Equations, vol. 24, no. 2, Art. no. 26, 2024, doi: 10.1007/s00028-024-00954-x.","ama":"Stinner C, Winkler M. A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. Journal of Evolution Equations. 2024;24(2). doi:10.1007/s00028-024-00954-x"},"intvolume":" 24","publication_status":"published","publication_identifier":{"issn":["1424-3199","1424-3202"]},"issue":"2","article_number":"26","language":[{"iso":"eng"}],"_id":"63257","user_id":"31496","abstract":[{"text":"AbstractThe quasilinear Keller–Segel system$$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t=\\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (S(u)\\nabla v), \\\\ v_t=\\Delta v-v+u, \\end{array}\\right. \\end{aligned}$$ut=∇·(D(u)∇u)-∇·(S(u)∇v),vt=Δv-v+u,endowed with homogeneous Neumann boundary conditions is considered in a bounded domain$$\\Omega \\subset {\\mathbb {R}}^n$$Ω⊂Rn,$$n \\ge 3$$n≥3, with smooth boundary for sufficiently regular functionsDandSsatisfying$$D>0$$D>0on$$[0,\\infty )$$[0,∞),$$S>0$$S>0on$$(0,\\infty )$$(0,∞)and$$S(0)=0$$S(0)=0. On the one hand, it is shown that if$$\\frac{S}{D}$$SDsatisfies the subcritical growth condition$$\\begin{aligned} \\frac{S(s)}{D(s)} \\le C s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha < \\frac{2}{n} \\end{aligned}$$S(s)D(s)≤Csαforalls≥1withsomeα<2nand$$C>0$$C>0, then for any sufficiently regular initial data there exists a global weak energy solution such that$${ \\mathrm{{ess}}} \\sup _{t>0} \\Vert u(t) \\Vert _{L^p(\\Omega )}<\\infty $$esssupt>0‖u(t)‖Lp(Ω)<∞for some$$p > \\frac{2n}{n+2}$$p>2nn+2. On the other hand, if$$\\frac{S}{D}$$SDsatisfies the supercritical growth condition$$\\begin{aligned} \\frac{S(s)}{D(s)} \\ge c s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha > \\frac{2}{n} \\end{aligned}$$S(s)D(s)≥csαforalls≥1withsomeα>2nand$$c>0$$c>0, then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value$$\\alpha = \\frac{2}{n}$$α=2nfor$$n \\ge 3$$n≥3, without any additional assumption on the behavior ofD(s) as$$s \\rightarrow \\infty $$s→∞, in particular without requiring any algebraic lower bound forD. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type$$Q(s) = \\exp (-s^\\beta )$$Q(s)=exp(-sβ),$$s \\ge 0$$s≥0, for global solvability the exponent$$\\beta = \\frac{n-2}{n}$$β=n-2nis seen to be critical.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Journal of Evolution Equations"},{"year":"2024","citation":{"apa":"Ding, M., & Winkler, M. (2024). Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture. Nonlinearity, 37(12), Article 125006. https://doi.org/10.1088/1361-6544/ad871a","bibtex":"@article{Ding_Winkler_2024, title={Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture}, volume={37}, DOI={10.1088/1361-6544/ad871a}, number={12125006}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Ding, Mengyao and Winkler, Michael}, year={2024} }","short":"M. Ding, M. Winkler, Nonlinearity 37 (2024).","mla":"Ding, Mengyao, and Michael Winkler. “Radial Blow-up in Quasilinear Keller-Segel Systems: Approaching the Full Picture.” Nonlinearity, vol. 37, no. 12, 125006, IOP Publishing, 2024, doi:10.1088/1361-6544/ad871a.","ama":"Ding M, Winkler M. Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture. Nonlinearity. 2024;37(12). doi:10.1088/1361-6544/ad871a","ieee":"M. Ding and M. Winkler, “Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture,” Nonlinearity, vol. 37, no. 12, Art. no. 125006, 2024, doi: 10.1088/1361-6544/ad871a.","chicago":"Ding, Mengyao, and Michael Winkler. “Radial Blow-up in Quasilinear Keller-Segel Systems: Approaching the Full Picture.” Nonlinearity 37, no. 12 (2024). https://doi.org/10.1088/1361-6544/ad871a."},"intvolume":" 37","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"issue":"12","title":"Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture","doi":"10.1088/1361-6544/ad871a","date_updated":"2025-12-18T20:13:49Z","publisher":"IOP Publishing","author":[{"first_name":"Mengyao","full_name":"Ding, Mengyao","last_name":"Ding"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_created":"2025-12-18T19:04:45Z","volume":37,"abstract":[{"lang":"eng","text":"Abstract\r\n The Neumann problem for the Keller-Segel system \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n {\r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n ∇\r\n ⋅\r\n \r\n (\r\n D\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n u\r\n )\r\n \r\n −\r\n ∇\r\n ⋅\r\n \r\n (\r\n S\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n v\r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n −\r\n μ\r\n +\r\n u\r\n ,\r\n \r\n μ\r\n =\r\n \r\n −\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n u\r\n d\r\n x\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered in n-dimensional balls Ω with \r\n \r\n \r\n \r\n n\r\n ⩾\r\n 2\r\n \r\n \r\n , with suitably regular and radially symmetric, radially nonincreasing initial data u\r\n 0. The functions D and S are only assumed to belong to \r\n \r\n \r\n \r\n \r\n C\r\n 2\r\n \r\n (\r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n )\r\n \r\n \r\n and to satisfy D > 0 and \r\n \r\n \r\n \r\n S\r\n ⩾\r\n 0\r\n \r\n \r\n on \r\n \r\n \r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n as well as \r\n \r\n \r\n \r\n S\r\n (\r\n 0\r\n )\r\n =\r\n 0\r\n \r\n \r\n ; in particular, diffusivities with arbitrarily fast decay are included.\r\n In this general context, it is shown that it is merely the asymptotic behavior as \r\n \r\n \r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n of the expression \r\n \r\n \r\n \r\n \r\n \r\n \r\n I\r\n \r\n (\r\n ξ\r\n )\r\n \r\n :=\r\n \r\n \r\n S\r\n \r\n (\r\n ξ\r\n )\r\n \r\n \r\n \r\n \r\n ξ\r\n \r\n 2\r\n n\r\n \r\n \r\n D\r\n \r\n (\r\n ξ\r\n )\r\n \r\n \r\n \r\n ,\r\n \r\n ξ\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n which decides about the occurrence of blow-up: Namely, it is seen that\r\n\r\n \r\n •\r\n if \r\n \r\n \r\n \r\n \r\n lim\r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n I\r\n (\r\n ξ\r\n )\r\n =\r\n 0\r\n \r\n \r\n , then any such solution is global and bounded, that\r\n \r\n \r\n •\r\n if \r\n \r\n \r\n \r\n \r\n lim sup\r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n I\r\n (\r\n ξ\r\n )\r\n <\r\n ∞\r\n \r\n \r\n and \r\n \r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n u\r\n 0\r\n \r\n \r\n \r\n is suitably small, then the corresponding solution is global and bounded, and that\r\n \r\n \r\n •\r\n if \r\n \r\n \r\n \r\n \r\n lim inf\r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n I\r\n (\r\n ξ\r\n )\r\n >\r\n 0\r\n \r\n \r\n , then at each appropriately large mass level m, there exist radial initial data u\r\n 0 such that \r\n \r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n u\r\n 0\r\n \r\n =\r\n m\r\n \r\n \r\n , and that the associated solution blows up either in finite or in infinite time.\r\n \r\n \r\n \r\n This especially reveals the presence of critical mass phenomena whenever \r\n \r\n \r\n \r\n \r\n lim\r\n \r\n ξ\r\n →\r\n ∞\r\n \r\n \r\n I\r\n (\r\n ξ\r\n )\r\n ∈\r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n exists."}],"status":"public","type":"journal_article","publication":"Nonlinearity","article_number":"125006","language":[{"iso":"eng"}],"_id":"63253","user_id":"31496"},{"article_number":"60","language":[{"iso":"eng"}],"_id":"63254","user_id":"31496","abstract":[{"lang":"eng","text":"AbstractThe chemotaxis-Navier–Stokes system $$\\begin{aligned} \\left\\{ \\begin{array}{rcl} n_t+u\\cdot \\nabla n & =& \\Delta \\big (n c^{-\\alpha } \\big ), \\\\ c_t+ u\\cdot \\nabla c & =& \\Delta c -nc,\\\\ u_t + (u\\cdot \\nabla ) u & =& \\Delta u+\\nabla P + n\\nabla \\Phi , \\qquad \\nabla \\cdot u=0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n n\r\n t\r\n \r\n +\r\n u\r\n ·\r\n ∇\r\n n\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n \r\n (\r\n \r\n n\r\n \r\n c\r\n \r\n -\r\n α\r\n \r\n \r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n c\r\n t\r\n \r\n +\r\n u\r\n ·\r\n ∇\r\n c\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n c\r\n -\r\n n\r\n c\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n +\r\n \r\n (\r\n u\r\n ·\r\n ∇\r\n )\r\n \r\n u\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n u\r\n +\r\n ∇\r\n P\r\n +\r\n n\r\n ∇\r\n Φ\r\n ,\r\n \r\n ∇\r\n ·\r\n u\r\n =\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain $$\\Omega \\subset \\mathbb R^2$$\r\n \r\n Ω\r\n ⊂\r\n \r\n R\r\n 2\r\n \r\n \r\n . For all $$\\alpha > 0$$\r\n \r\n α\r\n >\r\n 0\r\n \r\n and all sufficiently regular $$\\Phi $$\r\n Φ\r\n , we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for u at a point in the proof when knowledge about n is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time $$L^p$$\r\n \r\n L\r\n p\r\n \r\n estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time $$L^2$$\r\n \r\n L\r\n 2\r\n \r\n norm of the force term raised to an arbitrary small power."}],"status":"public","type":"journal_article","publication":"Journal of Mathematical Fluid Mechanics","title":"Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing","doi":"10.1007/s00021-024-00899-8","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-18T20:13:58Z","date_created":"2025-12-18T19:05:09Z","author":[{"first_name":"Mario","full_name":"Fuest, Mario","last_name":"Fuest"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"volume":26,"year":"2024","citation":{"ieee":"M. Fuest and M. Winkler, “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing,” Journal of Mathematical Fluid Mechanics, vol. 26, no. 4, Art. no. 60, 2024, doi: 10.1007/s00021-024-00899-8.","chicago":"Fuest, Mario, and Michael Winkler. “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing.” Journal of Mathematical Fluid Mechanics 26, no. 4 (2024). https://doi.org/10.1007/s00021-024-00899-8.","ama":"Fuest M, Winkler M. Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing. Journal of Mathematical Fluid Mechanics. 2024;26(4). doi:10.1007/s00021-024-00899-8","bibtex":"@article{Fuest_Winkler_2024, title={Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing}, volume={26}, DOI={10.1007/s00021-024-00899-8}, number={460}, journal={Journal of Mathematical Fluid Mechanics}, publisher={Springer Science and Business Media LLC}, author={Fuest, Mario and Winkler, Michael}, year={2024} }","mla":"Fuest, Mario, and Michael Winkler. “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing.” Journal of Mathematical Fluid Mechanics, vol. 26, no. 4, 60, Springer Science and Business Media LLC, 2024, doi:10.1007/s00021-024-00899-8.","short":"M. Fuest, M. Winkler, Journal of Mathematical Fluid Mechanics 26 (2024).","apa":"Fuest, M., & Winkler, M. (2024). Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing. Journal of Mathematical Fluid Mechanics, 26(4), Article 60. https://doi.org/10.1007/s00021-024-00899-8"},"intvolume":" 26","publication_status":"published","publication_identifier":{"issn":["1422-6928","1422-6952"]},"issue":"4"},{"article_number":"e12885","language":[{"iso":"eng"}],"_id":"63259","user_id":"31496","abstract":[{"text":"AbstractIn a smoothly bounded two‐dimensional domain and for a given nondecreasing positive unbounded , for each and the inequality\r\nis shown to hold for any positive fulfilling\r\nThis 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.","lang":"eng"}],"status":"public","publication":"Journal of the London Mathematical Society","type":"journal_article","title":"An interpolation inequality involving LlogL$L\\log L$ 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":"2025-12-18T20:14:39Z","volume":109,"author":[{"first_name":"Yulan","full_name":"Wang, Yulan","last_name":"Wang"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_created":"2025-12-18T19:07:25Z","year":"2024","intvolume":" 109","citation":{"apa":"Wang, Y., & Winkler, M. (2024). An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. Journal of the London Mathematical Society, 109(3), Article e12885. https://doi.org/10.1112/jlms.12885","short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).","mla":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” Journal of the London Mathematical Society, vol. 109, no. 3, e12885, Wiley, 2024, doi:10.1112/jlms.12885.","bibtex":"@article{Wang_Winkler_2024, title={An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={10.1112/jlms.12885}, number={3e12885}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }","chicago":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” Journal of the London Mathematical Society 109, no. 3 (2024). https://doi.org/10.1112/jlms.12885.","ieee":"Y. Wang and M. Winkler, “An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” Journal of the London Mathematical Society, vol. 109, no. 3, Art. no. e12885, 2024, doi: 10.1112/jlms.12885.","ama":"Wang Y, Winkler M. An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. Journal of the London Mathematical Society. 2024;109(3). doi:10.1112/jlms.12885"},"publication_identifier":{"issn":["0024-6107","1469-7750"]},"publication_status":"published","issue":"3"},{"type":"journal_article","publication":"Proceedings of the American Mathematical Society","abstract":[{"text":"This manuscript studies a no-flux initial-boundary value problem for a four-component chemotaxis system that has been proposed as a model for the response of cytotoxic T-lymphocytes to a solid tumor. In contrast to classical Keller-Segel type situations focusing on two-component interplay of chemotaxing populations with a signal directly secreted by themselves, the presently considered system accounts for a certain indirect mechanism of attractant evolution. Despite the presence of a zero-order exciting nonlinearity of quadratic type that forms a core mathematical feature of the model, the manuscript asserts the global existence of classical solutions for initial data of arbitrary size in three-dimensional domains.
","lang":"eng"}],"status":"public","_id":"63258","user_id":"31496","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0002-9939","1088-6826"]},"issue":"10","year":"2024","citation":{"chicago":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Chemotaxis System Modeling Immune Response to a Solid Tumor.” Proceedings of the American Mathematical Society 152, no. 10 (2024): 4325–41. https://doi.org/10.1090/proc/16867.","ieee":"Y. Tao and M. Winkler, “Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor,” Proceedings of the American Mathematical Society, vol. 152, no. 10, pp. 4325–4341, 2024, doi: 10.1090/proc/16867.","ama":"Tao Y, Winkler M. Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor. Proceedings of the American Mathematical Society. 2024;152(10):4325-4341. doi:10.1090/proc/16867","mla":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Chemotaxis System Modeling Immune Response to a Solid Tumor.” Proceedings of the American Mathematical Society, vol. 152, no. 10, American Mathematical Society (AMS), 2024, pp. 4325–41, doi:10.1090/proc/16867.","bibtex":"@article{Tao_Winkler_2024, title={Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor}, volume={152}, DOI={10.1090/proc/16867}, number={10}, journal={Proceedings of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Tao, Youshan and Winkler, Michael}, year={2024}, pages={4325–4341} }","short":"Y. Tao, M. Winkler, Proceedings of the American Mathematical Society 152 (2024) 4325–4341.","apa":"Tao, Y., & Winkler, M. (2024). Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor. Proceedings of the American Mathematical Society, 152(10), 4325–4341. https://doi.org/10.1090/proc/16867"},"intvolume":" 152","page":"4325-4341","publisher":"American Mathematical Society (AMS)","date_updated":"2025-12-18T20:14:30Z","author":[{"first_name":"Youshan","full_name":"Tao, Youshan","last_name":"Tao"},{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T19:07:03Z","volume":152,"title":"Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor","doi":"10.1090/proc/16867"},{"status":"public","type":"journal_article","publication":"Nonlinear Analysis","article_number":"113600","language":[{"iso":"eng"}],"_id":"63256","user_id":"31496","year":"2024","citation":{"apa":"Nikolić, V., & Winkler, M. (2024). <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation. Nonlinear Analysis, 247, Article 113600. https://doi.org/10.1016/j.na.2024.113600","mla":"Nikolić, Vanja, and Michael Winkler. “<mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\" Altimg=\"si15.Svg\" Display=\"inline\" Id=\"d1e25\"><mml:Msup><mml:Mrow><mml:Mi>L</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mi>∞</Mml:Mi></Mml:Mrow></Mml:Msup></Mml:Math> Blow-up in the Jordan–Moore–Gibson–Thompson Equation.” Nonlinear Analysis, vol. 247, 113600, Elsevier BV, 2024, doi:10.1016/j.na.2024.113600.","bibtex":"@article{Nikolić_Winkler_2024, title={<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation}, volume={247}, DOI={10.1016/j.na.2024.113600}, number={113600}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Nikolić, Vanja and Winkler, Michael}, year={2024} }","short":"V. Nikolić, M. Winkler, Nonlinear Analysis 247 (2024).","ama":"Nikolić V, Winkler M. <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation. Nonlinear Analysis. 2024;247. doi:10.1016/j.na.2024.113600","chicago":"Nikolić, Vanja, and Michael Winkler. “<mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\" Altimg=\"si15.Svg\" Display=\"inline\" Id=\"d1e25\"><mml:Msup><mml:Mrow><mml:Mi>L</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mi>∞</Mml:Mi></Mml:Mrow></Mml:Msup></Mml:Math> Blow-up in the Jordan–Moore–Gibson–Thompson Equation.” Nonlinear Analysis 247 (2024). https://doi.org/10.1016/j.na.2024.113600.","ieee":"V. Nikolić and M. Winkler, “<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si15.svg\" display=\"inline\" id=\"d1e25\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math> blow-up in the Jordan–Moore–Gibson–Thompson equation,” Nonlinear Analysis, vol. 247, Art. no. 113600, 2024, doi: 10.1016/j.na.2024.113600."},"intvolume":" 247","publication_status":"published","publication_identifier":{"issn":["0362-546X"]},"title":"L∞ blow-up in the Jordan–Moore–Gibson–Thompson equation","doi":"10.1016/j.na.2024.113600","date_updated":"2025-12-18T20:14:12Z","publisher":"Elsevier BV","date_created":"2025-12-18T19:06:09Z","author":[{"last_name":"Nikolić","full_name":"Nikolić, Vanja","first_name":"Vanja"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"volume":247},{"status":"public","abstract":[{"lang":"eng","text":"AbstractA no‐flux initial‐boundary value problem for\r\nis considered in a ball , where and .Under the assumption that , it is shown that for each , there exist and a positive with the property that whenever is nonnegative with , the global solutions to () emanating from the initial data have the property that\r\n"}],"type":"journal_article","publication":"Mathematische Nachrichten","language":[{"iso":"eng"}],"user_id":"31496","_id":"63260","citation":{"apa":"Wang, Y., & Winkler, M. (2024). A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities. Mathematische Nachrichten, 297(6), 2353–2364. https://doi.org/10.1002/mana.202300361","mla":"Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type Parabolic System Involving Density‐suppressed Motilities.” Mathematische Nachrichten, vol. 297, no. 6, Wiley, 2024, pp. 2353–64, doi:10.1002/mana.202300361.","short":"Y. Wang, M. Winkler, Mathematische Nachrichten 297 (2024) 2353–2364.","bibtex":"@article{Wang_Winkler_2024, title={A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities}, volume={297}, DOI={10.1002/mana.202300361}, number={6}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024}, pages={2353–2364} }","ama":"Wang Y, Winkler M. A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities. Mathematische Nachrichten. 2024;297(6):2353-2364. doi:10.1002/mana.202300361","ieee":"Y. Wang and M. Winkler, “A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities,” Mathematische Nachrichten, vol. 297, no. 6, pp. 2353–2364, 2024, doi: 10.1002/mana.202300361.","chicago":"Wang, Yulan, and Michael Winkler. “A Singular Growth Phenomenon in a Keller–Segel–Type Parabolic System Involving Density‐suppressed Motilities.” Mathematische Nachrichten 297, no. 6 (2024): 2353–64. https://doi.org/10.1002/mana.202300361."},"intvolume":" 297","page":"2353-2364","year":"2024","issue":"6","publication_status":"published","publication_identifier":{"issn":["0025-584X","1522-2616"]},"doi":"10.1002/mana.202300361","title":"A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities","author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:07:48Z","volume":297,"publisher":"Wiley","date_updated":"2025-12-18T20:14:46Z"},{"date_updated":"2025-12-18T20:14:59Z","publisher":"Springer Science and Business Media LLC","author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T19:08:34Z","volume":263,"title":"Complete infinite-time mass aggregation in a quasilinear Keller–Segel system","doi":"10.1007/s11856-024-2618-9","publication_status":"published","publication_identifier":{"issn":["0021-2172","1565-8511"]},"issue":"1","year":"2024","citation":{"short":"M. Winkler, Israel Journal of Mathematics 263 (2024) 93–127.","bibtex":"@article{Winkler_2024, title={Complete infinite-time mass aggregation in a quasilinear Keller–Segel system}, volume={263}, DOI={10.1007/s11856-024-2618-9}, number={1}, journal={Israel Journal of Mathematics}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2024}, pages={93–127} }","mla":"Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear Keller–Segel System.” Israel Journal of Mathematics, vol. 263, no. 1, Springer Science and Business Media LLC, 2024, pp. 93–127, doi:10.1007/s11856-024-2618-9.","apa":"Winkler, M. (2024). Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. Israel Journal of Mathematics, 263(1), 93–127. https://doi.org/10.1007/s11856-024-2618-9","chicago":"Winkler, Michael. “Complete Infinite-Time Mass Aggregation in a Quasilinear Keller–Segel System.” Israel Journal of Mathematics 263, no. 1 (2024): 93–127. https://doi.org/10.1007/s11856-024-2618-9.","ieee":"M. Winkler, “Complete infinite-time mass aggregation in a quasilinear Keller–Segel system,” Israel Journal of Mathematics, vol. 263, no. 1, pp. 93–127, 2024, doi: 10.1007/s11856-024-2618-9.","ama":"Winkler M. Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. Israel Journal of Mathematics. 2024;263(1):93-127. doi:10.1007/s11856-024-2618-9"},"page":"93-127","intvolume":" 263","_id":"63262","user_id":"31496","language":[{"iso":"eng"}],"type":"journal_article","publication":"Israel Journal of Mathematics","abstract":[{"text":"AbstractRadially symmetric global unbounded solutions of the chemotaxis system $$\\left\\{ {\\matrix{{{u_t} = \\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (uS(u)\\nabla v),} \\hfill & {} \\hfill \\cr {0 = \\Delta v - \\mu + u,} \\hfill & {\\mu = {1 \\over {|\\Omega |}}\\int_\\Omega {u,} } \\hfill \\cr } } \\right.$$\r\n \r\n \r\n {\r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n ∇\r\n ⋅\r\n (\r\n D\r\n (\r\n u\r\n )\r\n ∇\r\n u\r\n )\r\n −\r\n ∇\r\n ⋅\r\n (\r\n u\r\n S\r\n (\r\n u\r\n )\r\n ∇\r\n v\r\n )\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n −\r\n μ\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n μ\r\n =\r\n \r\n 1\r\n \r\n |\r\n Ω\r\n |\r\n \r\n \r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n \r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n are considered in a ball Ω = BR(0) ⊂ ℝn, where n ≥ 3 and R > 0.Under the assumption that D and S suitably generalize the prototypes given by D(ξ) = (ξ + ι)m−1 and S(ξ) = (ξ + 1)−λ−1 for all ξ > 0 and some m ∈ ℝ, λ >0 and ι ≥ 0 fulfilling $$m + \\lambda < 1 - {2 \\over n}$$\r\n m\r\n +\r\n λ\r\n <\r\n 1\r\n −\r\n \r\n 2\r\n n\r\n \r\n , a considerably large set of initial data u0 is found to enforce a complete mass aggregation in infinite time in the sense that for any such u0, an associated Neumann type initial-boundary value problem admits a global classical solution (u, v) satisfying $${1 \\over C} \\cdot {(t + 1)^{{1 \\over \\lambda }}} \\le ||u( \\cdot ,t)|{|_{{L^\\infty }(\\Omega )}} \\le C \\cdot {(t + 1)^{{1 \\over \\lambda }}}\\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,t > 0$$\r\n \r\n \r\n 1\r\n C\r\n \r\n \r\n ⋅\r\n \r\n (\r\n t\r\n +\r\n 1\r\n \r\n )\r\n \r\n \r\n \r\n 1\r\n λ\r\n \r\n \r\n \r\n \r\n \r\n ≤\r\n \r\n |\r\n \r\n \r\n |\r\n \r\n u\r\n (\r\n ⋅\r\n ,\r\n t\r\n )\r\n \r\n |\r\n \r\n \r\n \r\n \r\n |\r\n \r\n \r\n \r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n ≤\r\n C\r\n ⋅\r\n \r\n (\r\n t\r\n +\r\n 1\r\n \r\n )\r\n \r\n \r\n \r\n 1\r\n λ\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n f\r\n o\r\n r\r\n \r\n \r\n \r\n \r\n \r\n \r\n a\r\n l\r\n l\r\n \r\n \r\n \r\n \r\n t\r\n >\r\n 0\r\n as well as $$||u( \\cdot \\,,t)|{|_{{L^1}(\\Omega \\backslash {B_{{r_0}}}(0))}} \\to 0\\,\\,\\,{\\rm{as}}\\,\\,t \\to \\infty \\,\\,\\,{\\rm{for}}\\,\\,{\\rm{all}}\\,\\,{r_0} \\in (0,R)$$\r\n |\r\n |\r\n u\r\n (\r\n ⋅\r\n ,\r\n t\r\n )\r\n |\r\n \r\n |\r\n \r\n \r\n L\r\n 1\r\n \r\n (\r\n Ω\r\n \\\r\n \r\n B\r\n \r\n \r\n r\r\n 0\r\n \r\n \r\n \r\n (\r\n 0\r\n )\r\n )\r\n \r\n \r\n →\r\n 0\r\n as\r\n t\r\n →\r\n ∞\r\n for all\r\n \r\n r\r\n 0\r\n \r\n ∈\r\n (\r\n 0\r\n ,\r\n R\r\n )\r\n with some C > 0.","lang":"eng"}],"status":"public"},{"doi":"10.1016/j.jde.2024.04.028","title":"L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux","volume":400,"author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T19:09:07Z","publisher":"Elsevier BV","date_updated":"2025-12-18T20:15:05Z","intvolume":" 400","page":"423-456","citation":{"ama":"Winkler M. L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux. Journal of Differential Equations. 2024;400:423-456. doi:10.1016/j.jde.2024.04.028","chicago":"Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient Taxis System with General Cross-Diffusive Flux.” Journal of Differential Equations 400 (2024): 423–56. https://doi.org/10.1016/j.jde.2024.04.028.","ieee":"M. Winkler, “L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux,” Journal of Differential Equations, vol. 400, pp. 423–456, 2024, doi: 10.1016/j.jde.2024.04.028.","short":"M. Winkler, Journal of Differential Equations 400 (2024) 423–456.","mla":"Winkler, Michael. “L∞ Bounds in a Two-Dimensional Doubly Degenerate Nutrient Taxis System with General Cross-Diffusive Flux.” Journal of Differential Equations, vol. 400, Elsevier BV, 2024, pp. 423–56, doi:10.1016/j.jde.2024.04.028.","bibtex":"@article{Winkler_2024, title={L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux}, volume={400}, DOI={10.1016/j.jde.2024.04.028}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2024}, pages={423–456} }","apa":"Winkler, M. (2024). L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux. Journal of Differential Equations, 400, 423–456. https://doi.org/10.1016/j.jde.2024.04.028"},"year":"2024","publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","language":[{"iso":"eng"}],"user_id":"31496","_id":"63263","status":"public","publication":"Journal of Differential Equations","type":"journal_article"},{"doi":"10.1364/oe.522549","date_updated":"2025-12-19T11:37:41Z","volume":32,"author":[{"first_name":"René","last_name":"Pollmann","full_name":"Pollmann, René","id":"78890"},{"last_name":"Roeder","full_name":"Roeder, Franz","id":"88149","first_name":"Franz"},{"last_name":"Quiring","full_name":"Quiring, Victor","first_name":"Victor"},{"first_name":"Raimund","full_name":"Ricken, Raimund","last_name":"Ricken"},{"first_name":"Christof","last_name":"Eigner","orcid":"https://orcid.org/0000-0002-5693-3083","full_name":"Eigner, Christof","id":"13244"},{"first_name":"Benjamin","last_name":"Brecht","orcid":"0000-0003-4140-0556 ","id":"27150","full_name":"Brecht, Benjamin"},{"full_name":"Silberhorn, Christine","id":"26263","last_name":"Silberhorn","first_name":"Christine"}],"intvolume":" 32","citation":{"apa":"Pollmann, R., Roeder, F., Quiring, V., Ricken, R., Eigner, C., Brecht, B., & Silberhorn, C. (2024). Integrated, bright broadband, two-colour parametric down-conversion source. Optics Express, 32(14), Article 23945. https://doi.org/10.1364/oe.522549","short":"R. Pollmann, F. Roeder, V. Quiring, R. Ricken, C. Eigner, B. Brecht, C. Silberhorn, Optics Express 32 (2024).","mla":"Pollmann, René, et al. “Integrated, Bright Broadband, Two-Colour Parametric down-Conversion Source.” Optics Express, vol. 32, no. 14, 23945, Optica Publishing Group, 2024, doi:10.1364/oe.522549.","bibtex":"@article{Pollmann_Roeder_Quiring_Ricken_Eigner_Brecht_Silberhorn_2024, title={Integrated, bright broadband, two-colour parametric down-conversion source}, volume={32}, DOI={10.1364/oe.522549}, number={1423945}, journal={Optics Express}, publisher={Optica Publishing Group}, author={Pollmann, René and Roeder, Franz and Quiring, Victor and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}, year={2024} }","ieee":"R. Pollmann et al., “Integrated, bright broadband, two-colour parametric down-conversion source,” Optics Express, vol. 32, no. 14, Art. no. 23945, 2024, doi: 10.1364/oe.522549.","chicago":"Pollmann, René, Franz Roeder, Victor Quiring, Raimund Ricken, Christof Eigner, Benjamin Brecht, and Christine Silberhorn. “Integrated, Bright Broadband, Two-Colour Parametric down-Conversion Source.” Optics Express 32, no. 14 (2024). https://doi.org/10.1364/oe.522549.","ama":"Pollmann R, Roeder F, Quiring V, et al. Integrated, bright broadband, two-colour parametric down-conversion source. Optics Express. 2024;32(14). doi:10.1364/oe.522549"},"publication_identifier":{"issn":["1094-4087"]},"publication_status":"published","article_type":"original","article_number":"23945","_id":"54815","department":[{"_id":"15"},{"_id":"623"},{"_id":"288"}],"user_id":"78890","status":"public","type":"journal_article","title":"Integrated, bright broadband, two-colour parametric down-conversion source","publisher":"Optica Publishing Group","date_created":"2024-06-19T06:58:17Z","year":"2024","issue":"14","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Broadband quantum light is a vital resource for quantum metrology and spectroscopy applications such as quantum optical coherence tomography or entangled two photon absorption. For entangled two photon absorption in particular, very high photon flux combined with high time-frequency entanglement is crucial for observing a signal. So far these conditions could be met by using high power lasers driving degenerate, type 0 bulk-crystal spontaneous parametric down conversion (SPDC) sources. This naturally limits the available wavelength ranges and precludes deterministic splitting of the generated output photons. In this work we demonstrate an integrated two-colour SPDC source utilising a group-velocity matched lithium niobate waveguide, reaching both exceptional brightness 1.52⋅106pairssmWGHz and large bandwidth (7.8 THz FWHM) while pumped with a few mW of continuous wave (CW) laser light. By converting a narrow band pump to broadband pulses the created photon pairs show correlation times of Δτ ≈ 120 fs while maintaining the narrow bandwidth Δω\r\n p\r\n ≪ 1 MHz of the CW pump light, yielding strong time-frequency entanglement. Furthermore our process can be adapted to a wide range of central wavelengths."}],"publication":"Optics Express"},{"status":"public","abstract":[{"lang":"eng","text":"The latest applications in ultrafast quantum metrology require bright, broadband bi-photon sources with one of the photons in the mid-infrared and the other in the visible to near infrared. However, existing sources based on bulk crystals are limited in brightness due to the short interaction length and only allow for limited dispersion engineering. Here, we present an integrated PDC source based on a Ti:LiNbO3 waveguide that generates broadband bi-photons with central wavelengths at 860 nm and 2800 nm. Their spectral bandwidth exceeds 25 THz and is achieved by simultaneous matching of the group velocities (GVs) and cancellation of GV dispersion for the signal and idler field. We provide an intuitive understanding of the process by studying our source’s behavior at different temperatures and pump wavelengths, which agrees well with simulations."}],"type":"journal_article","publication":"New Journal of Physics","language":[{"iso":"eng"}],"article_number":"123025","article_type":"original","user_id":"78890","department":[{"_id":"288"},{"_id":"623"},{"_id":"15"}],"project":[{"name":"MIRAQLS: MIRAQLS: Mid-infrared Quantum Technology for Sensing","_id":"571"},{"name":"E2TPA: Exploiting Entangled Two-Photon Absorption","_id":"190"}],"_id":"57862","citation":{"ieee":"F. Roeder et al., “Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared,” New Journal of Physics, vol. 26, no. 12, Art. no. 123025, 2024, doi: 10.1088/1367-2630/ad9f98.","chicago":"Roeder, Franz, Abira Gnanavel, René Pollmann, Olga Brecht, Michael Stefszky, Laura Padberg, Christof Eigner, Christine Silberhorn, and Benjamin Brecht. “Ultra-Broadband Non-Degenerate Guided-Wave Bi-Photon Source in the near and Mid-Infrared.” New Journal of Physics 26, no. 12 (2024). https://doi.org/10.1088/1367-2630/ad9f98.","ama":"Roeder F, Gnanavel A, Pollmann R, et al. Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared. New Journal of Physics. 2024;26(12). doi:10.1088/1367-2630/ad9f98","apa":"Roeder, F., Gnanavel, A., Pollmann, R., Brecht, O., Stefszky, M., Padberg, L., Eigner, C., Silberhorn, C., & Brecht, B. (2024). Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared. New Journal of Physics, 26(12), Article 123025. https://doi.org/10.1088/1367-2630/ad9f98","bibtex":"@article{Roeder_Gnanavel_Pollmann_Brecht_Stefszky_Padberg_Eigner_Silberhorn_Brecht_2024, title={Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared}, volume={26}, DOI={10.1088/1367-2630/ad9f98}, number={12123025}, journal={New Journal of Physics}, publisher={IOP Publishing}, author={Roeder, Franz and Gnanavel, Abira and Pollmann, René and Brecht, Olga and Stefszky, Michael and Padberg, Laura and Eigner, Christof and Silberhorn, Christine and Brecht, Benjamin}, year={2024} }","short":"F. Roeder, A. Gnanavel, R. Pollmann, O. Brecht, M. Stefszky, L. Padberg, C. Eigner, C. Silberhorn, B. Brecht, New Journal of Physics 26 (2024).","mla":"Roeder, Franz, et al. “Ultra-Broadband Non-Degenerate Guided-Wave Bi-Photon Source in the near and Mid-Infrared.” New Journal of Physics, vol. 26, no. 12, 123025, IOP Publishing, 2024, doi:10.1088/1367-2630/ad9f98."},"intvolume":" 26","year":"2024","issue":"12","publication_status":"published","publication_identifier":{"issn":["1367-2630"]},"doi":"10.1088/1367-2630/ad9f98","title":"Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared","author":[{"full_name":"Roeder, Franz","id":"88149","last_name":"Roeder","first_name":"Franz"},{"first_name":"Abira","full_name":"Gnanavel, Abira","last_name":"Gnanavel"},{"first_name":"René","id":"78890","full_name":"Pollmann, René","last_name":"Pollmann"},{"first_name":"Olga","last_name":"Brecht","full_name":"Brecht, Olga"},{"first_name":"Michael","last_name":"Stefszky","full_name":"Stefszky, Michael","id":"42777"},{"id":"40300","full_name":"Padberg, Laura","last_name":"Padberg","first_name":"Laura"},{"orcid":"https://orcid.org/0000-0002-5693-3083","last_name":"Eigner","full_name":"Eigner, Christof","id":"13244","first_name":"Christof"},{"first_name":"Christine","full_name":"Silberhorn, Christine","id":"26263","last_name":"Silberhorn"},{"orcid":"0000-0003-4140-0556 ","last_name":"Brecht","full_name":"Brecht, Benjamin","id":"27150","first_name":"Benjamin"}],"date_created":"2024-12-27T19:01:14Z","volume":26,"publisher":"IOP Publishing","date_updated":"2025-12-19T11:36:36Z"},{"intvolume":" 238","page":"2299-2306","citation":{"ama":"Borgert T, Köhler D, Wiens E, et al. In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications. 2024;238(12):2299-2306. doi:10.1177/14644207241232233","chicago":"Borgert, Thomas, D Köhler, Eugen Wiens, R Kupfer, J Troschitz, Werner Homberg, and M Gude. “In-Situ Computed Tomography Analysis of the Failure Mechanisms of Thermomechanically Manufactured Joints with Auxiliary Joining Element.” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 238, no. 12 (2024): 2299–2306. https://doi.org/10.1177/14644207241232233.","ieee":"T. Borgert et al., “In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element,” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, vol. 238, no. 12, pp. 2299–2306, 2024, doi: 10.1177/14644207241232233.","apa":"Borgert, T., Köhler, D., Wiens, E., Kupfer, R., Troschitz, J., Homberg, W., & Gude, M. (2024). In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 238(12), 2299–2306. https://doi.org/10.1177/14644207241232233","mla":"Borgert, Thomas, et al. “In-Situ Computed Tomography Analysis of the Failure Mechanisms of Thermomechanically Manufactured Joints with Auxiliary Joining Element.” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, vol. 238, no. 12, SAGE Publications, 2024, pp. 2299–306, doi:10.1177/14644207241232233.","short":"T. Borgert, D. Köhler, E. Wiens, R. Kupfer, J. Troschitz, W. Homberg, M. Gude, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 238 (2024) 2299–2306.","bibtex":"@article{Borgert_Köhler_Wiens_Kupfer_Troschitz_Homberg_Gude_2024, title={In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element}, volume={238}, DOI={10.1177/14644207241232233}, number={12}, journal={Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications}, publisher={SAGE Publications}, author={Borgert, Thomas and Köhler, D and Wiens, Eugen and Kupfer, R and Troschitz, J and Homberg, Werner and Gude, M}, year={2024}, pages={2299–2306} }"},"publication_identifier":{"issn":["1464-4207","2041-3076"]},"publication_status":"published","doi":"10.1177/14644207241232233","volume":238,"author":[{"id":"83141","full_name":"Borgert, Thomas","last_name":"Borgert","first_name":"Thomas"},{"last_name":"Köhler","full_name":"Köhler, D","first_name":"D"},{"first_name":"Eugen","id":"7888","full_name":"Wiens, Eugen","last_name":"Wiens"},{"first_name":"R","full_name":"Kupfer, R","last_name":"Kupfer"},{"full_name":"Troschitz, J","last_name":"Troschitz","first_name":"J"},{"first_name":"Werner","last_name":"Homberg","full_name":"Homberg, Werner","id":"233"},{"first_name":"M","last_name":"Gude","full_name":"Gude, M"}],"date_updated":"2025-12-22T10:40:28Z","status":"public","type":"journal_article","department":[{"_id":"156"}],"user_id":"7888","_id":"63346","year":"2024","issue":"12","quality_controlled":"1","title":"In-situ computed tomography analysis of the failure mechanisms of thermomechanically manufactured joints with auxiliary joining element","date_created":"2025-12-19T09:13:30Z","publisher":"SAGE Publications","abstract":[{"lang":"eng","text":" Lightweight design by using low-density and load-adapted materials can reduce the weight of vehicles and the emissions generated during operation. However, the usage of different materials requires innovative joining technologies with increased versatility. In this investigation, the focus is on describing and characterising the failure behaviour of connections manufactured by an innovative thermomechanical joining process with adaptable auxiliary joining elements in single-lap tensile-shear tests. In order to analyse the failure development in detail, the specimens are investigated using in-situ computed tomography (in-situ CT). Here, the tensile-shear test is interrupted at points of interest and CT scans are conducted under load. In addition, the interrupted in-situ testing procedure is validated by comparing the loading behaviour with conventional continuous tensile-shear tests. The results of the in-situ investigations of joints with varying material combinations clearly describe the cause of failure, allowing conclusions towards an improved joint design. "}],"publication":"Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications","language":[{"iso":"eng"}]}]