--- _id: '63219' abstract: - lang: eng text: "We introduce the framework of Bayesian relative belief that directly evaluates whether or not the experimental data at hand support a given hypothesis regarding a quantum system by directly comparing the prior and posterior probabilities for the hypothesis. In model-dimension certification tasks, we show that the relative-belief procedure typically chooses Hilbert spaces that are never smaller in dimension than those selected from optimizing a broad class of information criteria, including Akaike's criterion. As a concrete and focused exposition of this powerful evidence-based technique, we apply the relative-belief procedure to an important application: . In particular, just by comparing prior and posterior probabilities based on data, we demonstrate its capability of tracking multiphoton emissions using (realistically lossy) single-photon detectors in order to assess the actual quality of photon sources without making assumptions, thereby reliably safeguarding source integrity for general quantum-information and communication tasks with Bayesian reasoning. Finally, we discuss how relative belief can be exploited to carry out parametric model certification and estimate the total dimension of the quantum state for the combined (measured) physical and interacting external systems described by the Tavis-Cummings model.\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 " article_number: '012231' author: - first_name: Y. S. full_name: Teo, Y. S. last_name: Teo - first_name: S. U. full_name: Shringarpure, S. U. last_name: Shringarpure - first_name: H. full_name: Jeong, H. last_name: Jeong - first_name: Nidhin full_name: Prasannan, Nidhin id: '71403' last_name: Prasannan - first_name: Benjamin full_name: Brecht, Benjamin id: '27150' last_name: Brecht orcid: '0000-0003-4140-0556 ' - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn - first_name: M. full_name: Evans, M. last_name: Evans - first_name: D. full_name: Mogilevtsev, D. last_name: Mogilevtsev - first_name: L. L. full_name: Sánchez-Soto, L. L. last_name: Sánchez-Soto citation: ama: Teo YS, Shringarpure SU, Jeong H, et al. Relative-belief inference in quantum information theory. Physical Review A. 2024;110(1). doi:10.1103/physreva.110.012231 apa: Teo, Y. S., Shringarpure, S. U., Jeong, H., Prasannan, N., Brecht, B., Silberhorn, C., Evans, M., Mogilevtsev, D., & Sánchez-Soto, L. L. (2024). Relative-belief inference in quantum information theory. Physical Review A, 110(1), Article 012231. https://doi.org/10.1103/physreva.110.012231 bibtex: '@article{Teo_Shringarpure_Jeong_Prasannan_Brecht_Silberhorn_Evans_Mogilevtsev_Sánchez-Soto_2024, title={Relative-belief inference in quantum information theory}, volume={110}, DOI={10.1103/physreva.110.012231}, number={1012231}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Teo, Y. S. and Shringarpure, S. U. and Jeong, H. and Prasannan, Nidhin and Brecht, Benjamin and Silberhorn, Christine and Evans, M. and Mogilevtsev, D. and Sánchez-Soto, L. L.}, year={2024} }' chicago: Teo, Y. S., S. U. Shringarpure, H. Jeong, Nidhin Prasannan, Benjamin Brecht, Christine Silberhorn, M. Evans, D. Mogilevtsev, and L. L. Sánchez-Soto. “Relative-Belief Inference in Quantum Information Theory.” Physical Review A 110, no. 1 (2024). https://doi.org/10.1103/physreva.110.012231. ieee: 'Y. S. Teo et al., “Relative-belief inference in quantum information theory,” Physical Review A, vol. 110, no. 1, Art. no. 012231, 2024, doi: 10.1103/physreva.110.012231.' mla: Teo, Y. S., et al. “Relative-Belief Inference in Quantum Information Theory.” Physical Review A, vol. 110, no. 1, 012231, American Physical Society (APS), 2024, doi:10.1103/physreva.110.012231. short: Y.S. Teo, S.U. Shringarpure, H. Jeong, N. Prasannan, B. Brecht, C. Silberhorn, M. Evans, D. Mogilevtsev, L.L. Sánchez-Soto, Physical Review A 110 (2024). date_created: 2025-12-18T16:12:21Z date_updated: 2025-12-18T16:12:40Z department: - _id: '15' - _id: '623' doi: 10.1103/physreva.110.012231 intvolume: ' 110' issue: '1' language: - iso: eng publication: Physical Review A publication_identifier: issn: - 2469-9926 - 2469-9934 publication_status: published publisher: American Physical Society (APS) status: public title: Relative-belief inference in quantum information theory type: journal_article user_id: '27150' volume: 110 year: '2024' ... --- _id: '63216' abstract: - lang: eng text: The characterization of the complex spectral amplitude, that is, the spectrum and spectral phase, of single-photon-level light fields is a crucial capability for modern photonic quantum technologies. Since established pulse characterization techniques are not applicable at low intensities, alternative approaches are required. Here, we demonstrate the retrieval of the complex spectral amplitude of single-photon-level light pulses through measuring their chronocyclic Q −function. Our approach draws inspiration from quantum state tomography by exploiting the analogy between quadrature phase space and time-frequency phase space. In the experiment, we perform time-frequency projections with a quantum pulse gate (QPG), which directly yield the chronocyclic Q −function. We evaluate the complex spectral amplitude from the measured chronocyclic Q −function data with maximum likelihood estimation (MLE), which is the established technique for quantum state tomography. The MLE yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any a priori information, but also allows for, in principle, estimating the spectral-temporal coherence properties of the state. Our method accurately recovers features such as jumps in the spectral phase and is resistant against regions with zero spectral intensity, which makes it immediately beneficial for classical pulse characterization problems. article_number: '5551' author: - first_name: Abhinandan full_name: Bhattacharjee, Abhinandan id: '95902' last_name: Bhattacharjee - first_name: Patrick Fabian full_name: Folge, Patrick Fabian id: '88605' last_name: Folge - first_name: Laura Maria full_name: Serino, Laura Maria id: '88242' last_name: Serino - first_name: Jaroslav full_name: Řeháček, Jaroslav last_name: Řeháček - first_name: Zdeněk full_name: Hradil, Zdeněk last_name: Hradil - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn - first_name: Benjamin full_name: Brecht, Benjamin id: '27150' last_name: Brecht orcid: '0000-0003-4140-0556 ' citation: ama: Bhattacharjee A, Folge PF, Serino LM, et al. Pulse characterization at the single-photon level through chronocyclic Q-function measurements. Optics Express. 2024;33(3). doi:10.1364/oe.540125 apa: Bhattacharjee, A., Folge, P. F., Serino, L. M., Řeháček, J., Hradil, Z., Silberhorn, C., & Brecht, B. (2024). Pulse characterization at the single-photon level through chronocyclic Q-function measurements. Optics Express, 33(3), Article 5551. https://doi.org/10.1364/oe.540125 bibtex: '@article{Bhattacharjee_Folge_Serino_Řeháček_Hradil_Silberhorn_Brecht_2024, title={Pulse characterization at the single-photon level through chronocyclic Q-function measurements}, volume={33}, DOI={10.1364/oe.540125}, number={35551}, journal={Optics Express}, publisher={Optica Publishing Group}, author={Bhattacharjee, Abhinandan and Folge, Patrick Fabian and Serino, Laura Maria and Řeháček, Jaroslav and Hradil, Zdeněk and Silberhorn, Christine and Brecht, Benjamin}, year={2024} }' chicago: Bhattacharjee, Abhinandan, Patrick Fabian Folge, Laura Maria Serino, Jaroslav Řeháček, Zdeněk Hradil, Christine Silberhorn, and Benjamin Brecht. “Pulse Characterization at the Single-Photon Level through Chronocyclic Q-Function Measurements.” Optics Express 33, no. 3 (2024). https://doi.org/10.1364/oe.540125. ieee: 'A. Bhattacharjee et al., “Pulse characterization at the single-photon level through chronocyclic Q-function measurements,” Optics Express, vol. 33, no. 3, Art. no. 5551, 2024, doi: 10.1364/oe.540125.' mla: Bhattacharjee, Abhinandan, et al. “Pulse Characterization at the Single-Photon Level through Chronocyclic Q-Function Measurements.” Optics Express, vol. 33, no. 3, 5551, Optica Publishing Group, 2024, doi:10.1364/oe.540125. short: A. Bhattacharjee, P.F. Folge, L.M. Serino, J. Řeháček, Z. Hradil, C. Silberhorn, B. Brecht, Optics Express 33 (2024). date_created: 2025-12-18T16:08:16Z date_updated: 2025-12-18T16:08:40Z department: - _id: '15' - _id: '623' doi: 10.1364/oe.540125 intvolume: ' 33' issue: '3' language: - iso: eng publication: Optics Express publication_identifier: issn: - 1094-4087 publication_status: published publisher: Optica Publishing Group status: public title: Pulse characterization at the single-photon level through chronocyclic Q-function measurements type: journal_article user_id: '27150' volume: 33 year: '2024' ... --- _id: '63220' abstract: - lang: eng text: "Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and continuous variables that is fully evidence based, relying solely on the experimental data collected and no other unjustified assumptions whatsoever. Using the Bayesian concept of relative belief, we take the effective dimension of the state as the smallest one such that the posterior probability is larger than the prior, as dictated by the data. The posterior probabilities associated with the relative-belief ratios measure the strength of the evidence provide by these ratios so that we can assess whether there is weak or strong evidence in favor or against a particular dimension. Using experimental data from spectral-temporal and polarimetry measurements, we demonstrate how to correctly assign Bayesian plausible error bars for the obtained effective dimensions. This makes relative belief a conservative and easy-to-use model-selection method for any experiment.\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 " article_number: '050204' author: - first_name: Y. S. full_name: Teo, Y. S. last_name: Teo - first_name: S. U. full_name: Shringarpure, S. U. last_name: Shringarpure - first_name: H. full_name: Jeong, H. last_name: Jeong - first_name: Nidhin full_name: Prasannan, Nidhin id: '71403' last_name: Prasannan - first_name: Benjamin full_name: Brecht, Benjamin id: '27150' last_name: Brecht orcid: '0000-0003-4140-0556 ' - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn - first_name: M. full_name: Evans, M. last_name: Evans - first_name: D. full_name: Mogilevtsev, D. last_name: Mogilevtsev - first_name: L. L. full_name: Sánchez-Soto, L. L. last_name: Sánchez-Soto citation: ama: Teo YS, Shringarpure SU, Jeong H, et al. Evidence-Based Certification of Quantum Dimensions. Physical Review Letters. 2024;133(5). doi:10.1103/physrevlett.133.050204 apa: Teo, Y. S., Shringarpure, S. U., Jeong, H., Prasannan, N., Brecht, B., Silberhorn, C., Evans, M., Mogilevtsev, D., & Sánchez-Soto, L. L. (2024). Evidence-Based Certification of Quantum Dimensions. Physical Review Letters, 133(5), Article 050204. https://doi.org/10.1103/physrevlett.133.050204 bibtex: '@article{Teo_Shringarpure_Jeong_Prasannan_Brecht_Silberhorn_Evans_Mogilevtsev_Sánchez-Soto_2024, title={Evidence-Based Certification of Quantum Dimensions}, volume={133}, DOI={10.1103/physrevlett.133.050204}, number={5050204}, journal={Physical Review Letters}, publisher={American Physical Society (APS)}, author={Teo, Y. S. and Shringarpure, S. U. and Jeong, H. and Prasannan, Nidhin and Brecht, Benjamin and Silberhorn, Christine and Evans, M. and Mogilevtsev, D. and Sánchez-Soto, L. L.}, year={2024} }' chicago: Teo, Y. S., S. U. Shringarpure, H. Jeong, Nidhin Prasannan, Benjamin Brecht, Christine Silberhorn, M. Evans, D. Mogilevtsev, and L. L. Sánchez-Soto. “Evidence-Based Certification of Quantum Dimensions.” Physical Review Letters 133, no. 5 (2024). https://doi.org/10.1103/physrevlett.133.050204. ieee: 'Y. S. Teo et al., “Evidence-Based Certification of Quantum Dimensions,” Physical Review Letters, vol. 133, no. 5, Art. no. 050204, 2024, doi: 10.1103/physrevlett.133.050204.' mla: Teo, Y. S., et al. “Evidence-Based Certification of Quantum Dimensions.” Physical Review Letters, vol. 133, no. 5, 050204, American Physical Society (APS), 2024, doi:10.1103/physrevlett.133.050204. short: Y.S. Teo, S.U. Shringarpure, H. Jeong, N. Prasannan, B. Brecht, C. Silberhorn, M. Evans, D. Mogilevtsev, L.L. Sánchez-Soto, Physical Review Letters 133 (2024). date_created: 2025-12-18T16:13:00Z date_updated: 2025-12-18T16:13:14Z department: - _id: '15' - _id: '623' doi: 10.1103/physrevlett.133.050204 intvolume: ' 133' issue: '5' language: - iso: eng publication: Physical Review Letters publication_identifier: issn: - 0031-9007 - 1079-7114 publication_status: published publisher: American Physical Society (APS) status: public title: Evidence-Based Certification of Quantum Dimensions type: journal_article user_id: '27150' volume: 133 year: '2024' ... --- _id: '54288' abstract: - lang: eng 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 " article_number: L022040 author: - first_name: Syamsundar full_name: De, Syamsundar last_name: De - first_name: Vahid full_name: Ansari, Vahid last_name: Ansari - first_name: Jan full_name: Sperling, Jan id: '75127' last_name: Sperling orcid: 0000-0002-5844-3205 - first_name: Sonja full_name: Barkhofen, Sonja id: '48188' last_name: Barkhofen - first_name: Benjamin full_name: Brecht, Benjamin id: '27150' last_name: Brecht orcid: '0000-0003-4140-0556 ' - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn citation: 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 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} }' 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. 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.' 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). date_created: 2024-05-14T12:40:48Z date_updated: 2025-12-18T16:14:39Z department: - _id: '623' - _id: '288' - _id: '15' doi: 10.1103/physrevresearch.6.l022040 intvolume: ' 6' issue: '2' language: - iso: eng project: - _id: '216' name: 'QuPoPCoRN: QUPOPCORN: Quantum Particles on Programmable Complex Reconfigurable Networks' publication: Physical Review Research publication_identifier: issn: - 2643-1564 publication_status: published publisher: American Physical Society (APS) status: public title: Realization of high-fidelity unitary operations on up to 64 frequency bins type: journal_article user_id: '27150' volume: 6 year: '2024' ... --- _id: '63218' 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 " article_number: '040329' author: - first_name: Patrick Fabian full_name: Folge, Patrick Fabian id: '88605' last_name: Folge - first_name: Michael full_name: Stefszky, Michael id: '42777' last_name: Stefszky - first_name: Benjamin full_name: Brecht, Benjamin id: '27150' last_name: Brecht orcid: '0000-0003-4140-0556 ' - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn citation: 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 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} }' 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. 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.' 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. short: P.F. Folge, M. Stefszky, B. Brecht, C. Silberhorn, PRX Quantum 5 (2024). date_created: 2025-12-18T16:10:37Z date_updated: 2025-12-18T16:10:55Z department: - _id: '15' - _id: '623' doi: 10.1103/prxquantum.5.040329 intvolume: ' 5' issue: '4' language: - iso: eng publication: PRX Quantum publication_identifier: issn: - 2691-3399 publication_status: published publisher: American Physical Society (APS) status: public title: A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates type: journal_article user_id: '27150' volume: 5 year: '2024' ... --- _id: '63217' abstract: - lang: eng 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. article_number: '5577' author: - first_name: Laura Maria full_name: Serino, Laura Maria id: '88242' last_name: Serino - first_name: Christof full_name: Eigner, Christof id: '13244' last_name: Eigner orcid: https://orcid.org/0000-0002-5693-3083 - first_name: Benjamin full_name: Brecht, Benjamin id: '27150' last_name: Brecht orcid: '0000-0003-4140-0556 ' - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn 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 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} }' 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. 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.' 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. short: L.M. Serino, C. Eigner, B. Brecht, C. Silberhorn, Optics Express 33 (2024). date_created: 2025-12-18T16:09:22Z date_updated: 2025-12-18T16:09:44Z department: - _id: '15' - _id: '623' doi: 10.1364/oe.544206 intvolume: ' 33' issue: '3' language: - iso: eng publication: Optics Express publication_identifier: issn: - 1094-4087 publication_status: published publisher: Optica Publishing Group status: public title: Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate type: journal_article user_id: '27150' volume: 33 year: '2024' ... --- _id: '50840' abstract: - lang: eng 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. article_number: '1' author: - first_name: Maximilian full_name: Protte, Maximilian id: '46170' last_name: Protte - first_name: Timon full_name: Schapeler, Timon id: '55629' last_name: Schapeler orcid: 0000-0001-7652-1716 - first_name: Jan full_name: Sperling, Jan id: '75127' last_name: Sperling orcid: 0000-0002-5844-3205 - first_name: Tim full_name: Bartley, Tim id: '49683' last_name: Bartley 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 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} }' 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.' 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). date_created: 2024-01-25T11:48:02Z date_updated: 2025-12-18T17:06:27Z department: - _id: '15' - _id: '623' doi: 10.1364/opticaq.502201 intvolume: ' 2' issue: '1' language: - iso: eng main_file_link: - open_access: '1' oa: '1' project: - _id: '191' name: 'PhoQuant: Photonische Quantencomputer - Quantencomputing Testplattform' - _id: '239' name: 'ERC-Grant: QuESADILLA: Quantum Engineering Superconducting Array Detectors in Low-Light Applications' - _id: '209' name: 'ISOQC: Quantenkommunikation mit integrierter Optik im Zusammenhang mit supraleitender Elektronik' publication: Optica Quantum publication_identifier: issn: - 2837-6714 publication_status: published publisher: Optica Publishing Group status: public title: Low-noise balanced homodyne detection with superconducting nanowire single-photon detectors type: journal_article user_id: '55629' volume: 2 year: '2024' ... --- _id: '63227' abstract: - lang: eng 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. article_type: original author: - first_name: Michael full_name: Biermann, Michael last_name: Biermann - first_name: Christian full_name: Leppin, Christian id: '117722' last_name: Leppin - first_name: Arne full_name: Langhoff, Arne last_name: Langhoff - first_name: Thorben full_name: Ziemer, Thorben last_name: Ziemer - first_name: Christian full_name: Rembe, Christian last_name: Rembe - first_name: Diethelm full_name: Johannsmann, Diethelm last_name: Johannsmann 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 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 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} }' 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.' 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. date_created: 2025-12-18T17:01:44Z date_updated: 2025-12-18T17:42:48Z doi: 10.1039/d3an02210b extern: '1' intvolume: ' 149' issue: '7' language: - iso: eng page: 2138-2146 publication: The Analyst publication_identifier: issn: - 0003-2654 - 1364-5528 publication_status: published publisher: Royal Society of Chemistry (RSC) quality_controlled: '1' status: public title: An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition type: journal_article user_id: '117722' volume: 149 year: '2024' ... --- _id: '63264' abstract: - lang: eng 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]." author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 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 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} }' 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.' 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.' 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. short: M. Winkler, Advanced Nonlinear Studies 24 (2024) 592–615. date_created: 2025-12-18T19:09:41Z date_updated: 2025-12-18T20:10:00Z doi: 10.1515/ans-2023-0131 intvolume: ' 24' issue: '3' language: - iso: eng page: 592-615 publication: Advanced Nonlinear Studies publication_identifier: issn: - 2169-0375 publication_status: published publisher: Walter de Gruyter GmbH status: public title: A degenerate migration-consumption model in domains of arbitrary dimension type: journal_article user_id: '31496' volume: 24 year: '2024' ... --- _id: '63248' 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 \ ." author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 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 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} }' 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. date_created: 2025-12-18T19:02:09Z date_updated: 2025-12-18T20:13:05Z doi: 10.1007/s00208-024-02987-6 intvolume: ' 391' issue: '2' language: - iso: eng page: 3023-3054 publication: Mathematische Annalen publication_identifier: issn: - 0025-5831 - 1432-1807 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system type: journal_article user_id: '31496' volume: 391 year: '2024' ... --- _id: '63245' 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 " author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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. date_created: 2025-12-18T19:00:24Z date_updated: 2025-12-18T20:12:43Z doi: 10.4171/aihpc/141 intvolume: ' 42' issue: '6' language: - iso: eng page: 1601-1630 publication: Annales de l'Institut Henri Poincaré C, Analyse non linéaire publication_identifier: issn: - 0294-1449 - 1873-1430 publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system type: journal_article user_id: '31496' volume: 42 year: '2024' ... --- _id: '63257' abstract: - lang: eng 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. article_number: '26' author: - first_name: Christian full_name: Stinner, Christian last_name: Stinner - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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. short: C. Stinner, M. Winkler, Journal of Evolution Equations 24 (2024). date_created: 2025-12-18T19:06:36Z date_updated: 2025-12-18T20:14:21Z doi: 10.1007/s00028-024-00954-x intvolume: ' 24' issue: '2' language: - iso: eng publication: Journal of Evolution Equations publication_identifier: issn: - 1424-3199 - 1424-3202 publication_status: published publisher: Springer Science and Business Media LLC status: public title: A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects type: journal_article user_id: '31496' volume: 24 year: '2024' ... --- _id: '63253' 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." article_number: '125006' author: - first_name: Mengyao full_name: Ding, Mengyao last_name: Ding - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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' 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} }' 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.' 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.' 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.' short: M. Ding, M. Winkler, Nonlinearity 37 (2024). date_created: 2025-12-18T19:04:45Z date_updated: 2025-12-18T20:13:49Z doi: 10.1088/1361-6544/ad871a intvolume: ' 37' issue: '12' language: - iso: eng publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published publisher: IOP Publishing status: public title: 'Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture' type: journal_article user_id: '31496' volume: 37 year: '2024' ... --- _id: '63254' 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." article_number: '60' author: - first_name: Mario full_name: Fuest, Mario last_name: Fuest - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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. 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.' 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). date_created: 2025-12-18T19:05:09Z date_updated: 2025-12-18T20:13:58Z doi: 10.1007/s00021-024-00899-8 intvolume: ' 26' issue: '4' language: - iso: eng publication: Journal of Mathematical Fluid Mechanics publication_identifier: issn: - 1422-6928 - 1422-6952 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing type: journal_article user_id: '31496' volume: 26 year: '2024' ... --- _id: '63259' abstract: - lang: eng 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." article_number: e12885 author: - first_name: Yulan full_name: Wang, Yulan last_name: Wang - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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.' 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. short: Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024). date_created: 2025-12-18T19:07:25Z date_updated: 2025-12-18T20:14:39Z doi: 10.1112/jlms.12885 intvolume: ' 109' issue: '3' language: - iso: eng publication: Journal of the London Mathematical Society publication_identifier: issn: - 0024-6107 - 1469-7750 publication_status: published publisher: Wiley status: public 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 type: journal_article user_id: '31496' volume: 109 year: '2024' ... --- _id: '63258' abstract: - lang: eng 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.

author: - first_name: Youshan full_name: Tao, Youshan last_name: Tao - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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. short: Y. Tao, M. Winkler, Proceedings of the American Mathematical Society 152 (2024) 4325–4341. date_created: 2025-12-18T19:07:03Z date_updated: 2025-12-18T20:14:30Z doi: 10.1090/proc/16867 intvolume: ' 152' issue: '10' language: - iso: eng page: 4325-4341 publication: Proceedings of the American Mathematical Society publication_identifier: issn: - 0002-9939 - 1088-6826 publication_status: published publisher: American Mathematical Society (AMS) status: public title: Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor type: journal_article user_id: '31496' volume: 152 year: '2024' ... --- _id: '63256' article_number: '113600' author: - first_name: Vanja full_name: Nikolić, Vanja last_name: Nikolić - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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. short: V. Nikolić, M. Winkler, Nonlinear Analysis 247 (2024). date_created: 2025-12-18T19:06:09Z date_updated: 2025-12-18T20:14:12Z doi: 10.1016/j.na.2024.113600 intvolume: ' 247' language: - iso: eng publication: Nonlinear Analysis publication_identifier: issn: - 0362-546X publication_status: published publisher: Elsevier BV status: public title: L∞ blow-up in the Jordan–Moore–Gibson–Thompson equation type: journal_article user_id: '31496' volume: 247 year: '2024' ... --- _id: '63260' 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" author: - first_name: Yulan full_name: Wang, Yulan last_name: Wang - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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.' 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. date_created: 2025-12-18T19:07:48Z date_updated: 2025-12-18T20:14:46Z doi: 10.1002/mana.202300361 intvolume: ' 297' issue: '6' language: - iso: eng page: 2353-2364 publication: Mathematische Nachrichten publication_identifier: issn: - 0025-584X - 1522-2616 publication_status: published publisher: Wiley status: public title: A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities type: journal_article user_id: '31496' volume: 297 year: '2024' ... --- _id: '63262' abstract: - lang: eng 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." author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler citation: 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 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 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} }' 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.' 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. short: M. Winkler, Israel Journal of Mathematics 263 (2024) 93–127. date_created: 2025-12-18T19:08:34Z date_updated: 2025-12-18T20:14:59Z doi: 10.1007/s11856-024-2618-9 intvolume: ' 263' issue: '1' language: - iso: eng page: 93-127 publication: Israel Journal of Mathematics publication_identifier: issn: - 0021-2172 - 1565-8511 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Complete infinite-time mass aggregation in a quasilinear Keller–Segel system type: journal_article user_id: '31496' volume: 263 year: '2024' ... --- _id: '63263' author: - first_name: Michael full_name: Winkler, Michael id: '31496' last_name: Winkler 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 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 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} }' 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.' 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. short: M. Winkler, Journal of Differential Equations 400 (2024) 423–456. date_created: 2025-12-18T19:09:07Z date_updated: 2025-12-18T20:15:05Z doi: 10.1016/j.jde.2024.04.028 intvolume: ' 400' language: - iso: eng page: 423-456 publication: Journal of Differential Equations publication_identifier: issn: - 0022-0396 publication_status: published publisher: Elsevier BV status: public title: L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux type: journal_article user_id: '31496' volume: 400 year: '2024' ...