[{"user_id":"95394","doi":"10.48550/ARXIV.2603.11697","_id":"65746","language":[{"iso":"eng"}],"date_updated":"2026-06-01T09:40:38Z","author":[{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","orcid":"0000-0002-6085-8071","first_name":"Boris Edgar","last_name":"Wembe Moafo"},{"first_name":"Usman","last_name":"Ali","full_name":"Ali, Usman"},{"id":"344","full_name":"Meier, Torsten","orcid":"0000-0001-8864-2072","first_name":"Torsten","last_name":"Meier"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"}],"conference":{"location":"Reykjavík, Iceland","start_date":"2026-07-07","name":"European Control Conference","end_date":"2026-07-10"},"year":"2026","status":"public","title":"Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control","department":[{"_id":"94"}],"type":"conference","date_created":"2026-06-01T09:38:06Z","abstract":[{"lang":"eng","text":"This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformulate the forward and backward propagation steps using Cayley-type schemes that preserve unitarity and symmetry at the discrete level. This approach eliminates the need for matrix exponentials and commutators, leading to significant computational savings while maintaining higher-order accuracy. We first recall the standard linear setting and then extend the formulation to nonlinear Schrödinger and Gross-Pitaevskii equations using a Cayley-polynomial interpolation strategy. Numerical experiments on state-transfer problems illustrate that the CF-Cayley method achieves the same accuracy as high-order exponential or Cayley-Magnus schemes at substantially lower cost, especially for longtime or highly oscillatory dynamics. In the nonlinear regime, the structure-preserving properties of the method ensure stability and norm conservation, making it a robust tool for large-scale quantum control simulations. The proposed framework thus bridges geometric integration and optimal control, offering an efficient and reliable alternative to existing exponential-based propagators."}],"citation":{"chicago":"Wembe Moafo, Boris Edgar, Usman Ali, Torsten Meier, and Sina Ober-Blöbaum. “Cayley Commutator-Free Methods for Krotov-Type Algorithms in Quantum Optimal Control,” 2026. <a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">https://doi.org/10.48550/ARXIV.2603.11697</a>.","short":"B.E. Wembe Moafo, U. Ali, T. Meier, S. Ober-Blöbaum, in: 2026.","apa":"Wembe Moafo, B. E., Ali, U., Meier, T., &#38; Ober-Blöbaum, S. (2026). <i>Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control</i>. European Control Conference, Reykjavík, Iceland. <a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">https://doi.org/10.48550/ARXIV.2603.11697</a>","ieee":"B. E. Wembe Moafo, U. Ali, T. Meier, and S. Ober-Blöbaum, “Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control,” presented at the European Control Conference, Reykjavík, Iceland, 2026, doi: <a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">10.48550/ARXIV.2603.11697</a>.","ama":"Wembe Moafo BE, Ali U, Meier T, Ober-Blöbaum S. Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control. In: ; 2026. doi:<a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">10.48550/ARXIV.2603.11697</a>","bibtex":"@inproceedings{Wembe Moafo_Ali_Meier_Ober-Blöbaum_2026, title={Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">10.48550/ARXIV.2603.11697</a>}, author={Wembe Moafo, Boris Edgar and Ali, Usman and Meier, Torsten and Ober-Blöbaum, Sina}, year={2026} }","mla":"Wembe Moafo, Boris Edgar, et al. <i>Cayley Commutator-Free Methods for Krotov-Type Algorithms in Quantum Optimal Control</i>. 2026, doi:<a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">10.48550/ARXIV.2603.11697</a>."}},{"_id":"65744","language":[{"iso":"eng"}],"user_id":"95394","year":"2026","status":"public","title":"Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions","author":[{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"id":"95394","last_name":"Wembe Moafo","orcid":"0000-0002-6085-8071","first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar"}],"date_updated":"2026-06-01T09:35:13Z","publication_status":"submitted","date_created":"2026-06-01T09:31:15Z","type":"preprint","department":[{"_id":"94"}],"citation":{"bibtex":"@article{Maslovskaya_Ober-Blöbaum_Wembe Moafo, title={Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar} }","ama":"Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions.","mla":"Maslovskaya, Sofya, et al. <i>Non Static Exponential Turnpike Property for Optimal Control Problems with Symmetries and Boundary Conditions</i>.","chicago":"Maslovskaya, Sofya, Sina Ober-Blöbaum, and Boris Edgar Wembe Moafo. “Non Static Exponential Turnpike Property for Optimal Control Problems with Symmetries and Boundary Conditions,” n.d.","short":"S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, (n.d.).","ieee":"S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions.” .","apa":"Maslovskaya, S., Ober-Blöbaum, S., &#38; Wembe Moafo, B. E. (n.d.). <i>Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions</i>."},"abstract":[{"text":"Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this paper we establish an exponential trim turnpike property for a class of optimal control problems with structural properties related to Abelian Lie group symmetries. The key ingredient of our approach is the introduction of an appropriate reduced optimal control problem. We show that extremals of the original problem can be characterized through a reduced Hamiltonian boundary value problem that coincides with the optimality system of the reduced problem. Under a hyperbolicity assumption on the equilibrium of the corresponding reduced Hamiltonian system we prove that optimal trajectories remain exponentially close, up to boundary layers near the endpoints, to a trim primitive defined by the static reduced problem. The theoretical results are illustrated on three representative examples: linear and nonlinear problems with quadratic cost and the Kepler orbital transfer problem.","lang":"eng"}]},{"doi":"10.1088/1751-8121/ae6d51","language":[{"iso":"eng"}],"article_number":"225303","intvolume":"        59","publication_status":"published","date_updated":"2026-06-05T07:38:44Z","publication_identifier":{"issn":["1751-8113","1751-8121"]},"author":[{"first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian"},{"first_name":"Boris Edgar","orcid":"0000-0002-6085-8071","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394"},{"full_name":"Ares, Laura","last_name":"Ares","first_name":"Laura"},{"id":"75127","full_name":"Sperling, Jan","first_name":"Jan","orcid":"0000-0002-5844-3205","last_name":"Sperling"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"title":"Numerical approaches to entangling dynamics from variational principles","year":"2026","department":[{"_id":"623"},{"_id":"15"},{"_id":"170"},{"_id":"706"},{"_id":"429"}],"type":"journal_article","date_created":"2026-06-05T07:37:43Z","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n                  <jats:p>In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the ‘first-discretize-then-restrict’ method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.</jats:p>"}],"issue":"22","publication":"Journal of Physics A: Mathematical and Theoretical","volume":59,"user_id":"75127","publisher":"IOP Publishing","_id":"65777","status":"public","citation":{"ama":"Offen C, Wembe Moafo BE, Ares L, Sperling J, Ober-Blöbaum S. Numerical approaches to entangling dynamics from variational principles. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2026;59(22). doi:<a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">10.1088/1751-8121/ae6d51</a>","bibtex":"@article{Offen_Wembe Moafo_Ares_Sperling_Ober-Blöbaum_2026, title={Numerical approaches to entangling dynamics from variational principles}, volume={59}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">10.1088/1751-8121/ae6d51</a>}, number={22225303}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing}, author={Offen, Christian and Wembe Moafo, Boris Edgar and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}, year={2026} }","mla":"Offen, Christian, et al. “Numerical Approaches to Entangling Dynamics from Variational Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 59, no. 22, 225303, IOP Publishing, 2026, doi:<a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">10.1088/1751-8121/ae6d51</a>.","short":"C. Offen, B.E. Wembe Moafo, L. Ares, J. Sperling, S. Ober-Blöbaum, Journal of Physics A: Mathematical and Theoretical 59 (2026).","chicago":"Offen, Christian, Boris Edgar Wembe Moafo, Laura Ares, Jan Sperling, and Sina Ober-Blöbaum. “Numerical Approaches to Entangling Dynamics from Variational Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i> 59, no. 22 (2026). <a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">https://doi.org/10.1088/1751-8121/ae6d51</a>.","apa":"Offen, C., Wembe Moafo, B. E., Ares, L., Sperling, J., &#38; Ober-Blöbaum, S. (2026). Numerical approaches to entangling dynamics from variational principles. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>59</i>(22), Article 225303. <a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">https://doi.org/10.1088/1751-8121/ae6d51</a>","ieee":"C. Offen, B. E. Wembe Moafo, L. Ares, J. Sperling, and S. Ober-Blöbaum, “Numerical approaches to entangling dynamics from variational principles,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 59, no. 22, Art. no. 225303, 2026, doi: <a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">10.1088/1751-8121/ae6d51</a>."}},{"date_created":"2025-05-05T09:23:38Z","department":[{"_id":"636"}],"type":"journal_article","citation":{"bibtex":"@article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim turnpikes for optimal control problems with symmetries}, DOI={<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Flaßkamp, Kathrin and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}, year={2025} }","short":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics of Control, Signals, and Systems (2025).","ama":"Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>","chicago":"Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, 2025. <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">https://doi.org/10.1007/s00498-025-00408-w</a>.","ieee":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim turnpikes for optimal control problems with symmetries,” <i>Mathematics of Control, Signals, and Systems</i>, 2025, doi: <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>.","apa":"Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., &#38; Wembe Moafo, B. E. (2025). Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">https://doi.org/10.1007/s00498-025-00408-w</a>","mla":"Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>."},"publication":"Mathematics of Control, Signals, and Systems","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing certain symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788 2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized the classical concept of <jats:italic>static turnpike to manifold turnpike</jats:italic> we extend the <jats:italic>exponential turnpike property</jats:italic> to the <jats:italic>exponential trim turnpike</jats:italic> for control systems with symmetries induced by abelian or non-abelian groups. Our analysis is mainly based on the geometric reduction of control systems with symmetries. More concretely, we first reduce the control system on the quotient space and state the turnpike theorem for the reduced problem. Then we use the group properties to obtain the <jats:italic>trim turnpike theorem</jats:italic> for the full problem. Finally, we illustrate our results on the Kepler problem and the rigid body problem.\r\n</jats:p>"}],"_id":"59792","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"doi":"10.1007/s00498-025-00408-w","user_id":"87909","publication_identifier":{"issn":["0932-4194","1435-568X"]},"author":[{"full_name":"Flaßkamp, Kathrin","first_name":"Kathrin","last_name":"Flaßkamp"},{"full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya","id":"87909"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Wembe Moafo, Boris Edgar","first_name":"Boris Edgar","last_name":"Wembe Moafo","id":"95394"}],"title":"Trim turnpikes for optimal control problems with symmetries","status":"public","year":"2025","date_updated":"2025-05-05T09:24:09Z","publication_status":"published"},{"abstract":[{"lang":"eng","text":"The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep networks are often unable to handle time-series data appearing at irregular intervals. These issues can be resolved by considering continuous-depth networks based on the neural ODE framework in combination with reversible integration methods that allow for variable time-steps. Reversibility of the method ensures that the memory requirement for training is independent of network depth, while variable time-steps are required for assimilating time-series data on irregular intervals. However, at present, there are no known higher-order reversible methods with this property. High-order methods are especially important when a high level of accuracy in learning is required or when small time-steps are necessary due to large errors in time integration of neural ODEs, for instance in context of complex dynamical systems such as Kepler systems and molecular dynamics. The requirement of small time-steps when using a low-order method can significantly increase the computational cost of training as well as inference. In this work, we present an approach for constructing high-order reversible methods that allow adaptive time-stepping. Our numerical tests show the advantages in computational speed when applied to the task of learning dynamical systems."}],"citation":{"ieee":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, and B. E. Wembe Moafo, “Adaptive higher order reversible integrators for memory efficient deep learning.” 2025.","apa":"Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., &#38; Wembe Moafo, B. E. (2025). <i>Adaptive higher order reversible integrators for memory efficient deep learning</i>.","short":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).","chicago":"Maslovskaya, Sofya, Sina Ober-Blöbaum, Christian Offen, Pranav Singh, and Boris Edgar Wembe Moafo. “Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning,” 2025.","mla":"Maslovskaya, Sofya, et al. <i>Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning</i>. 2025.","bibtex":"@article{Maslovskaya_Ober-Blöbaum_Offen_Singh_Wembe Moafo_2025, title={Adaptive higher order reversible integrators for memory efficient deep learning}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina and Offen, Christian and Singh, Pranav and Wembe Moafo, Boris Edgar}, year={2025} }","ama":"Maslovskaya S, Ober-Blöbaum S, Offen C, Singh P, Wembe Moafo BE. Adaptive higher order reversible integrators for memory efficient deep learning. Published online 2025."},"file_date_updated":"2025-05-05T09:28:02Z","department":[{"_id":"636"}],"type":"preprint","date_created":"2025-05-05T09:25:28Z","file":[{"content_type":"application/pdf","success":1,"file_id":"59795","date_updated":"2025-05-05T09:28:02Z","relation":"main_file","file_size":1830758,"access_level":"closed","file_name":"2410.09537v2.pdf","date_created":"2025-05-05T09:28:02Z","creator":"sofyam"}],"external_id":{"arxiv":["2410.09537"]},"has_accepted_license":"1","date_updated":"2025-09-30T15:16:09Z","author":[{"full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya","id":"87909"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"id":"85279","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian"},{"full_name":"Singh, Pranav","last_name":"Singh","first_name":"Pranav"},{"full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar","id":"95394"}],"year":"2025","status":"public","title":"Adaptive higher order reversible integrators for memory efficient deep learning","user_id":"85279","ddc":["510"],"_id":"59794","language":[{"iso":"eng"}]},{"publication":"Physical Review Research","issue":"3","abstract":[{"text":"<jats:p>We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.</jats:p>","lang":"eng"}],"date_created":"2025-12-09T09:08:39Z","department":[{"_id":"15"},{"_id":"569"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"35"},{"_id":"230"},{"_id":"429"},{"_id":"623"}],"type":"journal_article","author":[{"last_name":"Kopylov","first_name":"Denis A.","full_name":"Kopylov, Denis A."},{"first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279"},{"first_name":"Laura","last_name":"Ares","full_name":"Ares, Laura"},{"full_name":"Wembe Moafo, Boris Edgar","first_name":"Boris Edgar","last_name":"Wembe Moafo","id":"95394"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"},{"orcid":"0000-0001-8864-2072","first_name":"Torsten","last_name":"Meier","full_name":"Meier, Torsten","id":"344"},{"last_name":"Sharapova","first_name":"Polina R.","full_name":"Sharapova, Polina R.","id":"60286"},{"id":"75127","full_name":"Sperling, Jan","last_name":"Sperling","first_name":"Jan","orcid":"0000-0002-5844-3205"}],"publication_identifier":{"issn":["2643-1564"]},"year":"2025","title":"Multiphoton, multimode state classification for nonlinear optical circuits","intvolume":"         7","date_updated":"2025-12-09T09:10:01Z","publication_status":"published","language":[{"iso":"eng"}],"article_number":"033062","doi":"10.1103/sv6z-v1gk","citation":{"mla":"Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i>, vol. 7, no. 3, 033062, American Physical Society (APS), 2025, doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, volume={7}, DOI={<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>}, number={3033062}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Kopylov, Denis A. and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina R. and Sperling, Jan}, year={2025} }","ama":"Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>. 2025;7(3). doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>","ieee":"D. A. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits,” <i>Physical Review Research</i>, vol. 7, no. 3, Art. no. 033062, 2025, doi: <a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","apa":"Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P. R., &#38; Sperling, J. (2025). Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>, <i>7</i>(3), Article 033062. <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>","chicago":"Kopylov, Denis A., Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina R. Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i> 7, no. 3 (2025). <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>.","short":"D.A. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P.R. Sharapova, J. Sperling, Physical Review Research 7 (2025)."},"project":[{"name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen","_id":"53"},{"name":"TRR 142 - Project Area C","_id":"56"},{"_id":"174","name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse"},{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"status":"public","publisher":"American Physical Society (APS)","_id":"62980","volume":7,"user_id":"16199"},{"abstract":[{"text":"Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they respect important physical laws of the dynamical system, such as unitarity and energy conservation in the context of quantum dynamical systems, for instance. In this article we develop a high-order commutator free Lie group integrator for non-autonomous differential equations evolving on quadratic Lie groups. Instead of matrix exponentials, which are expensive to evaluate and need to be approximated by appropriate rational functions in order to preserve the Lie group structure, the proposed method is obtained as a composition of Cayley transforms which naturally respect the structure of quadratic Lie groups while being computationally efficient to evaluate. Unlike Cayley-Magnus methods the method is also free from nested matrix commutators.","lang":"eng"}],"issue":"15","publication":"J. Comput. Appl. Math","citation":{"short":"B.E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, P. Singh, J. Comput. Appl. Math 477 (n.d.).","chicago":"Wembe Moafo, Boris Edgar, Cristian  Offen, Sofya Maslovskaya, Sina Ober-Blöbaum, and Pranav Singh. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i> 477, no. 15 (n.d.). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>.","ieee":"B. E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, and P. Singh, “Commutator-free Cayley methods,” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi: <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>.","apa":"Wembe Moafo, B. E., Offen, C., Maslovskaya, S., Ober-Blöbaum, S., &#38; Singh, P. (n.d.). Commutator-free Cayley methods. <i>J. Comput. Appl. Math</i>, <i>477</i>(15). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>","bibtex":"@article{Wembe Moafo_Offen_Maslovskaya_Ober-Blöbaum_Singh, title={Commutator-free Cayley methods}, volume={477}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>}, number={15}, journal={J. Comput. Appl. Math}, author={Wembe Moafo, Boris Edgar and Offen, Cristian  and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Singh, Pranav} }","ama":"Wembe Moafo BE, Offen C, Maslovskaya S, Ober-Blöbaum S, Singh P. Commutator-free Cayley methods. <i>J Comput Appl Math</i>. 477(15). doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>","mla":"Wembe Moafo, Boris Edgar, et al. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>."},"type":"journal_article","department":[{"_id":"94"}],"date_created":"2025-04-10T14:42:52Z","publication_status":"submitted","date_updated":"2025-12-16T15:17:27Z","intvolume":"       477","status":"public","title":"Commutator-free Cayley methods","year":"2025","author":[{"first_name":"Boris Edgar","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394"},{"full_name":"Offen, Cristian ","last_name":"Offen","first_name":"Cristian "},{"full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya","id":"87909"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"last_name":"Singh","first_name":"Pranav","full_name":"Singh, Pranav"}],"user_id":"95394","doi":"10.1016/j.cam.2025.117184","volume":477,"language":[{"iso":"eng"}],"_id":"59507"},{"citation":{"ieee":"D. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits .” .","apa":"Kopylov, D., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P., &#38; Sperling, J. (n.d.). <i>Multiphoton, multimode state classification for nonlinear optical circuits </i>.","short":"D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P. Sharapova, J. Sperling, (n.d.).","chicago":"Kopylov, Denis, Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits ,” n.d.","mla":"Kopylov, Denis, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits </i>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling, title={Multiphoton, multimode state classification for nonlinear optical circuits }, author={Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and Sperling, Jan} }","ama":"Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits ."},"abstract":[{"lang":"eng","text":"We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes. "}],"date_created":"2025-02-10T08:26:45Z","external_id":{"arxiv":["2502.05123"]},"oa":"1","department":[{"_id":"623"},{"_id":"15"},{"_id":"636"}],"type":"preprint","author":[{"first_name":"Denis","last_name":"Kopylov","full_name":"Kopylov, Denis","id":"98502"},{"full_name":"Offen, Christian","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","id":"85279"},{"full_name":"Ares, Laura","first_name":"Laura","last_name":"Ares"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"id":"344","last_name":"Meier","first_name":"Torsten","orcid":"0000-0001-8864-2072","full_name":"Meier, Torsten"},{"full_name":"Sharapova, Polina","first_name":"Polina","last_name":"Sharapova","id":"60286"},{"full_name":"Sperling, Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205","first_name":"Jan","id":"75127"}],"status":"public","year":"2025","title":"Multiphoton, multimode state classification for nonlinear optical circuits ","date_updated":"2025-02-10T08:36:12Z","publication_status":"submitted","language":[{"iso":"eng"}],"_id":"58544","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2502.05123"}],"user_id":"85279"},{"author":[{"first_name":"Bernard","last_name":"Bonnard","full_name":"Bonnard, Bernard"},{"full_name":"Rouot, Jérémy","last_name":"Rouot","first_name":"Jérémy"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"publication_identifier":{"issn":["2156-8472","2156-8499"]},"year":"2022","status":"public","title":"Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies","publication_status":"published","date_updated":"2023-01-16T12:07:51Z","_id":"35206","publisher":"American Institute of Mathematical Sciences (AIMS)","language":[{"iso":"eng"}],"page":"0-0","volume":"0","user_id":"95394","doi":"10.3934/mcrf.2022052","citation":{"ieee":"B. Bonnard, J. Rouot, and B. E. Wembe Moafo, “Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies,” <i>Mathematical Control and Related Fields</i>, vol. 0, no. 0, pp. 0–0, 2022, doi: <a href=\"https://doi.org/10.3934/mcrf.2022052\">10.3934/mcrf.2022052</a>.","mla":"Bonnard, Bernard, et al. “Accessibility Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies.” <i>Mathematical Control and Related Fields</i>, vol. 0, no. 0, American Institute of Mathematical Sciences (AIMS), 2022, pp. 0–0, doi:<a href=\"https://doi.org/10.3934/mcrf.2022052\">10.3934/mcrf.2022052</a>.","apa":"Bonnard, B., Rouot, J., &#38; Wembe Moafo, B. E. (2022). Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies. <i>Mathematical Control and Related Fields</i>, <i>0</i>(0), 0–0. <a href=\"https://doi.org/10.3934/mcrf.2022052\">https://doi.org/10.3934/mcrf.2022052</a>","bibtex":"@article{Bonnard_Rouot_Wembe Moafo_2022, title={Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies}, volume={0}, DOI={<a href=\"https://doi.org/10.3934/mcrf.2022052\">10.3934/mcrf.2022052</a>}, number={0}, journal={Mathematical Control and Related Fields}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Bonnard, Bernard and Rouot, Jérémy and Wembe Moafo, Boris Edgar}, year={2022}, pages={0–0} }","chicago":"Bonnard, Bernard, Jérémy Rouot, and Boris Edgar Wembe Moafo. “Accessibility Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies.” <i>Mathematical Control and Related Fields</i> 0, no. 0 (2022): 0–0. <a href=\"https://doi.org/10.3934/mcrf.2022052\">https://doi.org/10.3934/mcrf.2022052</a>.","short":"B. Bonnard, J. Rouot, B.E. Wembe Moafo, Mathematical Control and Related Fields 0 (2022) 0–0.","ama":"Bonnard B, Rouot J, Wembe Moafo BE. Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies. <i>Mathematical Control and Related Fields</i>. 2022;0(0):0-0. doi:<a href=\"https://doi.org/10.3934/mcrf.2022052\">10.3934/mcrf.2022052</a>"},"publication":"Mathematical Control and Related Fields","issue":"0","date_created":"2023-01-04T10:26:56Z","keyword":["Applied Mathematics","Control and Optimization","General Medicine"],"type":"journal_article"},{"publication":"Systems &amp; Control Letters","citation":{"mla":"Bonnard, B., et al. “Abnormal Geodesics in 2D-Zermelo Navigation Problems in the Case of Revolution and the Fan Shape of the Small Time Balls.” <i>Systems &#38;amp; Control Letters</i>, vol. 161, 105140, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">10.1016/j.sysconle.2022.105140</a>.","bibtex":"@article{Bonnard_Cots_Gergaud_Wembe Moafo_2022, title={Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution and the fan shape of the small time balls}, volume={161}, DOI={<a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">10.1016/j.sysconle.2022.105140</a>}, number={105140}, journal={Systems &#38;amp; Control Letters}, publisher={Elsevier BV}, author={Bonnard, B. and Cots, O. and Gergaud, J. and Wembe Moafo, Boris Edgar}, year={2022} }","ama":"Bonnard B, Cots O, Gergaud J, Wembe Moafo BE. Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution and the fan shape of the small time balls. <i>Systems &#38;amp; Control Letters</i>. 2022;161. doi:<a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">10.1016/j.sysconle.2022.105140</a>","ieee":"B. Bonnard, O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution and the fan shape of the small time balls,” <i>Systems &#38;amp; Control Letters</i>, vol. 161, Art. no. 105140, 2022, doi: <a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">10.1016/j.sysconle.2022.105140</a>.","apa":"Bonnard, B., Cots, O., Gergaud, J., &#38; Wembe Moafo, B. E. (2022). Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution and the fan shape of the small time balls. <i>Systems &#38;amp; Control Letters</i>, <i>161</i>, Article 105140. <a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">https://doi.org/10.1016/j.sysconle.2022.105140</a>","short":"B. Bonnard, O. Cots, J. Gergaud, B.E. Wembe Moafo, Systems &#38;amp; Control Letters 161 (2022).","chicago":"Bonnard, B., O. Cots, J. Gergaud, and Boris Edgar Wembe Moafo. “Abnormal Geodesics in 2D-Zermelo Navigation Problems in the Case of Revolution and the Fan Shape of the Small Time Balls.” <i>Systems &#38;amp; Control Letters</i> 161 (2022). <a href=\"https://doi.org/10.1016/j.sysconle.2022.105140\">https://doi.org/10.1016/j.sysconle.2022.105140</a>."},"date_created":"2022-10-24T12:54:24Z","keyword":["Electrical and Electronic Engineering","Mechanical Engineering","General Computer Science","Control and Systems Engineering"],"type":"journal_article","year":"2022","status":"public","title":"Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution and the fan shape of the small time balls","author":[{"last_name":"Bonnard","first_name":"B.","full_name":"Bonnard, B."},{"first_name":"O.","last_name":"Cots","full_name":"Cots, O."},{"last_name":"Gergaud","first_name":"J.","full_name":"Gergaud, J."},{"full_name":"Wembe Moafo, Boris Edgar","first_name":"Boris Edgar","last_name":"Wembe Moafo","id":"95394"}],"publication_identifier":{"issn":["0167-6911"]},"publication_status":"published","date_updated":"2023-01-16T12:08:58Z","intvolume":"       161","article_number":"105140","_id":"33869","publisher":"Elsevier BV","language":[{"iso":"eng"}],"user_id":"95394","doi":"10.1016/j.sysconle.2022.105140","volume":161},{"status":"public","page":"43-53","_id":"33871","publisher":"EDP Sciences","user_id":"95394","volume":71,"citation":{"apa":"Cots, O., Gergaud, J., &#38; Wembe Moafo, B. E. (2021). Homotopic approach for turnpike and singularly perturbed optimal control problems. <i>ESAIM: Proceedings and Surveys</i>, <i>71</i>, 43–53. <a href=\"https://doi.org/10.1051/proc/202171105\">https://doi.org/10.1051/proc/202171105</a>","ieee":"O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Homotopic approach for turnpike and singularly perturbed optimal control problems,” <i>ESAIM: Proceedings and Surveys</i>, vol. 71, pp. 43–53, 2021, doi: <a href=\"https://doi.org/10.1051/proc/202171105\">10.1051/proc/202171105</a>.","short":"O. Cots, J. Gergaud, B.E. Wembe Moafo, ESAIM: Proceedings and Surveys 71 (2021) 43–53.","chicago":"Cots, Olivier, Joseph Gergaud, and Boris Edgar Wembe Moafo. “Homotopic Approach for Turnpike and Singularly Perturbed Optimal Control Problems.” <i>ESAIM: Proceedings and Surveys</i> 71 (2021): 43–53. <a href=\"https://doi.org/10.1051/proc/202171105\">https://doi.org/10.1051/proc/202171105</a>.","mla":"Cots, Olivier, et al. “Homotopic Approach for Turnpike and Singularly Perturbed Optimal Control Problems.” <i>ESAIM: Proceedings and Surveys</i>, vol. 71, EDP Sciences, 2021, pp. 43–53, doi:<a href=\"https://doi.org/10.1051/proc/202171105\">10.1051/proc/202171105</a>.","ama":"Cots O, Gergaud J, Wembe Moafo BE. Homotopic approach for turnpike and singularly perturbed optimal control problems. <i>ESAIM: Proceedings and Surveys</i>. 2021;71:43-53. doi:<a href=\"https://doi.org/10.1051/proc/202171105\">10.1051/proc/202171105</a>","bibtex":"@article{Cots_Gergaud_Wembe Moafo_2021, title={Homotopic approach for turnpike and singularly perturbed optimal control problems}, volume={71}, DOI={<a href=\"https://doi.org/10.1051/proc/202171105\">10.1051/proc/202171105</a>}, journal={ESAIM: Proceedings and Surveys}, publisher={EDP Sciences}, author={Cots, Olivier and Gergaud, Joseph and Wembe Moafo, Boris Edgar}, year={2021}, pages={43–53} }"},"title":"Homotopic approach for turnpike and singularly perturbed optimal control problems","year":"2021","author":[{"full_name":"Cots, Olivier","first_name":"Olivier","last_name":"Cots"},{"last_name":"Gergaud","first_name":"Joseph","full_name":"Gergaud, Joseph"},{"last_name":"Wembe Moafo","first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar","id":"95394"}],"publication_identifier":{"issn":["2267-3059"]},"publication_status":"published","date_updated":"2023-01-16T12:08:28Z","intvolume":"        71","language":[{"iso":"eng"}],"doi":"10.1051/proc/202171105","publication":"ESAIM: Proceedings and Surveys","abstract":[{"text":"<jats:p>The first aim of this article is to present the link between the turnpike property and the singular perturbations theory: the first one being a particular case of the second one. Then, thanks to this link, we set up a new framework based on continuation methods for the resolution of singularly perturbed optimal control problems. We consider first the turnpike case, then, we generalize the approach to general control problems with singular perturbations (that is with fast but also slow variables). We illustrate each step with an example.</jats:p>","lang":"eng"}],"date_created":"2022-10-24T13:00:10Z","type":"journal_article","keyword":["Immunology"]},{"has_accepted_license":"1","date_updated":"2023-01-16T12:09:11Z","publication_status":"submitted","author":[{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"title":"Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications","status":"public","year":"2021","ddc":["510"],"user_id":"95394","_id":"33872","language":[{"iso":"fre"}],"page":"180","related_material":{"link":[{"url":"https://hal.archives-ouvertes.fr/tel-03601394v2","relation":"confirmation"}]},"extern":"1","citation":{"ieee":"B. E. Wembe Moafo, <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>. .","mla":"Wembe Moafo, Boris Edgar. <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>.","apa":"Wembe Moafo, B. E. (n.d.). <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>.","bibtex":"@book{Wembe Moafo, title={Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications}, author={Wembe Moafo, Boris Edgar} }","chicago":"Wembe Moafo, Boris Edgar. <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>, n.d.","ama":"Wembe Moafo BE. <i>Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications</i>.","short":"B.E. Wembe Moafo, Geometric and Numerical Methods in Optimal Control and Zermelo Problems on Revolution Surfaces - Applications, n.d."},"file_date_updated":"2022-10-25T09:07:57Z","oa":"1","type":"dissertation","date_created":"2022-10-25T09:08:05Z","file":[{"date_created":"2022-10-25T09:07:57Z","creator":"wboris","file_id":"33873","content_type":"application/pdf","relation":"main_file","date_updated":"2022-10-25T09:07:57Z","file_name":"These_Hal.pdf","file_size":6662644,"access_level":"open_access"}]},{"date_created":"2022-10-24T12:59:19Z","place":"Cham","type":"book_chapter","citation":{"ama":"Balsa C, Cots O, Gergaud J, Wembe Moafo BE. Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow. In: <i>Lecture Notes in Electrical Engineering</i>. Springer International Publishing; 2020. doi:<a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">10.1007/978-3-030-58653-9_22</a>","bibtex":"@inbook{Balsa_Cots_Gergaud_Wembe Moafo_2020, place={Cham}, title={Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">10.1007/978-3-030-58653-9_22</a>}, booktitle={Lecture Notes in Electrical Engineering}, publisher={Springer International Publishing}, author={Balsa, Carlos and Cots, Olivier and Gergaud, Joseph and Wembe Moafo, Boris Edgar}, year={2020} }","mla":"Balsa, Carlos, et al. “Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow.” <i>Lecture Notes in Electrical Engineering</i>, Springer International Publishing, 2020, doi:<a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">10.1007/978-3-030-58653-9_22</a>.","short":"C. Balsa, O. Cots, J. Gergaud, B.E. Wembe Moafo, in: Lecture Notes in Electrical Engineering, Springer International Publishing, Cham, 2020.","chicago":"Balsa, Carlos, Olivier Cots, Joseph Gergaud, and Boris Edgar Wembe Moafo. “Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow.” In <i>Lecture Notes in Electrical Engineering</i>. Cham: Springer International Publishing, 2020. <a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">https://doi.org/10.1007/978-3-030-58653-9_22</a>.","apa":"Balsa, C., Cots, O., Gergaud, J., &#38; Wembe Moafo, B. E. (2020). Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow. In <i>Lecture Notes in Electrical Engineering</i>. Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-58653-9_22\">https://doi.org/10.1007/978-3-030-58653-9_22</a>","ieee":"C. Balsa, O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow,” in <i>Lecture Notes in Electrical Engineering</i>, Cham: Springer International Publishing, 2020."},"publication":"Lecture Notes in Electrical Engineering","_id":"33870","publisher":"Springer International Publishing","language":[{"iso":"eng"}],"user_id":"95394","doi":"10.1007/978-3-030-58653-9_22","publication_identifier":{"issn":["1876-1100","1876-1119"],"isbn":["9783030586522","9783030586539"]},"author":[{"last_name":"Balsa","first_name":"Carlos","full_name":"Balsa, Carlos"},{"full_name":"Cots, Olivier","first_name":"Olivier","last_name":"Cots"},{"full_name":"Gergaud, Joseph","first_name":"Joseph","last_name":"Gergaud"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"status":"public","year":"2020","title":"Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow","publication_status":"published","date_updated":"2023-01-16T12:08:44Z"},{"user_id":"95394","volume":27,"_id":"33866","publisher":"EDP Sciences","status":"public","citation":{"short":"B. Bonnard, O. Cots, B.E. Wembe Moafo, ESAIM: Control, Optimisation and Calculus of Variations 27 (2020).","ama":"Bonnard B, Cots O, Wembe Moafo BE. A Zermelo navigation problem with a vortex singularity. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>. 2020;27. doi:<a href=\"https://doi.org/10.1051/cocv/2020058\">10.1051/cocv/2020058</a>","chicago":"Bonnard, Bernard, Olivier Cots, and Boris Edgar Wembe Moafo. “A Zermelo Navigation Problem with a Vortex Singularity.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i> 27 (2020). <a href=\"https://doi.org/10.1051/cocv/2020058\">https://doi.org/10.1051/cocv/2020058</a>.","bibtex":"@article{Bonnard_Cots_Wembe Moafo_2020, title={A Zermelo navigation problem with a vortex singularity}, volume={27}, DOI={<a href=\"https://doi.org/10.1051/cocv/2020058\">10.1051/cocv/2020058</a>}, number={S10}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, publisher={EDP Sciences}, author={Bonnard, Bernard and Cots, Olivier and Wembe Moafo, Boris Edgar}, year={2020} }","mla":"Bonnard, Bernard, et al. “A Zermelo Navigation Problem with a Vortex Singularity.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, vol. 27, S10, EDP Sciences, 2020, doi:<a href=\"https://doi.org/10.1051/cocv/2020058\">10.1051/cocv/2020058</a>.","apa":"Bonnard, B., Cots, O., &#38; Wembe Moafo, B. E. (2020). A Zermelo navigation problem with a vortex singularity. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, <i>27</i>, Article S10. <a href=\"https://doi.org/10.1051/cocv/2020058\">https://doi.org/10.1051/cocv/2020058</a>","ieee":"B. Bonnard, O. Cots, and B. E. Wembe Moafo, “A Zermelo navigation problem with a vortex singularity,” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, vol. 27, Art. no. S10, 2020, doi: <a href=\"https://doi.org/10.1051/cocv/2020058\">10.1051/cocv/2020058</a>."},"doi":"10.1051/cocv/2020058","article_number":"S10","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-01-16T12:09:22Z","intvolume":"        27","title":"A Zermelo navigation problem with a vortex singularity","year":"2020","publication_identifier":{"issn":["1292-8119","1262-3377"]},"author":[{"first_name":"Bernard","last_name":"Bonnard","full_name":"Bonnard, Bernard"},{"last_name":"Cots","first_name":"Olivier","full_name":"Cots, Olivier"},{"id":"95394","first_name":"Boris Edgar","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar"}],"keyword":["Computational Mathematics","Control and Optimization","Control and Systems Engineering"],"type":"journal_article","date_created":"2022-10-24T12:51:05Z","abstract":[{"lang":"eng","text":"<jats:p>Helhmoltz–Kirchhoff equations of motions of vortices of an incompressible fluid in the plane define a dynamics with singularities and this leads to a Zermelo navigation problem describing the ship travel in such a field where the control is the heading angle. Considering one vortex, we define a time minimization problem which can be analyzed with the technics of geometric optimal control combined with numerical simulations, the geometric frame being the extension of Randers metrics in the punctured plane, with rotational symmetry. Candidates as minimizers are parameterized thanks to the Pontryagin Maximum Principle as extremal solutions of a Hamiltonian vector field. We analyze the time minimal solution to transfer the ship between two points where during the transfer the ship can be either in a strong current region in the vicinity of the vortex or in a weak current region. The analysis is based on a micro-local classification of the extremals using mainly the integrability properties of the dynamics due to the rotational symmetry. The discussion is complex and related to the existence of an isolated extremal (Reeb) circle due to the vortex singularity. The explicit computation of cut points where the extremal curves cease to be optimal is given and the spheres are described in the case where at the initial point the current is weak.</jats:p>"}],"publication":"ESAIM: Control, Optimisation and Calculus of Variations"}]