---
_id: '65746'
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.
author:
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
orcid: 0000-0002-6085-8071
- first_name: Usman
full_name: Ali, Usman
last_name: Ali
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
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:10.48550/ARXIV.2603.11697'
apa: Wembe Moafo, B. E., Ali, U., Meier, T., & Ober-Blöbaum, S. (2026). Cayley
Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control.
European Control Conference, Reykjavík, Iceland. https://doi.org/10.48550/ARXIV.2603.11697
bibtex: '@inproceedings{Wembe Moafo_Ali_Meier_Ober-Blöbaum_2026, title={Cayley Commutator-free
Methods for Krotov-Type Algorithms in Quantum Optimal Control}, DOI={10.48550/ARXIV.2603.11697},
author={Wembe Moafo, Boris Edgar and Ali, Usman and Meier, Torsten and Ober-Blöbaum,
Sina}, year={2026} }'
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. https://doi.org/10.48550/ARXIV.2603.11697.
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: 10.48550/ARXIV.2603.11697.'
mla: Wembe Moafo, Boris Edgar, et al. Cayley Commutator-Free Methods for Krotov-Type
Algorithms in Quantum Optimal Control. 2026, doi:10.48550/ARXIV.2603.11697.
short: 'B.E. Wembe Moafo, U. Ali, T. Meier, S. Ober-Blöbaum, in: 2026.'
conference:
end_date: 2026-07-10
location: Reykjavík, Iceland
name: European Control Conference
start_date: 2026-07-07
date_created: 2026-06-01T09:38:06Z
date_updated: 2026-06-01T09:40:38Z
department:
- _id: '94'
doi: 10.48550/ARXIV.2603.11697
language:
- iso: eng
status: public
title: Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal
Control
type: conference
user_id: '95394'
year: '2026'
...
---
_id: '65744'
abstract:
- lang: eng
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.'
author:
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
orcid: 0000-0002-6085-8071
citation:
ama: Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Non static exponential turnpike
property for optimal control problems with symmetries and boundary conditions.
apa: Maslovskaya, S., Ober-Blöbaum, S., & Wembe Moafo, B. E. (n.d.). Non
static exponential turnpike property for optimal control problems with symmetries
and boundary conditions.
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}
}'
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.
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.”
.
mla: Maslovskaya, Sofya, et al. Non Static Exponential Turnpike Property for
Optimal Control Problems with Symmetries and Boundary Conditions.
short: S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, (n.d.).
date_created: 2026-06-01T09:31:15Z
date_updated: 2026-06-01T09:35:13Z
department:
- _id: '94'
language:
- iso: eng
publication_status: submitted
status: public
title: Non static exponential turnpike property for optimal control problems with
symmetries and boundary conditions
type: preprint
user_id: '95394'
year: '2026'
...
---
_id: '65777'
abstract:
- lang: eng
text: "Abstract\r\n 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."
article_number: '225303'
author:
- first_name: Christian
full_name: Offen, Christian
last_name: Offen
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
orcid: 0000-0002-6085-8071
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Offen C, Wembe Moafo BE, Ares L, Sperling J, Ober-Blöbaum S. Numerical approaches
to entangling dynamics from variational principles. Journal of Physics A: Mathematical
and Theoretical. 2026;59(22). doi:10.1088/1751-8121/ae6d51'
apa: 'Offen, C., Wembe Moafo, B. E., Ares, L., Sperling, J., & Ober-Blöbaum,
S. (2026). Numerical approaches to entangling dynamics from variational principles.
Journal of Physics A: Mathematical and Theoretical, 59(22), Article
225303. https://doi.org/10.1088/1751-8121/ae6d51'
bibtex: '@article{Offen_Wembe Moafo_Ares_Sperling_Ober-Blöbaum_2026, title={Numerical
approaches to entangling dynamics from variational principles}, volume={59}, DOI={10.1088/1751-8121/ae6d51},
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} }'
chicago: 'Offen, Christian, Boris Edgar Wembe Moafo, Laura Ares, Jan Sperling, and
Sina Ober-Blöbaum. “Numerical Approaches to Entangling Dynamics from Variational
Principles.” Journal of Physics A: Mathematical and Theoretical 59, no.
22 (2026). https://doi.org/10.1088/1751-8121/ae6d51.'
ieee: 'C. Offen, B. E. Wembe Moafo, L. Ares, J. Sperling, and S. Ober-Blöbaum, “Numerical
approaches to entangling dynamics from variational principles,” Journal of
Physics A: Mathematical and Theoretical, vol. 59, no. 22, Art. no. 225303,
2026, doi: 10.1088/1751-8121/ae6d51.'
mla: 'Offen, Christian, et al. “Numerical Approaches to Entangling Dynamics from
Variational Principles.” Journal of Physics A: Mathematical and Theoretical,
vol. 59, no. 22, 225303, IOP Publishing, 2026, doi:10.1088/1751-8121/ae6d51.'
short: 'C. Offen, B.E. Wembe Moafo, L. Ares, J. Sperling, S. Ober-Blöbaum, Journal
of Physics A: Mathematical and Theoretical 59 (2026).'
date_created: 2026-06-05T07:37:43Z
date_updated: 2026-06-05T07:38:44Z
department:
- _id: '623'
- _id: '15'
- _id: '170'
- _id: '706'
- _id: '429'
doi: 10.1088/1751-8121/ae6d51
intvolume: ' 59'
issue: '22'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
issn:
- 1751-8113
- 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: Numerical approaches to entangling dynamics from variational principles
type: journal_article
user_id: '75127'
volume: 59
year: '2026'
...
---
_id: '59792'
abstract:
- lang: eng
text: "Abstract\r\n 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 static turnpike to manifold turnpike
we extend the exponential turnpike property to the
exponential trim turnpike 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
trim turnpike theorem for the full problem. Finally,
we illustrate our results on the Kepler problem and the rigid body problem.\r\n"
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for
optimal control problems with symmetries. Mathematics of Control, Signals,
and Systems. Published online 2025. doi:10.1007/s00498-025-00408-w
apa: Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., & Wembe Moafo, B. E. (2025).
Trim turnpikes for optimal control problems with symmetries. Mathematics of
Control, Signals, and Systems. https://doi.org/10.1007/s00498-025-00408-w
bibtex: '@article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim
turnpikes for optimal control problems with symmetries}, DOI={10.1007/s00498-025-00408-w},
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} }'
chicago: Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar
Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” Mathematics
of Control, Signals, and Systems, 2025. https://doi.org/10.1007/s00498-025-00408-w.
ieee: 'K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim
turnpikes for optimal control problems with symmetries,” Mathematics of Control,
Signals, and Systems, 2025, doi: 10.1007/s00498-025-00408-w.'
mla: Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with
Symmetries.” Mathematics of Control, Signals, and Systems, Springer Science
and Business Media LLC, 2025, doi:10.1007/s00498-025-00408-w.
short: K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics
of Control, Signals, and Systems (2025).
date_created: 2025-05-05T09:23:38Z
date_updated: 2025-05-05T09:24:09Z
department:
- _id: '636'
doi: 10.1007/s00498-025-00408-w
language:
- iso: eng
publication: Mathematics of Control, Signals, and Systems
publication_identifier:
issn:
- 0932-4194
- 1435-568X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Trim turnpikes for optimal control problems with symmetries
type: journal_article
user_id: '87909'
year: '2025'
...
---
_id: '59794'
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.
author:
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Pranav
full_name: Singh, Pranav
last_name: Singh
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
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.
apa: Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., & Wembe Moafo,
B. E. (2025). Adaptive higher order reversible integrators for memory efficient
deep learning.
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} }'
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.
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.
mla: Maslovskaya, Sofya, et al. Adaptive Higher Order Reversible Integrators
for Memory Efficient Deep Learning. 2025.
short: S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).
date_created: 2025-05-05T09:25:28Z
date_updated: 2025-09-30T15:16:09Z
ddc:
- '510'
department:
- _id: '636'
external_id:
arxiv:
- '2410.09537'
file:
- access_level: closed
content_type: application/pdf
creator: sofyam
date_created: 2025-05-05T09:28:02Z
date_updated: 2025-05-05T09:28:02Z
file_id: '59795'
file_name: 2410.09537v2.pdf
file_size: 1830758
relation: main_file
success: 1
file_date_updated: 2025-05-05T09:28:02Z
has_accepted_license: '1'
language:
- iso: eng
status: public
title: Adaptive higher order reversible integrators for memory efficient deep learning
type: preprint
user_id: '85279'
year: '2025'
...
---
_id: '62980'
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 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.
article_number: '033062'
author:
- first_name: Denis A.
full_name: Kopylov, Denis A.
last_name: Kopylov
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification
for nonlinear optical circuits. Physical Review Research. 2025;7(3). doi:10.1103/sv6z-v1gk
apa: Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S.,
Meier, T., Sharapova, P. R., & Sperling, J. (2025). Multiphoton, multimode
state classification for nonlinear optical circuits. Physical Review Research,
7(3), Article 033062. https://doi.org/10.1103/sv6z-v1gk
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={10.1103/sv6z-v1gk},
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} }'
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.” Physical Review
Research 7, no. 3 (2025). https://doi.org/10.1103/sv6z-v1gk.
ieee: 'D. A. Kopylov et al., “Multiphoton, multimode state classification
for nonlinear optical circuits,” Physical Review Research, vol. 7, no.
3, Art. no. 033062, 2025, doi: 10.1103/sv6z-v1gk.'
mla: Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for
Nonlinear Optical Circuits.” Physical Review Research, vol. 7, no. 3, 033062,
American Physical Society (APS), 2025, doi:10.1103/sv6z-v1gk.
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).
date_created: 2025-12-09T09:08:39Z
date_updated: 2025-12-09T09:10:01Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '35'
- _id: '230'
- _id: '429'
- _id: '623'
doi: 10.1103/sv6z-v1gk
intvolume: ' 7'
issue: '3'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: Physical Review Research
publication_identifier:
issn:
- 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: journal_article
user_id: '16199'
volume: 7
year: '2025'
...
---
_id: '62979'
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.
author:
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: Meier T, Sharapova PR, Sperling J, Ober-Blöbaum S, Wembe Moafo BE, Offen C.
Multiphoton, multimode state classification for nonlinear optical circuits. Published
online 2025.
apa: Meier, T., Sharapova, P. R., Sperling, J., Ober-Blöbaum, S., Wembe Moafo, B.
E., & Offen, C. (2025). Multiphoton, multimode state classification for
nonlinear optical circuits.
bibtex: '@article{Meier_Sharapova_Sperling_Ober-Blöbaum_Wembe Moafo_Offen_2025,
title={Multiphoton, multimode state classification for nonlinear optical circuits},
author={Meier, Torsten and Sharapova, Polina R. and Sperling, Jan and Ober-Blöbaum,
Sina and Wembe Moafo, Boris Edgar and Offen, Christian}, year={2025} }'
chicago: Meier, Torsten, Polina R. Sharapova, Jan Sperling, Sina Ober-Blöbaum, Boris
Edgar Wembe Moafo, and Christian Offen. “Multiphoton, Multimode State Classification
for Nonlinear Optical Circuits,” 2025.
ieee: T. Meier, P. R. Sharapova, J. Sperling, S. Ober-Blöbaum, B. E. Wembe Moafo,
and C. Offen, “Multiphoton, multimode state classification for nonlinear optical
circuits.” 2025.
mla: Meier, Torsten, et al. Multiphoton, Multimode State Classification for Nonlinear
Optical Circuits. 2025.
short: T. Meier, P.R. Sharapova, J. Sperling, S. Ober-Blöbaum, B.E. Wembe Moafo,
C. Offen, (2025).
date_created: 2025-12-09T08:59:27Z
date_updated: 2025-12-09T09:10:23Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '230'
- _id: '623'
- _id: '429'
- _id: '35'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _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
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: preprint
user_id: '16199'
year: '2025'
...
---
_id: '59507'
abstract:
- lang: eng
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.
author:
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: 'Cristian '
full_name: 'Offen, Cristian '
last_name: Offen
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Pranav
full_name: Singh, Pranav
last_name: Singh
citation:
ama: Wembe Moafo BE, Offen C, Maslovskaya S, Ober-Blöbaum S, Singh P. Commutator-free
Cayley methods. J Comput Appl Math. 477(15). doi:10.1016/j.cam.2025.117184
apa: Wembe Moafo, B. E., Offen, C., Maslovskaya, S., Ober-Blöbaum, S., & Singh,
P. (n.d.). Commutator-free Cayley methods. J. Comput. Appl. Math, 477(15).
https://doi.org/10.1016/j.cam.2025.117184
bibtex: '@article{Wembe Moafo_Offen_Maslovskaya_Ober-Blöbaum_Singh, title={Commutator-free
Cayley methods}, volume={477}, DOI={10.1016/j.cam.2025.117184},
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} }'
chicago: Wembe Moafo, Boris Edgar, Cristian Offen, Sofya Maslovskaya, Sina Ober-Blöbaum,
and Pranav Singh. “Commutator-Free Cayley Methods.” J. Comput. Appl. Math
477, no. 15 (n.d.). https://doi.org/10.1016/j.cam.2025.117184.
ieee: 'B. E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, and P. Singh,
“Commutator-free Cayley methods,” J. Comput. Appl. Math, vol. 477, no.
15, doi: 10.1016/j.cam.2025.117184.'
mla: Wembe Moafo, Boris Edgar, et al. “Commutator-Free Cayley Methods.” J. Comput.
Appl. Math, vol. 477, no. 15, doi:10.1016/j.cam.2025.117184.
short: B.E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, P. Singh, J.
Comput. Appl. Math 477 (n.d.).
date_created: 2025-04-10T14:42:52Z
date_updated: 2025-12-16T15:17:27Z
department:
- _id: '94'
doi: 10.1016/j.cam.2025.117184
intvolume: ' 477'
issue: '15'
language:
- iso: eng
publication: J. Comput. Appl. Math
publication_status: submitted
status: public
title: Commutator-free Cayley methods
type: journal_article
user_id: '95394'
volume: 477
year: '2025'
...
---
_id: '58544'
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. '
author:
- first_name: Denis
full_name: Kopylov, Denis
id: '98502'
last_name: Kopylov
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina
full_name: Sharapova, Polina
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Kopylov D, Offen C, Ares L, et al. 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., & Sperling, J. (n.d.). Multiphoton, multimode state
classification for nonlinear optical circuits .
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} }'
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.
ieee: D. Kopylov et al., “Multiphoton, multimode state classification for
nonlinear optical circuits .” .
mla: Kopylov, Denis, et al. Multiphoton, Multimode State Classification for Nonlinear
Optical Circuits .
short: D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier,
P. Sharapova, J. Sperling, (n.d.).
date_created: 2025-02-10T08:26:45Z
date_updated: 2025-02-10T08:36:12Z
department:
- _id: '623'
- _id: '15'
- _id: '636'
external_id:
arxiv:
- '2502.05123'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2502.05123
oa: '1'
publication_status: submitted
status: public
title: 'Multiphoton, multimode state classification for nonlinear optical circuits '
type: preprint
user_id: '85279'
year: '2025'
...
---
_id: '35206'
author:
- first_name: Bernard
full_name: Bonnard, Bernard
last_name: Bonnard
- first_name: Jérémy
full_name: Rouot, Jérémy
last_name: Rouot
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Bonnard B, Rouot J, Wembe Moafo BE. Accessibility properties of abnormal geodesics
in optimal control illustrated by two case studies. Mathematical Control and
Related Fields. 2022;0(0):0-0. doi:10.3934/mcrf.2022052
apa: Bonnard, B., Rouot, J., & Wembe Moafo, B. E. (2022). Accessibility properties
of abnormal geodesics in optimal control illustrated by two case studies. Mathematical
Control and Related Fields, 0(0), 0–0. https://doi.org/10.3934/mcrf.2022052
bibtex: '@article{Bonnard_Rouot_Wembe Moafo_2022, title={Accessibility properties
of abnormal geodesics in optimal control illustrated by two case studies}, volume={0},
DOI={10.3934/mcrf.2022052},
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.”
Mathematical Control and Related Fields 0, no. 0 (2022): 0–0. https://doi.org/10.3934/mcrf.2022052.'
ieee: 'B. Bonnard, J. Rouot, and B. E. Wembe Moafo, “Accessibility properties of
abnormal geodesics in optimal control illustrated by two case studies,” Mathematical
Control and Related Fields, vol. 0, no. 0, pp. 0–0, 2022, doi: 10.3934/mcrf.2022052.'
mla: Bonnard, Bernard, et al. “Accessibility Properties of Abnormal Geodesics in
Optimal Control Illustrated by Two Case Studies.” Mathematical Control and
Related Fields, vol. 0, no. 0, American Institute of Mathematical Sciences
(AIMS), 2022, pp. 0–0, doi:10.3934/mcrf.2022052.
short: B. Bonnard, J. Rouot, B.E. Wembe Moafo, Mathematical Control and Related
Fields 0 (2022) 0–0.
date_created: 2023-01-04T10:26:56Z
date_updated: 2023-01-16T12:07:51Z
doi: 10.3934/mcrf.2022052
issue: '0'
keyword:
- Applied Mathematics
- Control and Optimization
- General Medicine
language:
- iso: eng
page: 0-0
publication: Mathematical Control and Related Fields
publication_identifier:
issn:
- 2156-8472
- 2156-8499
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Accessibility properties of abnormal geodesics in optimal control illustrated
by two case studies
type: journal_article
user_id: '95394'
volume: '0'
year: '2022'
...
---
_id: '33869'
article_number: '105140'
author:
- first_name: B.
full_name: Bonnard, B.
last_name: Bonnard
- first_name: O.
full_name: Cots, O.
last_name: Cots
- first_name: J.
full_name: Gergaud, J.
last_name: Gergaud
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
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. Systems & Control Letters. 2022;161. doi:10.1016/j.sysconle.2022.105140
apa: Bonnard, B., Cots, O., Gergaud, J., & 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. Systems & Control Letters, 161,
Article 105140. https://doi.org/10.1016/j.sysconle.2022.105140
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={10.1016/j.sysconle.2022.105140},
number={105140}, journal={Systems & Control Letters}, publisher={Elsevier
BV}, author={Bonnard, B. and Cots, O. and Gergaud, J. and Wembe Moafo, Boris Edgar},
year={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.” Systems & Control Letters 161
(2022). https://doi.org/10.1016/j.sysconle.2022.105140.
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,” Systems & Control Letters, vol. 161,
Art. no. 105140, 2022, doi: 10.1016/j.sysconle.2022.105140.'
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.” Systems
& Control Letters, vol. 161, 105140, Elsevier BV, 2022, doi:10.1016/j.sysconle.2022.105140.
short: B. Bonnard, O. Cots, J. Gergaud, B.E. Wembe Moafo, Systems & Control
Letters 161 (2022).
date_created: 2022-10-24T12:54:24Z
date_updated: 2023-01-16T12:08:58Z
doi: 10.1016/j.sysconle.2022.105140
intvolume: ' 161'
keyword:
- Electrical and Electronic Engineering
- Mechanical Engineering
- General Computer Science
- Control and Systems Engineering
language:
- iso: eng
publication: Systems & Control Letters
publication_identifier:
issn:
- 0167-6911
publication_status: published
publisher: Elsevier BV
status: public
title: Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution
and the fan shape of the small time balls
type: journal_article
user_id: '95394'
volume: 161
year: '2022'
...
---
_id: '33871'
abstract:
- lang: eng
text: '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.'
author:
- first_name: Olivier
full_name: Cots, Olivier
last_name: Cots
- first_name: Joseph
full_name: Gergaud, Joseph
last_name: Gergaud
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: 'Cots O, Gergaud J, Wembe Moafo BE. Homotopic approach for turnpike and singularly
perturbed optimal control problems. ESAIM: Proceedings and Surveys. 2021;71:43-53.
doi:10.1051/proc/202171105'
apa: 'Cots, O., Gergaud, J., & Wembe Moafo, B. E. (2021). Homotopic approach
for turnpike and singularly perturbed optimal control problems. ESAIM: Proceedings
and Surveys, 71, 43–53. https://doi.org/10.1051/proc/202171105'
bibtex: '@article{Cots_Gergaud_Wembe Moafo_2021, title={Homotopic approach for turnpike
and singularly perturbed optimal control problems}, volume={71}, DOI={10.1051/proc/202171105},
journal={ESAIM: Proceedings and Surveys}, publisher={EDP Sciences}, author={Cots,
Olivier and Gergaud, Joseph and Wembe Moafo, Boris Edgar}, year={2021}, pages={43–53}
}'
chicago: 'Cots, Olivier, Joseph Gergaud, and Boris Edgar Wembe Moafo. “Homotopic
Approach for Turnpike and Singularly Perturbed Optimal Control Problems.” ESAIM:
Proceedings and Surveys 71 (2021): 43–53. https://doi.org/10.1051/proc/202171105.'
ieee: 'O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Homotopic approach for turnpike
and singularly perturbed optimal control problems,” ESAIM: Proceedings and
Surveys, vol. 71, pp. 43–53, 2021, doi: 10.1051/proc/202171105.'
mla: 'Cots, Olivier, et al. “Homotopic Approach for Turnpike and Singularly Perturbed
Optimal Control Problems.” ESAIM: Proceedings and Surveys, vol. 71, EDP
Sciences, 2021, pp. 43–53, doi:10.1051/proc/202171105.'
short: 'O. Cots, J. Gergaud, B.E. Wembe Moafo, ESAIM: Proceedings and Surveys 71
(2021) 43–53.'
date_created: 2022-10-24T13:00:10Z
date_updated: 2023-01-16T12:08:28Z
doi: 10.1051/proc/202171105
intvolume: ' 71'
keyword:
- Immunology
language:
- iso: eng
page: 43-53
publication: 'ESAIM: Proceedings and Surveys'
publication_identifier:
issn:
- 2267-3059
publication_status: published
publisher: EDP Sciences
status: public
title: Homotopic approach for turnpike and singularly perturbed optimal control problems
type: journal_article
user_id: '95394'
volume: 71
year: '2021'
...
---
_id: '33872'
author:
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Wembe Moafo BE. Geometric and Numerical Methods in Optimal Control and Zermelo
Problems on Revolution Surfaces - Applications.
apa: Wembe Moafo, B. E. (n.d.). Geometric and Numerical Methods in Optimal Control
and Zermelo Problems on Revolution Surfaces - Applications.
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. Geometric and Numerical Methods in Optimal
Control and Zermelo Problems on Revolution Surfaces - Applications, n.d.
ieee: B. E. Wembe Moafo, Geometric and Numerical Methods in Optimal Control and
Zermelo Problems on Revolution Surfaces - Applications. .
mla: Wembe Moafo, Boris Edgar. Geometric and Numerical Methods in Optimal Control
and Zermelo Problems on Revolution Surfaces - Applications.
short: B.E. Wembe Moafo, Geometric and Numerical Methods in Optimal Control and
Zermelo Problems on Revolution Surfaces - Applications, n.d.
date_created: 2022-10-25T09:08:05Z
date_updated: 2023-01-16T12:09:11Z
ddc:
- '510'
extern: '1'
file:
- access_level: open_access
content_type: application/pdf
creator: wboris
date_created: 2022-10-25T09:07:57Z
date_updated: 2022-10-25T09:07:57Z
file_id: '33873'
file_name: These_Hal.pdf
file_size: 6662644
relation: main_file
file_date_updated: 2022-10-25T09:07:57Z
has_accepted_license: '1'
language:
- iso: fre
oa: '1'
page: '180'
publication_status: submitted
related_material:
link:
- relation: confirmation
url: https://hal.archives-ouvertes.fr/tel-03601394v2
status: public
title: Geometric and Numerical Methods in Optimal Control and Zermelo Problems on
Revolution Surfaces - Applications
type: dissertation
user_id: '95394'
year: '2021'
...
---
_id: '33870'
author:
- first_name: Carlos
full_name: Balsa, Carlos
last_name: Balsa
- first_name: Olivier
full_name: Cots, Olivier
last_name: Cots
- first_name: Joseph
full_name: Gergaud, Joseph
last_name: Gergaud
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: 'Balsa C, Cots O, Gergaud J, Wembe Moafo BE. Minimum Energy Control of Passive
Tracers Advection in Point Vortices Flow. In: Lecture Notes in Electrical Engineering.
Springer International Publishing; 2020. doi:10.1007/978-3-030-58653-9_22'
apa: Balsa, C., Cots, O., Gergaud, J., & Wembe Moafo, B. E. (2020). Minimum
Energy Control of Passive Tracers Advection in Point Vortices Flow. In Lecture
Notes in Electrical Engineering. Springer International Publishing. https://doi.org/10.1007/978-3-030-58653-9_22
bibtex: '@inbook{Balsa_Cots_Gergaud_Wembe Moafo_2020, place={Cham}, title={Minimum
Energy Control of Passive Tracers Advection in Point Vortices Flow}, DOI={10.1007/978-3-030-58653-9_22},
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} }'
chicago: 'Balsa, Carlos, Olivier Cots, Joseph Gergaud, and Boris Edgar Wembe Moafo.
“Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow.”
In Lecture Notes in Electrical Engineering. Cham: Springer International
Publishing, 2020. https://doi.org/10.1007/978-3-030-58653-9_22.'
ieee: 'C. Balsa, O. Cots, J. Gergaud, and B. E. Wembe Moafo, “Minimum Energy Control
of Passive Tracers Advection in Point Vortices Flow,” in Lecture Notes in Electrical
Engineering, Cham: Springer International Publishing, 2020.'
mla: Balsa, Carlos, et al. “Minimum Energy Control of Passive Tracers Advection
in Point Vortices Flow.” Lecture Notes in Electrical Engineering, Springer
International Publishing, 2020, doi:10.1007/978-3-030-58653-9_22.
short: 'C. Balsa, O. Cots, J. Gergaud, B.E. Wembe Moafo, in: Lecture Notes in Electrical
Engineering, Springer International Publishing, Cham, 2020.'
date_created: 2022-10-24T12:59:19Z
date_updated: 2023-01-16T12:08:44Z
doi: 10.1007/978-3-030-58653-9_22
language:
- iso: eng
place: Cham
publication: Lecture Notes in Electrical Engineering
publication_identifier:
isbn:
- '9783030586522'
- '9783030586539'
issn:
- 1876-1100
- 1876-1119
publication_status: published
publisher: Springer International Publishing
status: public
title: Minimum Energy Control of Passive Tracers Advection in Point Vortices Flow
type: book_chapter
user_id: '95394'
year: '2020'
...
---
_id: '33866'
abstract:
- lang: eng
text: 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.
article_number: S10
author:
- first_name: Bernard
full_name: Bonnard, Bernard
last_name: Bonnard
- first_name: Olivier
full_name: Cots, Olivier
last_name: Cots
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: 'Bonnard B, Cots O, Wembe Moafo BE. A Zermelo navigation problem with a vortex
singularity. ESAIM: Control, Optimisation and Calculus of Variations. 2020;27.
doi:10.1051/cocv/2020058'
apa: 'Bonnard, B., Cots, O., & Wembe Moafo, B. E. (2020). A Zermelo navigation
problem with a vortex singularity. ESAIM: Control, Optimisation and Calculus
of Variations, 27, Article S10. https://doi.org/10.1051/cocv/2020058'
bibtex: '@article{Bonnard_Cots_Wembe Moafo_2020, title={A Zermelo navigation problem
with a vortex singularity}, volume={27}, DOI={10.1051/cocv/2020058},
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} }'
chicago: 'Bonnard, Bernard, Olivier Cots, and Boris Edgar Wembe Moafo. “A Zermelo
Navigation Problem with a Vortex Singularity.” ESAIM: Control, Optimisation
and Calculus of Variations 27 (2020). https://doi.org/10.1051/cocv/2020058.'
ieee: 'B. Bonnard, O. Cots, and B. E. Wembe Moafo, “A Zermelo navigation problem
with a vortex singularity,” ESAIM: Control, Optimisation and Calculus of Variations,
vol. 27, Art. no. S10, 2020, doi: 10.1051/cocv/2020058.'
mla: 'Bonnard, Bernard, et al. “A Zermelo Navigation Problem with a Vortex Singularity.”
ESAIM: Control, Optimisation and Calculus of Variations, vol. 27, S10,
EDP Sciences, 2020, doi:10.1051/cocv/2020058.'
short: 'B. Bonnard, O. Cots, B.E. Wembe Moafo, ESAIM: Control, Optimisation and
Calculus of Variations 27 (2020).'
date_created: 2022-10-24T12:51:05Z
date_updated: 2023-01-16T12:09:22Z
doi: 10.1051/cocv/2020058
intvolume: ' 27'
keyword:
- Computational Mathematics
- Control and Optimization
- Control and Systems Engineering
language:
- iso: eng
publication: 'ESAIM: Control, Optimisation and Calculus of Variations'
publication_identifier:
issn:
- 1292-8119
- 1262-3377
publication_status: published
publisher: EDP Sciences
status: public
title: A Zermelo navigation problem with a vortex singularity
type: journal_article
user_id: '95394'
volume: 27
year: '2020'
...