Quantum particle under dynamical confinement: from quantum fermi acceleration to high harmonic generation. - In: Physica scripta, ISSN 1402-4896, Bd. 99 (2024), 7, 075308, S. 1-13
Quantum dynamics of a particle confined in a box with time-dependent wall is revisited by considering some unexplored aspects of the problem. In particular, the case of dynamical confinement in a time-dependent box in the presence of purely time-varying external potential is treated by obtaining exact solution. Also, some external potentials approving separation of space and time variables in the Schrödinger equation with time-dependent boundary conditions are classified. Time-dependence of the average kinetic energy and average quantum force are analyzed. A model for optical high harmonic generation in the presence of dynamical confinement and external monochromatic time-dependent homogeneous electric field is proposed.
https://doi.org/10.1088/1402-4896/ad52c8
Perturbation and spectral theory for singular indefinite Sturm-Liouville operators. - In: Journal of differential equations, ISSN 1090-2732, Bd. 405 (2024), S. 151-178
https://doi.org/10.1016/j.jde.2024.05.043
Funnel MPC for nonlinear systems with arbitrary relative degree. - In: Automatica, ISSN 0005-1098, Bd. 167 (2024), 111759, S. 1-10
The model predictive control (MPC) scheme funnel MPC enables output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems with stable internal dynamics. Earlier works achieved the control objective for system with relative degree restricted to one or incorporated additional feasibility constraints in the optimal control problem. Here we resolve these limitations by introducing a modified stage cost function relying on a weighted sum of the tracking error derivatives. The weights need to be sufficiently large and we state explicit lower bounds. Under these assumptions we are able to prove initial and recursive feasibility of the novel funnel MPC scheme for systems with arbitrary relative degree - without requiring any terminal conditions, a sufficiently long prediction horizon or additional output constraints.
https://doi.org/10.1016/j.automatica.2024.111759
Rainbow bases in matroids. - In: SIAM journal on discrete mathematics, ISSN 1095-7146, Bd. 38 (2024), 2, S. 1472-1491
Recently, it was proved by Bérczi and Schwarcz that the problem of factorizing a matroid into rainbow bases with respect to a given partition of its ground set is algorithmically intractable. On the other hand, many special cases were left open. We first show that the problem remains hard if the matroid is graphic, answering a question of Bérczi and Schwarcz. As another special case, we consider the problem of deciding whether a given digraph can be factorized into subgraphs which are spanning trees in the underlying sense and respect upper bounds on the indegree of every vertex. We prove that this problem is also hard. This answers a question of Frank. In the second part of the article, we deal with the relaxed problem of covering the ground set of a matroid by rainbow bases. Among other results, we show that there is a linear function f such that every matroid that can be factorized into k bases for some k ≥ 3 can be covered by f(k) rainbow bases if every partition class contains at most 2 elements.
https://doi.org/10.1137/22M1516750
Generic observability for port-Hamiltonian descriptor systems. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 0 (2024), 0, insges. 43 S.
The present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359-377, 2021. https://doi.org/10.1007/s00498-021-00287-x), Ilchmann and Kirchhoff (Math Control Signals Syst 35:45-76, 2023. https://doi.org/10.1007/s00498-021-00287-x) on (relative) generic controllability of unstructured linear differential-algebraic systems and of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) on (relative) generic controllability of port-Hamiltonian descriptor systems. We extend their results to (relative) genericity of observability. For unstructured differential-algebraic systems, criteria for (relative) generic observability are derived from Ilchmann and Kirchhoff (Math Control Signals Syst 35:45-76, 2023. https://doi.org/10.1007/s00498-021-00287-x) using duality. This is not possible for port-Hamiltonian systems. Hence, we tweak the results of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) and derive similar criteria as for the unstructured case. Additionally, we consider certain rank constraints on the system matrices.
https://doi.org/10.1007/s00498-024-00388-3
PT-symmetric dynamical confinement: Fermi acceleration, quantum force, and Berry phase. - In: Physical review, ISSN 2469-9934, Bd. 109 (2024), 5, 053519
We consider a quantum particle under the dynamical confinement caused by PT-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schrödinger equation obeying the time-dependent PT-symmetric boundary conditions. The class of the functions, describing time dependence of the wall's position and keeping the system as PT-symmetric is found. Physically observable characteristics, such as average kinetic energy and the average quantum force are calculated as a function of time. It is found that the behavior of the average kinetic energy as a function of time is completely different than that for of Hermitian counterpart of the model, while the average quantum force behaves similarly to that for Hermitian system. Also, geometric phase is calculated for the harmonically oscillating wall regime. The experimental realization of the proposed model is discussed.
https://doi.org/10.1103/PhysRevA.109.053519
Sharp threshold for embedding balanced spanning trees in random geometric graphs. - In: Journal of graph theory, ISSN 1097-0118, Bd. 0 (2024), 0, S. 1-19
A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph G(n,r,d). In particular, we find the sharp threshold for balanced binary trees. More generally, we show that all sequences of balanced trees with uniformly bounded degrees and height tending to infinity appear above a sharp threshold, and none of these appears below the same value. Our results hold more generally for geometric graphs satisfying a mild condition on the distribution of their vertex set, and we provide a polynomial time algorithm to find such trees.
https://doi.org/10.1002/jgt.23106
Adjustable robust energy operation planning under uncertain renewable energy production. - In: Energies, ISSN 1996-1073, Bd. 17 (2024), 8, 1917, S. 1-14
In this paper, the application of the method of affinely adjustable robust optimization to a planning model of an energy system under uncertain parameters is presented, and the total scheduling costs in comparison with the deterministic model are evaluated. First, the basics of optimization under uncertain data are recapped, and it is described how these methods can be used in different applications for energy systems. This is followed by the methodology of adjustable robust optimization by defining the affinely adjustable robust counterpart. Finally, a numerical case study is conducted to compare the adjustable robust method with a rolling deterministic scheduling method. Both are implemented on a model of an energy system and compared with each other by simulation using real-world data. By calculating the total operating costs for both methods, it can be concluded that the adjustable robust optimization provides a significantly more cost-effective solution to the scheduling problem.
https://doi.org/10.3390/en17081917
GraphLearner: an approach to sequence recognition and generation. - In: IEEE Xplore digital library, ISSN 2473-2001, (2024), S. 445-451
This paper presents GraphLearner a neuromorphic sequence generator with similarities to Markov Chain Models. GraphLearner is proposed as an alternative to ‘black box’ deep neural network models which lack explainability and adaptability. Bloom Filters are used to simplify otherwise computationally expensive Markov chain probability calculations. It is demonstrated with Natural Language Processing tasks, generating sentences of remarkable quality.
https://doi.org/10.1109/BigComp60711.2024.00098
The mystery of Carleson frames. - In: Applied and computational harmonic analysis, ISSN 1096-603X, Bd. 72 (2024), 101659, S. 1-5
In 2016 Aldroubi et al. constructed the first class of frames having the form {Tkφ}k=0∞ for a bounded linear operator on the underlying Hilbert space. In this paper we show that a subclass of these frames has a number of additional remarkable features that have not been identified for any other frames in the literature. Most importantly, the subfamily obtained by selecting each Nth element from the frame is itself a frame, regardless of the choice of N∈N. Furthermore, the frame property is kept upon removal of an arbitrarily finite number of elements.
https://doi.org/10.1016/j.acha.2024.101659