Publikationen an der Fakultät für Mathematik und Naturwissenschaften ab 2019

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Philipp, Friedrich; Schaller, Manuel; Worthmann, Karl; Peitz, Sebastian; Nüske, Feliks
Error bounds for kernel-based approximations of the Koopman operator. - In: Applied and computational harmonic analysis, ISSN 1096-603X, Bd. 71 (2024), 101657, S. 1-25

We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations. We derive both an exact expression for the variance of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds for the finite-data estimation error. Moreover, we derive a bound on the prediction error of observables in the RKHS using a finite Mercer series expansion. Further, assuming Koopman-invariance of the RKHS, we provide bounds on the full approximation error. Numerical experiments using the Ornstein-Uhlenbeck process illustrate our results.



https://doi.org/10.1016/j.acha.2024.101657
Shen, Fengxia; Wu, Shuai; Zhao, Pengchong; Li, Yunfei; Miao, Shipeng; Liu, Jianxiong; Ostheimer, David; Hannappel, Thomas; Chen, Tianyou; Shi, Jin
Bipolar membrane Electrolyzer for CO2 electro-reduction to CO in organic electrolyte with NaClO produced as byproduct. - In: Electrochimica acta, ISSN 1873-3859, Bd. 483 (2024), 144056, S. 1-8

A novel electrolyzer has been proposed for CO2 reduction to CO, concurrently generating NaClO as a byproduct at the anode. The cell is divided into two compartments by a bipolar membrane, which plays a pivotal role in the dissociation of H2O into H^+ and OH^−. In the cathode compartment, CO2 is reduced to CO within a neutral organic solution. Simultaneously, in the anode compartment, Cl^− undergoes oxidation to form ClO^− within a basic aqueous solution. The electrolyzer remains stable during 10 h of electrolysis, and the current density reaches 76.35 mA cm^−2 at a potential of -2.4 V (vs SHE), with the Faradaic efficiency of CO formation stable at 93 %. By increasing the product values, CO2 electro-reduction technology can be promoted to industrial applications.



https://doi.org/10.1016/j.electacta.2024.144056
Hahn-Klimroth, Maximilian Grischa; Parczyk, Olaf; Person, Yury
Minimum degree conditions for containing an r-regular r-connected spanning subgraph. - In: European journal of combinatorics, Bd. 118 (2024), 103940, S. 1-23

We study optimal minimum degree conditions when an n-vertex graph G contains an r-regular r-connected spanning subgraph. We prove for r fixed and n large the condition to be δ (G) ≥ n+r-2 / 2 when nr ≡ 0 (mod 2). This answers a question of M. Kriesell.



https://doi.org/10.1016/j.ejc.2024.103940
Kunze, Thomas; Dreßler, Christian; Lauer, Christian; Paul, Wolfgang; Sebastiani, Daniel
Reverse mapping of coarse grained polyglutamine conformations from PRIME20 sampling. - In: ChemPhysChem, ISSN 1439-7641, (2024), e202300521, S. 1-11

An inverse coarse-graining protocol is presented for generating and validating atomistic structures of large (bio-) molecules from conformations obtained via a coarse-grained sampling method. Specifically, the protocol is implemented and tested based on the (coarse-grained) PRIME20 protein model (P20/SAMC), and the resulting all-atom conformations are simulated using conventional biomolecular force fields. The phase space sampling at the coarse-grained level is performed with a stochastical approximation Monte Carlo approach. The method is applied to a series of polypeptides, specifically dimers of polyglutamine with varying chain length in aqueous solution. The majority (>70 %) of the conformations obtained from the coarse-grained peptide model can successfully be mapped back to atomistic structures that remain conformationally stable during 10 ns of molecular dynamics simulations. This work can be seen as the first step towards the overarching goal of improving our understanding of protein aggregation phenomena through simulation methods.



https://doi.org/10.1002/cphc.202300521
Diederich, Jonathan; Velasquez Rojas, Jennifer; Zare Pour, Mohammad Amin; Ruiz Alvarado, Isaac Azahel; Paszuk, Agnieszka; Sciotto, Rachele; Höhn, Christian; Schwarzburg, Klaus; Ostheimer, David; Eichberger, Rainer; Schmidt, W. Gero; Hannappel, Thomas; Krol, Roel van de; Friedrich, Dennis
Unraveling electron dynamics in p-type indium phosphide (100): a time-resolved two-photon photoemission study. - In: Journal of the American Chemical Society, ISSN 1520-5126, Bd. 146 (2024), 13, S. 8949-8960

Renewable (“green”) hydrogen production through direct photoelectrochemical (PEC) water splitting is a potential key contributor to the sustainable energy mix of the future. We investigate the potential of indium phosphide (InP) as a reference material among III-V semiconductors for PEC and photovoltaic (PV) applications. The p(2 × 2)/c(4 × 2)-reconstructed phosphorus-terminated p-doped InP(100) (P-rich p-InP) surface is the focus of our investigation. We employ time-resolved two-photon photoemission (tr-2PPE) spectroscopy to study electronic states near the band gap with an emphasis on normally unoccupied conduction band states that are inaccessible through conventional single-photon emission methods. The study shows the complexity of the p-InP electronic band structure and reveals the presence of at least nine distinct states between the valence band edge and vacuum energy, including a valence band state, a surface defect state pinning the Fermi level, six unoccupied surface resonances within the conduction band, as well as a cluster of states about 1.6 eV above the CBM, identified as a bulk-to-surface transition. Furthermore, we determined the decay constants of five of the conduction band states, enabling us to track electron relaxation through the bulk and surface conduction bands. This comprehensive understanding of the electron dynamics in p-InP(100) lays the foundation for further exploration and surface engineering to enhance the properties and applications of p-InP-based III-V-compounds for, e.g., efficient and cost-effective PEC hydrogen production and highly efficient PV cells.



https://doi.org/10.1021/jacs.3c12487
Wu, Zhijun; Zheng, Chunfang; Lin, Qi; Fu, Qun; Zhao, Huaping; Lei, Yong
Unique gap-related SERS behaviors of p-aminothiophenol molecules absorbed on TiO2 surface in periodic TiO2/Ni nanopillar arrays. - In: Nanotechnology, ISSN 1361-6528, Bd. 35 (2024), 21, 215501, S. 1-11

We observed a unique interpillar gap-related surface-enhanced Raman scattering (SERS) behavior of p-aminothiophenol (PATP) molecules from periodic TiO2 nanopillar arrays with three gap sizes of 191, 297 and 401 nm, which is completely different from that on Ag and Ni nanopillar arrays. Especially, the gap-size-dependent charge-transfer (CT) resonance enhancement from TiO2/Ni has been indicated through comparisons of variation trend of SERS intensities with inter-pillar gap size between TiO2/Ni and Ag/TiO2/Ni as well as Ni nanoarrays, and been confirmed by spectra of ultraviolet-visible absorption and photoluminescence. Results demonstrate that the CT resonance enhancement is more susceptible to the change of the gap size compared with the surface plasmon resonance (SPR) enhancement in TiO2/Ni nanoarrays. Hence, SPR and CT enhancement showing different variation trend and rate with the gap size that leads to a different relative contribution of CT resonance to the overall SERS enhancement as gap size changes, and consequently results in a unique gap-related SERS behavior for TiO2/Ni nanoarrays. The present study is not only helpful for investigating SERS mechanism for semiconductors but also providing a method to design and optimize periodic metal/semiconductor SERS substrates in a controllable way.



https://doi.org/10.1088/1361-6528/ad2a5a
Abreu, Zita; Lieb, Julia; Pinto, Raquel; Rosenthal, Joachim
Criteria for the construction of MDS convolutional codes with good column distances. - In: Advances in mathematics of communications, ISSN 1930-5338, Bd. 18 (2024), 2, S. 595-613

Maximum-distance separable (MDS) convolutional codes are characterized by the property that their free distance reaches the generalized Singleton bound. In this paper, new criteria to construct MDS convolutional codes are presented. These codes also possess optimal first (reverse) column distances. The new criteria allow to relate the construction of MDS convolutional codes to those of reverse superregular Toeplitz matrices. Moreover, using the new criteria as well as the help of computer search, examples for MDS convolutional codes over small finite fields are given.



https://doi.org/10.3934/amc.2023060
He, Shijiang; Wang, Zidong; Qiu, Wenbo; Zhao, Huaping; Lei, Yong
Effect of partial cation replacement on anode performance of sodium-ion batteries. - In: Batteries, ISSN 2313-0105, Bd. 10 (2024), 2, 44, S. 1-13

Due to their high specific capacity and long cycle life, bimetallic sulfides are the preferred choice of researchers as anodes in sodium-ion batteries (SIBs). However, studies indicate that this class of materials often requires expensive elements such as Co, Sb, Sn, etc., and their performance is insufficient with the use of inexpensive Fe, V alone. Therefore, there is a need to explore the relationship between metal cations and anode performance so that the requirements of cost reduction and performance enhancement can be met simultaneously. In this work, a series of partially replaced sulfides with different cation ratios have been prepared by a hydrothermal method followed by heat treatment. By partially replacing Co in NiCo sulfides, all samples show improved capacity and stability over the original NiCo sulfides. As a result, the metal elements have different oxidation states, which leads to a higher capacity through their synergistic effects on each other. Mn-NiCoS with 10% replacement showed satisfactory capacity (721.09 mAh g^−1 at 300 mA g^−1, 662.58 mAh g^−1 after 20 cycles) and excellent cycle life (85.41% capacity retention after 1000 cycles at 2000 mA g^−1).



https://doi.org/10.3390/batteries10020044
Faulwasser, Timm; Flaßkamp, Kathrin; Röbenack, Klaus; Worthmann, Karl
Optimale Steuerung und Regelung - Analyse, Algorithmen und Anwendungen :
Optimal control - analysis, algorithms and applications. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 72 (2024), 2, S. 77-79

Optimal control has been at the center of many pivotal developments in systems and control in the 20th century. This includes the twin breakthroughs of Richard E. Bellman’s Dynamic Programming and Lew S. Pontryagin’s Maximimum Principle as well as the optimality does not imply stability punchline by Rudolf E. Kalman. Likewise the dissipativity notion for open systems conceived by Jan C. Willems is deeply routed and closely linked to optimal control theory. Moreover, model predictive control can be regarded as an industrially impactful attempt to overcome the difficulties of analytic computation of feedback laws for constrained systems by numerical online computation. First formulations of receding-horizon ideas for optimal control can be traced back to the 1960s. With this pretext one might be tempted to conclude that contemporary research on optimal control is limited to applications. This special issue on optimal control with its particular focus on analysis, algorithms as well as applications falsifies any adhoc conclusion of this kind. Indeed, it combines different contributions which cover a wide array of topics – ranging from hydropower plants and bicycle dynamics to port-Hamiltonian formulations for adaptive structures, distributed predictive control, and moving horizon estimation. Hence, even without drawing upon the currently prevailing trends of data-driven and learning-based control – which also admit optimization-based research avenues – optimal control continues to be a supporting pillar of modern systems and control research with manifold prospects for fundamental analysis, performant algorithms, and challenging applications. Following the established structure of the journal the articles of this special issue are clustered into two categories – methods and applications.



https://doi.org/10.1515/auto-2023-0235
Schaller, Manuel; Zeller, Amelie; Böhm, Michael; Sawodny, Oliver; Tarín, Cristina; Worthmann, Karl
Energie-optimale Steuerung adaptiver Gebäude :
Energy-optimal control of adaptive structures. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 72 (2024), 2, S. 107-119

Adaptive structures are equipped with sensors and actuators to actively counteract external loads such as wind. This can significantly reduce resource consumption and emissions during the life cycle compared to conventional structures. A common approach for active damping is to derive a port-Hamiltonian model and to employ linear-quadratic control. However, the quadratic control penalization lacks physical interpretation and merely serves as a regularization term. Rather, we propose a controller, which achieves the goal of vibration damping while acting energy-optimal. Leveraging the port-Hamiltonian structure, we show that the optimal control is uniquely determined, even on singular arcs. Further, we prove a stable long-time behavior of optimal trajectories by means of a turnpike property. Last, the proposed controller’s efficiency is evaluated in a numerical study.



https://doi.org/10.1515/auto-2023-0090