Publikationen an der Fakultät für Mathematik und Naturwissenschaften

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Derkach, Volodymyr; Hassi, Seppo; Malamud, Mark;
Generalized boundary triples, II : some applications of generalized boundary triples and form domain invariant Nevanlinna functions. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2021. - 1 Online-Ressource (54 Seiten). . - (Preprint. - M21,03)
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2021200058
Derkach, Volodymyr; Schmitz, Philipp; Trunk, Carsten;
PT-symmetric Hamiltonians as couplings of dual pairs. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2021. - 1 Online-Ressource (15 Seiten). . - (Preprint. - M21,02)
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2021200042
Wei, Huifang; Wang, Jiahui; Lin, Qian; Zou, Yanwen; Chen, Xi'an; Zhao, Huaping; Li, Jun; Jin, Huile; Lei, Yong; Wang, Shun;
Incorporating ultra-small N-doped Mo2C nanoparticles onto 3D N-doped flower-like carbon nanospheres for robust electrocatalytic hydrogen evolution. - In: Nano energy. - Amsterdam [u.a.] : Elsevier, ISSN 2211-2855, Bd. 86 (2021), 106047
- Im Titel ist "2" tiefgestellt

Developing highly-efficient and stable hydrogen evolution reaction (HER) electrocatalysts plays a crucial role in realizing the hydrogen production from electrocatalytic water splitting. Herein, ultra-small and nitrogen-doped molybdenum carbide (N-Mo2C) nanoparticles with oxidized surfaces are facilely synthesized with the assistance of cationic surfactants and simultaneously anchored onto three-dimensional nitrogen-doped flower-like carbon nanospheres (NFCNS), and the N-Mo2C/NFCNS composites are further investigated as HER electrocatalysts. Analysis results reveal that nitrogen atoms are doped into both the lattice and the carbon framework of Mo2C, resulting in low desorption energy of Mo-H bond for the easy evolution of hydrogen gas. Moreover, the high specific area of NFCNS enables enrichment of N-Mo2C nanoparticles, and its open framework facilitates fast ion diffusion. As a result, the N-Mo2C/NFCNS composites exhibit impressive HER activities with low overpotential, small Tafel slope, and excellent durability in both acidic and alkaline media, which outperform most of the reported Mo-based HER catalysts and are also highly comparable to the commercial Pt/C catalyst. Not limited to HER electrocatalysts, this work should open a new avenue for tailoring highly-efficient carbon/metal compounds-based electrocatalysts for oxygen reduction reaction, oxygen evolution reaction, nitrogen reduction reaction, etc.



https://doi.org/10.1016/j.nanoen.2021.106047
Zhang, Da; Zhao, Huaping; Liang, Feng; Ma, Wenhui; Lei, Yong;
Nanostructured arrays for metal-ion battery and metal-air battery applications. - In: Journal of power sources : the international journal on the science and technology of electrochemical energy systems.. - New York, NY [u.a.] : Elsevier, ISSN 1873-2755, Bd. 493 (2021), 229722

Rechargeable battery technology has been the research focus due to the largely increased global energy demand, while metal-ion batteries (MIBs) and metal-air batteries (MABs) are two major representatives. In addition to lithium-ion batteries, other MIBs such as sodium-ion batteries and aluminum-ion batteries have been drawn great attention. Regarding MABs, considerable research effort has been devoted to lithium-, zinc-, and sodium-air batteries. So far, significant progress in the performance improvement of both MIBs and MABs has been achieved through the material design and electrode design. Particularly, free-standing nanoarrays (NAs) directly grown on current collectors have been regarded as promising electrodes of both MIBs and MABs for improving the energy storage capability. In this review, recent advances in design, fabrication and application of NAs for MIBs and MABs have been summarized. Firstly, the motivation of employing NAs electrodes for MIBs and MABs is outlined. The principles and categories of MIBs and MABs, the construction, structural features, and resulting superiorities are also briefly reviewed. Secondly, the relationship of the conductive substrates, the structural features, and electrochemical performance of NAs electrodes is analyzed in depth. Finally, the future design focuses of NAs as advanced electrodes for MIBs and MABs are emphasized.



https://doi.org/10.1016/j.jpowsour.2021.229722
Link, Steffen; Kurniawan, Mario; Dimitrova, Anna; Krischok, Stefan; Bund, Andreas; Ivanov, Svetlozar;
Enhanced cycling performance of binder free silicon-based anode by application of electrochemically formed microporous substrate. - In: Electrochimica acta : the journal of the International Society of Electrochemistry (ISE).. - New York, NY [u.a.] : Elsevier, Bd. 380 (2021), 138216, S. 1-9

In this work, an electrochemically formed porous Cu current collector (p-Cu) is utilized for the development of a high-performance binder-free silicon anode. Two electrolyte compositions based on sulfolane (SL) and [BMP][TFSI] ionic liquid (IL) are implemented for silicon deposition. The electrochemical experiments confirm the advantages of applying the p-Cu structure in terms of specific capacity, rate capability, and long-term cycling, where the best electrochemical properties have been observed for the Si deposited from SL electrolyte. The Si-based p-Cu anodes formed in SL display stable 2500 mAh g^-1 reversible capacity during the first 250 cycles and promising capacity retention. Compared to this result, the cycling performance of the same type of material deposited on flat Cu foil (f-Cu) showed significantly reduced capacity (1400 mAh g^-1) and inferior cycling performance. The positive effect can be attributed to the improved mechanical stability of the active material and accelerated ionic transport in the porous structure of the anode. The improved functional properties of the electrochemically deposited Si from SL electrolyte in p-Cu samples compared to those obtained in IL can be ascribed to differences in the chemical composition. While the layers deposited in SL electrolyte involve Si domains incorporated in a matrix containing C and O that offer high mechanical stability, the Si material obtained in IL is additionally influenced by N and F chemical species, resulting from active IL decomposition. These differences in the chemical surrounding of the Si domains are the primary reason for the inferior electrochemical performance of the material deposited from [BMP][TFSI] electrolyte. XPS analysis shows that the initial composition of the as deposited layers, containing a considerable amount of elemental Si, is changed after lithiation and that the electrochemical activity of the anode is governed by switching between the intermediate redox states of Si, where the carbon-oxygen matrix is also involved.



https://doi.org/10.1016/j.electacta.2021.138216
Kurniawan, Mario; Stich, Michael; Marimon, Mayra; Camargo, Magali K.; Peipmann, Ralf; Hannappel, Thomas; Bund, Andreas;
Electrodeposition of cuprous oxide on a porous copper framework for an improved photoelectrochemical performance. - In: Journal of materials science. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1573-4803, (2021), insges. 15 S.

https://doi.org/10.1007/s10853-021-06058-y
Herrfurth, Oliver; Richter, Steffen; Rebarz, Mateusz; Espinoza, Shirley; Zúñiga-Pérez, Jesus; Deparis, Christiane; Leveillee, Joshua; Schleife, André; Grundmann, Marius; Andreasson, Jakob; Schmidt-Grund, Rüdiger;
Transient birefringence and dichroism in ZnO studied with fs-time-resolved spectroscopic ellipsometry. - In: Physical review research. - College Park, MD : APS, ISSN 2643-1564, Bd. 3 (2021), 1, S. 013246-1-013246-12

The full transient dielectric-function (DF) tensor of ZnO after UV-laser excitation in the spectral range 1.4-3.6 eV is obtained by measuring an m-plane-oriented ZnO thin film with femtosecond (fs)-time-resolved spectroscopic ellipsometry. From the merits of the method, we can distinguish between changes in the real and the imaginary part of the DF as well as changes in birefringence and dichroism, respectively. We find pump-induced switching from positive to negative birefringence in almost the entire measured spectral range for about 1 ps. Simultaneously, weak dichroism in the spectral range below 3.0 eV hints at contributions of inter-valence-band transitions. Line-shape analysis of the DF above the band gap based on discrete exciton, exciton-continuum, and exciton-phonon-complex contributions shows a maximal dynamic increase in the transient exciton energy by 80 meV. The absorption coefficient below the band gap reveals an exponential line shape attributed to Urbach-rule absorption mediated by exciton-longitudinal-optic-phonon interaction. The transient DF is supported by first-principles calculations for 1020cm^-3 excited electron-hole pairs in ideal bulk ZnO.



https://doi.org/10.1103/PhysRevResearch.3.013246
Bosch, Martí; Behrens, Arne; Sinzinger, Stefan; Hentschel, Martina;
Husimi functions for coupled optical resonators. - In: Journal of the Optical Society of America : JOSA.. - Washington, DC : Soc., ISSN 1520-8532, Bd. 38 (2021), 4, S. 573-578

Phase-space analysis has been widely used in the past for the study of optical resonant systems. While it is usually employed to analyze the far-field behavior of resonant systems, we focus here on its applicability to coupling problems. By looking at the phase-space description of both the resonant mode and the exciting source, it is possible to understand the coupling mechanisms as well as to gain insights and approximate the coupling behavior with reduced computational effort. In this work, we develop the framework for this idea and apply it to a system of an asymmetric dielectric resonator coupled to a waveguide.



https://doi.org/10.1364/JOSAA.422740
Leben, Leslie; Martínez Pería, Francisco; Philipp, Friedrich; Trunk, Carsten; Winkler, Henrik;
Finite rank perturbations of linear relations and matrix pencils. - In: Complex analysis and operator theory. - Cham (ZG) : Springer International Publishing AG, ISSN 1661-8262, Bd. 15 (2021), 2, S. 1-37

We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their number of Jordan chains of length at least n. In the operator case, it was recently proved that the difference of these numbers is independent of n and is at most the defect between the operators. One of the main results of this paper shows that in the case of linear relations this number has to be multiplied by n+1 and that this bound is sharp. The reason for this behavior is the existence of singular chains. We apply our results to one-dimensional perturbations of singular and regular matrix pencils. This is done by representing matrix pencils via linear relations. This technique allows for both proving known results for regular pencils as well as new results for singular ones.



https://doi.org/10.1007/s11785-021-01082-x
Berger, Thomas; Ilchmann, Achim; Ryan, Eugene P.;
Funnel control of nonlinear systems. - In: Mathematics of control, signals, and systems : MCSS.. - London : Springer, ISSN 1435-568X, Bd. 33 (2021), 1, S. 151-194

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).



https://doi.org/10.1007/s00498-021-00277-z