Publikationen an der Fakultät für Mathematik und Naturwissenschaften ab 2019

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Beddig, Rebekka S.; Benner, Peter; Dorschky, Ines; Reis, Timo; Schwerdtner, Paul; Voigt, Matthias; Werner, Steffen W. R.
Structure-preserving model reduction for dissipative mechanical systems. - In: Calm, smooth and smart, (2024), S. 209-230

Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model order reduction to construct easy-to-evaluate surrogates for the original dynamical system having the same structure. In our work, we present an overview of recently developed structure-preserving model reduction methods for second-order systems. These methods are based on modal and balanced truncation in different variants, as well as on rational interpolation. Numerical examples are used to illustrate the effectiveness of all described methods.
Espuny Díaz, Alberto; Janzer, Barnabás; Kronenberg, Gal; Lada, Joanna
Long running times for hypergraph bootstrap percolation. - In: European journal of combinatorics, Bd. 115 (2024), 103783, S. 1-18

Consider the hypergraph bootstrap percolation process in which, given a fixed r-uniform hypergraph H and starting with a given hypergraph G0, at each step we add to G0 all edges that create a new copy of H. We are interested in maximising the number of steps that this process takes before it stabilises. For the case where H = Kr+1(r) with r ≥ 3, we provide a new construction for G0 that shows that the number of steps of this process can be of order Θ (nr). This answers a recent question of Noel and Ranganathan. To demonstrate that different running times can occur, we also prove that, if H is K4(3) minus an edge, then the maximum possible running time is 2n − ⌊log2(n−2)⌋ − 6. However, if H is K5(3) minus an edge, then the process can run for Θ (n3) steps.
Kröger, Jörg; Néel, Nicolas; Crampin, Simon
Quantum confinement of electrons at metal surfaces. - In: Materials lab, ISSN 2653-4878, Bd. 2 (2023), 3, 230006, S. 1-11

Scanning tunneling microscopy and spectroscopy experiments on surface-localized electron states confined to nanometer-scaled resonators are reviewed from the first observations to the recently discovered novel reflection mechanism of electron de Broglie waves. The focus of the presented work is on lateral confinement and on processes leading to finite decay rates of the confined states.
Amann, Silas; Kucska, Nóra; Lászlóffy, András; Néel, Nicolas; Újfalussy, Balázs; Rózsa, Levente; Palotás, Krisztián; Kröger, Jörg
Magnetic bound states of iron clusters on a superconductor. - In: Physical review, ISSN 2469-9969, Bd. 108 (2023), 19, 195403, S. 195403-1-195403-13

The magnetic exchange interaction of Fen (n = 1, 2, 3) clusters with the quasiparticles of superconducting Pb(111) is probed by scanning tunneling spectroscopy of Yu-Shiba-Rusinov states. The spectral weight of the Yu-Shiba-Rusinov resonances is shifted from the coherence peaks in the Fe monomer spectrum towards the Fermi energy in the Fe dimer spectrum. Unexpectedly, the linear Fe trimer does not follow this trend, as it exhibits an almost identical spectrum to the single Fe atom. Kinked Fe trimers where one of the end atoms deviates from the linear orientation, in contrast, show strong Yu-Shiba-Rusinov resonances well within the Bardeen-Cooper-Schrieffer energy gap of the substrate. First-principles simulations of the Yu-Shiba-Rusinov states reveal which adsorption geometries and magnetic structures of the clusters can reproduce the experimental spectra most accurately.
Kröger, Jörg; Uchihashi, Takashi
Electron spin finds a fresh excitation. - In: Nature physics, ISSN 1745-2481, Bd. 0 (2023), 0, insges. 2 S.

The Kondo effect - the screening of an impurity spin by conduction electrons - is a fundamental many-body effect. However, recent experiments combined with simulations have caused a long-standing model system for the single-atom Kondo effect to fail.
Böhme, Thomas; Harant, Jochen; Kriesell, Matthias; Mohr, Samuel; Schmidt, Jens M.
Rooted minors and locally spanning subgraphs. - In: Journal of graph theory, ISSN 1097-0118, Bd. n/a (2023), n/a, S. 1-21

Results on the existence of various types of spanning subgraphs of graphs are milestones in structural graph theory and have been diversified in several directions. In the present paper, we consider “local” versions of such statements. In 1966, for instance, D. W. Barnette proved that a 3-connected planar graph contains a spanning tree of maximum degree at most 3. A local translation of this statement is that if G is a planar graph, X is a subset of specified vertices of G such that X cannot be separated in G by removing two or fewer vertices of G, then G has a tree of maximum degree at most 3 containing all vertices of X. Our results constitute a general machinery for strengthening statements about k-connected graphs (for 1 ≤ k ≤ 4) to locally spanning versions, that is, subgraphs containing a set X ⊆ V (G) of a (not necessarily planar) graph G in which only X has high connectedness. Given a graph G and X ⊆ V (G), we say M is a minor of G rooted at X, if M is a minor of G such that each bag of M contains at most one vertex of X and X is a subset of the union of all bags. We show that G has a highly connected minor rooted at X if X ⊆ V (G) cannot be separated in G by removing a few vertices of G. Combining these investigations and the theory of Tutte paths in the planar case yields locally spanning versions of six well-known results about degree-bounded trees, Hamiltonian paths and cycles, and 2-connected subgraphs of graphs.
Witt, Michael; Papmahl, Eric; Genov, Ivan; Dimitrova, Anna; Gabryelczyk, Agnieszka; Krischok, Stefan; Lota, Grzegorz; Ivanov, Svetlozar
In-situ electrogravimetric detection of the cathodic process during the galvanic coupling between lithium and copper. - In: Electrochimica acta, ISSN 1873-3859, Bd. 463 (2023), 142853

With the development of the energy system transformation the quality and efficiency of the rechargeable batteries, particularly the Li ion technology, gain major importance. In spite of the enormous advances, along with many other technological challenges corrosion of the metallic battery parts is often a difficult obstacle for producers and researchers. Li-metal batteries and especially the “anode-free” battery concept could significantly increase the energy density. However, contact corrosion of the Li anode, can occur in this cell configuration since there is a high probability of a three-phase contact between Li-metal, current collector and electrolyte, a condition triggering an intensive Li corrosion. In this work, a new in-situ analytical methodology based on combining electrochemical (ZRA) and microgravimetric (QCM) techniques is proposed for studying the galvanic corrosion. The applicability of this approach is explored in three different electrolyte compositions. Beside the analysis of the conventional electrochemical parameters an in-situ gravimetric detection of the deposited electrolyte decomposition products on the cathode surface is demonstrated. Adsorbed polymer layer on the Cu surface is applied for cathodic inhibition of the galvanic corrosion process, which is studied by means of the novel ZRA-QCM approach.
Mijalkov, Mite; Gerboles, Blanca Zufiria; Vereb, Daniel; Lüdge, Kathy; Brunner, Daniel; Volpe, Giovanni; Pereira, Joana B.
Uncovering vulnerable connections in the aging brain using reservoir computing. - In: Emerging Topics in Artificial Intelligence (ETAI) 2023, (2023), PC1265508

We used reservoir computing to explore the changes in the connectivity patterns of whole-brain anatomical networks derived by diffusion-weighted imaging, and their impact on cognition during aging. The networks showed optimal performance at small densities. This performance decreased with increasing density, with the rate of decrease being strongly associated with age and performance on behavioural tasks measuring cognitive function. This suggests that a network core of anatomical hubs is crucial for optimal functioning, while weaker connections are more susceptible to aging effects. This study highlights the potential utility of reservoir computing in understanding age-related changes in cognitive function.
Xu, Changfan; Qiu, Jiajia; Dong, Yulian; Li, Yueliang; Shen, Yonglong; Zhao, Huaping; Kaiser, Ute; Shao, Guosheng; Lei, Yong
Dual-functional electrode promoting dendrite-free and CO2 utilization enabled high-reversible symmetric Na-CO2 batteries. - In: Energy & Environmental Materials, ISSN 2575-0356, Bd. n/a (2023), n/a, e12626, S. 1-10

Sodium-carbon dioxide (Na-CO2) batteries are regarded as promising energy storage technologies because of their impressive theoretical energy density and CO2 reutilization, but their practical applications are restricted by uncontrollable sodium dendrite growth and poor electrochemical kinetics of CO2 cathode. Constructing suitable multifunctional electrodes for dendrite-free anodes and kinetics-enhanced CO2 cathodes is considered one of the most important ways to advance the practical application of Na-CO2 batteries. Herein, RuO2 nanoparticles encapsulated in carbon paper (RuCP) are rationally designed and employed as both Na anode host and CO2 cathode in Na-CO2 batteries. The outstanding sodiophilicity and high catalytic activity of RuCP electrodes can simultaneously contribute to homogenous Na+ distribution and dendrite-free sodium structure at the anode, as well as strengthen discharge and charge kinetics at the cathode. The morphological evolution confirmed the uniform deposition of Na on RuCP anode with dense and flat interfaces, delivering enhanced Coulombic efficiency of 99.5% and cycling stability near 1500 cycles. Meanwhile, Na-CO2 batteries with RuCP cathode demonstrated excellent cycling stability (>350 cycles). Significantly, implementation of a dendrite-free RuCPNa anode and catalytic-site-rich RuCP cathode allowed for the construction of a symmetric Na-CO2 battery with long-duration cyclability, offering inspiration for extensive practical uses of Na-CO2 batteries.
Behrndt, Jussi; Gesztesy, Fritz; Schmitz, Philipp; Trunk, Carsten
Lower bounds for self-adjoint Sturm-Liouville operators. - In: Proceedings of the American Mathematical Society, ISSN 1088-6826, Bd. 151 (2023), 12, S. 5313-5323