Publications at the Department of Mathematics and Natural Sciences from 2019

Results: 873
Created on: Wed, 27 Mar 2024 23:21:20 +0100 in 0.0866 sec


Espuny Díaz, Alberto; Morris, Patrick; Perarnau, Guillem; Serra, Oriol
Speeding up random walk mixing by starting from a uniform vertex. - In: Electronic journal of probability, ISSN 1083-6489, Bd. 29 (2024), 26, S. 1-25

The theory of rapid mixing random walks plays a fundamental role in the study of modern randomised algorithms. Usually, the mixing time is measured with respect to the worst initial position. It is well known that the presence of bottlenecks in a graph hampers mixing and, in particular, starting inside a small bottleneck significantly slows down the diffusion of the walk in the first steps of the process. The average mixing time is defined to be the mixing time starting at a uniformly random vertex and hence is not sensitive to the slow diffusion caused by these bottlenecks. In this paper we provide a general framework to show logarithmic average mixing time for random walks on graphs with small bottlenecks. The framework is especially effective on certain families of random graphs with heterogeneous properties. We demonstrate its applicability on two random models for which the mixing time was known to be of order (log n)2, speeding up the mixing to order logn. First, in the context of smoothed analysis on connected graphs, we show logarithmic average mixing time for randomly perturbed graphs of bounded degeneracy. A particular instance is the Newman-Watts small-world model. Second, we show logarithmic average mixing time for supercritically percolated expander graphs. When the host graph is complete, this application gives an alternative proof that the average mixing time of the giant component in the supercritical Erd˝os-Rényi graph is logarithmic.



https://doi.org/10.1214/24-EJP1091
Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-Hamiltonian systems’ modelling in electrical engineering. - In: Scientific computing in electrical engineering, (2024), S. 133-143

The port-Hamiltonian (pH) modelling framework allows for models that preserve essential physical properties such as energy conservation or dissipative inequalities. If all subsystems are modelled as pH systems and the inputs are related to the output in a linear manner, the overall system can be modelled as a pH system, too, which preserves the properties of the underlying subsystems. If the coupling is given by a skew-symmetric matrix, as usual in many applications, the overall system can be easily derived from the subsystems without the need of introducing dummy variables and therefore artificially increasing the complexity of the system. Hence the framework of pH systems is especially suitable for modelling multiphysical systems.



https://doi.org/10.1007/978-3-031-54517-7_15
Jaurigue, Lina; Lüdge, Kathy
Reducing reservoir computer hyperparameter dependence by external timescale tailoring. - In: Neuromorphic computing and engineering, ISSN 2634-4386, Bd. 4 (2024), 1, 014001, S. 1-16

Task specific hyperparameter tuning in reservoir computing is an open issue, and is of particular relevance for hardware implemented reservoirs. We investigate the influence of directly including externally controllable task specific timescales on the performance and hyperparameter sensitivity of reservoir computing approaches. We show that the need for hyperparameter optimisation can be reduced if timescales of the reservoir are tailored to the specific task. Our results are mainly relevant for temporal tasks requiring memory of past inputs, for example chaotic timeseries prediction. We consider various methods of including task specific timescales in the reservoir computing approach and demonstrate the universality of our message by looking at both time-multiplexed and spatially-multiplexed reservoir computing.



https://doi.org/10.1088/2634-4386/ad1d32
âCurgus, Branko; Derkach, Volodymyr; Trunk, Carsten
Indefinite Sturm-Liouville operators in polar form. - In: Integral equations and operator theory, ISSN 1420-8989, Bd. 96 (2024), 2, S. 1-58

https://doi.org/10.1007/s00020-023-02746-3
Yang, Hong; Huang, Yuanyong; Luo, Bifu; Xie, Zhongkai; Li, Di; Xu, Dongbo; Lei, Yong; Shi, Weidong
Infrared light dual excitation of Ni-phytate-sensitized ZnIn2S4 with sulfur vacancies for enhanced NIR-driven photocatalysis. - In: Chemical communications, ISSN 1364-548X, Bd. 60 (2024), 8, S. 1035-1038

Near-infrared (NIR) light accounts for about half of the solar spectrum, and the effective utilization of low-energy NIR light is an important but challenging task in the field of photocatalysis. Molecular semiconductor photocatalytic systems (MSPSs) are highly tunable, available and stable, and are considered to be one of the most promising ways to achieve efficient NIR hydrogen production. Here, we demonstrate efficient dual-excitation in MSPS consisting of ZnIn2S4−x (ZIS1−x) with sulfur vacancies and phytic acid nickel (PA-Ni), which differs from other NIR-responsive photosensitized systems. The system achieves a hydrogen evolution reaction (HER) of 119.85 μmol h−1 g−1 at λ > 800 nm illumination, which is an excellent performance among all reported NIR catalysts and even outperforms the noble metal catalysts when compared to the reported literature. The superior activity is attributed to the unique charge dynamics and higher carrier concentration of the system. This work demonstrates the potential of dual-excitation systems for efficient utilization of low-energy NIR light.



https://doi.org/10.1039/D3CC05089K
Wu, Zhijun; Sha, Mo; Ji, Deyang; Zhao, Huaping; Li, Liqiang; Lei, Yong
Ordered anodic aluminum oxide-based nanostructures for surface-enhanced Raman scattering: a review. - In: ACS applied nano materials, ISSN 2574-0970, Bd. 7 (2024), 1, S. 11-31

As a promising spectroscopic technique, surface enhanced raman spectroscopy (SERS) has been intensively used in bio/chemical sensing, attributing to its unique advantages of ultrasensitive and accurate detection of trace amounts of analytes, high specific fingerprint-like features, fast response, and noninvasive sensing. The robustness and consistency of SERS signals in practical analytical applications highly rely on the composition, structural morphology, and uniformity of SERS substrates. These factors play a pivotal role in determining the intensity and reproducibility of the detected signals. SERS substrates based on ordered nanostructures that are fabricated from anodic aluminum oxide (AAO)-template-assisted approaches are of significant interest due to their cost effectiveness, scalability, precise structural control, and exceptionally ordered features. In this review, recent progress in SERS substrates with high sensitivity and reproducibility prepared from AAO templates is highlighted. We emphasize the optimization strategies toward achieving efficient SERS-active substrates by fine-tuning the size, composition, and morphology of AAO-derived ordered nanostructures. Furthermore, we delve into the discussion of flexible and smart SERS substrates, while also exploring key aspects pertinent to further amplifying SERS signals. Overall, this review aims to offer insights into the future integration of the AAO templates technique with SERS, providing crucial perspectives for forthcoming research in this field.



https://doi.org/10.1021/acsanm.3c04652
Bohm, Sebastian; Runge, Erich
Efficient analytical evaluation of the singular BEM integrals for the three-dimensional Laplace and Stokes equations over polygonal elements. - In: Engineering analysis with boundary elements, ISSN 0955-7997, Bd. 161 (2024), S. 70-77

Singularities in the fundamental solutions pose a mathematical challenge for all applications of the boundary element method, if the source and field point lie on the same element. To avoid complex and error-prone numerical procedures, analytical solutions for the integrals that arise are desirable. In this work, easy and efficiently to implement analytical solutions are presented for the fundamental solutions of the three-dimensional Stokes equation as well as Laplace’s equation. Explicit expressions are derived for general triangular elements using constant shape functions. In addition, options for extending to arbitrary polygonal elements are shown. In particular, the three cases that the incenter, the centroid or the vertices of the triangles are used as source points for the calculation are addressed. The impressive numerical efficiency of the method is demonstrated by explicit examples.



https://doi.org/10.1016/j.enganabound.2024.01.013
Čindrak, Saud; Donvil, Brecht; Lüdge, Kathy; Jaurigue, Lina
Enhancing the performance of quantum reservoir computing and solving the time-complexity problem by artificial memory restriction. - In: Physical review research, ISSN 2643-1564, Bd. 6 (2024), 1, 013051, S. 013051-1-013051-11

We propose a scheme that can enhance the performance and reduce the computational cost of quantum reservoir computing. Quantum reservoir computing is a computing approach which aims at utilizing the complexity and high dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The suitability of quantum reservoir computing for solving temporal tasks is hindered by the collapse of the quantum system when measurements are made. This leads to the erasure of the memory of the reservoir. Hence, for every output, the entire input signal is needed to reinitialize the reservoir, leading to quadratic time complexity. Another critical issue for the hardware implementation of quantum reservoir computing is the need for an experimentally accessible means of tuning the nonlinearity of the quantum reservoir. We present an approach which addresses both of these issues. We propose artificially restricting the memory of the quantum reservoir by only using a small number inputs to reinitialize the reservoir after measurements are performed. This strongly influences the nonlinearity of the reservoir response due to the influence of the initial reservoir state, while also substantially reducing the number of quantum operations needed to perform time-series prediction tasks due to the linear rather than quadratic time complexity. The reinitialization length therefore provides an experimental accessible means of tuning the nonlinearity of the response of the reservoir, which can lead to significant task-specific performance improvement. We numerically study the linear and quadratic algorithms for a fully connected transverse Ising model and a quantum processor model.



https://doi.org/10.1103/PhysRevResearch.6.013051
Dong, Yulian; Huo, Jingyao; Xu, Changfan; Ji, Deyang; Zhao, Huaping; Li, Liqiang; Lei, Yong
Research progress on vanadium sulfide anode materials for sodium and potassium-ion batteries. - In: Advanced Materials Technologies, ISSN 2365-709X, Bd. n/a (2024), n/a, 2301840, S. 1-28

Considering environmental changes and the demand for more sustainable energy sources, stricter requirements have been placed on electrode materials for sodium and potassium-ion batteries, which are expected to provide higher energy and power density while being affordable and sustainable. Vanadium sulfide-based materials have emerged as intriguing contenders for the next generation of anode materials due to their high theoretical capacity, abundant reserves, and cost-effectiveness. Despite these advantages, challenges such as limited cycle life and restricted ion diffusion coefficients continue to impede their effective application in sodium and potassium-ion batteries. To overcome the limitations associated with electrochemical performance and circumvent bottlenecks imposed by the inherent properties of materials at the bulk scale, this review comprehensively summarizes and analyzes the crystal structures, modification strategies, and energy storage processes of vanadium sulfide-based electrode materials for sodium and potassium-ion batteries. The objective is to guide the development of high-performance vanadium-based sulfide electrode materials with refined morphologies and/or structures, employing environmentally friendly and cost-efficient methods. Finally, future perspectives and research suggestions for vanadium sulfide-based materials are presented to propel practical applications forward.



https://doi.org/10.1002/admt.202301840
Küstner, Merle Johanna; Eckstein, Diana; Brauer, Dana; Mai, Patrick; Hampl, Jörg; Weise, Frank; Schuhmann, Berit; Hause, Gerd; Glahn, Felix; Foth, Heidi; Schober, Andreas
Modular air-liquid interface aerosol exposure system (MALIES) to study toxicity of nanoparticle aerosols in 3D-cultured A549 cells in vitro. - In: Archives of toxicology, ISSN 1432-0738, Bd. 0 (2024), 0, insges. 20 S.

We present a novel lung aerosol exposure system named MALIES (modular air-liquid interface exposure system), which allows three-dimensional cultivation of lung epithelial cells in alveolar-like scaffolds (MatriGrids®) and exposure to nanoparticle aerosols. MALIES consists of multiple modular units for aerosol generation, and can be rapidly assembled and commissioned. The MALIES system was proven for its ability to reliably produce a dose-dependent toxicity in A549 cells using CuSO4 aerosol. Cytotoxic effects of BaSO4- and TiO2-nanoparticles were investigated using MALIES with the human lung tumor cell line A549 cultured at the air-liquid interface. Experiments with concentrations of up to 5.93 × 10^5 (BaSO4) and 1.49 × 10^6 (TiO2) particles/cm^3, resulting in deposited masses of up to 26.6 and 74.0 µg/cm^2 were performed using two identical aerosol exposure systems in two different laboratories. LDH, resazurin reduction and total glutathione were measured. A549 cells grown on MatriGrids® form a ZO-1- and E-Cadherin-positive epithelial barrier and produce mucin and surfactant protein. BaSO4-NP in a deposited mass of up to 26.6 µg/cm^2 resulted in mild, reversible damage (˜ 10% decrease in viability) to lung epithelium 24 h after exposure. TiO2-NP in a deposited mass of up to 74.0 µg/cm^2 did not induce any cytotoxicity in A549 cells 24 h and 72 h after exposure, with the exception of a 1.7 fold increase in the low exposure group in laboratory 1. These results are consistent with previous studies showing no significant damage to lung epithelium by short-term treatment with low concentrations of nanoscale BaSO4 and TiO2 in in vitro experiments.



https://doi.org/10.1007/s00204-023-03673-3