Department Angewandte Mathematik und Physik
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In this work we discuss a parameter σ on weighted k-element multisets of [n]={1,…,n}. The sums of weighted k-multisets are related to k-subsets, k-multisets, as well as special instances of truncated interpolated multiple zeta values. We study properties of this parameter using symbolic combinatorics. We rederive and extend certain identities for ζtn({m}k). Moreover, we introduce random variables on the k-element multisets and derive their distributions, as well as limit laws for k or n tending to infinity.
In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields – so-called hidden Killing vector fields – are constructed, which solve the Killing equation not globally, but only locally, i.e. in local subregions of spacetime. Taking advantage of the fact that the vector fields coincide locally with Killing fields and therefore allow the consideration of integral laws that convert into exact physical conservation laws on local scales, balance laws in dynamical systems without global Killing symmetries are derived that mimic as closely as possible the conservation laws for energy and angular momentum of highly symmetric models. The utility of said balance laws is demonstrated by a concrete geometric example, namely a toy model for the binary merger of two extremal Reissner–Nordström black holes.
In this paper, using the quasilocal formalism of Brown and York, the flow of energy through a closed surface containing a gravitating physical system is calculated in a way that augments earlier results on the subject by Booth and Creighton. To this end, by performing a variation of the total gravitational Hamiltonian (bulk plus boundary part), it is shown that associated tidal heating and deformation effects generally are larger than expected. This is because the aforementioned variation leads to previously unrecognized correction terms, including a bulk-to-boundary inflow term that does not appear in the original calculation of the time derivative of the Brown-York energy and leads to corrective extensions of Einstein’s quadrupole formula in the large sphere limit.
It has recently been shown that matter-wave interferometry can be used to imprint a periodic nanostructure onto a molecular beam, which provides a highly sensitive tool for beam displacement measurements. Herein, we used this feature to measure electronic properties of provitamin A, vitamin E, and vitamin K1 in the gas phase for the first time. The shift of the matter-wave fringes in a static electric field encodes the molecular susceptibility and the time-averaged dynamic electric dipole moment. The dependence of the fringe pattern on the intensity of the central light-wave diffraction grating was used to determine the molecular optical polarizability. Comparison of our experimental findings with molecular dynamics simulations and density functional theory provides a rich picture of the electronic structures and dynamics of these biomolecules in the gas phase with β-carotene as a particularly interesting example.
Designing experiments which delocalize ever more complex and more massive particles requires a quantitative assessment of new interferometer configurations. Here, we introduce a figure of
merit which quantifies the difference between a genuine quantum interference pattern and a classical shadow and use it to compare a number of near-field interferometer schemes. This allows us to identify the most promising setups for future tests of the quantum superposition principle, and to discuss the perspectives of interferometry with complex molecules and clusters.
After a discussion about the possibilities and status of augmented reality in education, a good
practice example of an augmented reality application is presented. This case study examines the
use of an augmented reality app in higher education to support abstract STEM content, such as
vectors. Based on this example, the implementation of such apps in didactic concepts and self -
directed learning will be discussed. Furthermore, aspects of integration into digital learning and
teaching will be addressed.
Matter-wave interference and deflection of tripeptides decorated with fluorinated alkyl chains
(2020)
A permutation can be locally classified according to the four local types: peaks, valleys, double rises and double falls. The corresponding classification of binary increasing trees uses four different types of nodes. Flajolet demonstrated the continued fraction representation of the generating function of local types, using a classical bijection between permutations, binary increasing trees, and suitably defined path diagrams induced by Motzkin paths.
The aim of this article is to extend the notion of local types from permutations to k-Stirling permutations (also known as k-multipermutations). We establish a bijection of these local types to node types of (k+1)-ary increasing trees. We present a branched continued fraction representation of the generating function of these local types through a bijection with path diagrams induced by Łukasiewicz paths, generalizing the results from permutations to arbitrary k-Stirling permutations.
We further show that the generating function of ordinary Stirling permutation has at least three branched continued fraction representations, using correspondences between non-standard increasing trees, k-Stirling permutations and path diagrams.
Stellar evolution models with entropy-calibrated mixing-length parameter: application to red giants
(2021)
Surface effects and turbulent pressure. Assessing the Gas-Γ1 and Reduced-Γ1 empirical models.
(2021)
In this work, the field of a gravitational shockwave generated by a massless point-like particle is calculated at the event horizon of a stationary Kerr–Newman black hole. Using the geometric framework of generalized Kerr–Schild deformations in combination with the spin-coefficient formalism of Newman and Penrose, it is shown that the field equations of the theory, at the event horizon of the black hole, can be reduced to a single linear ordinary differential equation for the so-called profile function of the geometry. This differential relation is solved exactly. Based on the results obtained, a physical interpretation is given for the found shockwave spacetime, and it is clarified how these results lead back to those of previous works on the subject, which deal with the much simpler cases of gravitational shockwaves in static black hole backgrounds.
In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. This framework is used to show that two Lorentzian manifolds can be matched by considering local deformations of the associated spacetime metrics. Based on the fact that metrics can be suitably matched in this way, it is shown that the underlying geometric approach allows the characterization of local spacetimes in general relativity. Furthermore, it is shown that said approach not only extends the conventional thin shell formalism, but also allows the treatment of geometric problems that cannot be treated with standard gluing techniques.
Driver disregard for the minimum safety distance increases the probability of rear-end collisions. In order to contribute to active safety on the road, we propose in this work a low-cost Forward Collision Warning system that captures and processes images. Using cameras located in the rear section of a leading vehicle, this system serves the purpose of discouraging tailgating behavior from the vehicle driving behind. We perform in this paper the pertinent field tests to assess system performance, focusing on the calculated distance from the processing of images and the error margins in a straight line, as well as in a curve. Based on the evaluation results, the current version of the Tailigator can be used at speeds up to 50 km per hour without any restrictions. The measurements showed similar characteristics both on the straight line and in the curve. At close distances, between 3 and 5 m, the values deviated from the real value. At average distances, around 10 to 15 m, the Tailigator achieved the best results. From distances higher than 20 m, the deviations increased steadily with the distance. We contribute to the state of the art with an innovative low-cost system to identify tailgating behavior and raise awareness, which works independently of the rear vehicle's communication capabilities or equipment.