Development and application of a logistic model to estimate the past and future hail potential in Germany

This study investigates to what extent the frequency of hail events in the summer months has changed during the past decades and which changes are expected to occur in the future. To improve the diagnostics of hail events by considering various factors relevant for the formation of hail, a logistic hail model has been developed by means of a multivariate analysis method. This statistical model is based on a combination of appropriate meteorological parameters (convective parameter, moisture content, etc.) and synoptic weather types. The output of the model is a new index that estimates the potential of the atmosphere for hailstorm development, referred to as potential hail index. Validations with independent data sets confirm the reliability of the model results. For Germany, the logistic hail model applied to reanalysis data over the past decades shows a markedly north-to-south gradient with most of the potential hail days occurring in the south. Applied to an ensemble of seven regional climate model simulations, it is found that the potential for hail events will increase in the future (2021–2050) compared to the past (1971–2000), but only statistically significant in the northwest and south of Germany

On Axially Symmetric Solutions in the Electroweak Theory

We present the general ansatz, the energy density and the Chern-Simons charge for static axially symmetric configurations in the bosonic sector of the electroweak theory. Containing the sphaleron, the multisphalerons and the sphaleron-antisphaleron pair at finite mixing angle, the ansatz further allows the construction of the sphaleron and multisphaleron barriers and of the bisphalerons at finite mixing angle. We conjecture that further solutions exist.Comment: 17 pages, latex, THU-94/0

Orbits in the Field of a Gravitating Magnetic Monopole

Orbits of test particles and light rays are an important tool to study the properties of space-time metrics. Here we systematically study the properties of the gravitational field of a globally regular magnetic monopole in terms of the geodesics of test particles and light. The gravitational field depends on two dimensionless parameters, defined as ratios of the characteristic mass scales present. For critical values of these parameters the resulting metric coefficients develop a singular behavior, which has profound influence on the properties of the resulting space-time and which is clearly reflected in the orbits of the test particles and light rays.Comment: 24 pages, 15 figures. Accepted for publication in GR

Toric rings, inseparability and rigidity

This article provides the basic algebraic background on infinitesimal deformations and presents the proof of the well-known fact that the non-trivial infinitesimal deformations of a $K$-algebra $R$ are parameterized by the elements of cotangent module $T^1(R)$ of $R$. In this article we focus on deformations of toric rings, and give an explicit description of $T^1(R)$ in the case that $R$ is a toric ring. In particular, we are interested in unobstructed deformations which preserve the toric structure. Such deformations we call separations. Toric rings which do not admit any separation are called inseparable. We apply the theory to the edge ring of a finite graph. The coordinate ring of a convex polyomino may be viewed as the edge ring of a special class of bipartite graphs. It is shown that the coordinate ring of any convex polyomino is inseparable. We introduce the concept of semi-rigidity, and give a combinatorial description of the graphs whose edge ring is semi-rigid. The results are applied to show that for $m-k=k=3$, $G_{k,m-k}$ is not rigid while for $m-k\geq k\geq 4$, $G_{k,m-k}$ is rigid. Here $G_{k,m-k}$ is the complete bipartite graph $K_{m-k,k}$ with one edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and Applications>> 2018, Springer International Publishing AG, part of Springer Natur

Electron rescattering at metal nanotips induced by ultrashort laser pulses

We report on the first investigation of plateau and cut-off structures in photoelectron spectra from nano-scale metal tips interacting with few-cycle near-infrared laser pulses. These hallmarks of electron rescattering, well-known from atom-laser interaction in the strong-field regime, appear at remarkably low laser intensities with nominal Keldysh parameters of the order of $\gtrsim 10$. Quantum and quasi-classical simulations reveal that a large field enhancement near the tip and the increased backscattering probability at a solid-state target play a key role. Plateau electrons are by an order of magnitude more abundant than in comparable atomic spectra, reflecting the high density of target atoms at the surface. The position of the cut-off serves as an in-situ probe for the locally enhanced electric field at the tip apex

On the question of universality in \RPn and \On Lattice Sigma Models

We argue that there is no essential violation of universality in the continuum limit of mixed \RPn and \On lattice sigma models in 2 dimensions, contrary to opposite claims in the literature.Comment: 16 pages (latex) + 3 figures (Postscript), uuencode

New Universality Classes for Two-Dimensional σ\sigma-Models

We argue that the two-dimensional $O(N)$-invariant lattice $\sigma$-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum $\sigma$-model constructed by conventional perturbation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for $N=3,4$ on lattices up to $512 \times 512$, using a Wolff-type embedding algorithm. [CPU time $\approx$ 7 years IBM RS-6000/320H] The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the $RP^{N-1}$ and $N$-vector models do not lie in the same universality class.Comment: 10 pages (includes 2 figures), 211176 bytes Postscript, NYU-TH-93/07/03, IFUP-TH 34/9

Impact of heavy hole-light hole coupling on optical selection rules in GaAs quantum dots

We report strong heavy hole-light mixing in GaAs quantum dots grown by droplet epitaxy. Using the neutral and charged exciton emission as a monitor we observe the direct consequence of quantum dot symmetry reduction in this strain free system. By fitting the polar diagram of the emission with simple analytical expressions obtained from k$\cdot$p theory we are able to extract the mixing that arises from the heavy-light hole coupling due to the geometrical asymmetry of the quantum dot.Comment: 4 pages, 2 figure

Metal nanofilm in strong ultrafast optical fields

We predict that a metal nanofilm subjected to an ultrashort (single oscillation) optical pulse of a high field amplitude $\sim 3 \mathrm{V/\AA}$ at normal incidence undergoes an ultrafast (at subcycle times $\lesssim 1 \mathrm{fs}$) transition to a state resembling semimetal. Its reflectivity is greatly reduced, while the transmissivity and the optical field inside the metal are greatly increased. The temporal profiles of the optical fields are predicted to exhibit pronounced subcycle oscillations, which are attributed to the Bloch oscillations and formation of the Wannier-Stark ladder of electronic states. The reflected, transmitted, and inside-the-metal pulses have non-zero areas approaching half-cycle pulses. The effects predicted are promising for applications to nanoplasmonic modulators and field-effect transistors with petahertz bandwidth