QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show the rather surprising structural result that a disjoint union of cycles is the complement of a disk graph if and only if at most one of those cycles is of odd length. From that, we derive the first QPTAS and subexponential algorithm running in time 2^{O~(n^{2/3})} for Maximum Clique on disk graphs. In stark contrast, Maximum Clique on intersection graphs of filled ellipses or filled triangles is unlikely to have such algorithms, even when the ellipses are close to unit disks. Indeed, we show that there is a constant ratio of approximation which cannot be attained even in time 2^{n^{1-epsilon}}, unless the Exponential Time Hypothesis fails

Dynamics and High Energy Emission of the Flaring HST-1 Knot in the M 87 Jet

Stimulated by recent observations of a radio-to-X-ray synchrotron flare from HST-1, the innermost knot of the M 87 jet, as well as by a detection of a very high energy gamma-ray emission from M 87, we investigated the dynamics and multiwavelength emission of the HST-1 region. We study thermal pressure of the hot interstellar medium in M 87 and argue for a presence of a gaseous condensation in its central parts. Interaction of the jet with such a feature is likely to result in formation of a converging reconfinement shock in the innermost parts of the M 87 jet. We show that for a realistic set of the outflow parameters, a stationary and a flaring part of the HST-1 knot located \~100 pc away from the active center can be associated with the decelerated portion of the jet matter placed immediately downstream of the point where the reconfinement shock reaches the jet axis. We discuss a possible scenario explaining a broad-band brightening of the HST-1 region related to the variable activity of the central core. We show that assuming a previous epoch of the high central black hole activity resulting in ejection of excess particles and photons down along the jet, one may first expect a high-energy flare of HST-1 due to inverse-Comptonisation of the nuclear radiation, followed after a few years by an increase in the synchrotron continuum of this region. If this is the case, then the recently observed increase in the knot luminosity in all spectral bands could be regarded as an unusual echo of the outburst that had happened previously in the active core of the M 87 radio galaxy.Comment: 30 pages, 7 figures included. Accepted for publication in MNRA

Extraction of the electron mass from gg factor measurements on light hydrogenlike ions

The determination of the electron mass from Penning-trap measurements with $^{12}$C$^{5+}$ ions and from theoretical results for the bound-electron $g$ factor is described in detail. Some recently calculated contributions slightly shift the extracted mass value. Prospects of a further improvement of the electron mass are discussed both from the experimental and from the theoretical point of view. Measurements with $^4$He$^+$ ions will enable a consistency check of the electron mass value, and in future an improvement of the $^4$He nuclear mass and a determination of the fine-structure constant

On Pair Content and Variability of Sub-Parsec Jets in Quasars

X-ray observations of blazars associated with the OVV (Optically Violently Variable) quasars put strong constraints on the electron - positron pair content of radio-loud quasar jets. From those observations, we infer that jets in quasars contain many more electron - positron pairs than protons, but dynamically are still dominated by protons. In particular, we show that pure electron - positron jet models can be excluded, as they overpredict soft X-ray radiation; likewise, pure proton - electron jets can be excluded, as they predict too weak nonthermal X-ray radiation. An intermediate case is viable. We demonstrate that jets which are initially proton-electron ("proto-jets") can be pair-loaded via interaction with 100 - 300 keV photons produced in hot accretion disc coronae, likely to exist in active galactic nuclei in general. If the coronal radiation is powered by magnetic flares, the pair loading is expected to be non-uniform and non-axisymmetric. Together with radiation drag, this leads to velocity and density perturbations in a jet and formation of shocks, where the pairs are accelerated. Such a scenario can explain rapid (time scale of about a day) variability observed in OVV quasars.Comment: Accepted for publication in the Astrophysical Journa

Three-dimensional topological lattice models with surface anyons

We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they may well capture the topological behavior of some strongly correlated systems. In this work we give a full pedagogical treatment of a special simple case of these models, which we call the 3D semion model: We calculate its ground state degeneracies for a variety of boundary conditions, and classify its low-lying excitations. While point defects in the bulk are confined in pairs connected by energetic strings, the surface excitations are more interesting: the model has deconfined point defects pinned to the boundary of the lattice, and these exhibit semionic braiding statistics. The surface physics is reminiscent of a $\nu=1/2$ bosonic fractional quantum Hall effect in its topological limit, and these considerations help motivate an effective field theoretic description for the lattice models as variants of $bF$ theories. Our special example of the 3D semion model captures much of the behavior of more general `confined Walker-Wang models'. We contrast the 3D semion model with the closely related 3D version of the toric code (a lattice gauge theory) which has deconfined point excitations in the bulk and we discuss how more general models may have some confined and some deconfined excitations. Having seen that there exist lattice models whose surfaces have the same topological order as a bosonic fractional quantum Hall effect on a confining bulk, we construct a lattice model whose surface has similar topological order to a fermionic quantum hall effect. We find that in these models a fermion is always deconfined in the three dimensional bulk

Samenfeste Sorten oder Hybriden - Untersuchungen an Speisemöhren aus einem Anbauvergleich an zwei Standorten des Ökologischen Landbaus

An zwei Standorten des Ökologischen Landbaus (Neu-Eichenberg, Nordhessen: mittlerer bis schwerer Boden; Queck, Osthessen: leichter Boden) wurden Feldversuche mit Möhren durchgeführt, um sechs samenfeste Sorten und sechs Hybriden auf ihre Anbautauglichkeit zu prüfen. Außer der Roh- und Handelswarenerträge wurden die Einheitlichkeit des Erntegutes (cv%) bestimmt und die Gehalte an Mineralstoffen (K, Ca, P, Mg) und Zuckern (D-Glucose, D-Fructose, Saccharose) analysiert. Auch sogenannte Bildschaffende Methoden (Kupferchloridkristallisation, Steigbild, Rundfilterchromatogramm) kamen zur Anwendung. Die untersuchten Hybriden erzielten Mehrerträge von 25 bis 29% und in den meisten Fällen auch gleichmäßiger lange Rüben als die Samenfesten. Die Inhaltsstoffuntersuchungen zeigten höhere Mineralstoffgehalte und niedrigere Quotienten von Mono- zu Disaccharide bei den samenfesten Sorten. Mithilfe der Bildschaffenden Methoden konnten die Proben blind klar in zwei unterschiedliche Gruppen differenziert werden: Die Bilder der samenfesten Sorten waren im Vergleich zu denjenigen der Hybriden geprägt durch einen höheren Grad an Formintensität und Reife

Inequivalent routes across the Mott transition in V2O3 explored by X-ray absorption

The changes in the electronic structure of V2O3 across the metal-insulator transition induced by temperature, doping and pressure are identified using high resolution x-ray absorption spectroscopy at the V pre K-edge. Contrary to what has been taken for granted so far, the metallic phase reached under pressure is shown to differ from the one obtained by changing doping or temperature. Using a novel computational scheme, we relate this effect to the role and occupancy of the a1g orbitals. This finding unveils the inequivalence of different routes across the Mott transition in V2O

Highly sensitive thermal conductivity measurements of suspended membranes (SiN and diamond) using a 3w-Volklein method

A suspended system for measuring the thermal properties of membranes is presented. The sensitive thermal measurement is based on the 3$\omega$ dynamic method coupled to a V$\ddot{o}$lklein geometry. The device obtained using micro-machining processes allows the measurement of the in-plane thermal conductivity of a membrane with a sensitivity of less than 10nW/K (+/-$5x10^{-3}$Wm$^{-1}K^{-1}$ at room temperature) and a very high resolution ($\Delta K/K =10^{-3}$). A transducer (heater/thermometer) centered on the membrane is used to create an oscillation of the heat flux and to measure the temperature oscillation at the third harmonic using a Wheatstone bridge set-up. Power as low as 0.1nanoWatt has been measured at room temperature. The method has been applied to measure thermal properties of low stress silicon nitride and polycrystalline diamond membranes with thickness ranging from 100 nm to 400 nm. The thermal conductivity measured on the polycrystalline diamond membrane support a significant grain size effect on the thermal transport.Comment: 17 page