Contact line stability of ridges and drops

Within the framework of a semi-microscopic interface displacement model we analyze the linear stability of sessile ridges and drops of a non-volatile liquid on a homogeneous, partially wet substrate, for both signs and arbitrary amplitudes of the three-phase contact line tension. Focusing on perturbations which correspond to deformations of the three-phase contact line, we find that drops are generally stable while ridges are subject only to the long-wavelength Rayleigh-Plateau instability leading to a breakup into droplets, in contrast to the predictions of capillary models which take line tension into account. We argue that the short-wavelength instabilities predicted within the framework of the latter macroscopic capillary theory occur outside its range of validity and thus are spurious.Comment: 6 pages, 1 figur

Generalized Symmetries of Impulsive Gravitational Waves

We generalize previous \cite{AiBa2} work on the classification of ($C^\infty$) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normal-form-preserving diffeomorphisms to include non-smooth transformations. This extension entails a richer structure of the symmetry algebra generated by the (non-smooth) Killing vectors.Comment: 18 pages, latex2e, no figure

Radio-loud Active Galaxies in the Northern ROSAT All-Sky Survey III: New Spectroscopic Identifications from the RGB BL Lac Survey

We present new spectroscopic identifications for 169 objects in the RASS-Green Bank (RGB) catalog of radio- and X-ray-emitting AGN. These data significantly increase the fraction of bright RGB objects with classifications. Specifically, we report and discuss the classification of 66 radio-loud quasars, 53 BL Lacs, 33 Broad Line Radio Galaxies, 5 Narrow Line Radio Galaxies, 1 Seyfert I galaxy and 11 galaxies or galaxies in clusters. Over 78% of the identifications we present here are new. The observations we report were undertaken as part of our targeted search program to identify a new, large unbiased sample of BL Lac Objects and we therefore discuss the BL Lac sample extensively. Unlike many previous surveys, we impose no selection criteria based on optical morphology, color or broadband spectral energy distribution. Our classifications are based solely on a carefully defined set of self-consistent spectroscopic classification criteria. We show the 53 RGB presented here exhibit transitional properties between normal galaxies and BL Lacs discovered previously. We show there is no clear separation in CaII break strength between RGB BL Lacs and galaxies, with the distribution of break strengths varying smoothly between 0% and 50%. We also show that the newly discovered RGB BL Lacs reside in a "zone of avoidance" in the log(S_x/S_r) vs. log(S_o/S_r) diagram. This has important implications for BL Lac search strategies since it shows that RASS BL Lac samples will be severely incomplete if candidates are chosen only from among those objects with the highest S_x/S_r flux ratios.Comment: 21 pages text, 189 Figures, 4 tables, LaTeX2E, 4.2MB tar file (compressed); special style file paper.sty provide

The Optical Emission from Gamma-ray Quasars

We present photometric observations of six radio-loud quasars that were detected by the COMPTEL gamma-ray telescope. The data encompasses seven wavebands in the optical and near-infrared. After correction for Galactic extinction, we find a wide range in optical slopes. Two sources are as blue as optically-selected quasars, and are likely to be dominated by the accretion disc emission, while three others show colours consistent with a red synchrotron component. We discuss the properties of the COMPTEL sample of quasars, as well as the implications our observations have for multi-wavelength modelling of gamma-ray quasars.Comment: 12 pages, 3 figures, accepted for publication in P.A.S.A; minor typos correcte

Synthetic X-ray light curves of BL Lacs from relativistic hydrodynamic simulations

We present the results of relativistic hydrodynamic simulations of the collision of two dense shells in a uniform external medium, as envisaged in the internal shock model for BL Lac jets. The non-thermal radiation produced by highly energetic electrons injected at the relativistic shocks is computed following their temporal and spatial evolution. The acceleration of electrons at the relativistic shocks is parametrized using two different models and the corresponding X-ray light curves are computed. We find that the interaction time scale of the two shells is influenced by an interaction with the external medium. For the chosen parameter sets, the efficiency of the collision in converting dissipated kinetic energy into the observed X-ray radiation is of the order of one percent.Comment: 22 pages, 6 figures, accepted to A&

Investigation of the Spin-Peierls transition in CuGeO_3 by Raman scattering

Raman experiments on the spin-Peierls compound CuGeO$_3$ and the substituted (Cu$_{1- x}$,Zn$_x$)GeO$_3$ and Cu(Ge$_{1-x}$,Ga$_x$)O$_3$ compounds were performed in order to investigate the response of specific magnetic excitations of the one-dimensional spin-1/2 chain to spin anisotropies and substitution-induced disorder. In pure CuGeO$_3$, in addition to normal phonon scattering which is not affected at all by the spin-Peierls transition, four types of magnetic scattering features were observed. Below T$_{SP}$=14 K a singlet-triplet excitation at 30 cm$^{-1}$, two-magnon scattering from 30 to 227 cm$^{-1}$ and folded phonon modes at 369 and 819 cm$^{-1}$ were identified. They were assigned by their temperature dependence and lineshape. For temperatures between the spin-Peierls transition T$_{SP}$ and approximately 100 K a broad intensity maximum centered at 300 cm$^{-1}$ is observed.Comment: 7 pages, LaTex2e, including 3 figures (eps) to be published in Physica B (1996

Beam Based Alignment of Interaction Region Magnets

In conventional beam based alignment (BBA) procedures, the relative alignment of a quadrupole to a nearby beam position monitor is determined by finding a beam position in the quadrupole at which the closed orbit does not change when the quadrupole field is varied. The final focus magnets of the interaction regions (IR) of circular colliders often have some specialized properties that make it difficult to perform conventional beam based alignment procedures. At the HERA interaction points, for example, these properties are: (a) The quadrupoles are quite strong and long. Therefore a thin lens approximation is quite imprecise. (b) The effects of angular magnet offsets become significant. (c) The possibilities to steer the beam are limited as long as the alignment is not within specifications. (d) The beam orbit has design offsets and design angles with respect to the axis of the low-beta quadrupoles. (e) Often quadrupoles do not have a beam position monitor in their vicinity. Here we present a beam based alignment procedure that determines the relative offset of the closed orbit from a quadrupole center without requiring large orbit changes or monitors next to the quadrupole. Taking into account the alignment angle allows us to reduce the sensitivity to optical errors by one to two orders of magnitude. We also show how the BBA measurements of all IR quadrupoles can be used to determine the global position of the magnets. The sensitivity to errors of this method is evaluated and its applicability to HERA is shown

Topological Designs

We give an exponential upper and a quadratic lower bound on the number of pairwise non-isotopic simple closed curves can be placed on a closed surface of genus g such that any two of the curves intersects at most once. Although the gap is large, both bounds are the best known for large genus. In genus one and two, we solve the problem exactly. Our methods generalize to variants in which the allowed number of pairwise intersections is odd, even, or bounded, and to surfaces with boundary components.Comment: 14 p., 4 Figures. To appear in Geometriae Dedicat