Non-Weyl Resonance Asymptotics for Quantum Graphs

We consider the resonances of a quantum graph $\mathcal G$ that consists of a compact part with one or more infinite leads attached to it. We discuss the leading term of the asymptotics of the number of resonances of $\mathcal G$ in a disc of a large radius. We call $\mathcal G$ a \emph{Weyl graph} if the coefficient in front of this leading term coincides with the volume of the compact part of $\mathcal G$. We give an explicit topological criterion for a graph to be Weyl. In the final section we analyze a particular example in some detail to explain how the transition from the Weyl to the non-Weyl case occurs.Comment: 29 pages, 2 figure

Non-Weyl asymptotics for quantum graphs with general coupling conditions

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in case of Kirchhoff or anti-Kirchhoff conditions, while for graphs without permutation numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight helping to understand what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with nonequal edge weights.Comment: minor changes, to appear in Pierre Duclos memorial issue of J. Phys. A: Math. Theo

LpL^p-Spectral theory of locally symmetric spaces with QQ-rank one

We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one

Probing the Inner Disk Emission of the Herbig Ae Stars HD 163296 and HD 190073

The physical processes occurring within the inner few astronomical units of proto-planetary disks surrounding Herbig Ae stars are crucial to setting the environment in which the outer planet-forming disk evolves and put critical constraints on the processes of accretion and planet migration. We present the most complete published sample of high angular resolution H- and K-band observations of the stars HD 163296 and HD 190073, including 30 previously unpublished nights of observations of the former and 45 nights of the latter with the CHARA long-baseline interferometer, in addition to archival VLTI data. We confirm previous observations suggesting significant near-infrared emission originates within the putative dust evaporation front of HD 163296 and show this is the case for HD 190073 as well. The H- and K-band sizes are the same within $(3 \pm 3)\%$ for HD 163296 and within $(6 \pm 10)\%$ for HD 190073. The radial surface brightness profiles for both disks are remarkably Gaussian-like with little or no sign of the sharp edge expected for a dust evaporation front. Coupled with spectral energy distribution analysis, our direct measurements of the stellar flux component at H and K bands suggest that HD 190073 is much younger (<400 kyr) and more massive (~5.6 M$_\odot$) than previously thought, mainly as a consequence of the new Gaia distance (891 pc).Comment: 19 pages, 6 figure

Preliminary imaging results from the second Mercury encounter

The second Mercury encounter has resulted in the acquisition of about 360 pictures of the south polar regions which provide a reliable cartographic and geologic tie between the two sides of the planet photographed on the first encounter. Stereoscopic coverage of large areas of the southern hemisphere was obtained by combining Mercury 1 and 2 pictures taken at different viewing angles. The south polar regions consist of heavily cratered terrain and intercrater plains interspersed with patches of smooth plains. No large areas of smooth plains similar to those surrounding Caloris occur in the south polar regions. No new types of terrain have been recognized, but lobate scarps are common. The second largest basin seen by Mariner 10 (∼600-km diameter) has been confirmed on the new photography. At high solar elevations the surface displays an abundance of rays and rayed craters

The ANU WiFeS SuperNovA Program (AWSNAP)

This paper presents the first major data release and survey description for the ANU WiFeS SuperNovA Program (AWSNAP). AWSNAP is an ongoing supernova spectroscopy campaign utilising the Wide Field Spectrograph (WiFeS) on the Australian National University (ANU) 2.3m telescope. The first and primary data release of this program (AWSNAP-DR1) releases 357 spectra of 175 unique objects collected over 82 equivalent full nights of observing from July 2012 to August 2015. These spectra have been made publicly available via the WISeREP supernova spectroscopy repository. We analyse the AWSNAP sample of Type Ia supernova spectra, including measurements of narrow sodium absorption features afforded by the high spectral resolution of the WiFeS instrument. In some cases we were able to use the integral-field nature of the WiFeS instrument to measure the rotation velocity of the SN host galaxy near the SN location in order to obtain precision sodium absorption velocities. We also present an extensive time series of SN 2012dn, including a near-nebular spectrum which both confirms its "super-Chandrasekhar" status and enables measurement of the sub-solar host metallicity at the SN site.Comment: Submitted to Publications of the Astronomical Society of Australia (PASA). Spectra publicly released via WISeREP at http://wiserep.weizmann.ac.il

Metal ion-dependent, reversible, protein filament formation by designed beta-roll polypeptides

<p>Abstract</p> <p>Background</p> <p>A right-handed, calcium-dependent β-roll structure found in secreted proteases and repeat-in-toxin proteins was used as a template for the design of minimal, soluble, monomeric polypeptides that would fold in the presence of Ca²⁺. Two polypeptides were synthesised to contain two and four metal-binding sites, respectively, and exploit stacked tryptophan pairs to stabilise the fold and report on the conformational state of the polypeptide.</p> <p>Results</p> <p>Initial analysis of the two polypeptides in the presence of calcium suggested the polypeptides were disordered. The addition of lanthanum to these peptides caused aggregation. Upon further study by right angle light scattering and electron microscopy, the aggregates were identified as ordered protein filaments that required lanthanum to polymerize. These filaments could be disassembled by the addition of a chelating agent. A simple head-to-tail model is proposed for filament formation that explains the metal ion-dependency. The model is supported by the capping of one of the polypeptides with biotin, which disrupts filament formation and provides the ability to control the average length of the filaments.</p> <p>Conclusion</p> <p>Metal ion-dependent, reversible protein filament formation is demonstrated for two designed polypeptides. The polypeptides form filaments that are approximately 3 nm in diameter and several hundred nm in length. They are not amyloid-like in nature as demonstrated by their behaviour in the presence of congo red and thioflavin T. A capping strategy allows for the control of filament length and for potential applications including the "decoration" of a protein filament with various functional moieties.</p