A Survey of Classical and Recent Results in RLC Circuit Synthesis

This is the final version of the article. Available from the publisher via the link in this record.The motivation provided by mechanical network synthesis to make a fresh attack on certain questions in circuit synthesis will be briefly recalled. The classical early work on RLC synthesis, beginning with the works of Foster and Cauer and culminating in the Bott-Duffin construction, will be explained in a tutorial manner. Recent work on RLC synthesis by Jiang and Smith and Hughes and Smith will be introduced. The proof in T.H. Hughes and M.C. Smith, 2014, " On the minimality and uniqueness of the Bott-Duffin procedure " , IEEE Trans. Aut. Contr., (to appear), showing the surprising result that the Bott-Duffin construction for a biquadratic minimum function is the simplest possible among series-parallel circuits, will be explained.This work was supported by the Engineering and Physical Sciences Research Council under Grant EP/G066477/

Hierarchical fragmentation and collapse signatures in a high-mass starless region

Aims: Understanding the fragmentation and collapse properties of the dense gas during the onset of high-mass star formation. Methods: We observed the massive (~800M_sun) starless gas clump IRDC18310-4 with the Plateau de Bure Interferometer (PdBI) at sub-arcsecond resolution in the 1.07mm continuum andN2H+(3-2) line emission. Results: Zooming from a single-dish low-resolution map to previous 3mm PdBI data, and now the new 1.07mm continuum observations, the sub-structures hierarchically fragment on the increasingly smaller spatial scales. While the fragment separations may still be roughly consistent with pure thermal Jeans fragmentation, the derived core masses are almost two orders of magnitude larger than the typical Jeans mass at the given densities and temperatures. However, the data can be reconciled with models using non-homogeneous initial density structures, turbulence and/or magnetic fields. While most sub-cores remain (far-)infrared dark even at 70mum, we identify weak 70mum emission toward one core with a comparably low luminosity of ~16L_sun, re-enforcing the general youth of the region. The spectral line data always exhibit multiple spectral components toward each core with comparably small line widths for the individual components (in the 0.3 to 1.0km/s regime). Based on single-dish C18O(2-1) data we estimate a low virial-to-gas-mass ratio <=0.25. We discuss that the likely origin of these spectral properties may be the global collapse of the original gas clump that results in multiple spectral components along each line of sight. Even within this dynamic picture the individual collapsing gas cores appear to have very low levels of internal turbulence.Comment: 8 pages, 4 figures, A&A in pres

Discovery of > 200 RR Lyrae Variables in M62: An Oosterhoff I Globular Cluster with a Predominantly Blue HB

We report on the discovery of a large number of RR Lyrae variable stars in the moderately metal-rich Galactic globular cluster M62 (NGC 6266), which places it among the top three most RR Lyrae-rich globular clusters known. Likely members of the cluster in our studied field, from our preliminary number counts, include about 130 fundamental-mode (RRab) pulsators, with = 0.548 d, and about 75 first-overtone (RRc) pulsators, with = 0.300 d. The average periods and the position of the RRab variables with well-defined light curves in the Bailey diagram both suggest that the cluster is of Oosterhoff type I. However, the morphology of the cluster's horizontal branch (HB) is strikingly similar to that of the Oosterhoff type II globular cluster M15 (NGC 7078), with a dominant blue HB component and a very extended blue tail. Since M15 and M62 differ in metallicity by about one dex, we conclude that metallicity, at a fixed HB type, is a key parameter determining the Oosterhoff status of a globular cluster and the position of its variables in the Bailey diagram.Comment: 5 pages, 4 figures. ApJ Letters, in pres

Kinematic and Thermal Structure at the onset of high-mass star formation

We want to understand the kinematic and thermal properties of young massive gas clumps prior to and at the earliest evolutionary stages of high-mass star formation. Do we find signatures of gravitational collapse? Do we find temperature gradients in the vicinity or absence of infrared emission sources? Do we find coherent velocity structures toward the center of the dense and cold gas clumps? To determine kinematics and gas temperatures, we used ammonia, because it is known to be a good tracer and thermometer of dense gas. We observed the NH$_3$(1,1) and (2,2) lines within seven very young high-mass star-forming regions with the VLA and the Effelsberg 100m telescope. This allows us to study velocity structures, linewidths, and gas temperatures at high spatial resolution of 3-5$"$, corresponding to $\sim$0.05 pc. We find on average cold gas clumps with temperatures in the range between 10 K and 30 K. The observations do not reveal a clear correlation between infrared emission peaks and ammonia temperature peaks. We report an upper limit for the linewidth of $\sim$1.3 km s$^{-1}$, at the spectral resolution limit of our VLA observation. This indicates a relatively low level of turbulence on the scale of the observations. Velocity gradients are present in almost all regions with typical velocity differences of 1 to 2 km s$^{-1}$ and gradients of 5 to 10 km s$^{-1}$ pc$^{-1}$. These velocity gradients are smooth in most cases, but there is one exceptional source (ISOSS23053), for which we find several velocity components with a steep velocity gradient toward the clump centers that is larger than 30 km s$^{-1}$ pc$^{-1}$. This steep velocity gradient is consistent with recent models of cloud collapse. Furthermore, we report a spatial correlation of ammonia and cold dust, but we also find decreasing ammonia emission close to infrared emission sources.Comment: 20 pages, 10 figure

RR Lyrae Stars in NGC 6388 and NGC 6441: A New Oosterhoff Group?

NGC 6388 and NGC 6441 are anomalies among Galactic globular clusters in that they cannot be readily place into either Oosterhoff group I or Oosterhoff group II despite their significant numbers of RR Lyrae variables. The mean pulsation periods, , of their RRab variables, at 0.71 d and 0.76 d, respectively, are even larger than for Oosterhoff II clusters. Moreover, Oosterhoff II clusters are very metal-poor, whereas NGC 6388 and NGC 6441 are the most metal-rich globular clusters known to contain RR Lyrae stars. The location of the NGC 6388 and NGC 6441 RRab variables in the period-amplitude diagram implies that the RR Lyrae stars in those two clusters are brighter than expected for their metallicities. Our results therefore indicate that a universal relationship may not exist between the luminosity and the metallicity of RR Lyrae variables.Comment: Four pages, three figures. ApJ (Letters), in pres

High-resolution UV spectrum of the benzene—N2 van der Waals complex

The rotationally resolved spectrum of the 610 band of the S1 ← S0 electronic transition of the benzene—N2 van der Waals complex has been recorded and 119 transitions assigned. The C6H6·N2 complex, produced in a pulsed molecular beam, was detected by mass-selected two-photon two-colour ionization employing a high-resolution (ΔνUV = 100 MHz, fwhm) pulsed-amplified cw laser for the resonant intermediate excitation. The observed rotational structure is that of a rigid symmetric top with weaker additional rotational transitions most likely arising from the free internal rotation of the N2 in the plane parallel to the benzene ring. The N2 is located parallel to the benzene ring at a distance of 3.50 Å; this decreases by 45 mÅ in the excited electronic state

Fragmentation and dynamical collapse of the starless high-mass star-forming region IRDC18310-4

Aims: We study the fragmentation and dynamical properties of a massive starless gas clump at the onset of high-mass star formation. Methods: Based on Herschel continuum data we identify a massive gas clump that remains far-infrared dark up to 100mum wavelengths. The fragmentation and dynamical properties are investigated by means of Plateau de Bure Interferometer and Nobeyama 45m single-dish spectral line and continuum observations. Results: The massive gas reservoir fragments at spatial scales of ~18000AU in four cores. Comparing the spatial extent of this high-mass region with intermediate- to low-mass starless cores from the literature, we find that linear sizes do not vary significantly over the whole mass regime. However, the high-mass regions squeeze much more gas into these similar volumes and hence have orders of magnitude larger densities. The fragmentation properties of the presented low-to high-mass regions are consistent with gravitational instable Jeans fragmentation. Furthermore, we find multiple velocity components associated with the resolved cores. Recent radiative transfer hydrodynamic simulations of the dynamic collapse of massive gas clumps also result in multiple velocity components along the line of sight because of the clumpy structure of the regions. This result is supported by a ratio between viral and total gas mass for the whole region <1. Conclusions: This apparently still starless high-mass gas clump exhibits clear signatures of early fragmentation and dynamic collapse prior to the formation of an embedded heating source. A comparison with regions of lower mass reveals that the linear size of star-forming regions does not necessarily have to vary much for different masses, however, the mass reservoirs and gas densities are orders of magnitude enhanced for high-mass regions compared to their lower-mass siblings.Comment: 11 pages, 10 figures, accepted to Astronomy and Astrophysics, high-resolution version with all figures included can be found at http://www.mpia.de/homes/beuther/papers.htm

Thermodynamic properties of spin-1/2 transverse XY chain with Dzyaloshinskii-Moriya interaction: Exact solution for correlated Lorentzian disorder

We extend the consideration of the spin-1/2 transverse XY chain with correlated Lorentzian disorder (Phys. Rev. B {\bf 55,} 14298 (1997)) for the case of additional Dzyaloshinskii-Moriya interspin interaction. It is shown how the averaged density of states can be calculated exactly. Results are presented for the density of states and the transverse magnetization.Comment: 2 figure

Geochemical comparison of K-T boundaries from the Northern and Southern Hemispheres

Closely spaced (cm-scale) traverses through the K-T boundary at Stevns Klint (Denmark), Woodside Creek (New Zealand) and a new Southern Hemisphere site at Richards Bay (South Africa) were subjected to trace element and isotopic (C, O, Sr) investigation. Intercomparison between these data-sets, and correlation with the broad K-T database available in the literature, indicate that the chemistry of the boundary clays is not globally constant. Variations are more common than similarities, both of absolute concentrations, and interelement ratios. For example, the chondrite normalized platinum-group elements (PGE) patterns of Stevns Klint are not like those of Woodside Creek, with the Pt/Os ratios showing the biggest variation. These differences in PGE patterns are difficult to explain by secondary alteration of a layer that was originally chemically homogeneous, especially for elements of such dubious crustal mobility as Os and Ir. The data also show that enhanced PGE concentrations, with similar trends to those of the boundary layers, occur in the Cretaceous sediments below the actual boundary at Stevns Klint and all three the New Zealand localities. This confirms the observations of others that the geochemistry of the boundary layers apparently does not record a unique component. It is suggested that terrestrial processes, eg. an extended period of Late Cretaceous volcanism can offer a satisfactory explanation for the features of the K-T geochemical anomaly. Such models would probably be more consistent with the observed stepwise, or gradual, palaeontological changes across this boundary, than the instant catastrophe predicated by the impact theory

Tubular structures of GaS

In this Brief Report we demonstrate, using density-functional tight-binding theory, that gallium sulfide (GaS) tubular nanostructures are stable and energetically viable. The GaS-based nanotubes have a semiconducting direct gap which grows towards the value of two-dimensional hexagonal GaS sheet and is in contrast to carbon nanotubes largely independent of chirality. We further report on the mechanical properties of the GaS-based nanotubes