Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

CaII K interstellar observations towards early-type disc and halo stars - distances to intermediate- and high-velocity clouds

We compare existing high spectral resolution (R = lambda/Deltalambda similar to 40 000) Ca II Kobservations (lambda(air) = 3933.66 Angstrom) towards 88 mainly B-type stars, and new observations taken using the Intermediate dispersion Spectrograph and Imaging System (ISIS) on the William Herschel Telescope at R similar to 10 000 towards three stars taken from the Palomar-Green Survey, with 21-cm HI emission-line profiles, in order to search for optical absorption towards known intermediate- and high-velocity cloud complexes. Given certain assumptions, limits to the gas phase abundance of Ca II are estimated for the cloud components. We use the data to derive the following distances from the Galactic plane (z). (i) Tentative lower z-height limits of 2800 and 4100 pc towards complex C using lack of absorption in the spectra of HD341617 and PG 0855 + 294, respectively. (ii) A weak lower z-height of 1400 pc towards complex WA-WB using lack of absorption in EC 09470-1433 and a weak lower limit of 2470 pc using lack of absorption in EC 09452-1403. (iii) An upper z- height of 2470 pc towards a southern intermediate- velocity cloud (IVC) with v(LSR) = -55 km s(-1) using PG 2351 + 198. (iv) Detection of a possible IVC in Ca II absorption at v(LSR) = +52 km s(-1) using EC 20104-2944. No associated HI in emission is detected. At this position, normal Galactic rotation predicts velocities of up to similar to+ 25 km s(-1). The detection puts an upper z-height of 1860 pc to the cloud. (v) Tentative HI and Ca II K detections towards an IVC at similar to+70 km s(-1) in the direction of high-velocity cloud (HVC) complex WE, sightline EC 06387-8045, indicating that the IVC may be at a z-height lower than 1770 pc. (vi) Detection of Ca II K absorption in the spectrum of PG 0855 + 294 in the direction of IV20, indicating that this IVC has a z-height smaller than 4100 pc. (vii) A weak lower z-height of 4300 pc towards a small HVC with v(LSR) = +115 km s(-1) at l, b = 200degrees, + 52degrees, using lack of absorption in the Ca II K spectrum of PG 0955 + 291.

CaIIKinterstellar observations towards early-type disc and halo stars, abundances and distances of intermediate- and high-velocity clouds

We present Ca II K (lambda(air) = 3933.661 angstrom) interstellar observations towards 20 early-type stars, to place lower distance limits to intermediate- and high-velocity clouds (IHVCs) in their lines of sight. The spectra are also employed to estimate the Ca abundance in the low-velocity gas towards these objects, when combined with Leiden-Dwingeloo 21-cm HI survey data of spatial resolution 0 degrees.5. Nine of the stars, which lie towards IHVC complexes H, K and gp, were observed with the intermediate dispersion spectrograph on the Isaac Newton Telescope at a resolution R = lambda/Delta lambda of 9000 (similar to 33 km s(-1)) and signal-to-noise ratio (S/N) per pixel of 75-140. A further nine objects were observed with the Utrecht Echelle Spectrograph on the William Herschel Telescope at R = 40 000 (similar to 7.5 km s(-1)) and S/N per pixel of 10-25. Finally, two objects were observed in both Ca II K and Na I D lines using the 2D COUDE on the McDonald 2.7-m telescope at R = 35 000 (similar to 8.5 km s(-1)). The abundance of Ca II K {log(10)(A) = log(10)[N(Ca II K)]-log(10)[N(HI)]} plotted against HI column density for the objects in the current sample with heights above the Galactic plane (z) exceeding 1000 pc is found to obey the Wakker & Mathis (2000) relation. Also, the reduced column density of Ca II K as function of z is consistent with the larger sample taken from Smoker et al. (2003). Higher S/N observations than those previously taken towards HVC complex H stars HD 13256 and HILT 190 reinforce the assertion that this lies at a distance exceeding 4000 pc. No obvious absorption is detected in observations of ALS 10407 and HD 357657 towards IVC complex gp. The latter star has a spectroscopically estimated distance of similar to 2040 pc, although this was derived assuming the star lies on the main sequence and without any reddening correction being applied. Finally, no Ca II K absorption is detected towards two stars along the line of sight to complex K, namely PG 1610+529 and PG 1710+490. The latter is at a distance of similar to 700 pc, hence placing a lower distance limit to this complex, where previously only an upper distance limit of 6800 pc was available.

Natural three-qubit interactions in one-way quantum computing

We address the effects of natural three-qubit interactions on the computational power of one-way quantum computation. A benefit of using more sophisticated entanglement structures is the ability to construct compact and economic simulations of quantum algorithms with limited resources. We show that the features of our study are embodied by suitably prepared optical lattices, where effective three-spin interactions have been theoretically demonstrated. We use this to provide a compact construction for the Toffoli gate. Information flow and two-qubit interactions are also outlined, together with a brief analysis of relevant sources of imperfection.

Hydrocarbon Anions in Interstellar Clouds and Circumstellar Envelopes

The recent detection of the hydrocarbon anion C$_6$H$^-$ in the interstellar medium has led us to investigate the synthesis of hydrocarbon anions in a variety of interstellar and circumstellar environments. We find that the anion/neutral abundance ratio can be quite large, on the order of at least a few percent, once the neutral has more than five carbon atoms. Detailed modeling shows that the column densities of C$_6$H$^-$ observed in IRC+10216 and TMC-1 can be reproduced. Our calculations also predict that other hydrocarbon anions, such as C$_{4}$H$^{-}$ and C$_8$H$^-$, are viable candidates for detection in IRC+10216, TMC-1 and photon-dominated regions such as the Horsehead Nebula.

The VLT-FLAMES survey of massive stars: evolution of surface N abundances and effective temperature scales in the Galaxy and Magellanic Clouds

We present an analysis of high resolution VLT-FLAMES spectra of 61 B-type stars with relatively narrow-lined spectra located in 4 fields centered on the Milky Way clusters; NGC 3293 and NGC 4755 and the Large and Small Magellanic cloud clusters; NGC 2004 and NGC 330. For each object a quantitative analysis was carried out using the non-LTE model atmosphere code TLUSTY; resulting in the determination of their atmospheric parameters and photospheric abundances of the dominant metal species (C, N, O, Mg, Si, Fe). The results are discussed in relation to our earlier work on 3 younger clusters in these galaxies; NGC 6611, N11 and NGC 346 paying particular attention to the nitrogen abundances which are an important probe of the role of rotation in the evolution of stars. This work along with that of the younger clusters provides a consistent dataset of abundances and atmospheric parameters for over 100 B-type stars in the three galaxies. We provide effective temperature scales for B-type dwarfs in all three galaxies and for giants and supergiants in the SMC and LMC. In each galaxy a dependence on luminosity is found between the three classes with the unevolved dwarf objects having significantly higher effective temperatures. A metallicity dependence is present between the SMC and Galactic dwarf objects, and whilst the LMC stars are only slightly cooler than the SMC stars, they are significantly hotter than their Galactic counterparts.

Galactic Edge Clouds I. Molecular Line Observations and Chemical Modelling of Edge Cloud 2

Edge Cloud 2 (EC2) is a molecular cloud, about 35 pc in size, with one of the largest galactocentric distances known to exist in the Milky Way. We present observations of a peak CO emission region in the cloud and use these to determine its physical characteristics. We calculate a gas temperature of 20 K and a density of n(H2)~10^4 cm-3. Based on our CO maps, we estimate the mass of EC2 at around 10^4 Msolar and continuum observations suggest a dust-to-gas mass ratio as low as 0.001. Chemical models have been developed to reproduce the abundances in EC2, and they indicate that heavy element abundances may be reduced by a factor of 5 relative to the solar neighborhood (similar to dwarf irregular galaxies and damped Lya systems), very low extinction (A_V <4 mag) due to a very low dust-to-gas mass ratio, an enhanced cosmic-ray ionization rate, and a higher UV field compared to local interstellar values. The reduced abundances may be attributed to the low level of star formation in this region and are probably also related to the continuing infall of primordial (or low-metallicity) halo gas since the Milky Way formed. Finally, we note that shocks from the old supernova remnant GSH 138-01-94 may have determined the morphology and dynamics of EC2.

The VLT-FLAMES survey of massive stars: atmospheric parameters and rotational velocity distributions for B-type stars in the Magellanic Clouds

Aims.We aim to provide the atmospheric parameters and rotational velocities for a large sample of O- and early B-type stars, analysed in a homogeneous and consistent manner, for use in constraining theoretical models. Methods: Atmospheric parameters, stellar masses, and rotational velocities have been estimated for approximately 250 early B-type stars in the Large (LMC) and Small (SMC) Magellanic Clouds from high-resolution VLT-FLAMES data using the non-LTE TLUSTY model atmosphere code. This data set has been supplemented with our previous analyses of some 50 O-type stars (Mokiem et al. 2006, 2007) and 100 narrow-lined early B-type stars (Hunter et al. 2006; Trundle et al. 2007) from the same survey, providing a sample of ~400 early-type objects. Results: Comparison of the rotational velocities with evolutionary tracks suggests that the end of core hydrogen burning occurs later than currently predicted and we argue for an extension of the evolutionary tracks. We also show that the large number of the luminous blue supergiants observed in the fields are unlikely to have directly evolved from main-sequence massive O-type stars as neither their low rotational velocities nor their position on the H-R diagram are predicted. We suggest that blue loops or mass-transfer binary systems may populate the blue supergiant regime. By comparing the rotational velocity distributions of the Magellanic Cloud stars to a similar Galactic sample, we find that (at 3s confidence level) massive stars (above 8 M?) in the SMC rotate faster than those in the solar neighbourhood. However there appears to be no significant difference between the rotational velocity distributions in the Galaxy and the LMC. We find that the v sin i distributions in the SMC and LMC can modelled with an intrinsic rotational velocity distribution that is a Gaussian peaking at 175 km s-1 (SMC) and 100 km s-1 (LMC) with a 1/e half width of 150 km s-1. We find that in NGC 346 in the SMC, the 10-25 M? main-sequence stars appear to rotate faster than their higher mass counterparts. It is not expected that O-type stars spin down significantly through angular momentum loss via stellar winds at SMC metallicity, hence this could be a reflection of mass dependent birth spin rates. Recently Yoon et al. (2006) have determined rates of GRBs by modelling rapidly rotating massive star progenitors. Our measured rotational velocity distribution for the 10-25 M? stars is peaked at slightly higher velocities than they assume, supporting the idea that GRBs could come from rapid rotators with initial masses as low as 14 M? at low metallicities.