An algebraic formula for the index of a vector field on an isolated complete intersection singularity

Let (V,0) be a germ of a complete intersection variety in \CC^{n+k}, n>0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on \CC^{n+k} tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space \CC^{n+k} we give a formula for the homological index in terms of local linear algebra.Comment: 18 pages; added an example which is not quasi homogeneous. A script calculating this example can be found at http://www.iag.uni-hannover.de/~bothmer/gobelin/ or at the and of the source file of this articl

Response of a particle in a one-dimensional lattice to an applied force: Dynamics of the effective mass

We study the behaviour of the expectation value of the acceleration of a particle in a one-dimensional periodic potential when an external homogeneous force is suddenly applied. The theory is formulated in terms of modified Bloch states that include the interband mixing induced by the force. This approach allows us to understand the behaviour of the wavepacket, which responds with a mass that is initially the bare mass, and subsequently oscillates around the value predicted by the effective mass. If Zener tunneling can be neglected, the expression obtained for the acceleration of the particle is valid over timescales of the order of a Bloch oscillation, which are of interest for experiments with cold atoms in optical lattices. We discuss how these oscillations can be tuned in an optical lattice for experimental detection.Comment: 15 pages, 12 figure

Electrospray synthesis of PLGA TIPS microspheres

We successfully demonstrate the synthesis of polymer microspheres using a single electrospray source, and show their physical characterisation. Electrospray has proven to be a versatile method to manufacture particles, giving tight control over size with quasi-monodisperse size distributions. It is a liquid atomisation technique that generates a monodisperse population of highly charged liquid droplets over a broad size range (nanometres to tens of microns). The droplets contain liquid precursors for the in-flight synthesis of particles, and control over the trajectory of these droplets can be precisely manipulated with the use of electric fields to drive them to a grounded substrate. This study reports a method to synthesize poly(lactic-co-glycolic) acid (PLGA) microspheres using the electrospray and thermally induced phase separation (TIPS) techniques, followed by subsequent freeze-drying, for particle production. These microspheres are of interest as vehicles for controlled drug release systems

Specific Heat of the Dilute Ising Magnet LiHox_xY1−x_{1-x}F4_4

We present specific heat data on three samples of the dilute Ising magnet \HoYLF with $x = 0.018$, 0.045 and 0.080. Previous measurements of the ac susceptibility of an $x = 0.045$ sample showed the Ho$^{3+}$ moments to remain dynamic down to very low temperatures and the specific heat was found to have unusually sharp features. In contrast, our measurements do not exhibit these sharp features in the specific heat and instead show a broad feature, for all three samples studied, which is qualitatively consistent with a spin glass state. Integrating $C/T$, however, reveals an increase in residual entropy with lower Ho concentration, consistent with recent Monte Carlo simulations showing a lack of spin glass transition for low x.Comment: 10 pages, 3 figurs, accepted for publication in Phys. Rev. Let

Controlling the quality factor of a tuning-fork resonance between 9 K and 300 K for scanning-probe microscopy

We study the dynamic response of a mechanical quartz tuning fork in the temperature range from 9 K to 300 K. Since the quality factor Q of the resonance strongly depends on temperature, we implement a procedure to control the quality factor of the resonance. We show that we are able to dynamically change the quality factor and keep it constant over the whole temperature range. This procedure is suitable for applications in scanning probe microscopy.Comment: 5 pages, 6 figure

A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting

Scaling in the time-dependent failure of a fiber bundle with local load sharing

We study the scaling behaviors of a time-dependent fiber-bundle model with local load sharing. Upon approaching the complete failure of the bundle, the breaking rate of fibers diverges according to $r(t)\propto (T_f-t)^{-\xi}$, where $T_f$ is the lifetime of the bundle, and $\xi \approx 1.0$ is a quite universal scaling exponent. The average lifetime of the bundle $$ scales with the system size as $N^{-\delta}$, where $\delta$ depends on the distribution of individual fiber as well as the breakdown rule.Comment: 5 pages, 4 eps figures; to appear in Phys. Rev.

The Herschel exploitation of local galaxy Andromeda (HELGA) V: Strengthening the case for substantial interstellar grain growth

In this paper we consider the implications of the distributions of dust and metals in the disc of M31. We derive mean radial dust distributions using a dust map created from Herschel images of M31 sampling the entire far-infrared (FIR) peak. Modified blackbodies are fit to approximately 4000 pixels with a varying, as well as a fixed, dust emissivity index (beta). An overall metal distribution is also derived using data collected from the literature. We use a simple analytical model of the evolution of the dust in a galaxy with dust contributed by stellar sources and interstellar grain growth, and fit this model to the radial dust-to-metals distribution across the galaxy. Our analysis shows that the dust-to-gas gradient in M31 is steeper than the metallicity gradient, suggesting interstellar dust growth is (or has been) important in M31. We argue that M31 helps build a case for cosmic dust in galaxies being the result of substantial interstellar grain growth, while the net dust production from stars may be limited. We note, however, that the efficiency of dust production in stars, e.g., in supernovae (SNe) ejecta and/or stellar atmospheres, and grain destruction in the interstellar medium (ISM) may be degenerate in our simple model. We can conclude that interstellar grain growth by accretion is likely at least as important as stellar dust production channels in building the cosmic dust component in M31.Comment: 12 pages, 7 figures. Published in MNRAS 444, 797. This version is updated to match the published versio

H2O Maser Observations of Candidate Post-AGB Stars and Discovery of Three High-velocity Water Sources

We present the results of 22 GHz H_2O maser observations of a sample of 85 post-Asymptotic Giant Branch (post-AGB) candidate stars, selected on the basis of their OH 1612 MHz maser and far-infrared properties. All sources were observed with the Tidbinbilla 70-m radio telescope and 21 detections were made. 86 GHz SiO Mopra observations of a subset of the sample are also presented. Of the 21 H_2O detections, 15 are from sources that are likely to be massive AGB stars and most of these show typical, regular H_2O maser profiles. In contrast, nearly all the detections of more evolved stars exhibited high-velocity H_2O maser emission. Of the five sources seen, v223 (W43A, IRAS 18450-0148) is a well known `water-fountain' source which belongs to a small group of post-AGB stars with highly collimated, high-velocity H_2O maser emission. A second source in our sample, v270 (IRAS 18596+0315), is also known to have high-velocity emission. We report the discovery of similar emission from a further three sources, d46 (IRAS 15445-5449), d62 (IRAS 15544-5332) and b292 (IRAS 18043-2116). The source d46 is an evolved post-AGB star with highly unusual maser properties. The H_2O maser emission from d62 is probably associated with a massive star. The source b292 is a young post-AGB star that is highly likely to be a water-fountain source, with masers detected over a velocity range of 210 km s^{-1}.Comment: 47 pages, 9 figures, 4 tables, accepted by Ap