Gravitational instantons and internal dimensions

We Study instanton solutions in general relativity with a scalar field. The metric ansatz we use is composed of a particular warp product of general Einstein metrics, such as those found in a number of cosmological settings, including string cosmology, supergravity compactifications and general Kaluza Klein reductions. Using the Hartle-Hawking prescription the instantons we obtain determine whether metrics involving extra compact dimensions of this type are favoured as initial conditions for the universe. Specifically, we find that these product metric instantons, viewed as constrained instantons, do have a local minima in the action. These minima are then compared with the higher dimensional version of the Hawking-Turok instantons, and we argue that the latter always have lower action than those associated with these product metrics.Comment: 10 pages, 5 figure

A quantum mechanical approach to establishing the magnetic field orientation from a maser Zeeman profile

Recent comparisons of magnetic field directions derived from maser Zeeman splitting with those derived from continuum source rotation measures have prompted new analysis of the propagation of the Zeeman split components, and the inferred field orientation. In order to do this, we first review differing electric field polarization conventions used in past studies. With these clearly and consistently defined, we then show that for a given Zeeman splitting spectrum, the magnetic field direction is fully determined and predictable on theoretical grounds: when a magnetic field is oriented away from the observer, the left-hand circular polarization is observed at higher frequency and the right-hand polarization at lower frequency. This is consistent with classical Lorentzian derivations. The consequent interpretation of recent measurements then raises the possibility of a reversal between the large-scale field (traced by rotation measures) and the small-scale field (traced by maser Zeeman splitting).Comment: 10 pages, 5 Figures, accepted for publication in MNRA

Microlensing of Extended Stellar Sources

We investigate the feasibility of reconstructing the radial intensity profile of extended stellar sources by inverting their microlensed light curves. Using a simple, linear, limb darkening law as an illustration, we show that the intensity profile can be accurately determined, at least over the outer part of the stellar disc, with realistic light curve sampling and photometric errors. The principal requirement is that the impact parameter of the lens be less than or equal to the stellar radius. Thus, the analysis of microlensing events provides a powerful method for testing stellar atmosphere models.Comment: 4 pages LaTeX, to appear in New Astronomy Reviews - proceedings of the Oxford Workshop `Gravitational Lensing: Nature's Own Weighing Scales'. Uses elsart.cls. Paper also available at ftp://info.astro.gla.ac.uk/pub/martin/extended.p

Unified molecular field theory of nematic, smectic-A, and smectic-C phases

A unified mean-field molecular theory of nematic (NU), smectic A (SmA), and smectic C (SmC) liquid crystal phases, composed of uniaxial nonpolar molecules, is developed taking into account the variation of all orientational and translational order parameters in these phases. Numerical results, obtained by direct global minimization of the free energy, are presented in the form of three typical phase diagrams of different topology. Temperature variation of the relevant order parameters in different sequences of phases is analyzed for various cross sections of the phase diagrams. The present model enables one to reproduce all possible sequences of phase transitions between the given phases including isotropic (Iso)-NU-SmA-SmC, Iso-NU-SmC, Iso-SmA-SmC, and Iso-SmC. The properties of the NAC point, where the NU, SmA, and SmC structures coexist, are considered in detail and the shape of the phase diagram in the vicinity of the NAC point is compared with existing experimental data

AdS Strings with Torsion: Non-complex Heterotic Compactifications

Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a ten-dimensional approach to find a new class of four-dimensional supersymmetric AdS compactifications on almost-Hermitian manifolds of SU(3) structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly Kahler. We argue that all moduli are fixed, and we show that the Kahler potential and superpotential proposed in the literature yield the correct AdS radius. In the nearly Kahler case, we are able to solve the H Bianchi using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate.Comment: 42 pages; v2. added refs, revised discussion of Bianchi for N

Polarization morphology of SiO masers in the circumstellar envelope of the AGB star R Cassiopeiae

Silicon monoxide maser emission has been detected in the circumstellar envelopes of many evolved stars in various vibrationally-excited rotational transitions. It is considered a good tracer of the wind dynamics close to the photosphere of the star. We have investigated the polarization morphology in the circumstellar envelope of an AGB star, R Cas. We mapped the linear and circular polarization of SiO masers in the v=1, J=1-0 transition. The linear polarization is typically a few tens of percent while the circular polarization is a few percent. The fractional polarization tends to be higher for emission of lower total intensity. We found that, in some isolated features the fractional linear polarization appears to exceed 100%. We found the Faraday rotation is not negligible but is ~15 deg., which could produce small scale structure in polarized emission whilst total intensity is smoother and partly resolved out. The polarization angles vary considerably from feature to feature but there is a tendency to favour the directions parallel or perpendicular to the radial direction with respect to the star. In some features, the polarization angle abruptly flips 90 deg. We found that our data are in the regime where the model of Goldreich et al (1973) can be applied and the polarization angle flip is caused when the magnetic field is at close to 55 deg. to the line of sight. The polarization angle configuration is consistent with a radial magnetic field although other configurations are not excluded.Comment: 14 pages, 15 figures. Accepted for publication in MNRA

Fluid-Induced Propulsion of Rigid Particles in Wormlike Micellar Solutions

In the absence of inertia, a reciprocal swimmer achieves no net motion in a viscous Newtonian fluid. Here, we investigate the ability of a reciprocally actuated particle to translate through a complex fluid that possesses a network using tracking methods and birefringence imaging. A geometrically polar particle, a rod with a bead on one end, is reciprocally rotated using magnetic fields. The particle is immersed in a wormlike micellar (WLM) solution that is known to be susceptible to the formation of shear bands and other localized structures due to shear-induced remodeling of its microstructure. Results show that the nonlinearities present in this WLM solution break time-reversal symmetry under certain conditions, and enable propulsion of an artificial "swimmer." We find three regimes dependent on the Deborah number (De): net motion towards the bead-end of the particle at low De, net motion towards the rod-end of the particle at intermediate De, and no appreciable propulsion at high De. At low De, where the particle time-scale is longer then the fluid relaxation time, we believe that propulsion is caused by an imbalance in the fluid first normal stress differences between the two ends of the particle (bead and rod). At De~1, however, we observe the emergence of a region of network anisotropy near the rod using birefringence imaging. This anisotropy suggests alignment of the micellar network, which is "locked in" due to the shorter time-scale of the particle relative to the fluid

Strong latitudinal shear in the shallow convection zone of a rapidly rotating A-star

We have derived the mean broadening profile of the star V102 in the region of the open cluster IC4665 from high resolution spectroscopy. At a projected equatorial rotation velocity of vsini = (105 +- 12)km/s we find strong deviation from classical rotation. We discuss several scenarios, the most plausible being strong differential rotation in latitudinal direction. For this scenario we find a difference in angular velocity of DeltaOmega = 3.6 +- 0.8 rad/d (DeltaOmega/Omega = 0.42 +- 0.09). From the Halpha line we derive a spectral type of A9 and support photometric measurements classifying IC4665 V102 as a non-member of IC4665. At such early spectral type this is the strongest case of differential rotation observed so far. Together with three similar stars, IC4665 V102 seems to form a new class of objects that exhibit extreme latitudinal shear in a very shallow convective envelope.Comment: accepted for A&A Letter

Current flow in a plasma caused by dielectric breakdown

Spacecraft with a thin dielectric coating on the outer surface of the structure which are biased (-200 V) negative relative to the atmospheric plasma are susceptible to dielectric breakdown. This paper will present experimental tests designed to measure the electron current flow from the structure through the plasma during the arc. The current path was examined in three parts: the electrons supplied through the structure and the arc to the outer structure, the expansion of the arc into the ambient plasma, and the return current through the ambient plasma. The measured electron current either flowing from the plasma or supplied to the plasma by the arc in each case was compared to the random thermal electron current which could be collected. The results of the tests show a spacecraft is capable of supporting arcs with peak currents greater than thermal electron currents, and these currents will be dependent upon the amount of stored charge in the structure (i.e., the structure's surface area and dielectric thickness). Also, the results of these tests show that it is possible for structures with a self capacitance of 10 microFarads to see peak currents of 90 A and structures with 1000 microFarads (i.e., capacitance of one Space Station Freedom module) to produce peak currents of 1000 A

Conformally Einstein Products and Nearly K\"ahler Manifolds

In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 6--dimensional almost Hermitian manifolds of type W_1+W_4 in the Gray--Hervella classification admitting a parallel vector field and show that (under some regularity assumption) they are obtained as mapping tori of isometries of compact Sasaki-Einstein 5-dimensional manifolds. In particular, we obtain examples of inhomogeneous locally (non-globally) conformal nearly K\"ahler compact manifolds