The discovery and dynamical evolution of an object at the outer edge of Saturn's A ring

This work was supported by the Science and Technology Facilities Council (Grant No. ST/F007566/1) and we are grateful to them for financial assistance. C.D.M. is also grateful to the Leverhulme Trust for the award of a Research Fellowshippublisher PDF not permitted, withdraw

On the General Analytical Solution of the Kinematic Cosserat Equations

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure

Killing spinors in supergravity with 4-fluxes

We study the spinorial Killing equation of supergravity involving a torsion 3-form \T as well as a flux 4-form \F. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We investigate the constraint \T \cdot \Psi = 0, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically

Stable bundles on hypercomplex surfaces

A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin's and Gualtieri's generalized complex geometry, (4,4)-manifolds are called ``generalized hyperkaehler manifolds''. We show that the moduli space of anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a (4,4)-structure.Comment: 17 pages. Version 3.0: reference adde

Classification of Generalized Symmetries for the Vacuum Einstein Equations

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. To begin, we analyze symmetries that can be built from the metric, curvature, and covariant derivatives of the curvature to any order; these are called natural symmetries and are globally defined on any spacetime manifold. We next classify first-order generalized symmetries, that is, symmetries that depend on the metric and its first derivatives. Finally, using results from the classification of natural symmetries, we reduce the classification of all higher-order generalized symmetries to the first-order case. In each case we find that the generalized symmetries are infinitesimal generalized diffeomorphisms and constant metric scalings. There are no non-trivial conservation laws associated with these symmetries. A novel feature of our analysis is the use of a fundamental set of spinorial coordinates on the infinite jet space of Ricci-flat metrics, which are derived from Penrose's ``exact set of fields'' for the vacuum equations.Comment: 57 pages, plain Te

Thin film coatings which inhibit spin relaxation of polarized potassium atoms

A prototype of a polarized deuterium target which employs the spin exchange method is being developed. The mixing cell for mixing deuterium atoms and potassium vapor requires a surface that will reflect these atoms without being destroyed by the corrosive potassium. Thin film coating methods and a technique for coating pyrex are described. Results of spin relaxation measurements are given. (LEW

Formulation, Casting, and Evaluation of Paraffin-Based Solid Fuels Containing Energetic and Novel Additives for Hybrid Rockets

This investigation studied the inclusion of various additives to paraffin wax for use in a hybrid rocket motor. Some of the paraffin-based fuels were doped with various percentages of LiAlH4 (up to 10%). Addition of LiAlH4 at 10% was found to increase regression rates between 7 - 10% over baseline paraffin through tests in a gaseous oxygen hybrid rocket motor. Mass burn rates for paraffin grains with 10% LiAlH4 were also higher than those of the baseline paraffin. RDX was also cast into a paraffin sample via a novel casting process which involved dissolving RDX into dimethylformamide (DMF) solvent and then drawing a vacuum on the mixture of paraffin and RDX/DMF in order to evaporate out the DMF. It was found that although all DMF was removed, the process was not conducive to generating small RDX particles. The slow boiling generated an inhomogeneous mixture of paraffin and RDX. It is likely that superheating the DMF to cause rapid boiling would likely reduce RDX particle sizes. In addition to paraffin/LiAlH4 grains, multi-walled carbon nanotubes (MWNT) were cast in paraffin for testing in a hybrid rocket motor, and assorted samples containing a range of MWNT percentages in paraffin were imaged using SEM. The fuel samples showed good distribution of MWNT in the paraffin matrix, but the MWNT were often agglomerated, indicating that a change to the sonication and mixing processes were required to achieve better uniformity and debundled MWNT. Fuel grains with MWNT fuel grains had slightly lower regression rate, likely due to the increased thermal conductivity to the fuel subsurface, reducing the burning surface temperature

A Measurement of Time-Averaged Aerosol Optical Depth using Air-Showers Observed in Stereo by HiRes

Air fluorescence measurements of cosmic ray energy must be corrected for attenuation of the atmosphere. In this paper we show that the air-showers themselves can yield a measurement of the aerosol attenuation in terms of optical depth, time-averaged over extended periods. Although the technique lacks statistical power to make the critical hourly measurements that only specialized active instruments can achieve, we note the technique does not depend on absolute calibration of the detector hardware, and requires no additional equipment beyond the fluorescence detectors that observe the air showers. This paper describes the technique, and presents results based on analysis of 1258 air-showers observed in stereo by the High Resolution Fly's Eye over a four year span.Comment: 7 pages, 3 figures, accepted for publication by Astroparticle Physics Journa

Exploring Curved Superspace

We systematically analyze Riemannian manifolds M that admit rigid supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R symmetry. We find that M admits a single supercharge, if and only if it is a Hermitian manifold. The supercharge transforms as a scalar on M. We then consider the restrictions imposed by the presence of additional supercharges. Two supercharges of opposite R-charge exist on certain fibrations of a two-torus over a Riemann surface. Upon dimensional reduction, these give rise to an interesting class of supersymmetric geometries in three dimensions. We further show that compact manifolds admitting two supercharges of equal R-charge must be hyperhermitian. Finally, four supercharges imply that M is locally isometric to M_3 x R, where M_3 is a maximally symmetric space.Comment: 39 pages; minor change