Weyl calculus and dual pairs

We consider a dual pair $(G,G')$, in the sense of Howe, with $G$ compact acting on $L^2(\mathbb R^n)$ for an appropriate $n$ via the Weil Representation. Let $\widetilde{G}$ be the preimage of $G$ in the metaplectic group. Given a genuine irreducible unitary representation $\Pi$ of $\widetilde{G}$ we compute the Weyl symbol of orthogonal projection onto $L^2(\mathbb R^n)_\Pi$, the $\Pi$-isotypic component. We apply the result to obtain an explicit formula for the character of the corresponding irreducible unitary representation $\Pi'$ of $\widetilde{G'}$ and to compute of the wave front set of $\Pi'$ by elementary means

Semisimple orbital integrals on the symplectic space for a real reductive dual pair

We prove a Weyl Harish-Chandra integration formula for the action of a reductive dual pair on the corresponding symplectic space $W$. As an intermediate step, we introduce a notion of a Cartan subspace and a notion of an almost semisimple element in the symplectic space $W$. We prove that the almost semisimple elements are dense in $W$. Finally, we provide estimates for the orbital integrals associated with the different Cartan subspaces in $W$

The wave front set correspondence for dual pairs with one member compact

Let W be a real symplectic space and (G,G') an irreducible dual pair in Sp(W), in the sense of Howe, with G compact. Let $\widetilde{\mathrm{G}}$ be the preimage of G in the metaplectic group $\widetilde{\mathrm{Sp}}(\mathrm{W})$. Given an irreducible unitary representation $\Pi$ of $\widetilde{\mathrm{G}}$ that occurs in the restriction of the Weil representation to $\widetilde{\mathrm{G}}$, let $\Theta_\Pi$ denote its character. We prove that, for the embedding $T$ of $\widetilde{\mathrm{Sp}}(\mathrm{W})$ in the space of tempered distributions on W given by the Weil representation, the distribution $T(\check\Theta_\Pi)$ has an asymptotic limit. This limit is an orbital integral over a nilpotent orbit $\mathcal O_m\subseteq \mathrm{W}$. The closure of the image of $\mathcal O_m$ in $\mathfrak{g}'$ under the moment map is the wave front set of $\Pi'$, the representation of $\widetilde{\mathrm{G}'}$ dual to $\Pi$.Comment: arXiv admin note: substantial text overlap with arXiv:1405.243

Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: I. Turbulence Statistics

Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256^3 and 512^3 simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li, McKee, & Klein (2006). Our calculations are based on the assumption that the number of ions is conserved, but we show that these results approximately apply to the case of time-dependent ionization in molecular clouds as well. Convergence studies allow us to determine the optimal value of the ionization mass fraction when using the heavy-ion approximation for low Mach number, sub-Alfvenic turbulent systems. We find that ambipolar diffusion steepens the velocity and magnetic power spectra compared to the ideal MHD case. Changes in the density PDF, total magnetic energy, and ionization fraction are determined as a function of the AD Reynolds number. The power spectra for the neutral gas properties of a strongly magnetized medium with a low AD Reynolds number are similar to those for a weakly magnetized medium; in particular, the power spectrum of the neutral velocity is close to that for Burgers turbulence.Comment: 37 pages, 11 figures, 4 table

Self-organising management of Grid environments

This paper presents basic concepts, architectural principles and algorithms for efficient resource and security management in cluster computing environments and the Grid. The work presented in this paper is funded by BTExacT and the EPSRC project SO-GRM (GR/S21939)

A Methodology for Public-Planner Interaction in Multiobjective Project Planning and Evaluation

A review of current multiple objective planning techniques is presented. A critique of certain classes of these techniques is offered, especially in terms of the degree to which they facilitate certain information needs of the planning process. Various tools in operations research are used to constructed a new multiple objective planning methodology, called the Vector Optimization Decision Convergence Algorithm (VODCA). An application of the methodology pertaining to water resources development in Utah is documented

A Profile of Pornography Users in Australia: Findings From the Second Australian Study of Health and Relationships

Copyright © The Society for the Scientific Study of Sexuality. There are societal concerns that looking at pornography has adverse consequences among those exposed. However, looking at sexually explicit material could have educative and relationship benefits. This article identifies factors associated with looking at pornography ever or within the past 12 months for men and women in Australia, and the extent to which reporting an “addiction” to pornography is associated with reported bad effects. Data from the Second Australian Study of Health and Relationships (ASHR2) were used: computer-assisted telephone interviews (CASIs) completed by a representative sample of 9,963 men and 10,131 women aged 16 to 69 years from all Australian states and territories, with an overall participation rate of 66%. Most men (84%) and half of the women (54%) had ever looked at pornographic material. Three-quarters of these men (76%) and more than one-third of these women (41%) had looked at pornographic material in the past year. Very few respondents reported that they were addicted to pornography (men 4%, women 1%), and of those who said they were addicted about half also reported that using pornography had had a bad effect on them. Looking at pornographic material appears to be reasonably common in Australia, with adverse effects reported by a small minority

An upper limit on the X-ray luminosity of the black hole - microlens OGLE-1999-BUL-32

We present an upper limit on the 3--20 keV X-ray flux from the black hole - microlens OGLE-1999-BUL-32, based on RXTE/PCA scans over the Galactic Center region in 1999-2000. It is shown that the X-ray luminosity of the black hole did not exceed L(3-20 keV)<3e33(d/1kpc)^2 ergs/s (where d is the distance to the black hole). Near the maximum of the background star amplification by the microlens (July 6, 1999), the upper limit on the X-ray flux corresponds to an X-ray luminosity L(3-20 keV)<7e33(d/1kpc)^2 ergs/s.Comment: 4 pages, 3 figures. Accepted for publication in Astronomy Letter

The Circumstellar Environment of High Mass Protostellar Objects. III Evidence of Infall?

The results are presented of a molecular line survey to search for the spectral signature of infall towards 77 850 micron continuum sources believed to be candidate high mass protostellar objects. Up to six different transitions, HCO+ 1-0, 3-2 and 4-3, H2CO 2_12-1_11, N2H+ and H13CO+ 3-2, were observed towards each source. Towards the peak of the 850 micron emission, N2H+ was typically strong, with a peak antenna temperature of ~1.5K, with a typical linewidth of ~2km/s. The good agreement between the velocity and velocity width of the N2H+ and H13CO+ emission suggests that both species are tracing similar material in the sources. With respect to the velocity of the N2H+, there is a statistically significant excess of blue asymmetric line profiles in both the HCO+ 1-0 and H2CO transitions. This excess reaches levels similar to that seen towards samples of low mass protostars, and suggests that the material around these high mass sources is infalling. We identify 22 promising candidate infall sources which show at least one blue asymmetric line profile and no red asymmetric profiles. The infall velocity is estimated to be in the range of 0.1 km/s to 1 km/s with an implied mass accretion rate of between 2x10^{-4} Msol/yr and 10^{-3}Msol/yr.Comment: Accepted for publication in Astronomy and Astrophysics. Higher resolution versions of Figures 1 and 2 are available from http://www.jb.man.ac.uk/~gaf/Papers.htm

The Influence of a Biologically Relevant Substratum Topography on Human Aortic and Umbilical Vein Endothelial Cells

AbstractA topographically patterned substrate with stochastic surface order that closely mimics the topographic features of native basement membranes has been fabricated to investigate the influence of topographic biophysical cueing on human aortic and umbilical vein endothelial cells. The stochastic substrate was fabricated by first generating a highly porous polyelectrolyte multilayer film of poly(acrylic acid) and poly(allylamine hydrochloride) followed by replicate production of this biomimetic topography via soft lithography. These substrates, which are easy to prepare and replicate, possess a number of prominent features associated with in vivo vascular basement membrane (interwoven ridges and grooves, bumps, and pores), which have typically been studied as singular features that frequently possess anisotropic surface order (e.g., alternating ridges and grooves). When compared to a flat surface of identical chemistry, these biomimetic topographies influenced a number of important cellular behaviors associated with the homeostasis and degradation of vascular tissues. These include modulating cell migration rate and directional persistence, proliferation rate, and gene expression associated with regulation and remodeling of vascular tissues as well as inflammation