5,646 research outputs found
Weyl calculus and dual pairs
We consider a dual pair , in the sense of Howe, with compact
acting on for an appropriate via the Weil
Representation. Let be the preimage of in the metaplectic
group. Given a genuine irreducible unitary representation of
we compute the Weyl symbol of orthogonal projection onto
, the -isotypic component. We apply the result to
obtain an explicit formula for the character of the corresponding irreducible
unitary representation of and to compute of the wave
front set of 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 . As an
intermediate step, we introduce a notion of a Cartan subspace and a notion of
an almost semisimple element in the symplectic space . We prove that the
almost semisimple elements are dense in . Finally, we provide estimates for
the orbital integrals associated with the different Cartan subspaces in
Symmetry breaking operators for dual pairs with one member compact
We consider a dual pair , in the sense of Howe, with G compact
acting on , for an appropriate , via the Weil
representation . Let be the preimage of G in the
metaplectic group. Given a genuine irreducible unitary representation of
, let be the corresponding irreducible unitary
representation of in the Howe duality. The orthogonal
projection onto , the -isotypic component, is the
essentially unique symmetry breaking operator in
. We study this
operator by computing its Weyl symbol. Our results allow us to recover the
known list of highest weights of irreducible representations of
occurring in Howe's correspondence when the rank of
is strictly bigger than the rank of .
They also allow us to compute the wavefront set of by elementary means.Comment: 94 pages. The present paper subsumes and extends sections 2,3,4 and 6
of the (unpublished) preprint arXiv:1405.243
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 be
the preimage of G in the metaplectic group
. Given an irreducible unitary
representation of that occurs in the restriction
of the Weil representation to , let denote
its character. We prove that, for the embedding of
in the space of tempered distributions on
W given by the Weil representation, the distribution has
an asymptotic limit. This limit is an orbital integral over a nilpotent orbit
. The closure of the image of
in under the moment map is the wave front set of , the
representation of dual to .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
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