6,173 research outputs found
Shape maps for second order partial differential equations
We analyse the singularity formation of congruences of solutions of systems
of second order PDEs via the construction of \emph{shape maps}. The trace of
such maps represents a congruence volume whose collapse we study through an
appropriate evolution equation, akin to Raychaudhuri's equation. We develop the
necessary geometric framework on a suitable jet space in which the shape maps
appear naturally associated with certain linear connections. Explicit
computations are given, along with a nontrivial example
Tangent bundle geometry induced by second order partial differential equations
We show how the tangent bundle decomposition generated by a system of
ordinary differential equations may be generalized to the case of a system of
second order PDEs `of connection type'. Whereas for ODEs the decomposition is
intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold
of independent variables, together with a transverse local vector field. The
resulting decomposition provides several natural curvature operators. The
harmonic map equation is examined, and in this case both the 1-form and the
vector field arise naturally
The Power Spectrum of the PSC Redshift Survey
We measure the redshift-space power spectrum P(k) for the recently completed
IRAS Point Source Catalogue (PSC) redshift survey, which contains 14500
galaxies over 84% of the sky with 60 micron flux >= 0.6 Jansky. Comparison with
simulations shows that our estimated errors on P(k) are realistic, and that
systematic errors due to the finite survey volume are small for wavenumbers k
>~ 0.03 h Mpc^-1. At large scales our power spectrum is intermediate between
those of the earlier QDOT and 1.2 Jansky surveys, but with considerably smaller
error bars; it falls slightly more steeply to smaller scales. We have fitted
families of CDM-like models using the Peacock-Dodds formula for non-linear
evolution; the results are somewhat sensitive to the assumed small-scale
velocity dispersion \sigma_V. Assuming a realistic \sigma_V \approx 300 km/s
yields a shape parameter \Gamma ~ 0.25 and normalisation b \sigma_8 ~ 0.75; if
\sigma_V is as high as 600 km/s then \Gamma = 0.5 is only marginally excluded.
There is little evidence for any `preferred scale' in the power spectrum or
non-Gaussian behaviour in the distribution of large-scale power.Comment: Latex, uses mn.sty, 14 pages including 11 Postscript figures.
Accepted by MNRA
High-speed noise-free optical quantum memory
Quantum networks promise to revolutionise computing, simulation, and
communication. Light is the ideal information carrier for quantum networks, as
its properties are not degraded by noise in ambient conditions, and it can
support large bandwidths enabling fast operations and a large information
capacity. Quantum memories, devices that store, manipulate, and release on
demand quantum light, have been identified as critical components of photonic
quantum networks, because they facilitate scalability. However, any noise
introduced by the memory can render the device classical by destroying the
quantum character of the light. Here we introduce an intrinsically noise-free
memory protocol based on two-photon off-resonant cascaded absorption (ORCA). We
consequently demonstrate for the first time successful storage of GHz-bandwidth
heralded single photons in a warm atomic vapour with no added noise; confirmed
by the unaltered photon statistics upon recall. Our ORCA memory platform meets
the stringent noise-requirements for quantum memories whilst offering technical
simplicity and high-speed operation, and therefore is immediately applicable to
low-latency quantum networks
Spacetime locality in Sp(2) symmetric lagrangian formalism
The existence of a local solution to the Sp(2) master equation for gauge
field theory is proven in the framework of perturbation theory and under
standard assumptions on regularity of the action. The arbitrariness of
solutions to the Sp(2) master equation is described, provided that they are
proper. It is also shown that the effective action can be chosen to be Sp(2)
and Lorentz invariant (under the additional assumption that the gauge
transformation generators are Lorentz tensors).Comment: LaTeX, 13 pages, minor misprints correcte
High resolution mid-infrared spectroscopy of ultraluminous infrared galaxies
(Abridged) We present R~600, 10-37um spectra of 53 ULIRGs at z<0.32, taken
using the IRS on board Spitzer. All of the spectra show fine structure emission
lines of Ne, O, S, Si and Ar, as well as molecular Hydrogen lines. Some ULIRGs
also show emission lines of Cl, Fe, P, and atomic Hydrogen, and/or absorption
features from C_2H_2, HCN, and OH. We employ diagnostics based on the
fine-structure lines, as well as the EWs and luminosities of PAH features and
the strength of the 9.7um silicate absorption feature (S_sil), to explore the
power source behind the infrared emission in ULIRGs. We show that the IR
emission from the majority of ULIRGs is powered mostly by star formation, with
only ~20% of ULIRGs hosting an AGN with a comparable or greater IR luminosity
than the starburst. The detection of the 14.32um [NeV] line in just under half
the sample however implies that an AGN contributes significantly to the mid-IR
flux in ~42% of ULIRGs. The emission line ratios, luminosities and PAH EWs are
consistent with the starbursts and AGN in ULIRGs being more extincted, and for
the starbursts more compact, versions of those in lower luminosity systems. The
excitations and electron densities in the NLRs of ULIRGs appear comparable to
those of lower luminosity starbursts, though there is evidence that the NLR gas
in ULIRGs is more dense. We show that the combined luminosity of the 12.81um
[NeII] and 15.56um [NeIII] lines correlates with both IR luminosity and the
luminosity of the 6.2 micron and 11.2 micron PAH features in ULIRGs, and use
this to derive a calibration between PAH luminosity and star formation rate.
Finally, we show that ULIRGs with 0.8 < S_sil < 2.4 are likely to be powered
mainly by star formation, but that ULIRGs with S_sil < 0.8, and possibly those
with S_sil > 2.4, contain an IR-luminous AGN.Comment: 62 pages in preprint format, 4 tables, 23 figures. ApJ accepte
Locally Biased Galaxy Formation and Large Scale Structure
We examine the influence of the morphology-density(MD) relation and a wide
range of simple models for biased galaxy formation on statistical measures of
large scale structure. We contrast the behavior of local biasing models, in
which the efficiency of galaxy formation is determined by density, geometry, or
velocity dispersion of the local mass distribution, with that of non-local
biasing models, in which galaxy formation is modulated coherently over scales
larger than the galaxy correlation length. If morphological segregation of
galaxies is governed by a local MD relation, then the correlation function of
E/S0 galaxies should be steeper and stronger than that of spiral galaxies on
small scales, as observed, while on large scales the correlation functions of
E/S0 and spiral galaxies should have the same shape but different amplitudes.
Similarly, all of our local bias models produce scale-independent amplification
of the correlation function and power spectrum in the linear and mildly
non-linear regimes; only a non-local biasing mechanism can alter the shape of
the power spectrum on large scales. Moments of the biased galaxy distribution
retain the hierarchical pattern of the mass moments, but biasing alters the
values and scale-dependence of the hierarchical amplitudes S3 and S4.
Pair-weighted moments of the galaxy velocity distribution are sensitive to the
details of the biasing prescription. The non-linearity of the relation between
galaxy density and mass density depends on the biasing prescription and the
smoothing scale, and the scatter in this relation is a useful diagnostic of the
physical parameters that determine the bias. Although the sensitivity of galaxy
clustering statistics to the details of biasing is an obstacle to testing
cosmological models, it is an asset for testing galaxy formation theories.Comment: 47 pages including 17 Figures, submitted to Ap
The difference that tenure makes
This paper argues that housing tenures cannot be reduced to either production relations or consumption relations. Instead, they need to be understood as modes of housing distribution, and as having complex and dynamic relations with social classes. Building on a critique of both the productionist and the consumptionist literature, as well as of formalist accounts of the relations between tenure and class, the paper attempts to lay the foundations for a new theory of housing tenure. In order to do this, a new theory of class is articulated, which is then used to throw new light on the nature of class-tenure relations
The Science Case for PILOT I: Summary and Overview
Original article can be found at: http://www.publish.csiro.au/?nid=139&aid=108 DOI: 10.1071/AS08048 [Open access article]PILOT (the Pathfinder for an International Large Optical Telescope) is a proposed 2.5-m optical/infrared telescope to be located at Dome C on the Antarctic plateau. Conditions at Dome C are known to be exceptional for astronomy. The seeing (above ∼30 m height), coherence time, and isoplanatic angle are all twice as good as at typical mid-latitude sites, while the water-vapour column, and the atmosphere and telescope thermal emission are all an order of magnitude better. These conditions enable a unique scientific capability for PILOT, which is addressed in this series of papers. The current paper presents an overview of the optical and instrumentation suite for PILOT and its expected performance, a summary of the key science goals and observational approach for the facility, a discussion of the synergies between the science goals for PILOT and other telescopes, and a discussion of the future of Antarctic astronomy. Paper II and Paper III present details of the science projects divided, respectively, between the distant Universe (i.e. studies of first light, and the assembly and evolution of structure) and the nearby Universe (i.e. studies of Local Group galaxies, the Milky Way, and the Solar System).Peer reviewe
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