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

Microwave observations of spinning dust emission in NGC6946

We report new cm-wave measurements at five frequencies between 15 and 18GHz of the continuum emission from the reportedly anomalous "region 4" of the nearby galaxy NGC6946. We find that the emission in this frequency range is significantly in excess of that measured at 8.5GHz, but has a spectrum from 15-18GHz consistent with optically thin free-free emission from a compact HII region. In combination with previously published data we fit four emission models containing different continuum components using the Bayesian spectrum analysis package radiospec. These fits show that, in combination with data at other frequencies, a model with a spinning dust component is slightly preferred to those that possess better-established emission mechanisms.Comment: submitted MNRA