A Complete Sample of Megaparsec Size Double Radio Sources from SUMSS

We present a complete sample of megaparsec-size double radio sources compiled from the Sydney University Molonglo Sky Survey (SUMSS). Almost complete redshift information has been obtained for the sample. The sample has the following defining criteria: Galactic latitude |b| > 12.5 deg, declination < -50 deg and angular size > 5 arcmin. All the sources have projected linear size larger than 0.7 Mpc (assuming H_o = 71 km/s/Mpc). The sample is chosen from a region of the sky covering 2100 square degrees. In this paper, we present 843-MHz radio images of the extended radio morphologies made using the Molonglo Observatory Synthesis Telescope (MOST), higher resolution radio observations of any compact radio structures using the Australia Telescope Compact Array (ATCA), and low resolution optical spectra of the host galaxies from the 2.3-m Australian National University (ANU) telescope at Siding Spring Observatory. The sample presented here is the first in the southern hemisphere and significantly enhances the database of known giant radio sources. The giant radio sources with linear size exceeding 0.7 Mpc have an abundance of (215 Mpc)^(-3) at the sensitivity of the survey. In the low redshift universe, the survey may be suggesting the possibility that giant radio sources with relict lobes are more numerous than giant sources in which beams from the centre currently energize the lobes.Comment: 67 pages, 29 figures, for full resolution figures see http://www.astrop.physics.usyd.edu.au/SUMSS/PAPERS/Submit-May11-ms.pd

Variational water-wave model with accurate dispersion and vertical vorticity

A new water-wave model has been derived which is based on variational techniques and combines a depth-averaged vertical (component of) vorticity with depth-dependent potential flow. The model facilitates the further restriction of the vertical profile of the velocity potential to n-th order polynomials or a finite-element profile with a small number of elements (say), leading to a framework for efficient modeling of the interaction of steepening and breaking waves near the shore with a large-scale horizontal flow. The equations are derived from a constrained variational formulation which leads to conservation laws for energy, mass, momentum and vertical vorticity. It is shown that the potential-flow water-wave equations and the shallow-water equations are recovered in the relevant limits. Approximate shock relations are provided, which can be used in numerical schemes to model breaking waves

On the rate of convergence of the Hamiltonian particle-mesh method

The Hamiltonian Particle-Mesh (HPM) method is a particle-in-cell method for compressible fluid flow with Hamiltonian structure. We present a numer- ical short-time study of the rate of convergence of HPM in terms of its three main governing parameters. We find that the rate of convergence is much better than the best available theoretical estimates. Our results indicate that HPM performs best when the number of particles is on the order of the number of grid cells, the HPM global smoothing kernel has fast decay in Fourier space, and the HPM local interpolation kernel is a cubic spline

Multi-path interferometry using single photons

In most experiments which search for violations of Born's rule using light the diffractive elements are formed from material slits, or waveguides, which are treated classically. In this article we propose an alternative approach where the internal energy levels of particles are used instead of slits to test the superposition principle, thus removing the effect of the finite width of the slits. By quantising both the light field and the diffraction elements we propose a new way to probe Born's rule for light in a fully quantum mechanical way

Un-reduction

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.Comment: 25 pages, revised versio

Comparing placentas from normal and abnormal pregnancies

This report describes work carried out at a Mathematics-in-Medicine Study Group. It is believed that placenta shape villous network characteristics are strongly linked to the placenta’s efficiency, and hence to pregnancy outcome. We were asked to consider mathematical ways to describe the shape and other characteristics of a placenta, as well as forming mathematical models for placenta development. In this report we propose a number of possible measure of placental shape, form, and efficiency, which can be computed from images already obtained. We also consider various models for the early development of placentas and the growth of the villous tree

The Lifetime of FRIIs in Groups and Clusters: Implications for Radio-Mode Feedback

We determine the maximum lifetime t_max of 52 FRII radio sources found in 26 central group galaxies from cross correlation of the Berlind SDSS group catalog with the VLA FIRST survey. Mock catalogs of FRII sources were produced to match the selection criteria of FIRST and the redshift distribution of our parent sample, while an analytical model was used to calculate source sizes and luminosities. The maximum lifetime of FRII sources was then determined via a comparison of the observed and model projected length distributions. We estimate the average FRII lifetime is 1.5x10^7 years and the duty cycle is ~8x10^8 years. Degeneracies between t_max and the model parameters: jet power distribution, axial ratio, energy injection index, and ambient density introduce at most a factor of two uncertainty in our lifetime estimate. In addition, we calculate the radio active galactic nuclei (AGN) fraction in central group galaxies as a function of several group and host galaxy properties. The lifetime of radio sources recorded here is consistent with the quasar lifetime, even though these FRIIs have substantially sub-Eddington accretion. These results suggest a fiducial time frame for energy injection from AGN in feedback models. If the morphology of a given extended radio source is set by large-scale environment, while the lifetime is determined by the details of the accretion physics, this FRII lifetime is relevant for all extended radio sources.Comment: 18 pages, 7 figures. Accepted for publication in ApJ. High resolution paper available at http://www.astronomy.ohio-state.edu/~bird/BMK07.pd

Multiwavelength Observations of the Second Largest Known FR II Radio Galaxy, NVSS 2146+82

We present multi-frequency VLA, multicolor CCD imaging, optical spectroscopy, and ROSAT HRI observations of the giant FR II radio galaxy NVSS 2146+82. This galaxy, which was discovered by the NRAO VLA Sky Survey (NVSS), has an angular extent of nearly 20' from lobe to lobe. The radio structure is normal for an FR II source except for its large size and regions in the lobes with unusually flat radio spectra. Our spectroscopy indicates that the optical counterpart of the radio core is at a redshift of z=0.145, so the linear size of the radio structure is ~4 h_50^-1 Mpc. This object is therefore the second largest FR II known (3C 236 is ~6 h_50^-1 Mpc). Optical imaging of the field surrounding the host galaxy reveals an excess number of candidate galaxy cluster members above the number typically found in the field surrounding a giant radio galaxy. WIYN HYDRA spectra of a sample of the candidate cluster members reveal that six share the same redshift as NVSS 2146+82, indicating the presence of at least a ``rich group'' containing the FR II host galaxy. ROSAT HRI observations of NVSS 2146+82 place upper limits on the X-ray flux of 1.33 x 10^-13 ergs cm^-2 s^-1 for any hot IGM and 3.52 x 10^-14 ergs cm^-2 s^-1 for an X-ray AGN, thereby limiting any X-ray emission at the distance of the radio galaxy to that typical of a poor group or weak AGN. Several other giant radio galaxies have been found in regions with overdensities of nearby galaxies, and a separate study has shown that groups containing FR IIs are underluminous in X-rays compared to groups without radio sources. We speculate that the presence of the host galaxy in an optically rich group of galaxies that is underluminous in X-rays may be related to the giant radio galaxy phenomenon.Comment: 46 pages, 15 figures, AASTeX aaspp4 style, accepted for publication in A

Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies

Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page