Newtonian and Relativistic Cosmologies

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed, which allows for such nonlinearity at small scales. We propose a relatively straightforward "dictionary"---which is exact at the linearized level---that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our "ordering scheme" to determine the degree to which the resulting metric and matter distribution solve Einstein's equation. We find that Einstein's equation fails to hold at "order 1" at small scales and at "order $\epsilon$" at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein's equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.Comment: 35 pages; minor change

Morse matchings on polytopes

We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works. This involves constructing explicit complete acyclic Morse matchings on the face lattice of the half cube; this procedure may be of independent interest for other highly symmetric polytopes

Deconvolution and analysis of wide-angle longwave radiation data from Nimbus 6 Earth radiation budget experiment for the first year

One year of longwave radiation data from July 1975 through June 1976 from the Nimbus 6 satellite Earth radiation budget experiment is analyzed by representing the radiation field by a spherical harmonic expansion. The data are from the wide field of view instrument. Contour maps of the longwave radiation field and spherical harmonic coefficients to degree 12 and order 12 are presented for a 12 month data period

In-work poverty in the East Midlands

Research that explores the nature and scale of in-work poverty in the East Midlands, using several established measures

A strong 3.4 micron emission feature in comet Austin 1989c1

High resolution 2.8-4.0 micron spectra of the 'new' comet Austin 1989c1, taken on 15-16 May 1990 confirm the presence of the broad emission features around 3.4 and 3.52 micron seen in a number of bright comets and ascribed to organic material. Both the 3.4 micron band strength and the 3.52/3.36 micron flux ratios are among the largest so far observed. The data are consistent with the relationship between band strength and water production rate that was recently derived. Excess emission at 3.28 and 3.6 micron cannot be unambiguously identified as features due to the poor signal-to-noise ratio

A digitalized solar ultraviolet spectrum

Digitalized solar ultraviolet spectrum obtained in rocket experiments for use in analysis of upper atmosphere experiment

The Molonglo Galactic Plane Survey (MGPS-2): Compact Source Catalogue

We present the first data release from the second epoch Molonglo Galactic Plane Survey (MGPS-2). MGPS-2 was carried out with the Molonglo Observatory Synthesis Telescope at a frequency of 843 MHz and with a restoring beam of 45 arcsec x 45 arcsec cosec(dec), making it the highest resolution large scale radio survey of the southern Galactic plane. It covers the range |b| < 10 deg and 245 deg < l < 365 deg and is the Galactic counterpart to the Sydney University Molonglo Sky Survey (SUMSS) which covers the whole southern sky with dec 10 deg). In this paper we present the MGPS-2 compact source catalogue. The catalogue has 48,850 sources above a limiting peak brightness of 10 mJy/beam. Positions in the catalogue are accurate to 1 arcsec - 2 arcsec. A full catalogue including extended sources is in preparation. We have carried out an analysis of the compact source density across the Galactic plane and find that the source density is not statistically higher than the density expected from the extragalactic source density alone. We also present version 2.0 of the SUMSS image data and catalogue which are now available online. The data consists of 629 4.3 deg x 4.3 deg mosaic images covering the 8100 deg^2 of sky with dec 10 deg. The catalogue contains 210,412 radio sources to a limiting peak brightness of 6 mJy/beam at dec -50 deg. We describe the updates and improvements made to the SUMSS cataloguing process.Comment: 12 pages, 9 figures, to be published in MNRAS Note that Figures 8 and 9 are much lower resolution than in the published versio

The Sun's position in the sky

We express the position of the Sun in the sky as a function of time and the observer's geographic coordinates. Our method is based on applying rotation matrices to vectors describing points on the celestial sphere. We also derive direct expressions, as functions of date of the year and geographic latitude, for the duration of daylight, the maximum and minimum altitudes of the Sun, and the cardinal directions to sunrise and sunset. We discuss how to account for the eccentricity of the earth's orbit, the precessions of the equinoxes and the perihelion, the size of the solar disk, and atmospheric refraction. We illustrate these results by computing the dates of "Manhattanhenge" (when sunset aligns with the east-west streets on the main traffic grid for Manhattan, in New York City), by plotting the altitude of the Sun over representative cities as a function of time, and by showing plots ("analemmas") for the position of the Sun in the sky at a given hour of the day.Comment: 19 pages, 16 figures. v3: Replaced to match published version and to re-package Mathematica notebook as an ancillary fil

Four-quark flux distribution and binding in lattice SU(2)

The full spatial distribution of the color fields of two and four static quarks is measured in lattice SU(2) field theory at separations up to 1 fm at beta=2.4. The four-quark case is equivalent to a qbar q qbar q system in SU(2) and is relevant to meson-meson interactions. By subtracting two-body flux tubes from the four-quark distribution we isolate the flux contribution connected with the four-body binding energy. This contribution is further studied using a model for the binding energies. Lattice sum rules for two and four quarks are used to verify the results.Comment: 46 pages including 71 eps figures. 3D color figures are available at www.physics.helsinki.fi/~ppennane/pics