2,545 research outputs found
Constructive spherical codes on layers of flat tori
A new class of spherical codes is constructed by selecting a finite subset of
flat tori from a foliation of the unit sphere S^{2L-1} of R^{2L} and designing
a structured codebook on each torus layer. The resulting spherical code can be
the image of a lattice restricted to a specific hyperbox in R^L in each layer.
Group structure and homogeneity, useful for efficient storage and decoding, are
inherited from the underlying lattice codebook. A systematic method for
constructing such codes are presented and, as an example, the Leech lattice is
used to construct a spherical code in R^{48}. Upper and lower bounds on the
performance, the asymptotic packing density and a method for decoding are
derived.Comment: 9 pages, 5 figures, submitted to IEEE Transactions on Information
Theor
Curves on torus layers and coding for continuous alphabet sources
In this paper we consider the problem of transmitting a continuous alphabet
discrete-time source over an AWGN channel. The design of good curves for this
purpose relies on geometrical properties of spherical codes and projections of
-dimensional lattices. We propose a constructive scheme based on a set of
curves on the surface of a 2N-dimensional sphere and present comparisons with
some previous works.Comment: 5 pages, 4 figures. Accepted for presentation at 2012 IEEE
International Symposium on Information Theory (ISIT). 2th version: typos
corrected. 3rd version: some typos corrected, a footnote added in Section III
B, a comment added in the beggining of Section V and Theorem I adde
Benchmark problems for continuum radiative transfer. High optical depths, anisotropic scattering, and polarisation
Solving the continuum radiative transfer equation in high opacity media
requires sophisticated numerical tools. In order to test the reliability of
such tools, we present a benchmark of radiative transfer codes in a 2D disc
configuration. We test the accuracy of seven independently developed radiative
transfer codes by comparing the temperature structures, spectral energy
distributions, scattered light images, and linear polarisation maps that each
model predicts for a variety of disc opacities and viewing angles. The test
cases have been chosen to be numerically challenging, with midplane optical
depths up 10^6, a sharp density transition at the inner edge and complex
scattering matrices. We also review recent progress in the implementation of
the Monte Carlo method that allow an efficient solution to these kinds of
problems and discuss the advantages and limitations of Monte Carlo codes
compared to those of discrete ordinate codes. For each of the test cases, the
predicted results from the radiative transfer codes are within good agreement.
The results indicate that these codes can be confidently used to interpret
present and future observations of protoplanetary discs.Comment: 15 pages, 10 figures, accepted for publication in A&
2-Dust : a Dust Radiative Transfer Code for an Axisymmetric System
We have developed a general purpose dust radiative transfer code for an
axisymmetric system, 2-Dust, motivated by the recent increasing availability of
high-resolution images of circumstellar dust shells at various wavelengths.
This code solves the equation of radiative transfer following the principle of
long characteristic in a 2-D polar grid while considering a 3-D radiation field
at each grid point. A solution is sought through an iterative scheme in which
self-consistency of the solution is achieved by requiring a global luminosity
constancy throughout the shell. The dust opacities are calculated through Mie
theory from the given size distribution and optical properties of the dust
grains. The main focus of the code is to obtain insights on (1) the global
energetics of dust grains in the shell (2) the 2-D projected morphologies that
are strongly dependent on the mixed effects of the axisymmetric dust
distribution and inclination angle of the shell. Here, test models are
presented with discussion of the results. The code can be supplied with a
user-defined density distribution function, and thus, is applicable to a
variety of dusty astronomical objects possessing the axisymmetric geometry.Comment: To be published in ApJ, April 2003 issue; 13 pages, 4 tables, 17
figures, 5-page appendix (no figures for the main text included in this
preprint). For the complete preprint and code distribution, contact the
author
Evolution of magnetized, differentially rotating neutron stars: Simulations in full general relativity
We study the effects of magnetic fields on the evolution of differentially
rotating neutron stars, which can form in stellar core collapse or binary
neutron star coalescence. Magnetic braking and the magnetorotational
instability (MRI) both redistribute angular momentum; the outcome of the
evolution depends on the star's mass and spin. Simulations are carried out in
axisymmetry using our recently developed codes which integrate the coupled
Einstein-Maxwell-MHD equations. For initial data, we consider three categories
of differentially rotating, equilibrium configurations, which we label normal,
hypermassive and ultraspinning. Hypermassive stars have rest masses exceeding
the mass limit for uniform rotation. Ultraspinning stars are not hypermassive,
but have angular momentum exceeding the maximum for uniform rotation at the
same rest mass. We show that a normal star will evolve to a uniformly rotating
equilibrium configuration. An ultraspinning star evolves to an equilibrium
state consisting of a nearly uniformly rotating central core, surrounded by a
differentially rotating torus with constant angular velocity along magnetic
field lines, so that differential rotation ceases to wind the magnetic field.
In addition, the final state is stable against the MRI, although it has
differential rotation. For a hypermassive neutron star, the MHD-driven angular
momentum transport leads to catastrophic collapse of the core. The resulting
rotating black hole is surrounded by a hot, massive, magnetized torus
undergoing quasistationary accretion, and a magnetic field collimated along the
spin axis--a promising candidate for the central engine of a short gamma-ray
burst. (Abridged)Comment: 27 pages, 30 figure
AZEuS: An Adaptive Zone Eulerian Scheme for Computational MHD
A new adaptive mesh refinement (AMR) version of the ZEUS-3D astrophysical
magnetohydrodynamical (MHD) fluid code, AZEuS, is described. The AMR module in
AZEuS has been completely adapted to the staggered mesh that characterises the
ZEUS family of codes, on which scalar quantities are zone-centred and vector
components are face-centred. In addition, for applications using static grids,
it is necessary to use higher-order interpolations for prolongation to minimise
the errors caused by waves crossing from a grid of one resolution to another.
Finally, solutions to test problems in 1-, 2-, and 3-dimensions in both
Cartesian and spherical coordinates are presented.Comment: 52 pages, 17 figures; Accepted for publication in ApJ
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