829 research outputs found
Spherically symmetric static solution for colliding null dust
The Einstein equations are integrated in the presence of two (incoming and
outgoing) streams of null dust, under the assumptions of spherical symmetry and
staticity. The solution is also written in double null and radiation
coordinates and it is reinterpreted as an anisotropic fluid. Interior matching
with a static fluid and exterior matching with the Vaidya solution along null
hypersurfaces is discussed. The connection with two-dimensional dilaton gravity
is established.Comment: 12 pages, 7 figures, to appear in Phys. Rev.
Regularizing made-to-measure particle models of galaxies
Made-to-measure methods such as the parallel code NMAGIC are powerful tools
to build galaxy models reproducing observational data. They work by adapting
the particle weights in an N-body system until the target observables are well
matched. Here we introduce a moving prior regularization (MPR) method for such
particle models. It is based on determining from the particles a distribution
of priors in phase-space, which are updated in parallel with the weight
adaptation. This method allows one to construct smooth models from noisy data
without erasing global phase-space gradients. We first apply MPR to a spherical
system for which the distribution function can in theory be uniquely recovered
from idealized data. We show that NMAGIC with MPR indeed converges to the true
solution with very good accuracy, independent of the initial particle model.
Compared to the standard weight entropy regularization, biases in the
anisotropy structure are removed and local fluctuations in the intrinsic
distribution function are reduced. We then investigate how the uncertainties in
the inferred dynamical structure increase with less complete and noisier
kinematic data, and how the dependence on the initial particle model also
increases. Finally, we apply the MPR technique to the two
intermediate-luminosity elliptical galaxies NGC 4697 and NGC 3379, obtaining
smoother dynamical models in luminous and dark matter potentials.Comment: 16 pages, 15 figures, 2 tables. Accepted for publication in MNRA
CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions
CMB anisotropy measurements have brought the issue of global topology of the
universe from the realm of theoretical possibility to within the grasp of
observations. The global topology of the universe modifies the correlation
properties of cosmic fields. In particular, strong correlations are predicted
in CMB anisotropy patterns on the largest observable scales if the size of the
Universe is comparable to the distance to the CMB last scattering surface. We
describe in detail our completely general scheme using a regularized method of
images for calculating such correlation functions in models with nontrivial
topology, and apply it to the computationally challenging compact hyperbolic
spaces. Our procedure directly sums over images within a specified radius,
ideally many times the diameter of the space, effectively treats more distant
images in a continuous approximation, and uses Cesaro resummation to further
sharpen the results. At all levels of approximation the symmetries of the space
are preserved in the correlation function. This new technique eliminates the
need for the difficult task of spatial eigenmode decomposition on these spaces.
Although the eigenspectrum can be obtained by this method if desired, at a
given level of approximation the correlation functions are more accurately
determined. We use the 3-torus example to demonstrate that the method works
very well. We apply it to power spectrum as well as correlation function
evaluations in a number of compact hyperbolic (CH) spaces. Application to the
computation of CMB anisotropy correlations on CH spaces, and the observational
constraints following from them, are given in a companion paper.Comment: 27 pages, Latex, 11 figures, submitted to Phys. Rev. D, March 11,
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Computing CMB Anisotropy in Compact Hyperbolic Spaces
The measurements of CMB anisotropy have opened up a window for probing the
global topology of the universe on length scales comparable to and beyond the
Hubble radius. For compact topologies, the two main effects on the CMB are: (1)
the breaking of statistical isotropy in characteristic patterns determined by
the photon geodesic structure of the manifold and (2) an infrared cutoff in the
power spectrum of perturbations imposed by the finite spatial extent. We
present a completely general scheme using the regularized method of images for
calculating CMB anisotropy in models with nontrivial topology, and apply it to
the computationally challenging compact hyperbolic topologies. This new
technique eliminates the need for the difficult task of spatial eigenmode
decomposition on these spaces. We estimate a Bayesian probability for a
selection of models by confronting the theoretical pixel-pixel temperature
correlation function with the COBE-DMR data. Our results demonstrate that
strong constraints on compactness arise: if the universe is small compared to
the `horizon' size, correlations appear in the maps that are irreconcilable
with the observations. If the universe is of comparable size, the likelihood
function is very dependent upon orientation of the manifold wrt the sky. While
most orientations may be strongly ruled out, it sometimes happens that for a
specific orientation the predicted correlation patterns are preferred over the
conventional infinite models.Comment: 15 pages, LaTeX (IOP style included), 3 color figures (GIF) in
separate files. Minor revision to match the version accepted in Class.
Quantum Grav.: Proc. of Topology and Cosmology, Cleveland, 1997. The paper
can be also downloaded from
http://www.cita.utoronto.ca/~pogosyan/cwru_proc.ps.g
A Discrete Adapted Hierarchical Basis Solver For Radial Basis Function Interpolation
In this paper we develop a discrete Hierarchical Basis (HB) to efficiently
solve the Radial Basis Function (RBF) interpolation problem with variable
polynomial order. The HB forms an orthogonal set and is adapted to the kernel
seed function and the placement of the interpolation nodes. Moreover, this
basis is orthogonal to a set of polynomials up to a given order defined on the
interpolating nodes. We are thus able to decouple the RBF interpolation problem
for any order of the polynomial interpolation and solve it in two steps: (1)
The polynomial orthogonal RBF interpolation problem is efficiently solved in
the transformed HB basis with a GMRES iteration and a diagonal, or block SSOR
preconditioner. (2) The residual is then projected onto an orthonormal
polynomial basis. We apply our approach on several test cases to study its
effectiveness, including an application to the Best Linear Unbiased Estimator
regression problem
Computational morphogenesis of free form shells: Filter methods to create alternative solutions
p. 536-547Actual trends in numerical shape optimal design of structures deal with handling of very
large dimensions of design space. The goal is to allowing as much design freedom as
possible while considerably reducing the modelling effort. As a consequence, several
technical problems have to be solved to get procedures which are robust, easy to use and which can handle many design parameters efficiently. The paper briefly discusses several of the most important aspects in this context and presents many illustrative examples which show typical applications for the design of light weight shell and membrane structures.Bletzinger, K.; Firi, M.; Linhard, J.; Wüchner, R. (2009). Computational morphogenesis of free form shells: Filter methods to create alternative solutions. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654
Loop Quantum Cosmology I: Kinematics
The framework of quantum symmetry reduction is applied to loop quantum
gravity with respect to transitively acting symmetry groups. This allows to
test loop quantum gravity in a large class of minisuperspaces and to
investigate its features - e.g. the discrete volume spectrum - in certain
cosmological regimes. Contrary to previous studies of quantum cosmology
(minisuperspace quantizations) the symmetry reduction is carried out not at the
classical level but on an auxiliary Hilbert space of the quantum theory before
solving the constraints. Therefore, kinematical properties like volume
quantization survive the symmetry reduction. In this first part the kinematical
framework, i.e. implementation of the quantum symmetry reduction and
quantization of Gauss and diffeomorphism constraints, is presented for Bianchi
class A models as well as locally rotationally symmetric and spatially
isotropic closed and flat models.Comment: 24 page
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