5,535 research outputs found
Galaxy clusters and microwave background anisotropy
Previous estimates of the microwave background anisotropies produced by
freely falling spherical clusters are discussed. These estimates are based on
the Swiss-Cheese and Tolman-Bondi models. It is proved that these models give
only upper limits to the anisotropies produced by the observed galaxy clusters.
By using spherically symmetric codes including pressureless matter and a hot
baryonic gas, new upper limits are obtained. The contributions of the hot gas
and the pressureless component to the total anisotropy are compared. The
effects produced by the pressure are proved to be negligible; hence,
estimations of the cluster anisotropies based on N-body simulations are
hereafter justified. After the phenomenon of violent relaxation, any realistic
rich cluster can only produce small anisotropies with amplitudes of order
. During the rapid process of violent relaxation, the anisotropies
produced by nonlinear clusters are expected to range in the interval
. The angular scales of these anisotropies are discussed.Comment: 31 pages, 3 postscript figures, accepted MNRA
Learning from observations of the microwave background at small angular scales
In this paper, we focus our attention on the following question: How well can
we recover the power spectrum of the cosmic microwave background from the maps
of a given experiment?. Each experiment is described by a a pixelization scale,
a beam size, a noise level and a sky coverage. We use accurate numerical
simulations of the microwave sky and a cold dark matter model for structure
formation in the universe. Angular scales smaller than those of previous
simulations are included. The spectrum obtained from the simulated maps is
appropriately compared with the theoretical one. Relative deviations between
these spectra are estimated. Various contributions to these deviations are
analyzed. The method used for spectra comparisons is discussed.Comment: 15 pages (LATEX), 2 postcript figures, accepted in Ap
A paradox in bosonic energy computations via semidefinite programming relaxations
We show that the recent hierarchy of semidefinite programming relaxations
based on non-commutative polynomial optimization and reduced density matrix
variational methods exhibits an interesting paradox when applied to the bosonic
case: even though it can be rigorously proven that the hierarchy collapses
after the first step, numerical implementations of higher order steps generate
a sequence of improving lower bounds that converges to the optimal solution. We
analyze this effect and compare it with similar behavior observed in
implementations of semidefinite programming relaxations for commutative
polynomial minimization. We conclude that the method converges due to the
rounding errors occurring during the execution of the numerical program, and
show that convergence is lost as soon as computer precision is incremented. We
support this conclusion by proving that for any element p of a Weyl algebra
which is non-negative in the Schrodinger representation there exists another
element p' arbitrarily close to p that admits a sum of squares decomposition.Comment: 22 pages, 4 figure
Relaxation of the Curve Shortening Flow via the Parabolic Ginzburg-Landau equation
In this paper we study how to find solutions to the parabolic Ginzburg–Landau equation that as have as interface a given curve that evolves under curve shortening flow. Moreover, for compact embedded curves we find a uniform profile for the solution up the extinction time of the curve. We show that after the extinction time the solution converges uniformly to a constant
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