831 research outputs found
Geometry of weak lensing of CMB polarization
Hu [Phys. Rev. D62 (2000) 043007] has presented a harmonic-space method for
calculating the effects of weak gravitational lensing on the cosmic microwave
background (CMB) over the full sky. Computing the lensed power spectra to first
order in the deflection power requires one to formulate the lensing
displacement beyond the tangent-space approximation. We point out that for CMB
polarization this displacement must undergo geometric corrections on the
spherical sky to maintain statistical isotropy of the lensed fields. Although
not discussed by Hu, these geometric effects are implicit in his analysis.
However, there they are hidden by an overly-compact notation that is both
unconventional and rather confusing. Here we aim to ameliorate this deficiency
by providing a rigorous derivation of the lensed spherical power spectra.Comment: 3 page
CMB Lensing Reconstruction on the Full Sky
Gravitational lensing of the microwave background by the intervening dark
matter mainly arises from large-angle fluctuations in the projected
gravitational potential and hence offers a unique opportunity to study the
physics of the dark sector at large scales. Studies with surveys that cover
greater than a percent of the sky will require techniques that incorporate the
curvature of the sky. We lay the groundwork for these studies by deriving the
full sky minimum variance quadratic estimators of the lensing potential from
the CMB temperature and polarization fields. We also present a general
technique for constructing these estimators, with harmonic space convolutions
replaced by real space products, that is appropriate for both the full sky
limit and the flat sky approximation. This also extends previous treatments to
include estimators involving the temperature-polarization cross-correlation and
should be useful for next generation experiments in which most of the
additional information from polarization comes from this channel due to
sensitivity limitations.Comment: Accepted for publication in Phys. Rev. D; typos correcte
Relations as executable specifications: taming partiality and non-determinism using invariants
Comunicação publicada em "Lecture Notes in Computer Science", vol. 7560 (2012), pag. 146-161The calculus of relations has been widely used in program specification and reasoning. It is very tempting to use such specifications as running prototypes of the desired program, but, even considering finite domains, the inherent partiality and non-determinism of relations makes this impractical and highly inefficient. To tame partiality we prescribe the usage of invariants, represented by coreflexives, to characterize the exact domains and codomains of relational specifications. Such invariants can be used as pre-condition checkers to avoid runtime errors. Moreover, we show how such invariants can be used to narrow the non-deterministic execution of relational specifications, making it viable for a relevant class of problems. In particular, we show how the proposed techniques can be applied to execute specifications of bidirectional transformations, a domain where partiality and non-determinism are paramount.Fundação para a Ciência e a Tecnologi
CMBR Weak Lensing and HI 21-cm Cross-correlation Angular Power Spectrum
Weak gravitational lensing of the CMBR manifests as a secondary anisotropy in
the temperature maps. The effect, quantified through the shear and convergence
fields imprint the underlying large scale structure (LSS), geometry and
evolution history of the Universe. It is hence perceived to be an important
observational probe of cosmology. De-lensing the CMBR temperature maps is also
crucial for detecting the gravitational wave generated B-modes. Future
observations of redshifted 21-cm radiation from the cosmological neutral
hydrogen (HI) distribution hold the potential of probing the LSS over a large
redshift range. We have investigated the correlation between post-reionization
HI signal and weak lensing convergence field. Assuming that the HI follows the
dark matter distribution, the cross-correlation angular power spectrum at a
multipole \ell is found to be proportional to the cold dark matter power
spectrum evaluated at \ell/r, where r denotes the comoving distance to the
redshift where the HI is located. The amplitude of the ross-correlation depends
on quantities specific to the HI distribution, growth of perturbations and also
the underlying cosmological model. In an ideal ituation, we found that a
statistically significant detection of the cross-correlation signal is
possible. If detected, the cross-correlation signal hold the possibility of a
joint estimation of cosmological parameters and also test various CMBR
de-lensing estimators.Comment: 14 pages, 4 figures, publishe
Benchmark Parameters for CMB Polarization Experiments
The recently detected polarization of the cosmic microwave background (CMB)
holds the potential for revealing the physics of inflation and gravitationally
mapping the large-scale structure of the universe, if so called B-mode signals
below 10^{-7}, or tenths of a uK, can be reliably detected. We provide a
language for describing systematic effects which distort the observed CMB
temperature and polarization fields and so contaminate the B-modes. We identify
7 types of effects, described by 11 distortion fields, and show their
association with known instrumental systematics such as common mode and
differential gain fluctuations, line cross-coupling, pointing errors, and
differential polarized beam effects. Because of aliasing from the small-scale
structure in the CMB, even uncorrelated fluctuations in these effects can
affect the large-scale B modes relevant to gravitational waves. Many of these
problems are greatly reduced by having an instrumental beam that resolves the
primary anisotropies (FWHM << 10'). To reach the ultimate goal of an
inflationary energy scale of 3 \times 10^{15} GeV, polarization distortion
fluctuations must be controlled at the 10^{-2}-10^{-3} level and temperature
leakage to the 10^{-4}-10^{-3} level depending on effect. For example pointing
errors must be controlled to 1.5'' rms for arcminute scale beams or a percent
of the Gaussian beam width for larger beams; low spatial frequency differential
gain fluctuations or line cross-coupling must be eliminated at the level of
10^{-4} rms.Comment: 11 pages, 5 figures, submitted to PR
Cross-Correlation Studies with CMB Polarization Maps
The free-electron population during the reionized epoch rescatters CMB
temperature quadrupole and generates a now well-known polarization signal at
large angular scales. While this contribution has been detected in the
temperature-polarization cross power spectrum measured with WMAP data, due to
the large cosmic variance associated with anisotropy measurements at tens of
degree angular scales only limited information related to reionization, such as
the optical depth to electron scattering, can be extracted. The inhomogeneities
in the free-electron population lead to an additional secondary polarization
anisotropy contribution at arcminute scales. While the fluctuation amplitude,
relative to dominant primordial fluctuations, is small, we suggest that a
cross-correlation between arcminute scale CMB polarization data and a tracer
field of the high redshift universe, such as through fluctuations captured by
the 21 cm neutral Hydrogen background or those in the infrared background
related to first proto-galaxies, may allow one to study additional details
related to reionization. For this purpose, we discuss an optimized higher order
correlation measurement, in the form of a three-point function, including
information from large angular scale CMB temperature anisotropies in addition
to arcminute scale polarization signal related to inhomogeneous reionization.
We suggest that the proposed bispectrum can be measured with a substantial
signal-to-noise ratio and does not require all-sky maps of CMB polarization or
that of the tracer field. A measurement such as the one proposed may allow one
to establish the epoch when CMB polarization related to reionization is
generated and to address if the universe was reionized once or twice.Comment: 13 pages, 7 figures; Version in press with Phys. Rev.
Proteinlike behavior of a spin system near the transition between ferromagnet and spin glass
A simple spin system is studied as an analog for proteins. We investigate how
the introduction of randomness and frustration into the system effects the
designability and stability of ground state configurations. We observe that the
spin system exhibits protein-like behavior in the vicinity of the transition
between ferromagnet and spin glass.
Our results illuminate some guiding principles in protein evolution.Comment: 12 pages, 4 figure
Annual modulation of the Galactic binary confusion noise bakground and LISA data analysis
We study the anisotropies of the Galactic confusion noise background and its
effects on LISA data analysis. LISA has two data streams of the gravitational
waves signals relevant for low frequency regime. Due to the anisotropies of the
background, the matrix for their confusion noises has off-diagonal components
and depends strongly on the orientation of the detector plane. We find that the
sky-averaged confusion noise level could change by a factor of 2
in three months, and would be minimum when the orbital position of LISA is
either around the spring or autumn equinox.Comment: 13 pages, 6 figure
Nonlinear Modulation of Multi-Dimensional Lattice Waves
The equations governing weakly nonlinear modulations of -dimensional
lattices are considered using a quasi-discrete multiple-scale approach. It is
found that the evolution of a short wave packet for a lattice system with cubic
and quartic interatomic potentials is governed by generalized Davey-Stewartson
(GDS) equations, which include mean motion induced by the oscillatory wave
packet through cubic interatomic interaction. The GDS equations derived here
are more general than those known in the theory of water waves because of the
anisotropy inherent in lattices. Generalized Kadomtsev-Petviashvili equations
describing the evolution of long wavelength acoustic modes in two and three
dimensional lattices are also presented. Then the modulational instability of a
-dimensional Stokes lattice wave is discussed based on the -dimensional
GDS equations obtained. Finally, the one- and two-soliton solutions of
two-dimensional GDS equations are provided by means of Hirota's bilinear
transformation method.Comment: Submitted to PR
A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface
Cracks often exist in composite structures, especially at the interface of two different materials. These cracks can significantly affect the load bearing capacity of the structure and lead to premature failure of the structure. In this paper, a novel element for modeling the singular stress state around the inclined interface crack which terminates at the interface is developed. This new singular element is derived based on the explicit form of the high order eigen solution which is, for the first time, determined by using a symplectic approach. The developed singular element is then applied in finite element analysis and the stress intensity factors (SIFs) for a number of crack configurations are derived. It has been concluded that composites with complex geometric configurations of inclined interface cracks can be accurately simulated by the developed method, according to comparison of the results against benchmarks. It has been found that the stiffness matrix of the proposed singular element is independent of the element size and the SIFs of the crack can be solved directly without any post-processing
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