16,304 research outputs found
Revisiting the radio interferometer measurement equation. IV. A generalized tensor formalism
The radio interferometer measurement equation (RIME), especially in its 2x2
form, has provided a comprehensive matrix-based formalism for describing
classical radio interferometry and polarimetry, as shown in the previous three
papers of this series. However, recent practical and theoretical developments,
such as phased array feeds (PAFs), aperture arrays (AAs) and wide-field
polarimetry, are exposing limitations of the formalism. This paper aims to
develop a more general formalism that can be used to both clearly define the
limitations of the matrix RIME, and to describe observational scenarios that
lie outside these limitations. Some assumptions underlying the matrix RIME are
explicated and analysed in detail. To this purpose, an array correlation matrix
(ACM) formalism is explored. This proves of limited use; it is shown that
matrix algebra is simply not a sufficiently flexible tool for the job. To
overcome these limitations, a more general formalism based on tensors and the
Einstein notation is proposed and explored both theoretically, and with a view
to practical implementations. The tensor formalism elegantly yields generalized
RIMEs describing beamforming, mutual coupling, and wide-field polarimetry in
one equation. It is shown that under the explicated assumptions, tensor
equations reduce to the 2x2 RIME. From a practical point of view, some methods
for implementing tensor equations in an optimal way are proposed and analysed.
The tensor RIME is a powerful means of describing observational scenarios not
amenable to the matrix RIME. Even in cases where the latter remains applicable,
the tensor formalism can be a valuable tool for understanding the limits of
such applicability.Comment: 16 pages, no figures, accepted by A&
Element gain drifts as an imaging dynamic range limitation in PAF-based interferometers
Interferometry with phased-array feeds (PAFs) presents new calibration
challenges in comparison with single-pixel feeds. In particular, temporal
instability of the compound beam patterns due to element gain drifts (EGDs) can
produce calibration artefacts in interferometric images. To translate imaging
dynamic range requirements into PAF hardware and calibration requirements, we
must learn to relate EGD levels to imaging artefact levels. We present a
MeqTrees-based simulations framework that addresses this problem, and apply it
to the APERTIF prototype currently in development for the WSRT.Comment: 4 pages, 3 figures, poster presentation at the XXX URSI General
Assembly and Scientific Symposium (Istanbul, Turkey, August 13-20, 2011
Lepton mixing from the hidden sector
Experimental results indicate a possible relation between the lepton and
quark mixing matrices of the form U_PMNS \approx V_CKM^\dagger U_X, where U_X
is a matrix with special structure related to the mechanism of neutrino mass
generation. We propose a framework which can realize such a relation. The main
ingredients of the framework are the double seesaw mechanism, SO(10) Grand
Unification and a hidden sector of theory. The latter is composed of singlets
(fermions and bosons) of the GUT symmetry with masses between the GUT and
Planck scale. The interactions in this sector obey certain symmetries G_hidden.
We explore the conditions under which symmetries G_hidden can produce flavour
structures in the visible sector. Here the key elements are the basis-fixing
symmetry and mediators which communicate information about properties of the
hidden sector to the visible one. The interplay of SO(10) symmetry,
basis-fixing symmetry identified as Z2 x Z2 and G_hidden can lead to the
required form of U_X. A different kind of new physics is responsible for
generation of the CKM mixing. We present the simplest realizations of the
framework which differ by nature of the mediators and by symmetries of the
hidden sector.Comment: 30 pages, 6 figures; typo corrected, one reference added, version for
publication in Phys. Rev.
Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism
Since its formulation by Hamaker et al., the radio interferometer measurement
equation (RIME) has provided a rigorous mathematical basis for the development
of novel calibration methods and techniques, including various approaches to
the problem of direction-dependent effects (DDEs). This series of papers aims
to place recent developments in the treatment of DDEs into one RIME-based
mathematical framework, and to demonstrate the ease with which the various
effects can be described and understood. It also aims to show the benefits of a
RIME-based approach to calibration.
Paper I re-derives the RIME from first principles, extends the formalism to
the full-sky case, and incorporates DDEs. Paper II then uses the formalism to
describe self-calibration, both with a full RIME, and with the approximate
equations of older software packages, and shows how this is affected by DDEs.
It also gives an overview of real-life DDEs and proposed methods of dealing
with them. Applying this to WSRT data (Paper III) results in a noise-limited
image of the field around 3C 147 with a very high dynamic range (1.6 million),
and none of the off-axis artifacts that plague regular selfcal. The resulting
differential gain solutions contain significant information on DDEs, and can be
used for iterative improvements of sky models.
Perhaps most importantly, sources as faint as 2 mJy have been shown to yield
meaningful differential gain solutions, and thus can be used as potential
calibration beacons in other DDE-related schemes.Comment: 12 pages, no figures, published in A&
Atmospheric neutrinos: LMA oscillations, Ue3 induced interference and CP-violation
We consider oscillations of the low energy (sub-GeV sample) atmospheric
neutrinos in the three neutrino context. We present the semi-analytic study of
the neutrino evolution and calculate characteristics of the e-like events
(total number, energy spectra and zenith angle distributions) in the presence
of oscillations. At low energies there are three different contributions to the
number of events: the LMA contribution (from electron-neutrino oscillations
driven by the solar oscillation parameters), the Ue3-contribution proportional
to s13**2, and the Ue3 - induced interference of the two amplitudes driven by
the solar oscillation parameters. The interference term is sensitive to the
CP-violation phase. We describe in details properties of these contributions.
We find that the LMA, the interference and Ue3 contributions can reach 5 - 6%,
2 - 3% and 1 - 2 % correspondingly. An existence of the significant (> 3 - 5 %)
excess of the e-like events in the sub-GeV sample and the absence of the excess
in the multi-GeV range testifies for deviation of the 2-3 mixing from maximum.
We consider a possibility to measure the deviation as well as the CP- violation
phase in future atmospheric neutrino studies.Comment: 30 pages, RevTeX4.0, 11 figures; improved figure
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