14,746 research outputs found
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
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&
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&
Form factors of the XXZ model and the affine quantum group symmetry
We present new expressions of form factors of the XXZ model which satisfy
Smirnov's three axioms. These new form factors are obtained by acting the
affine quantum group to the known ones obtained
in our previous works. We also find the relations among all the new and known
form factors, i.e., all other form factors can be expressed as kind of
descendents of a special one.Comment: 11 pages, latex; Some explanation is adde
The potential of the ground state of NaRb
The X state of NaRb was studied by Fourier transform
spectroscopy. An accurate potential energy curve was derived from more than
8800 transitions in isotopomers NaRb and NaRb. This
potential reproduces the experimental observations within their uncertainties
of 0.003 \rcm to 0.007 \rcm. The outer classical turning point of the last
observed energy level (, ) lies at \AA, leading
to a energy of 4.5 \rcm below the ground state asymptote.Comment: 8 pages, 6 figures and 2 table
Using baseline-dependent window functions for data compression and field-of-interest shaping in radio interferometry
In radio interferometry, observed visibilities are intrinsically sampled at
some interval in time and frequency. Modern interferometers are capable of
producing data at very high time and frequency resolution; practical limits on
storage and computation costs require that some form of data compression be
imposed. The traditional form of compression is a simple averaging of the
visibilities over coarser time and frequency bins. This has an undesired side
effect: the resulting averaged visibilities "decorrelate", and do so
differently depending on the baseline length and averaging interval. This
translates into a non-trivial signature in the image domain known as
"smearing", which manifests itself as an attenuation in amplitude towards
off-centre sources. With the increasing fields of view and/or longer baselines
employed in modern and future instruments, the trade-off between data rate and
smearing becomes increasingly unfavourable. In this work we investigate
alternative approaches to low-loss data compression. We show that averaging of
the visibility data can be treated as a form of convolution by a boxcar-like
window function, and that by employing alternative baseline-dependent window
functions a more optimal interferometer smearing response may be induced. In
particular, we show improved amplitude response over a chosen field of
interest, and better attenuation of sources outside the field of interest. The
main cost of this technique is a reduction in nominal sensitivity; we
investigate the smearing vs. sensitivity trade-off, and show that in certain
regimes a favourable compromise can be achieved. We show the application of
this technique to simulated data from the Karl G. Jansky Very Large Array (VLA)
and the European Very-long-baseline interferometry Network (EVN)
Structure of Matrix Elements in Quantum Toda Chain
We consider the quantum Toda chain using the method of separation of
variables. We show that the matrix elements of operators in the model are
written in terms of finite number of ``deformed Abelian integrals''. The
properties of these integrals are discussed. We explain that these properties
are necessary in order to provide the correct number of independent operators.
The comparison with the classical theory is done.Comment: LaTeX, 17 page
Storage and retrieval of light pulses in atomic media with "slow" and "fast" light
We present experimental evidence that light storage, i.e. the controlled
release of a light pulse by an atomic sample dependent on the past presence of
a writing pulse, is not restricted to small group velocity media but can also
occur in a negative group velocity medium. A simple physical picture applicable
to both cases and previous light storage experiments is discussed.Comment: 4 pages, 3 figures, submitted to Physical Review Letter
Spin interfaces in the Ashkin-Teller model and SLE
We investigate the scaling properties of the spin interfaces in the
Ashkin-Teller model. These interfaces are a very simple instance of lattice
curves coexisting with a fluctuating degree of freedom, which renders the
analytical determination of their exponents very difficult. One of our main
findings is the construction of boundary conditions which ensure that the
interface still satisfies the Markov property in this case. Then, using a novel
technique based on the transfer matrix, we compute numerically the left-passage
probability, and our results confirm that the spin interface is described by an
SLE in the scaling limit. Moreover, at a particular point of the critical line,
we describe a mapping of Ashkin-Teller model onto an integrable 19-vertex
model, which, in turn, relates to an integrable dilute Brauer model.Comment: 12 pages, 6 figure
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