8,315 research outputs found
Modal decomposition of astronomical images with application to shapelets
The decomposition of an image into a linear combination of digitised basis
functions is an everyday task in astronomy. A general method is presented for
performing such a decomposition optimally into an arbitrary set of digitised
basis functions, which may be linearly dependent, non-orthogonal and
incomplete. It is shown that such circumstances may result even from the
digitisation of continuous basis functions that are orthogonal and complete. In
particular, digitised shapelet basis functions are investigated and are shown
to suffer from such difficulties. As a result the standard method of performing
shapelet analysis produces unnecessarily inaccurate decompositions. The optimal
method presented here is shown to yield more accurate decompositions in all
cases.Comment: 12 pages, 17 figures, submitted to MNRA
Ephemeral properties and the illusion of microscopic particles
Founding our analysis on the Geneva-Brussels approach to quantum mechanics,
we use conventional macroscopic objects as guiding examples to clarify the
content of two important results of the beginning of twentieth century:
Einstein-Podolsky-Rosen's reality criterion and Heisenberg's uncertainty
principle. We then use them in combination to show that our widespread belief
in the existence of microscopic particles is only the result of a cognitive
illusion, as microscopic particles are not particles, but are instead the
ephemeral spatial and local manifestations of non-spatial and non-local
entities
Bayes-X: a Bayesian inference tool for the analysis of X-ray observations of galaxy clusters
We present the first public release of our Bayesian inference tool, Bayes-X,
for the analysis of X-ray observations of galaxy clusters. We illustrate the
use of Bayes-X by analysing a set of four simulated clusters at z=0.2-0.9 as
they would be observed by a Chandra-like X-ray observatory. In both the
simulations and the analysis pipeline we assume that the dark matter density
follows a spherically-symmetric Navarro, Frenk and White (NFW) profile and that
the gas pressure is described by a generalised NFW (GNFW) profile. We then
perform four sets of analyses. By numerically exploring the joint probability
distribution of the cluster parameters given simulated Chandra-like data, we
show that the model and analysis technique can robustly return the simulated
cluster input quantities, constrain the cluster physical parameters and reveal
the degeneracies among the model parameters and cluster physical parameters. We
then analyse Chandra data on the nearby cluster, A262, and derive the cluster
physical profiles. To illustrate the performance of the Bayesian model
selection, we also carried out analyses assuming an Einasto profile for the
matter density and calculated the Bayes factor. The results of the model
selection analyses for the simulated data favour the NFW model as expected.
However, we find that the Einasto profile is preferred in the analysis of A262.
The Bayes-X software, which is implemented in Fortran 90, is available at
http://www.mrao.cam.ac.uk/facilities/software/bayesx/.Comment: 22 pages, 11 figure
Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector
Terahertz (THz) imaging has the ability to see through otherwise opaque
materials. However, due to the long wavelengths of THz radiation
({\lambda}=300{\mu}m at 1THz), far-field THz imaging techniques are heavily
outperformed by optical imaging in regards to the obtained resolution. In this
work we demonstrate near-field THz imaging with a single-pixel detector. We
project a time-varying optical mask onto a silicon wafer which is used to
spatially modulate a pulse of THz radiation. The far-field transmission
corresponding to each mask is recorded by a single element detector and this
data is used to reconstruct the image of an object placed on the far side of
the silicon wafer. We demonstrate a proof of principal application where we
image a printed circuit board on the underside of a 115{\mu}m thick silicon
wafer with ~100{\mu}m ({\lambda}/4) resolution. With subwavelength resolution
and the inherent sensitivity to local conductivity provided by the THz probe
frequencies, we show that it is possible to detect fissures in the circuitry
wiring of a few microns in size. Imaging systems of this type could have other
uses where non-invasive measurement or imaging of concealed structures with
high resolution is necessary, such as in semiconductor manufacturing or in
bio-imaging
Classifying LISA gravitational wave burst signals using Bayesian evidence
We consider the problem of characterisation of burst sources detected with
the Laser Interferometer Space Antenna (LISA) using the multi-modal nested
sampling algorithm, MultiNest. We use MultiNest as a tool to search for
modelled bursts from cosmic string cusps, and compute the Bayesian evidence
associated with the cosmic string model. As an alternative burst model, we
consider sine-Gaussian burst signals, and show how the evidence ratio can be
used to choose between these two alternatives. We present results from an
application of MultiNest to the last round of the Mock LISA Data Challenge, in
which we were able to successfully detect and characterise all three of the
cosmic string burst sources present in the release data set. We also present
results of independent trials and show that MultiNest can detect cosmic string
signals with signal-to-noise ratio (SNR) as low as ~7 and sine-Gaussian signals
with SNR as low as ~8. In both cases, we show that the threshold at which the
sources become detectable coincides with the SNR at which the evidence ratio
begins to favour the correct model over the alternative.Comment: 21 pages, 11 figures, accepted by CQG; v2 has minor changes for
consistency with accepted versio
Dust heating by the interstellar radiation field in models of turbulent molecular clouds
We have calculated the radiation field, dust grain temperatures, and far
infrared emissivity of numerical models of turbulent molecular clouds. When
compared to a uniform cloud of the same mean optical depth, most of the volume
inside the turbulent cloud is brighter, but most of the mass is darker. There
is little mean attenuation from center to edge, and clumping causes the
radiation field to be somewhat bluer. There is also a large dispersion,
typically by a few orders of magnitude, of all quantities relative to their
means. However, despite the scatter, the 850 micron emission maps are well
correlated with surface density. The fraction of mass as a function of
intensity can be reproduced by a simple hierarchical model of density
structure.Comment: 32 pages, 14 figures, submitted to Ap
Universality of optimal measurements
We present optimal and minimal measurements on identical copies of an unknown
state of a qubit when the quality of measuring strategies is quantified with
the gain of information (Kullback of probability distributions). We also show
that the maximal gain of information occurs, among isotropic priors, when the
state is known to be pure. Universality of optimal measurements follows from
our results: using the fidelity or the gain of information, two different
figures of merits, leads to exactly the same conclusions. We finally
investigate the optimal capacity of copies of an unknown state as a quantum
channel of information.Comment: Revtex, 5 pages, no figure
Alternative Fourier Expansions for Inverse Square Law Forces
Few-body problems involving Coulomb or gravitational interactions between
pairs of particles, whether in classical or quantum physics, are generally
handled through a standard multipole expansion of the two-body potentials. We
discuss an alternative based on a compact, cylindrical Green's function
expansion that should have wide applicability throughout physics. Two-electron
"direct" and "exchange" integrals in many-electron quantum systems are
evaluated to illustrate the procedure which is more compact than the standard
one using Wigner coefficients and Slater integrals.Comment: 10 pages, latex/Revtex4, 1 figure
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