1,434 research outputs found
Creation and characterization of vortex clusters in atomic Bose-Einstein condensates
We show that a moving obstacle, in the form of an elongated paddle, can
create vortices that are dispersed, or induce clusters of like-signed vortices
in 2D Bose-Einstein condensates. We propose new statistical measures of
clustering based on Ripley's K-function which are suitable to the small size
and small number of vortices in atomic condensates, which lack the huge number
of length scales excited in larger classical and quantum turbulent fluid
systems. The evolution and decay of clustering is analyzed using these
measures. Experimentally it should prove possible to create such an obstacle by
a laser beam and a moving optical mask. The theoretical techniques we present
are accessible to experimentalists and extend the current methods available to
induce 2D quantum turbulence in Bose-Einstein condensates.Comment: 9 pages, 9 figure
Two-dimensional supersolidity in a planar dipolar Bose gas
We investigate the crystalline stationary states of a dipolar Bose-Einstein
condensate in a planar trapping geometry. Our focus is on the ground state
phase diagram in the thermodynamic limit, where triangular, honeycomb and
stripe phases occur. We quantify the superfluid fraction by calculating the
non-classical translational inertia, which allows us to identify favorable
parameter regimes for observing supersolid ground states. We develop two
simplified theories to approximately describe the ground states, and consider
the relationship to roton softening in the uniform ground state. This also
allows us to extend the phase diagram to the low density regime. While the
triangular and honeycomb states have an isotropic superfluid response tensor,
the stripe state exhibits anisotropic superfluidity.Comment: 10 pages, 8 figure
A Bayesian reassessment of nearest-neighbour classification
The k-nearest-neighbour procedure is a well-known deterministic method used
in supervised classification. This paper proposes a reassessment of this
approach as a statistical technique derived from a proper probabilistic model;
in particular, we modify the assessment made in a previous analysis of this
method undertaken by Holmes and Adams (2002,2003), and evaluated by Manocha and
Girolami (2007), where the underlying probabilistic model is not completely
well-defined. Once a clear probabilistic basis for the k-nearest-neighbour
procedure is established, we derive computational tools for conducting Bayesian
inference on the parameters of the corresponding model. In particular, we
assess the difficulties inherent to pseudo-likelihood and to path sampling
approximations of an intractable normalising constant, and propose a perfect
sampling strategy to implement a correct MCMC sampler associated with our
model. If perfect sampling is not available, we suggest using a Gibbs sampling
approximation. Illustrations of the performance of the corresponding Bayesian
classifier are provided for several benchmark datasets, demonstrating in
particular the limitations of the pseudo-likelihood approximation in this
set-up
Limits of Abductivism About Logic
I argue against abductivism about logic, which is the view that rational theory choice in logic happens by abduction. Abduction cannot serve as a neutral arbiter in many foundational disputes in logic because, in order to use abduction, one must first identify the relevant data. Which data one deems relevant depends on what I call one's conception of logic. One's conception of logic is, however, not independent of one's views regarding many of the foundational disputes that one may hope to solve by abduction
A Naive Bayes Source Classifier for X-ray Sources
The Chandra Carina Complex Project (CCCP) provides a sensitive X-ray survey
of a nearby starburst region over >1 square degree in extent. Thousands of
faint X-ray sources are found, many concentrated into rich young stellar
clusters. However, significant contamination from unrelated Galactic and
extragalactic sources is present in the X-ray catalog. We describe the use of a
naive Bayes classifier to assign membership probabilities to individual
sources, based on source location, X-ray properties, and visual/infrared
properties. For the particular membership decision rule adopted, 75% of CCCP
sources are classified as members, 11% are classified as contaminants, and 14%
remain unclassified. The resulting sample of stars likely to be Carina members
is used in several other studies, which appear in a Special Issue of the ApJS
devoted to the CCCP.Comment: Accepted for the ApJS Special Issue on the Chandra Carina Complex
Project (CCCP), scheduled for publication in May 2011. All 16 CCCP Special
Issue papers are available at
http://cochise.astro.psu.edu/Carina_public/special_issue.html through 2011 at
least. 19 pages, 7 figure
Scaling and allometry in the building geometries of Greater London
Many aggregate distributions of urban activities such as city sizes reveal
scaling but hardly any work exists on the properties of spatial distributions
within individual cities, notwithstanding considerable knowledge about their
fractal structure. We redress this here by examining scaling relationships in a
world city using data on the geometric properties of individual buildings. We
first summarise how power laws can be used to approximate the size
distributions of buildings, in analogy to city-size distributions which have
been widely studied as rank-size and lognormal distributions following Zipf and
Gibrat. We then extend this analysis to allometric relationships between
buildings in terms of their different geometric size properties. We present
some preliminary analysis of building heights from the Emporis database which
suggests very strong scaling in world cities. The data base for Greater London
is then introduced from which we extract 3.6 million buildings whose scaling
properties we explore. We examine key allometric relationships between these
different properties illustrating how building shape changes according to size,
and we extend this analysis to the classification of buildings according to
land use types. We conclude with an analysis of two-point correlation functions
of building geometries which supports our non-spatial analysis of scaling.Comment: 28 pages, 8 figure
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