27,809 research outputs found
Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and double simple Hurwitz numbers
We derive explicit formulae for the generating series of mixed Grothendieck dessins d'enfant/monotone/simple Hurwitz numbers, via the semi-infinite wedge formalism. This reveals the strong piecewise polynomiality in the sense of Goulden–Jackson–Vakil, generalising a result of Johnson, and provides a new explicit proof of the piecewise polynomiality of the mixed case. Moreover, we derive wall-crossing formulae for the mixed case. These statements specialise to any of the three types of Hurwitz numbers, and to the mixed case of any pair
Axial symmetry and conformal Killing vectors
Axisymmetric spacetimes with a conformal symmetry are studied and it is shown
that, if there is no further conformal symmetry, the axial Killing vector and
the conformal Killing vector must commute. As a direct consequence, in
conformally stationary and axisymmetric spacetimes, no restriction is made by
assuming that the axial symmetry and the conformal timelike symmetry commute.
Furthermore, we prove that in axisymmetric spacetimes with another symmetry
(such as stationary and axisymmetric or cylindrically symmetric spacetimes) and
a conformal symmetry, the commutator of the axial Killing vector with the two
others mush vanish or else the symmetry is larger than that originally
considered. The results are completely general and do not depend on Einstein's
equations or any particular matter content.Comment: 15 pages, Latex, no figure
Spherical Orbifolds for Cosmic Topology
Harmonic analysis is a tool to infer cosmic topology from the measured
astrophysical cosmic microwave background CMB radiation. For overall positive
curvature, Platonic spherical manifolds are candidates for this analysis. We
combine the specific point symmetry of the Platonic manifolds with their deck
transformations. This analysis in topology leads from manifolds to orbifolds.
We discuss the deck transformations of the orbifolds and give eigenmodes for
the harmonic analysis as linear combinations of Wigner polynomials on the
3-sphere. These provide new tools for detecting cosmic topology from the CMB
radiation.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1011.427
A Bayesian method for pulsar template generation
Extracting Times of Arrival from pulsar radio signals depends on the
knowledge of the pulsars pulse profile and how this template is generated. We
examine pulsar template generation with Bayesian methods. We will contrast the
classical generation mechanism of averaging intensity profiles with a new
approach based on Bayesian inference. We introduce the Bayesian measurement
model imposed and derive the algorithm to reconstruct a "statistical template"
out of noisy data. The properties of these "statistical templates" are analysed
with simulated and real measurement data from PSR B1133+16. We explain how to
put this new form of template to use in analysing secondary parameters of
interest and give various examples: We implement a nonlinear filter for
determining ToAs of pulsars. Applying this method to data from PSR J1713+0747
we derive ToAs self consistently, meaning all epochs were timed and we used the
same epochs for template generation. While the average template contains
fluctuations and noise as unavoidable artifacts, we find that the "statistical
template" derived by Bayesian inference quantifies fluctuations and remaining
uncertainty. This is why the algorithm suggested turns out to reconstruct
templates of statistical significance from ten to fifty single pulses. A moving
data window of fifty pulses, taking out one single pulse at the beginning and
adding one at the end of the window unravels the characteristics of the methods
to be compared. It shows that the change induced in the classical
reconstruction is dominated by random fluctuations for the average template,
while statistically significant changes drive the dynamics of the proposed
method's reconstruction. The analysis of phase shifts with simulated data
reveals that the proposed nonlinear algorithm is able to reconstruct correct
phase information along with an acceptable estimation of the remaining
uncertainty.Comment: 21 pages, 16 figures, submitted to MNRA
Surface structure of i-Al(68)Pd(23)Mn(9): An analysis based on the T*(2F) tiling decorated by Bergman polytopes
A Fibonacci-like terrace structure along a 5fold axis of i-Al(68)Pd(23)Mn(9)
monograins has been observed by T.M. Schaub et al. with scanning tunnelling
microscopy (STM). In the planes of the terraces they see patterns of dark
pentagonal holes. These holes are well oriented both within and among terraces.
In one of 11 planes Schaub et al. obtain the autocorrelation function of the
hole pattern. We interpret these experimental findings in terms of the
Katz-Gratias-de Boisseu-Elser model. Following the suggestion of Elser that the
Bergman clusters are the dominant motive of this model, we decorate the tiling
T*(2F) by the Bergman polytopes only. The tiling T*(2F) allows us to use the
powerful tools of the projection techniques. The Bergman polytopes can be
easily replaced by the Mackay polytopes as the decoration objects. We derive a
picture of ``geared'' layers of Bergman polytopes from the projection
techniques as well as from a huge patch. Under the assumption that no surface
reconstruction takes place, this picture explains the Fibonacci-sequence of the
step heights as well as the related structure in the terraces qualitatively and
to certain extent even quantitatively. Furthermore, this layer-picture requires
that the polytopes are cut in order to allow for the observed step heights. We
conclude that Bergman or Mackay clusters have to be considered as geometric
building blocks of the i-AlPdMn structure rather than as energetically stable
entities
A Spherically Symmetric Closed Universe as an Example of a 2D Dilatonic Model
We study the two-dimensional (2D) dilatonic model describing a massless
scalar field minimally coupled to the spherically reduced Einstein-Hilbert
gravity. The general solution of this model is given in the case when a Killing
vector is present. When interpreted in four dimensions, the solution describes
either a static or a homogeneous collision of incoming and outgoing null dust
streams with spherical symmetry. The homogeneous Universe is closed.Comment: 5 pages, 2 figures, to appear in Physical Review
Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface
The single-mode Richtmyer–Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier–Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models
An investigation of pulsar searching techniques with the Fast Folding Algorithm
Here we present an in-depth study of the behaviour of the Fast Folding
Algorithm, an alternative pulsar searching technique to the Fast Fourier
Transform. Weaknesses in the Fast Fourier Transform, including a susceptibility
to red noise, leave it insensitive to pulsars with long rotational periods (P >
1 s). This sensitivity gap has the potential to bias our understanding of the
period distribution of the pulsar population. The Fast Folding Algorithm, a
time-domain based pulsar searching technique, has the potential to overcome
some of these biases. Modern distributed-computing frameworks now allow for the
application of this algorithm to all-sky blind pulsar surveys for the first
time. However, many aspects of the behaviour of this search technique remain
poorly understood, including its responsiveness to variations in pulse shape
and the presence of red noise. Using a custom CPU-based implementation of the
Fast Folding Algorithm, ffancy, we have conducted an in-depth study into the
behaviour of the Fast Folding Algorithm in both an ideal, white noise regime as
well as a trial on observational data from the HTRU-S Low Latitude pulsar
survey, including a comparison to the behaviour of the Fast Fourier Transform.
We are able to both confirm and expand upon earlier studies that demonstrate
the ability of the Fast Folding Algorithm to outperform the Fast Fourier
Transform under ideal white noise conditions, and demonstrate a significant
improvement in sensitivity to long-period pulsars in real observational data
through the use of the Fast Folding Algorithm.Comment: 19 pages, 15 figures, 3 table
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