12,518 research outputs found
Hausdorff dimension of some groups acting on the binary tree
Based on the work of Abercrombie, Barnea and Shalev gave an explicit formula
for the Hausdorff dimension of a group acting on a rooted tree. We focus here
on the binary tree T. Abert and Virag showed that there exist finitely
generated (but not necessarily level-transitive) subgroups of AutT of arbitrary
dimension in [0,1].
In this article we explicitly compute the Hausdorff dimension of the
level-transitive spinal groups. We then show examples of 3-generated spinal
groups which have transcendental Hausdroff dimension, and exhibit a
construction of 2-generated groups whose Hausdorff dimension is 1.Comment: 10 pages; full revision; simplified some proof
Aeolian sans ripples: experimental study of saturated states
We report an experimental investigation of aeolian sand ripples, performed
both in a wind tunnel and on stoss slopes of dunes. Starting from a flat bed,
we can identify three regimes: appearance of an initial wavelength, coarsening
of the pattern and finally saturation of the ripples. We show that both initial
and final wavelengths, as well as the propagative speed of the ripples, are
linear functions of the wind velocity. Investigating the evolution of an
initially corrugated bed, we exhibit non-linear stable solutions for a finite
range of wavelengths, which demonstrates the existence of a saturation in
amplitude. These results contradict most of the models.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Title changed,
figures corrected and simplified, more field data included, text clarifie
Intensity Mapping with Carbon Monoxide Emission Lines and the Redshifted 21 cm Line
We quantify the prospects for using emission lines from rotational
transitions of the CO molecule to perform an `intensity mapping' observation at
high redshift during the Epoch of Reionization (EoR). The aim of CO intensity
mapping is to observe the combined CO emission from many unresolved galaxies,
to measure the spatial fluctuations in this emission, and use this as a tracer
of large scale structure at very early times in the history of our Universe.
This measurement would help determine the properties of molecular clouds -- the
sites of star formation -- in the very galaxies that reionize the Universe. We
further consider the possibility of cross-correlating CO intensity maps with
future observations of the redshifted 21 cm line. The cross spectrum is less
sensitive to foreground contamination than the auto power spectra, and can
therefore help confirm the high redshift origin of each signal. Furthermore,
the cross spectrum measurement would help extract key information about the
EoR, especially regarding the size distribution of ionized regions. We discuss
uncertainties in predicting the CO signal at high redshift, and discuss
strategies for improving these predictions. Under favorable assumptions, and
feasible specifications for a CO survey mapping the CO(2-1) and CO(1-0) lines,
the power spectrum of CO emission fluctuations and its cross spectrum with
future 21 cm measurements from the MWA are detectable at high significance.Comment: 19 pages, 8 figures, submitted to Ap
Laser Guide Star for Large Segmented-Aperture Space Telescopes, Part I: Implications for Terrestrial Exoplanet Detection and Observatory Stability
Precision wavefront control on future segmented-aperture space telescopes
presents significant challenges, particularly in the context of high-contrast
exoplanet direct imaging. We present a new wavefront control architecture that
translates the ground-based artificial guide star concept to space with a laser
source aboard a second spacecraft, formation flying within the telescope
field-of-view. We describe the motivating problem of mirror segment motion and
develop wavefront sensing requirements as a function of guide star magnitude
and segment motion power spectrum. Several sample cases with different values
for transmitter power, pointing jitter, and wavelength are presented to
illustrate the advantages and challenges of having a non-stellar-magnitude
noise limited wavefront sensor for space telescopes. These notional designs
allow increased control authority, potentially relaxing spacecraft stability
requirements by two orders of magnitude, and increasing terrestrial exoplanet
discovery space by allowing high-contrast observations of stars of arbitrary
brightness.Comment: Submitted to A
A ring trap for ultracold atoms
We propose a new kind of toroidal trap, designed for ultracold atoms. It
relies on a combination of a magnetic trap for rf-dressed atoms, which creates
a bubble-like trap, and a standing wave of light. This new trap is well suited
for investigating questions of low dimensionality in a ring potential. We study
the trap characteristics for a set of experimentally accessible parameters. A
loading procedure from a conventional magnetic trap is also proposed. The
flexible nature of this new ring trap, including an adjustable radius and
adjustable transverse oscillation frequencies, will allow the study of
superfluidity in variable geometries and dimensionalities.Comment: 4 figures, 10 pages ; the order of the sections has been changed ; to
appear in Phys. Rev.
Practical learning method for multi-scale entangled states
We describe a method for reconstructing multi-scale entangled states from a
small number of efficiently-implementable measurements and fast
post-processing. The method only requires single particle measurements and the
total number of measurements is polynomial in the number of particles. Data
post-processing for state reconstruction uses standard tools, namely matrix
diagonalisation and conjugate gradient method, and scales polynomially with the
number of particles. Our method prevents the build-up of errors from both
numerical and experimental imperfections
Fine frequency shift of sigle vortex entrance and exit in superconducting loops
The heat capacity of an array of independent aluminum rings has been
measured under an external magnetic field using highly sensitive
ac-calorimetry based on a silicon membrane sensor. Each superconducting vortex
entrance induces a phase transition and a heat capacity jump and hence
oscillates with . This oscillatory and non-stationary behaviour
measured versus the magnetic field has been studied using the Wigner-Ville
distribution (a time-frequency representation). It is found that the
periodicity of the heat capacity oscillations varies significantly with the
magnetic field; the evolution of the period also depends on the sweeping
direction of the field. This can be attributed to a different behavior between
expulsion and penetration of vortices into the rings. A variation of more than
15% of the periodicity of the heat capacity jumps is observed as the magnetic
field is varied. A description of this phenomenon is given using an analytical
solution of the Ginzburg-Landau equations of superconductivity
Close limit evolution of Kerr-Schild type initial data for binary black holes
We evolve the binary black hole initial data family proposed by Bishop {\em
et al.} in the limit in which the black holes are close to each other. We
present an exact solution of the linearized initial value problem based on
their proposal and make use of a recently introduced generalized formalism for
studying perturbations of Schwarzschild black holes in arbitrary coordinates to
perform the evolution. We clarify the meaning of the free parameters of the
initial data family through the results for the radiated energy and waveforms
from the black hole collision.Comment: 8 pages, RevTex, four eps figure
Moving walls accelerate mixing
Mixing in viscous fluids is challenging, but chaotic advection in principle
allows efficient mixing. In the best possible scenario,the decay rate of the
concentration profile of a passive scalar should be exponential in time. In
practice, several authors have found that the no-slip boundary condition at the
walls of a vessel can slow down mixing considerably, turning an exponential
decay into a power law. This slowdown affects the whole mixing region, and not
just the vicinity of the wall. The reason is that when the chaotic mixing
region extends to the wall, a separatrix connects to it. The approach to the
wall along that separatrix is polynomial in time and dominates the long-time
decay. However, if the walls are moved or rotated, closed orbits appear,
separated from the central mixing region by a hyperbolic fixed point with a
homoclinic orbit. The long-time approach to the fixed point is exponential, so
an overall exponential decay is recovered, albeit with a thin unmixed region
near the wall.Comment: 17 pages, 13 figures. PDFLaTeX with RevTeX 4-1 styl
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