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 $C_{p}$ of an array of independent aluminum rings has been measured under an external magnetic field $\vec{H}$ 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 $C_{p}$ oscillates with $\vec{H}$. 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