FFTs for the 2-Sphere-Improvements and Variations

Earlier work by Driscoll and Healy has produced an efficient algorithm for computing the Fourier transform of band-limited functions on the 2-sphere. In this paper we present a reformulation and variation of the original algorithm which results in a greatly improved inverse transform, and consequent improved convolution algorithm for such functions. All require at most 0(N log2 N) operations where N is the number of sample points. We also address implementation considerations and give heuristics for allowing reliable floating point implementations of a slightly modified algorithm at little cost in either theoretical or actual performance. These claims are supported by extensive numerical experiments from our implementation in C on DEC and Sun workstations. These results give strong indications that the algorithm is both reliable and efficient for a large range of useful problem sizes. The paper concludes with a brief discussion of a few potential appications

Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence

We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1 dimensions [Phys. Rev. Lett. 104, 230601 (2010); Sci. Rep. 1, 34 (2011)]. Here we investigate both circular and flat interfaces and report their statistics in detail. First we demonstrate that their fluctuations show not only the KPZ scaling exponents but beyond: they asymptotically share even the precise forms of the distribution function and the spatial correlation function in common with solvable models of the KPZ class, demonstrating also an intimate relation to random matrix theory. We then determine other statistical properties for which no exact theoretical predictions were made, in particular the temporal correlation function and the persistence probabilities. Experimental results on finite-time effects and extreme-value statistics are also presented. Throughout the paper, emphasis is put on how the universal statistical properties depend on the global geometry of the interfaces, i.e., whether the interfaces are circular or flat. We thereby corroborate the powerful yet geometry-dependent universality of the KPZ class, which governs growing interfaces driven out of equilibrium.Comment: 31 pages, 21 figures, 1 table; references updated (v2,v3); Fig.19 updated & minor changes in text (v3); final version (v4); J. Stat. Phys. Online First (2012

Avalanche Dynamics in Evolution, Growth, and Depinning Models

The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and evolution is presented. Specifically, we include the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models into a unified treatment encompassing a large class of far from equilibrium processes. The formation of fractal structures, the appearance of $1/f$ noise, diffusion with anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be related to the same underlying avalanche dynamics. This dynamics can be represented as a fractal in $d$ spatial plus one temporal dimension. We develop a scaling theory that relates many of the critical exponents in this broad category of extremal models, representing different universality classes, to two basic exponents characterizing the fractal attractor. The exact equations and the derived set of scaling relations are consistent with numerical simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the manuscript supplied on reques

Effects of shoe sole geometry on toe clearance and walking stability in older adults

Thirty-five percent of people above age 65 fall each year, and half of their falls are associated with tripping: tripping, an apparently ‘mundane’ everyday problem, therefore significantly impacts on older people's health and associated medical costs. To avoid tripping and subsequent falling, sufficient toe clearance during the swing phase is crucial. We previously found that a rocker-shaped shoe sole enhances toe clearance in young adults, thereby decreasing their trip-risk. This study investigates whether such sole design also enhances older adults’ toe clearance, without inadvertently affecting their walking stability. Toe clearance and its variability are reported together with measures of walking stability for twelve older adults, walking in shoes with rocker angles of 10°, 15°, and 20° degrees. Surface inclinations (flat, incline, decline) were chosen to reflect a potential real-world environment. Toe clearance increased substantially from the 10° to the 15° degree rocker angle (p = 0.003) without compromising measures of walking stability (p > 0.05). A further increase in rocker angle to 20° degrees resulted in less substantial enhancement of toe clearance and came at the cost of a decrease in gait speed on the decline. The novelty of this investigation lies in the exploration of the trade-off between reduction of trip- risk through footwear design and adverse effects on walking stability on real-life relevant surfaces. A large amount of slip-resistant footwear is already available; our two studies highlight that footwear may also be designed to reduce trip-risk

Anisotropy studies around the galactic centre at EeV energies with the Auger Observatory

Data from the Pierre Auger Observatory are analyzed to search for anisotropies near the direction of the Galactic Centre at EeV energies. The exposure of the surface array in this part of the sky is already significantly larger than that of the fore-runner experiments. Our results do not support previous findings of localized excesses in the AGASA and SUGAR data. We set an upper bound on a point-like flux of cosmic rays arriving from the Galactic Centre which excludes several scenarios predicting sources of EeV neutrons from Sagittarius $A$. Also the events detected simultaneously by the surface and fluorescence detectors (the `hybrid' data set), which have better pointing accuracy but are less numerous than those of the surface array alone, do not show any significant localized excess from this direction.Comment: Matches published versio

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society