Local Decoders for the 2D and 4D Toric Code

We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a model of independent $X$ and $Z$ errors and faulty syndrome measurements with identical probability we report a threshold of $0.133\%$ for this Harrington decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings arXiv:1312.2546 . Incorporating a method for handling faulty syndromes we estimate a threshold of $1.59\%$ for the same noise model as in the 2D case. We compare the performance of this decoder with a decoder based on a 4D version of Toom's cellular automaton rule as well as the decoding method suggested by Dennis et al. arXiv:quant-ph/0110143 .Comment: 22 pages, 21 figures; fixed typos, updated Figures 6,7,8,

Forward acoustic performance of a model turbofan designed for a high specific flow (QF-14)

Forward noise and overall aerodynamic performance are presented for a high-tip-speed fan having an exceptionally high average axial Mach number at the rotor inlet. This high Mach number is intended to attenuate forward noise at both the design-speed takeoff point, and at the unconventional low-pressure-ratio, design-speed approach point. As speed was increased near design, all forward noise components were reduced, and rear noise in the discharge duct was increased, indicating that the high Mach number flow at the rotor face is attenuating forward noise at takeoff. The fan at takeoff is some 5.5 to 11 dB quieter than several reference fans. Data at the point closest to approach indicated tentatively that the design-speed approach mode was 3 dB quieter than the conventional mode

Demixing can occur in binary hard-sphere mixtures with negative non-additivity

A binary fluid mixture of non-additive hard spheres characterized by a size ratio $\gamma=\sigma_2/\sigma_1<1$ and a non-additivity parameter $\Delta=2\sigma_{12}/(\sigma_1+\sigma_2)-1$ is considered in infinitely many dimensions. From the equation of state in the second virial approximation (which is exact in the limit $d\to\infty$) a demixing transition with a critical consolute point at a packing fraction scaling as $\eta\sim d 2^{-d}$ is found, even for slightly negative non-additivity, if $\Delta>-{1/8}(\ln\gamma)^2$. Arguments concerning the stability of the demixing with respect to freezing are provided.Comment: 4 pages, 2 figures; title changed; final paragraph added; to be published in PRE as a Rapid Communicatio

Lie Symmetry Analysis for Cosserat Rods

We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s,t) and three arbitrary functions in t. Assuming analyticity of the arbitrary functions in a domain under consideration, we prove that the obtained solution is analytic and general. The Special Cosserat Theory of Rods describes the dynamic equilibrium of 1-dimensional continua, i.e. slender structures like fibers, by means of a system of partial differential equations.Comment: 12 Pages, 1 Figur

Parametric versus Nonparametric Treatment of Unobserved Heterogeneity in Multivariate Failure Times

Two contrary methods for the estimation of a frailty model of multivariate failure times are presented. The assumed Accelerated Failure Time Model includes censored data, observed covariates and unobserved heterogeneity. The parametric estimator maximizes the marginal likelihood whereas the method which does not require distributional assumptions combines the GEE approach (Liang and Zeger, 1986) with the Buckley-James (1979) estimator for censored data. Monte Carlo experiments are conducted to compare the methods under various conditions with regard to bias and efficiency. The ML estimator is found to be rather robust against some misspecifications and both methods seem to be interesting alternatives in uncertain circumstances which lack exact solutions. The methods are applied to data of recurrent purchase acts of yogurt brands

General health and residential proximity to the coast in Belgium : results from a cross-sectional health survey

The health risks of coastal areas have long been researched, but the potential benefits for health are only recently being explored. The present study compared the general health of Belgian citizens a) according to the EU's definition of coastal ( 50 km), and b) between eight more refined categories of residential proximity to the coast ( 250 km). Data was drawn from the Belgian Health Interview Survey (n = 60,939) and investigated using linear regression models and mediation analyses on several hypothesized mechanisms. Results indicated that populations living 50-100 km. Four commonly hypothesized mechanisms were considered but no indirect associations were found: scores for mental health, physical activity levels and social contacts were not higher at 0-5 km from the coast, and air pollution (PM ic , concentrations) was lower at 0-5 km from the coast but not statistically associated with better health. Results are controlled for typical variables such as age, sex, income, neighbourhood levels of green and freshwater blue space, etc. The spatial urban-rural-nature mosaic at the Belgian coast and alternative explanations are discussed. The positive associations between the ocean and human health observed in this study encourage policy makers to manage coastal areas sustainably to maintain associated public health benefits into the future

Structure of hard-hypersphere fluids in odd dimensions

The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities $d$ are studied with an analytical approximation method that generalizes the Rational Function Approximation earlier introduced in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A {\bf 43}, 5418 (1991)]. The theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in Laplace space, the coefficients being determined by simple physical requirements. Fourier transform in terms of reverse Bessel polynomials constitute the mathematical framework of this approximation, from which an analytical expression for the static structure factor is obtained. In its most elementary form, the method recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike equation for hyperspheres at odd dimension. The present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state. Excellent agreement with available computer simulation data at $d=5$ and $d=7$ is obtained. As a byproduct of this study, an exact and explicit polynomial expression for the intersection volume of two identical hyperspheres in arbitrary odd dimensions is given.Comment: 18 pages, 7 figures; v2: new references added plus minor changes; to be published in PR

Transient nucleation driven by solvent evaporation

We theoretically investigate homogeneous crystal nucleation in a solution containing a solute and a volatile solvent. The solvent evaporates from the solution, thereby continuously increasing the concentration of the solute. We view it as an idealized model for the far-out-of-equilibrium conditions present during the liquid-state manufacturing of organic electronic devices. Our model is based on classical nucleation theory, taking the solvent to be a source of the transient conditions in which the solute drops out of solution. Other than that, the solvent is not directly involved in the nucleation process itself. We approximately solve the kinetic master equations using a combination of Laplace transforms and singular perturbation theory, providing an analytical expression for the nucleation flux, predicting that (i) the nucleation flux lags slightly behind a commonly used quasi-steady-state approximation, an effect that is governed by two counteracting effects originating from the solvent evaporation: while a faster evaporation rate results in an increasingly larger influence of the lag time on the nucleation flux, this lag time itself we find to decrease with increasing evaporation rate, (ii) the nucleation flux and the quasi-steady-state nucleation flux are never identical, except trivially in the stationary limit and (iii) the initial induction period of the nucleation flux, which we characterize with a generalized induction time, decreases weakly with the evaporation rate. This indicates that the relevant time scale for nucleation also decreases with increasing evaporation rate. Our analytical theory compares favorably with results from numerical evaluation of the governing kinetic equations