Spectral Statistics for the Dirac Operator on Graphs

We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level statistics are expected, in the semiclassical limit, to correspond to those of random matrices from the Gaussian symplectic ensemble. This is confirmed by numerical investigation. The scattering matrix used to formulate the quantisation condition is found to be independent of the type of spinor. We derive an exact trace formula for the spectrum and use this to investigate the form factor in the diagonal approximation

Determinants of short-period heart rate variability in the general population

Decreased heart rate variability (HRV) is associated with a worse prognosis in a variety of diseases and disorders. We evaluated the determinants of short-period HRV in a random sample of 149 middle-aged men and 137 women from the general population. Spectral analysis was used to compute low-frequency (LF), high-frequency (HF) and total-frequency power. HRV showed a strong inverse association with age and heart rate in both sexes with a more pronounced effect of heart rate on HRV in women. Age and heart rate-adjusted LF was significantly higher in men and HF higher in women. Significant negative correlations of BMI, triglycerides, insulin and positive correlations of HDL cholesterol with LF and total power occurred only in men. In multivariate analyses, heart rate and age persisted as prominent independent predictors of HRV. In addition, BMI was strongly negatively associated with LF in men but not in women, We conclude that the more pronounced vagal influence in cardiac regulation in middle-aged women and the gender-different influence of heart rate and metabolic factors on HRV may help to explain the lower susceptibility of women for cardiac arrhythmias. Copyright (C) 2001 S. Karger AG, Basel

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

We determine the asymptotics of the two-point correlation function for quantum systems with half-integer spin which show chaotic behaviour in the classical limit using a method introduced by Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472-1475]. For time-reversal invariant systems we obtain the leading terms of the two-point correlation function of the Gaussian symplectic ensemble. Special attention has to be paid to the role of Kramers' degeneracy.Comment: 7 pages, no figure

Wind morphology around cool evolved stars in binaries: the case of slowly accelerating oxygen-rich outflows

The late stellar evolutionary phases of low and intermediate-mass stars are strongly constrained by their mass-loss rates. The wind surrounding cool evolved stars frequently shows non-spherical features, thought to be due to an unseen companion orbiting the donor star. We study the morphology of the circumbinary envelope, in particular around oxygen-rich asymptotic giant branch (AGB) stars. We run a grid of 70 3D hydrodynamics simulations of a progressively accelerating wind propagating in the Roche potential formed by a mass-loosing evolved star in orbit with a main sequence companion. We resolve the flow structure both in the immediate vicinity of the secondary, where bow shocks, outflows and wind-captured disks form, and up to 40 orbital separations, where spiral arms, arcs and equatorial density enhancements develop. When the companion is deeply engulfed in the wind, the lower terminal wind speeds and more progressive wind acceleration around oxygen-rich AGB stars make them more prone than carbon-rich AGB stars to display more disturbed outflows, a disk-like structure around the companion and a wind concentrated in the orbital plane. In these configurations, a large fraction of the wind is captured by the companion which leads to a significant shrinking of the orbit over the mass-loss timescale, if the donor star is at least a few times more massive than its companion. Provided the companion has a mass of at least a tenth of the mass of the donor star, it can compress the wind in the orbital plane up to large distances. Our grid of models covers a wide scope of configurations function of the dust chemical content, the terminal wind speed relative to the orbital speed, the extension of the dust condensation region around the cool evolved star and the mass ratio. It provides a frame of reference to interpret high-resolution maps of the outflows surrounding cool evolved stars

Proposal for a standard problem for micromagnetic simulations including spin-transfer torque

The spin-transfer torque between itinerant electrons and the magnetization in a ferromagnet is of fundamental interest for the applied physics community. To investigate the spin-transfer torque, powerful simulation tools are mandatory. We propose a micromagnetic standard problem includingthe spin-transfer torque that can be used for the validation and falsication of micromagnetic simulation tools. The work is based on the micromagnetic model extended by the spin-transfer torque in continuously varying magnetizations as proposed by Zhang and Li. The standard problem geometry is a permalloy cuboid of 100 nm edge length and 10 nm thickness, which contains a Landau pattern with a vortex in the center of the structure. A spin-polarized dc current density of 1012 A/m2 flows laterally through the cuboid and moves the vortex core to a new steady-state position. We show that the new vortex-core position is a sensitive measure for the correctness of micromagnetic simulatorsthat include the spin-transfer torque. The suitability of the proposed problem as a standard problem is tested by numerical results from four different finite-difference and finite-element-based simulation tools

Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2

The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the Gaussian symplectic ensemble is demonstrated. A duality between the underlying generating functions of the orthogonal and symplectic symmetry classes is semiclassically established

SPH modelling of companion-perturbed AGB outflows including a new morphology classification scheme

CONTEXT: Asymptotic giant branch (AGB) stars are known to lose a significant amount of mass by a stellar wind, which controls the remainder of their stellar lifetime. High angular-resolution observations show that the winds of these cool stars typically exhibit mid- to small-scale density perturbations such as spirals and arcs, believed to be caused by the gravitational interaction with a (sub-)stellar companion. AIMS: We aim to explore the effects of the wind-companion interaction on the 3D density and velocity distribution of the wind, as a function of three key parameters: wind velocity, binary separation and companion mass. For the first time, we compare the impact on the outflow of a planetary companion to that of a stellar companion. We intend to devise a morphology classification scheme based on a singular parameter. METHODS: We ran a small grid of high-resolution polytropic models with the smoothed particle hydrodynamics (SPH) numerical code PHANTOM to examine the 3D density structure of the AGB outflow in the orbital and meridional plane and around the poles. By constructing a basic toy model of the gravitational acceleration due to the companion, we analysed the terminal velocity reached by the outflow in the simulations. RESULTS: We find that models with a stellar companion, large binary separation and high wind speed obtain a wind morphology in the orbital plane consisting of a single spiral structure, of which the two edges diverge due to a velocity dispersion caused by the gravitational slingshot mechanism. In the meridional plane the spiral manifests itself as concentric arcs, reaching all latitudes. When lowering the wind velocity and/or the binary separation, the morphology becomes more complex: in the orbital plane a double spiral arises, which is irregular for the closest systems, and the wind material gets focussed towards the orbital plane, with the formation of an equatorial density enhancement (EDE) as a consequence. Lowering the companion mass from a stellar to a planetary mass, reduces the formation of density perturbations significantly. CONCLUSIONS: With this grid of models we cover the prominent morphology changes in a companion-perturbed AGB outflow: slow winds with a close, massive binary companion show a more complex morphology. Additionally, we prove that massive planets are able to significantly impact the density structure of an AGB wind. We find that the interaction with a companion affects the terminal velocity of the wind, which can be explained by the gravitational slingshot mechanism. We distinguish between two types of wind focussing to the orbital plane resulting from distinct mechanisms: global flattening of the outflow as a result of the AGB star’s orbital motion and the formation of an EDE as a consequence of the companion’s gravitational pull. We investigate different morphology classification schemes and uncover that the ratio of the gravitational potential energy density of the companion to the kinetic energy density of the AGB outflow yields a robust classification parameter for the models presented in this paper

SPH modelling of wind-companion interactions in eccentric AGB binary systems

The late evolutionary stages of low- and intermediate-mass stars are characterised by mass loss through a dust-driven stellar wind. Recent observations reveal complex structures within these winds, that are believed to be formed primarily via interaction with a companion. How these complexities arise, and which structures are formed in which type of systems, is still poorly understood. Particularly, there is a lack of studies investigating the structure formation in eccentric systems. We aim to improve our understanding of the wind morphology of eccentric AGB binary systems by investigating the mechanism responsible for the different small-scale structures and global morphologies that arise in a polytropic wind with different velocities. Using the smoothed particle hydrodynamics (SPH) code Phantom, we generate nine different high-resolution, 3D simulations of an AGB star with a solar-mass companion with various wind velocity and eccentricity combinations. The models assume a polytropic gas, with no additional cooling. We conclude that for models with a high wind velocity, the short interaction with the companion results in a regular spiral morphology, that is flattened. In the case of a lower wind velocity, the stronger interaction results in the formation of a high-energy region and bow-shock structure that can shape the wind into an irregular morphology if instabilities arise. High-eccentricity models show a complex, phase-dependent interaction leading to wind structures that are irregular in three dimensions. However, the significant interaction with the companion compresses matter into an equatorial density enhancement, irrespective of eccentricity.Comment: 23 pages, 22 figure

The Dwarf Galaxy Population of the Dorado group down to Mv=-11

We present V and I CCD photometry of suspected low-surface brightness dwarf galaxies detected in a survey covering ~2.4 deg^2 around the central region of the Dorado group of galaxies. The low-surface brightness galaxies were chosen based on their sizes and magnitudes at the limiting isophote of 26.0V\mu. The selected galaxies have magnitudes brighter than V=20 (Mv=-11 for an assumed distance to the group of 17.2 Mpc), with central surface brightnesses \mu0>22.5 V mag/arcsec^2, scale lengths h>2'', and diameters > 14'' at the limiting isophote. Using these criteria, we identified 69 dwarf galaxy candidates. Four of them are large very low-surface brightness galaxies that were detected on a smoothed image, after masking high surface brightness objects. Monte Carlo simulations performed to estimate completeness, photometric uncertainties and to evaluate our ability to detect extended low-surface brightness galaxies show that the completeness fraction is, on average, > 80% for dwarf galaxies with $-17<M_{V}<-10.5$ and 22.5<\mu0<25.5 V mag/arcsec^2, for the range of sizes considered by us (D>14''). The V-I colors of the dwarf candidates vary from -0.3 to 2.3 with a peak on V-I=0.98, suggesting a range of different stellar populations in these galaxies. The projected surface density of the dwarf galaxies shows a concentration towards the group center similar in extent to that found around five X-ray groups and the elliptical galaxy NGC1132 studied by Mulchaey and Zabludoff (1999), suggesting that the dwarf galaxies in Dorado are probably physically associated with the overall potential well of the group.Comment: 32 pages, 16 postscript figures and 3 figures in GIF format, aastex v5.0. To appear in The Astronomical Journal, January 200