Approximating the maximum ergodic average via periodic orbits

Let sigma: Sigma(A) -> Sigma(A) be a subshift of finite type, let M-sigma be the set of all sigma-invariant Borel probability measures on Sigma(A), and let f : Sigma(A) -> R be a Holder continuous observable. There exists at least one or-invariant measure A which maximizes integral f d mu. The following question was asked by B. R. Hunt, E. Ott and G. Yuan: how quickly can the maximum of the integrals integral f d mu be approximated by averages along periodic orbits of period less than p? We give an example of a Holder observable f for which this rate of approximation is slower than stretched-exponential in p

Implicit Large-Eddy Simulations of Hot and Cold Supersonic Jets in Loci-CHEM

This paper introduces a 4th-order accurate low-dissipation flux scheme for use on un- structured CFD codes, and compares this flux scheme with two others for LES calculations of hot and cold supersonic jets. The flux schemes are compared with experimental profiles of jet centerline Mach number, total temperature and total pressure, with jet spreading rate data, and with near- field acoustic measurements. The influence of grid resolution on these solution accuracy is also evaluated. The new low-dissipation flux scheme is shown to be stable on a high-speed compressible turbulent ow problem, and to be significantly more accurate than the existing baseline flux approach

On The Linearity of The Black Hole - Bulge Mass Relation in Active and in Nearby Galaxies

Analysis of PG quasar observations suggests a nonlinear relation between the black hole mass, M_BH, and the bulge mass, M_bulge, although a linear relation, as proposed for nearby galaxies, cannot be ruled out. New M_BH values for nearby galaxies from Gebhardt et al., and L_bulge measurements for Seyfert 1 galaxies from Virani et al., are used here to obtain a more accurate value for the slope of the M_BH-M_bulge relation. The combined sample of 40 active and non-active galaxies suggests a significantly nonlinear relation, M_BH\propto M_bulge^{1.53\pm 0.14}. Further support for a nonlinear relation is provided by the slope of the M_BH-stellar velocity dispersion relation found recently, and by the low M_BH found in late type spiral galaxies. The mean M_BH/M_bulge ratio is therefore not a universal constant, but rather drops from ~0.5% in bright (M_V ~ -22) ellipticals, to ~0.05% in low luminosity (M_V ~ -18) bulges. Hubble Space Telescope determinations of M_BH in late type spirals, and of the bulge magnitude in narrow line Seyfert 1 galaxies (both predicted to have low M_BH), can further test the validity of the nonlinear M_BH-M_bulge relation.Comment: Accepted for publication in ApJ, 9 pages inc. 2 figure

The local potential approximation in the background field formalism

Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f(R) approximation in asymptotic safety for gravity.Comment: 40 pages, version accepted by JHE

Role of androgen and gonadotrophins in the development and function of the Sertoli cells and Leydig cells: data from mutant and genetically modified mice

Development and maintenance of the male phenotype and establishment of fertility are all dependent upon the activity of the Sertoli cells and Leydig cells of the testis. This review examines the regulation and function of these cell during fetal and post-natal development. Fetal Leydig cells are sensitive to both luteinising hormone (LH) and adrenocorticotrophic hormone (ACTH) but Leydig cell function appears normal in fetal mice lacking both hormones or their receptors. Post-natally, the Sertoli cells and Leydig cells are reliant upon the pituitary gonadotrophins. Leydig cells are critically dependent on LH but follicle-stimulating hormone (FSH), presumably acting through the Sertoli cell, can also affect Leydig cell function. Testosterone secreted by the Leydig cells acts with FSH to stimulate Sertoli cell activity and spermatogenesis. Study of animals lacking FSH-receptors and androgen-receptors shows that both hormones can act to maintain the meiotic germ cell population but that androgens are critical for completion of meiosis

Assessing carbon-based anodes for lithium-ion batteries: A universal description of charge-transfer binding

Many key performance characteristics of carbon-based lithium-ion battery anodes are largely determined by the strength of binding between lithium (Li) and sp2 carbon (C), which can vary significantly with subtle changes in substrate structure, chemistry, and morphology. Here, we use density functional theory calculations to investigate the interactions of Li with a wide variety of sp2 C substrates, including pristine, defective, and strained graphene; planar C clusters; nanotubes; C edges; and multilayer stacks. In almost all cases, we find a universal linear relation between the Li-C binding energy and the work required to fill previously unoccupied electronic states within the substrate. This suggests that Li capacity is predominantly determined by two key factors -- namely, intrinsic quantum capacitance limitations and the absolute placement of the Fermi level. This simple descriptor allows for straightforward prediction of the Li-C binding energy and related battery characteristics in candidate C materials based solely on the substrate electronic structure. It further suggests specific guidelines for designing more effective C-based anodes. The method should be broadly applicable to charge-transfer adsorption on planar substrates, and provides a phenomenological connection to established principles in supercapacitor and catalyst design.Comment: accepted by Physical Review Letter

Creep-rupture of polymer-matrix composites

An accelerated characterization method for resin matrix composites is reviewed. Methods for determining modulus and strength master curves are given. Creep rupture analytical models are discussed as applied to polymers and polymer matrix composites. Comparisons between creep rupture experiments and analytical models are presented. The time dependent creep rupture process in graphite epoxy laminates is examined as a function of temperature and stress level