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

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

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

The fate of non-polynomial interactions in scalar field theory

We present an exact RG (renormalization group) analysis of $O(N)$-invariant scalar field theory about the Gaussian fixed point. We prove a series of statements that taken together show that the non-polynomial eigen-perturbations found in the LPA (local potential approximation) at the linearised level, do not lead to new interactions, \textit{i.e.} enlarge the universality class, neither in the LPA or treated exactly. Non-perturbatively, their RG flow does not emanate from the fixed point. For the equivalent Wilsonian effective action they can be re-expressed in terms of the usual couplings to polynomial interactions, which can furthermore be tuned to be as small as desired for all finite RG time. For the infrared cutoff Legendre effective action, this can also be done for the infrared evolution. We explain why this is nevertheless consistent with the fact that the large field behaviour is fixed by these perturbations.Comment: 32 pages, 1 figure; extended to exact treatmen

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

The accelerated characterization of viscoelastic composite materials

Necessary fundamentals relative to composite materials and viscoelasticity are reviewed. The accelerated characterization techniques of time temperature superposition and time temperature stress superposition are described. An experimental procedure for applying the latter to composites is given along with results obtained on a particular T300/934 graphite/epoxy. The accelerated characterization predictions are found in good agreement with actual long term tests. A postcuring phenomenon is discussed that necessitates thermal conditioning of the specimen prior to testing. A closely related phenomenon of physical aging is described as well as the effect of each on the glass transition temperature and strength. Creep rupture results are provided for a variety of geometries and temperatures for T300/934 graphite/epoxy. The results are found to compare reasonably with a modified kinetic rate theory

Local stabilisation of polar order at charged antiphase boundaries in antiferroelectric (Bi_0.85Nd_0.15)(Ti_0.1Fe_0.9)O₃

Observation of an unusual, negatively-charged antiphase boundary in (Bi<sub>0.85</sub>Nd<sub>0.15</sub>)(Ti<sub>0.1</sub>Fe<sub>0.9</sub>)O<sub>3</sub> is reported. Aberration corrected scanning transmission electron microscopy is used to establish the full three dimensional structure of this boundary including O-ion positions to ~ ± 10 pm. The charged antiphase boundary stabilises tetragonally distorted regions with a strong polar ordering to either side of the boundary, with a characteristic length scale determined by the excess charge trapped at the boundary. Far away from the boundary the crystal relaxes into the well-known Nd-stabilised antiferroelectric phase

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