Approximation of the acoustic radiation impedance of a cylindrical pipe

Useful approximation formulae for radiation impedance are given for the reflection coefficients of both infinitely flanged and unflanged rigid-walled cylindrical ducts. The expressions guarantee that simple but necessary physical and mathematical principles are met, like hermitian symmetry for the reflection coefficient (identical behaviour of positive and negative frequencies) and causality for the impulse response. A non causal but more accurate expression is also proposed that is suitable for frequency-domain applications. The formulae are obtained by analytical and numerical fitting to reference results from Levine & Schwinger for the unflanged case and extracted from the radiation impedance matrix given by Zorumski for the infinite flanged case.Comment: Journal of Sound and Vibration (2008) accepte

Anisotropic elasticity in confocal studies of colloidal crystals

We consider the theory of fluctuations of a colloidal solid observed in a confocal slice. For a cubic crystal we study the evolution of the projected elastic properties as a function of the anisotropy of the crystal using numerical methods based on the fast Fourier transform. In certain situations of high symmetry we find exact analytic results for the projected fluctuations.Comment: 6 pages, 7 figure

The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Transformation elastodynamics and active exterior acoustic cloaking

This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we study the effect of transformations on a mass-spring network model. The transformed networks can be realized with "torque springs", which are introduced here and are springs with a force proportional to the displacement in a direction other than the direction of the spring terminals. Possible homogenizations of the transformed networks are presented, with potential applications to cloaking. In the second and third parts we present cloaking methods that are based on cancelling an incident field using active devices which are exterior to the cloaked region and that do not generate significant fields far away from the devices. In the second part, the exterior cloaking problem for the Laplace equation is reformulated as the problem of polynomial approximation of analytic functions. An explicit solution is given that allows to cloak larger objects at a fixed distance from the cloaking device, compared to previous explicit solutions. In the third part we consider the active exterior cloaking problem for the Helmholtz equation in 3D. Our method uses the Green's formula and an addition theorem for spherical outgoing waves to design devices that mimic the effect of the single and double layer potentials in Green's formula.Comment: Submitted as a chapter for the volume "Acoustic metamaterials: Negative refraction, imaging, lensing and cloaking", Craster and Guenneau ed., Springe

Unilateral interactions in granular packings: A model for the anisotropy modulus

Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results.Comment: 6 pages, 5 figure

"Author! Author!" : Shakespeare and biography

Original article can be found at: http://www.informaworld.com/smpp/title~content=t714579626~db=all Copyright Informa / Taylor & Francis Group. DOI: 10.1080/17450910902764454Since 1996, not a year has passed without the publication of at least one Shakespeare biography. Yet for many years the place of the author in the practice of understanding literary works has been problematized, and even on occasions eliminated. Criticism reads the “works”, and may or may not refer to an author whose “life” contributed to their meaning. Biography seeks the author in the works, the personality that precedes the works and gives them their characteristic shape and meaning. But the form of literary biography addresses the unusual kind of “life” that puts itself into “works”, and this is particularly challenging where the “works” predominate massively over the salient facts of the “life”. This essay surveys the current terrain of Shakespeare biography, and considers the key questions raised by the medium: can we know anything of Shakespeare's “personality” from the facts of his life and the survival of his works? What is the status of the kind of speculation that inevitably plays a part in biographical reconstruction? Are biographers in the end telling us as much about themselves as they tell us about Shakespeare?Peer reviewe

Severity of asymptomatic carotid stenosis and risk of ipsilateral hemispheric ischaemic events: Results from the ACSRS study

Objectives. This study determines the risk of ipsilateral ischaemic neurological events in relation to the degree of asymptomatic carotid stenosis and other risk factors. Methods. Patients (n = 1115) with asymptomatic internal carotid artery (ICA) stenosis greater than 50% in relation to the bulb diameter were followed up for a period of 6-84 (mean 37.1) months. Stenosis was graded using duplex, and clinical and biochemical risk factors were recorded. Results. The relationship between ICA stenosis and event rate is linear when stenosis is expressed by the ECST method, but S-shaped if expressed by the NASCET method. In addition to the ECST grade of stenosis (RR 1.6; 95% CI 1.21-2.15), history of contralateral TIAs (RR 3.0; 95% CI 1.90-4.73) and creatinine in excess of 85 μmol/L (RR 2.1; 95% CI 1.23-3.65) were independent risk predictors. The combination of these three risk factors can identify a high-risk group (7.3% annual event rate and 4.3% annual stroke rate) and a low risk group (2.3% annual event rate and 0.7% annual stroke rate). Conclusions. Linearity between ECST percent stenosis and risk makes this method for grading stenosis more amenable to risk prediction without any transformation not only in clinical practice but also when multivariable analysis is to be used. Identification of additional risk factors provides a new approach to risk stratification and should help refine the indications for carotid endarterectomy. © 2005 Elsevier Ltd. All rights reserved

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc