131 research outputs found
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
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