The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

Padé approximants for the acoustical characteristics of rigid frame porous media

In this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media, especially those involving ratios of Bessel functions of complex argument, can be accurately approximated and greatly simplified by the use of Padé approximation techniques. In the case of the model of Attenborough [J. Acoust. Soc. Am. 81, 93–102 (1987)] rational approximations are produced for the characteristic impedance, propagation constant, dynamic compressibility, and dynamic density, as a function of frequency and the material parameters. The model proposed by Stinson and Champoux

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Time development of small disturbances to plane Couette Flow

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.

Optimal frame length for keeping normalized goodput with lowest requirement on BER

This paper presents an adaptive frame length mechanism based on a cross-layer analysis of intrinsic relations between the MAC frame length, bit error rate (BER) of the wireless link and normalized goodput. The proposed mechanism selects the optimal frame length that keeps the service normalized goodput at required levels while satisfying the lowest requirement on the BER, thus increasing the transmission reliability. Numerical results are provided and show that an optimal frame length satisfying the lowest BER requirement does indeed exist. The performance of BER requirement as a function of the MAC frame length is evaluated and compared for transmission scenarios with and without automatic repeat request (ARQ). Furthermore, issues related to the MAC overhead length are also discussed to illuminate the functionality and performance of the proposed mechanism.

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Influence of water flow rate on shear bond strength of resin composite to Er : YAG cavity preparation

Purpose: To evaluate in vitro the influence of water flow rate on shear bond strength of a resin composite to enamel and dentin after Er:YAG cavity preparation. Methods: Ten bovine incisors were selected and roots removed. Crowns were sectioned in four pieces, resulting in 40 samples that were individually embedded in polyester resin (n=10), and ground to plane the enamel and expose the dentin. The bonding site was delimited and samples were randomly assigned according to cavity preparation: (1) Er:YAG/1.0 mL/minute; (2) Er:YAG/1.5 mL/minute; (3) Er:YAG/2.0 mL/minute and (4) High speed handpiece/bur (control group). Samples were fixed to a metallic device, where composite resin cylinders were prepared. Subsequently, they were stored for 24 hours and subjected to a shear bond strength test (500N at 0.5 mm/minute). Results: Means (MPa) were: enamel: 1: 12.8; 2: 16.8; 3: 17.5; 4: 36.0 and Dentin: 1: 13.6; 2: 18.7; 3: 12.1; 4: 21.3. Data were submitted to ANOVA and Tukey`s test. Adhesion to enamel was more efficient than for dentin. The cavities prepared with conventional bur (control) presented higher statistically significant bond strength values (P<0.05) than for Er:YAG laser for both enamel and dentin. No significant differences were observed between water flow rates employed during enamel ablation. For dentin, the shear bond strength of 2.0 mL/minute water flow rate was lower than for 1.5 mL/minute and 1.0 mL/minute rates. The Er:YAG laser adversely affected shear bond strength of resin composite to both enamel and dentin, regardless of the water flow rate used.

Ablation of primary afferent neurons by neonatal capsaicin treatment reduces the susceptibility of the portal hypertensive gastric mucosa to ethanol-induced injury in cirrhotic rats

Primary sensory afferent neurons modulate the hyperdynamic circulation in Cirrhotic rats with portal hypertension.The stomach of cirrhotic rats is prone to damage induced by ethanol, a phenomenon associated with reduced gastric hyperemic response to acid-back diffusion. The aim of this study was to examine the impact of ablation of capsaicin-sensitive neurons and the tachykinin NK(1) receptor antagonist A5330 on the susceptibility of the portal hypertensive gastric mucosa, to ethanol-induced injury and its effects on gastric cyclooxygenase (COX) and nitric oxide synthase (NOS) mRNA expression. Capsaicin was administered to neonatal, male, Wistar rats and the animals were allowed to grow. Cirrhosis was then induced by bile duct ligation in adult rats while controls had sham operation. Ethanol-induced gastric damage was assessed using ex vivo gastric chamber experiments. Gastric blood flow was measured as well as COX/NOS mRNA expression. Topical application of ethanol produced significant gastric damage in cirrhotic rats compared to controls, which was reversed in capsaicin- and A5330-treated animals. Mean arterial and portal pressure was normalized in capsaicin-treated cirrhotic rats. Capsaicin and A5330 administration restored gastric blood flow responses to topical application of ethanol followed by acid in cirrhotic rats. Differential COX and NOS mRNA expression was noted in bile duct ligated rats relative to controls. Capsaicin treatment significantly modified gastric eNOS/iNOS/COX-2 mRNA expression in cirrhotic rats. Capsaicin-sensitive neurons modulate the susceptibility of the portal hypertensive gastric mucosa to injury induced by ethanol via tachykinin NK(1) receptors and signalling of prostaglandin and NO production/release. (c) 2008 Elsevier B.V. All rights reserved.

Plane curve diagrams and geometrical applications

We look at plane curve diagrams (f,alpha), which are given by a plane curve multigerm alpha : (R, S) -> R(2) and a function on it f : (R, S) -> R. We obtain a classification of all such diagrams, where alpha has e-codimension <= 2 and f has finite order. Then we define an equivalence between plane curves which we call Ah(alpha)-equivalence and which is determined by the class of the diagram (h(alpha), alpha). Here, h alpha denotes the height function of alpha with respect to its normal vector. This is an equivalence which not only takes into account the topology of the singularity of alpha, but also its flat geometry. Finally, we apply our results in order to obtain a classification of all the plane projections of a generic space curve gamma embedded in R(3).

Stress distribution in orthodontic mini-implants

The objective of this study was to evaluate the stress distribution in the resin in contact with the spirals of cylindrical and conical mini-implants, when submitted to lateral load and insertion torsion. A photoelastic model was fabricated using transparent gelatin to simulate the alveolar bone. The model was observed with a plane polariscope and photographically recorded before and after activation of the two screws with a lateral force and torsion. The lateral force application caused bending moments on both mini-implants, with the uprising of fringes or isochromatics, characteristics of stresses, along the threads of the mini-implants and in the apex. When the torsion was exerted in the mini-implants, a great concentration of stress upraised close to the apex. The conclusion was that, comparing conical with cylindrical mini-implants under lateral load, the stresses were similar on the traction sides. The differences appear (1) on the apex, where the cylindrical mini-implant showed a greater concentration of stress, and (2) along the spirals, in the compression side, where the conical mini-implant showed a greater concentration of stress. The greater part of the stress produced by both mini-implants, after torsion load in insertion, were concentrated on the apex. With the cylindrical mini-implant, the greater concentration of tension was close to the apex, while with the conical one, the stresses were distributed along a greater amount of apical threads.

Influence of quantum-dots density on average in-plane strain of optoelectronic devices investigated by high-resolution X-ray diffraction

High-resolution X-ray diffractometry is used to probe the nature of a diffraction-peak broadening previously noticed in quantum dots (QDs) systems with freestanding InAs islands on top of GaAs (001) substrates [Freitas et al., Phys. Status Solidi (A) 204, 2548 (2007)]. The procedure is hence extended to further investigate the capping process of InAs/GaAs QDs. A direct correlation is established between QDs growth rates and misorientation of lattice-planes at the samples surfaces. This effect provides an alternative too] for studying average strain fields on QDs systems in standard triple axis diffractometers running on X-ray tube sources, which are much more common than synchrotron facilities. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Reentrant quantum Hall effect in bilayer system at high filling factors

We report on the measurements of the quantum Hall effect states in double quantum well structures at the filling factors v = 4N + 1 and 4N + 3, where N is the Landau index number, in the presence of the in-plane magnetic field. The quantum Hall states at these filling factors vanish and reappear several times. Repeated reentrance of the transport gap occurs due to the periodic vanishing of the tunneling amplitude in the presence of the in-plane field. When the gap vanishes, the transport becomes anisotropic. The anisotropy persist at half-odd filling factors, when bilayer quantum Hall states are recovered with increase of the tilt angle. (C) 2007 Elsevier B.V. All rights reserved.