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.

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.

The impact of maternal cortisol concentrations on child arterial elasticity

Epidemiological studies suggest that glucocorticoid excess in the fetus may contribute to the pathophysiology of cardiovascular diseases in adulthood. However, the impact of maternal glucocorticoid on the cardiovascular system of the offspring has not been much explored in studies involving humans, especially in childhood. The objective of this study was to assess the influence of maternal cortisol concentrations on child arterial elasticity. One hundred and thirty pregnant women followed from 1997 to 2000, and respective children 5-7 years of age followed from 2004 to 2006 were included in the study. Maternal cortisol was determined in saliva by an enzyme immunoassay utilizing the mean concentration of nine samples of saliva. Arterial elasticity was assessed by the large artery elasticity index (LAEI; the capacitive elasticity of large arteries) by recording radial artery pulse wave, utilizing the equipment HDI/PulseWave CR-2000 Cardiovascular Profiling System (R). The nutritional status of the children was determined by the body mass index (BMI). Insulin concentration was assessed by chemiluminescence, and insulin resistance by the homeostasis model assessment. Blood glucose, total cholesterol and fractions (LDL-c and HDL-c) and triglyceride concentrations were determined by automated enzymatic methods. The association between maternal cortisol and child arterial elasticity was assessed by multivariate linear regression analysis. There was a statistically significant association between maternal cortisol and LAEI (P=0.02), controlling for birth weight, age, BMI and HDL-c of the children. This study suggests that exposure to higher glucocorticoid concentrations in the prenatal period is associated to lower arterial elasticity in childhood, an earlier cardiovascular risk marker.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 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).

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

Semiclassical and quantum motions on the non-commutative plane

We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man`ko states and circular squeezed states. The relation between these states and the ""classical"" trajectories is investigated, and we present numerical explorations of some semiclassical quantities. (C) 2009 Elsevier B.V. All rights reserved.

Two-dimensional electron states bound to an off-plane donor in a magnetic field

The states of an electron confined in a two-dimensional (2D) plane and bound to an off-plane donor impurity center, in the presence of a magnetic field, are investigated. The energy levels of the ground state and the first three excited states are calculated variationally. The binding energy and the mean orbital radius of these states are obtained as a function of the donor center position and the magnetic field strength. The limiting cases are discussed for an in-plane donor impurity (i.e. a 2D hydrogen atom) as well as for the donor center far away from the 2D plane in strong magnetic fields, which corresponds to a 2D harmonic oscillator.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the ( finite and infinite) virtually cyclic subgroups of the pure braid groups P(n)(RP(2)) of the projective plane. The maximal finite subgroups of P(n)(RP(2)) are isomorphic to the quaternion group of order 8 if n = 3, and to Z(4) if n >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

Formation of out of plane oxime metallacycles in [Cu(2)] and [Cu(4)] complexes

The reaction Of Cu(ClO(4))(2)center dot 6H(2)O with dimethylglyoxime (H(2)dmg) in a 1:1 mole ratio in aqueous methanol at room temperature affords the dinuclear complex [Cu(2)(mu-Hdmg)(4)] (1). Reaction of 1 with [Cu(bpy)(H(2)O)(2)](ClO(4))(2) (bpy = 2,2`-bipyridine) in a 1:1 mole ratio in aqueous methanol at room temperature yields the tetranuclear complex [Cu(2)(mu-HdMg)(2)(mu-dMg)(2)(bpy)(2)(H(2)O)(2)](ClO(4))(2) (2). The direct reaction of Cu(ClO(4))(2)center dot 6H(2)O with H(2)dmg and bpy in a 2:21 mole ratio in aqueous methanol at room temperature also yields 2 quantitatively. The complexes 1 and 2 were structurally characterized by X-ray crystallography. Unlike the binding in Ni/Co-dmg, two different types of N-O bridging modes during the oxime based metallacycle formation and stacking of square planar units have been identified in these complexes. The neutral dinuclear complex 1 has CuN(4)O coordination spheres and complex 2 consists of a dicationic [Cu(2)(mu-HdMg)(2)(mu-dMg)(2)(bpy)(2)(H(2)O)(2)](2+) unit and two uncoordinated ClO(4)(-) anions having CuN(4)O and CuN(2)O(3) coordination spheres. The two copper(II) ions are at a distance of 3.846(8) angstrom in 1 for the trans out of plane link and at 3.419(10) and 3.684(10) angstrom in 2 for the trans out of plane and cis in plane arrangements, respectively. The average Cu-N(oxime) distances are 1.953 and 1.935 angstrom, respectively. The average basal and apical Cu-N(oxime) distances are 1.945, 2.295 and 2.429 angstrom. The UV-Vis spectra of 2 is similar to the spectrum of the reaction mixture of 1 and [Cu(bpy)(H(2)O)(2)](2+). Variable temperature magnetic properties measurement shows that the interaction between the paramagnetic copper centers in complex I is antiferromagnetic in nature. The EPR spectra of frozen solution of the complexes at 77 K consist of axially symmetric fine-structure transitions (Delta M(S) = 1) and half-field signals (Delta M(S) = 2) at ca. 1600 G, suggesting the presence of appreciable Cu-Cu interactions. (C) 2009 Elsevier Ltd. All rights reserved.

Price elasticity of demand for cigarettes : The Case of Sweden

Due to health problems and the negative externalities associated with cigarette consumption, many governments try to discourage cigarette consumption by increasing its price through taxation. However, cigarette, like the other addictive goods, is viewed as that it is not sensitive to demand rules and the market forces. This study analyses the effect of price increase on cigarette consumption. We used Swedish time series data from 1970 to 2010. Our results reveal that though cigarette is addictive substance its demand is sensitive to changes in the price. Estimates from this study indicate short-run price-elasticity of -0.29 and the long run price elasticity of -0.47.