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.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

The role of the harmonic vector average in motion integration

The local speeds of object contours vary systematically with the cosine of the angle between the normal component of the local velocity and the global object motion direction. An array of Gabor elements whose speed changes with local spatial orientation in accordance with this pattern can appear to move as a single surface. The apparent direction of motion of plaids and Gabor arrays has variously been proposed to result from feature tracking, vector addition and vector averaging in addition to the geometrically correct global velocity as indicated by the intersection of constraints (IOC) solution. Here a new combination rule, the harmonic vector average (HVA), is introduced, as well as a new algorithm for computing the IOC solution. The vector sum can be discounted as an integration strategy as it increases with the number of elements. The vector average over local vectors that vary in direction always provides an underestimate of the true global speed. The HVA, however, provides the correct global speed and direction for an unbiased sample of local velocities with respect to the global motion direction, as is the case for a simple closed contour. The HVA over biased samples provides an aggregate velocity estimate that can still be combined through an IOC computation to give an accurate estimate of the global velocity, which is not true of the vector average. Psychophysical results for type II Gabor arrays show perceived direction and speed falls close to the IOC direction for Gabor arrays having a wide range of orientations but the IOC prediction fails as the mean orientation shifts away from the global motion direction and the orientation range narrows. In this case perceived velocity generally defaults to the HVA.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Strategies to Optimize Biosensors Based on Impedance Spectroscopy to Detect Phytic Acid Using Layer-by-Layer Films

Impedance spectroscopy has been proven a powerful tool for reaching high sensitivity in sensor arrays made with nanostructured films in the so-called electronic tongue systems, whose distinguishing ability may be enhanced with sensing units capable of molecular recognition. In this study we show that for optimized sensors and bio-sensors the dielectric relaxation processes involved in impedance measurements should also be considered, in addition to an adequate choice of sensing materials. We used sensing units made from layer-by-layer (LbL) films with alternating layers of the polyeletrolytes, poly(allylamine) hydrochloride (PAH) and poly(vinyl sulfonate) (PVS), or LbL films of PAH alternated with layers of the enzyme phytase, all adsorbed on gold interdigitate electrodes. Surprisingly, the detection of phytic acid was as effective in the PVS/PAH sensing system as with the PAH/phytase system, in spite of the specific interactions of the latter. This was attributed to the dependence of the relaxation processes on nonspecific interactions such as electrostatic cross-linking and possibly on the distinct film architecture as the phytase layers were found to grow as columns on the LbL film, in contrast to the molecularly thin PAH/PVS films. Using projection techniques, we were able to detect phytic acid at the micromolar level with either of the sensing units in a data analysis procedure that allows for further optimization.

Quantization of the damped harmonic oscillator revisited

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. (C) 2011 Elsevier B.V. All rights reserved.

In situ impedance spectroscopy study of the electrochemical corrosion of Ti and Ti-6Al-4V in simulated body fluid at 25 degrees C and 37 degrees C

The corrosion resistance of Ti and Ti-6Al-4V was investigated through electrochemical impedance spectroscopy, EIS, potentiodynamic polarisation curves and UV-Vis spectrophotometry. The tests were done in Hank solution at 25 degrees C and 37 degrees C. The EIS measurements were done at the open circuit potential at specific immersion times. An increase of the resistance as a function of the immersion time was observed, for Ti (at 25 degrees C and 37 degrees C), and for Ti-6Al-4V (at 25 degrees C), which was interpreted as the formation and growth of a passive film on the metallic surfaces. (C) 2009 Elsevier Ltd. All rights reserved.

Temperature effects on a network of dissipative quantum harmonic oscillators: collective damping and dispersion processes

In this paper we extend the results presented in (de Ponte, Mizrahi and Moussa 2007 Phys. Rev. A 76 032101) to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whatever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. These solutions are shown to be significantly involved when temperature effects are considered, making difficult the analysis of collective decoherence and dispersion in dissipative bosonic networks. To circumvent these difficulties, we turn to the Wigner distribution function which enables us to present a technique to estimate the decoherence time of network states. Our technique proceeds by computing separately the effects of dispersion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the dispersion mechanism is also presented through the evolution of the Wigner function. The interesting collective dispersion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.

Detection of phenolic compounds using impedance spectroscopy measurements

Langmuir-Blodgett (LB) and layer-by-layer films (LbL) of a PPV (p-phenylenevinylene) derivative, an azo compound and tetrasulfonated phthalocyanines were successfully employed as transducers in an ""electronic tongue"" system for detecting trace levels of phenolic compounds in water. The choice of the materials was based on their distinct electrical natures, which enabled the array to establish a fingerprint of very similar liquids. Impedance spectroscopy measurements were taken in the frequency range from 10 Hz to 1 MHz, with the data analysed with principal component analysis (PCA). The sensing units were obtained from five-layer LB films of (poly[(2-methoxy-5-n-hexyloxy)-p-phenylenevinylene]), OC(1)OC(18)-PPV (poly(2-methoxy,5-(n-octadecyl)-p-phenylenevinylene)), DR (HEMA-co-DR13MA (poly-(hydroxyethylmethacrylate-co-[4`-[[2-(methacryloyloxy)-ethyl]ethylamino]-2-chloro-4-nitroazobenzene]))) and five-bilayer LbL films of tetrasulfonated metallic phthalocyanines deposited onto gold interdigitated electrodes. The sensors were immersed into phenol, 2-chloro-4-methoxyphenol, 2-chlorophenol and 3-chlorophenol (isomers) solutions at 1 x 10(-9) mol L(-1), with control experiments carried out in ultra pure water. Samples could be distinguished if the principal component analysis (PCA) plots were made with capacitance values taken at 10(3) Hz, which is promising for detection of trace amounts of phenolic pollutants in natural water.

Search for first harmonic modulation in the right ascension distribution of cosmic rays detected at the Pierre Auger Observatory

We present the results of searches for dipolar-type anisotropies in different energy ranges above 2.5 x 10(17) eV with the surface detector array of the Pierre Auger Observatory, reporting on both the phase and the amplitude measurements of the first harmonic modulation in the right-ascension distribution. Upper limits on the amplitudes are obtained, which provide the most stringent bounds at present, being below 2% at 99% C.L. for EeV energies. We also compare our results to those of previous experiments as well as with some theoretical expectations. (C) 2011 Elsevier B.V. All rights reserved.

Computational aspects of harmonic wavelet Galerkin methods and an application to a precipitation front propagation model

This article is dedicated to harmonic wavelet Galerkin methods for the solution of partial differential equations. Several variants of the method are proposed and analyzed, using the Burgers equation as a test model. The computational complexity can be reduced when the localization properties of the wavelets and restricted interactions between different scales are exploited. The resulting variants of the method have computational complexities ranging from O(N(3)) to O(N) (N being the space dimension) per time step. A pseudo-spectral wavelet scheme is also described and compared to the methods based on connection coefficients. The harmonic wavelet Galerkin scheme is applied to a nonlinear model for the propagation of precipitation fronts, with the front locations being exposed in the sizes of the localized wavelet coefficients. (C) 2011 Elsevier Ltd. All rights reserved.

Exploiting the versatility of taste sensors based on impedance spectroscopy

The versatility of sensor arrays made from nanostructured Langmuir-Blodgett (LB) and layer-by-layer (LBL) films is demonstrated in two ways. First, different combinations of sensing units are employed to distinguish the basic tastes, viz. sweet, sour, bitter, and salty tastes, produced, respectively, by small concentrations (down to 0.01 g/mol) of sucrose, HCl, quinine, and NaCl solutions. The sensing units are comprised of LB and/or LBL films from semiconducting polymers, a ruthenium complex, and sulfonated lignin. Then, sensor arrays were used to identify wines from different sources, with the high distinguishing ability being demonstrated in principal component analysis (PCA) plots. Particularly important was the fact that the sensing ability does not depend on specific interactions between analytes and the film materials, but a judicious choice of materials is, nevertheless, required for the materials to respond differently to a given sample. It is also shown that the interaction with the analyte may affect the morphology of the nanostructured films, as indicated with scanning electron microscopy. For instance, in wine analysis these changes are not irreversible and the original film morphology is retrieved if the sensing unit is washed with copious amounts of water, thus allowing the sensor unit to be reused.