Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

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

Pure spinor partition function using Padé approximants

In a recent paper, the partition function (character) of ten-dimensional pure spinor worldsheet variables was calculated explicitly up to the fifth mass-level. In this letter, we propose a novel application of Padé approximants as a tool for computing the character of pure spinors. We get results up to the twelfth mass-level. This work is a first step towards an explicit construction of the complete pure spinor partition function.

Direct and Inverse Results on Row Sequences of Hermite-Pad, Approximants

We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants. Exact rates of convergence for these denominators and the simultaneous rational approximants are provided.

Padé approach to potential transients: Part 1. Electron transfer without and with coupling to first-order homogeneous reactions at planar electrodes

Potential transients are obtained by using “Padé approximants” (an accurate approximation procedure valid globally — not just perturbatively) for all amplitudes of concentration polarization and current densities. This is done for several mechanistic schemes under constant current conditions. We invert the non-linear current-potential relationship in the form (using the Lagrange or the Ramanujan method) of power series appropriate to the two extremes, namely near reversible and near irreversible. Transforming both into the Pad́e expressions, we construct the potential-time profile by retaining whichever is the more accurate of the two. The effectiveness of this method is demonstrated through illustrations which include couplings of homogeneous chemical reactions to the electron-transfer step.

On the two point Padé table for a distribution

Some additional recurrence relations for the denominator polynomials of two point Padé approximants are derived. An example in which the coefficients of one of the two series, from which the Padé approximants are derived, are moments of a distribution is considered. For this example, properties of the denominator polynomials, and their zeros, are described.

Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I(t) = I0(t−t0)q for t greater-or-equal, slanted t0, I(t) = 0 for t < t0; and (ii) I(t) = I0tq for t greater-or-equal, slanted t0, I(t) = 0 for t < t0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.

A finite-element analysis of viscoelastically damped sandwich plates

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

Some Extensions of M-Fractions Related to Strong Stieltjes Distributions

The purpose of this paper is to show the symmetric relations that appear between the coefficients of some even and odd extensions of the M-fractions related to a certain kind of symmetric strong Stieltjes distribution.

Frações contínuas que correspondem a séries de potências em dois pontos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Método da propagação de feixe de ângulo largo para análise de guias de ondas ópticos não-lineares

Este trabalho propõe uma extensão do método de propagação de feixe (BPM - Beam Propagation Method) para a análise de guias de ondas ópticos e acopladores baseados em materiais não-lineares do tipo Kerr. Este método se destina à investigação de estruturas onde a utilização da equação escalar de Helmholtz (EEH) em seu limite paraxial não mais se aplica. Os métodos desenvolvidos para este fim são denominados na literatura como métodos de propagação de feixe de ângulo largo. O formalismo aqui desenvolvido é baseado na técnica das diferenças finitas e nos esquemas de Crank-Nicholson (CN) e Douglas generalizado (GD). Estes esquemas apresentam como característica o fato de apresentarem um erro de truncamento em relação ao passo de discretização transversal, Δx, proporcional a O(Δx2) para o primeiro e O(Δx4). A convergência do método em ambos esquemas é otimizada pela utilização de um algoritmo interativo para a correção do campo no meio não-linear. O formalismo de ângulo largo é obtido pela expansão da EEH para os esquemas CN e GD em termos de polinômios aproximantes de Padé de ordem (1,0) e (1,1) para CN e GD, e (2,2) e (3,3) para CN. Os aproximantes de ordem superior a (1,1) apresentam sérios problemas de estabilidade. Este problema é eliminado pela rotação dos aproximantes no plano complexo. Duas condições de contorno nos extremos da janela computacional são também investigadas: 1) (TBC - Transparent Boundary Condition) e 2) condição de contorno absorvente (TAB - Transparent Absorbing Boundary). Estas condições de contorno possuem a facilidade de evitar que reflexões indesejáveis sejam transmitidas para dentro da janela computacional. Um estudo comparativo da influência destas condições de contorno na solução de guias de ondas ópticos não-lineares é também abordada neste trabalho.

Bulk compressive properties of the heel fat pad during walking: a pilot investigation in plantar heel pain

Background: Altered mechanical properties of the heel pad have been implicated in the development of plantar heel pain. However, the in vivo properties of the heel pad during gait remain largely unexplored in this cohort. The aim of the current study was to characterise the bulk compressive properties of the heel pad in individuals with and without plantar heel pain while walking. ---------- Methods: The sagittal thickness and axial compressive strain of the heel pad were estimated in vivo from dynamic lateral foot radiographs acquired from nine subjects with unilateral plantar heel pain and an equivalent number of matched controls, while walking at their preferred speed. Compressive stress was derived from simultaneously acquired plantar pressure data. Principal viscoelastic parameters of the heel pad, including peak strain, secant modulus and energy dissipation (hysteresis), were estimated from subsequent stress–strain curves.---------- Findings: There was no significant difference in loaded and unloaded heel pad thickness, peak stress, peak strain, or secant and tangent modulus in subjects with and without heel pain. However, the fat pad of symptomatic feet had a significantly lower energy dissipation ratio (0.55 ± 0.17 vs. 0.69 ± 0.08) when compared to asymptomatic feet (P < .05).---------- Interpretation: Plantar heel pain is characterised by reduced energy dissipation ratio of the heel pad when measured in vivo and under physiologically relevant strain rates.

Plantar enthesopathy : thickening of the enthesis is correlated with energy dissipation of the plantar fat pad during walking

Background: The enthesis of the plantar fascia is thought to play an important role in stress dissipation. However, the potential link between entheseal thickening characteristic of enthesopathy and the stress-dissipating properties of the intervening plantar fat pad have not been investigated. Purpose: This study was conducted to identify whether plantar fat pad mechanics explain variance in the thickness of the fascial enthesis in individuals with and without plantar enthesopathy. Study Design: Case-control study; Level of evidence, 3. Methods: The study population consisted of 9 patients with unilateral plantar enthesopathy and 9 asymptomatic, individually matched controls. The thickness of the enthesis of the symptomatic, asymptomatic, and a matched control limb was acquired using high-resolution ultrasound. The compressive strain of the plantar fat pad during walking was estimated from dynamic lateral radiographs acquired with a multifunction fluoroscopy unit. Peak compressive stress was simultaneously acquired via a pressure platform. Principal viscoelastic parameters were estimated from subsequent stress-strain curves. Results: The symptomatic fascial enthesis (6.7 ± 2.0 mm) was significantly thicker than the asymptomatic enthesis (4.2 ± 0.4 mm), which in turn was thicker than the enthesis (3.3 ± 0.4 mm) of control limbs (P < .05). There was no significant difference in the mean thickness, peak stress, peak strain, or secant modulus of the plantar fat pad between limbs. However, the energy dissipated by the fat pad during loading and unloading was significantly lower in the symptomatic limb (0.55 ± 0.17) when compared with asymptomatic (0.69 ± 0.13) and control (0.70 ± 0.09) limbs (P < .05). The sonographic thickness of the enthesis was correlated with the energy dissipation ratio of the plantar fat pad (r = .72, P < .05), but only in the symptomatic limb. Conclusion: The energy-dissipating properties of the plantar fat pad are associated with the sonograpic appearance of the enthesis in symptomatic limbs, providing a previously unidentified link between the mechanical behavior of the plantar fat pad and enthesopathy.

An isoviscous, isothermal model investigating the influence of hydrostatic recesses on a spring-supported tilting pad thrust bearing

Tilting-pad hydrodynamic thrust bearings are used in hydroelectric power stations around the world, reliably supporting turbines weighing hundreds of tonnes, over decades of service. Newer designs incorporate hydrostatic recesses machined into the sector-shaped pads to enhance oil film thickness at low rotational speeds. External pressurisation practically eliminates wear and enhances service life and reliability. It follows that older generating plants, lacking such assistance, stand to benefit from being retrofitted with hydrostatic lubrication systems. The design process is not trivial however. The need to increase the groove size to permit spontaneous lifting of the turbine under hydrostatic pressure, conflicts with the need to preserve performance of the original plane pad design. A haphazardly designed recess can induce a significant rise in bearing temperature concomitant with reduced mechanical efficiency and risk of thermal damage. In this work, a numerical study of a sector-shaped pad is undertaken to demonstrate how recess size and shape can affect the performance of a typical bearing.

Dynamic effects of electrical pitting in steam-turbine tilting-pad thrust-bearings

This paper merges the analysis of a case history and the simplified theoretical model related to a rather singular phenomenon that may happen in rotating machinery. Starting from the first, a small industrial steam turbine experienced a very strange behavior during megawatt load. When the unit was approaching the maximum allowed power, the temperature of the babbitt metal of the pads of the thrust bearing showed constant increase with an unrecoverable drift. Bearing inspection showed that pad trailing edge had the typical aspect of electrical pitting. This kind of damage was not reparable and bearing pads had to replaced. This problem occurred several times in sequence and was solved only by adding further ground brushes to the shaft-line. Failure analysis indicated electrodischarge machining as the root fault. A specific model, able to take into consideration the effect of electrical pitting and loading capacity decreasing as a consequence of the damage of the babbitt metal, is proposed in the paper and shows that the phenomenon causes the irretrievable failure of the thrust bearing.