Sound transmission in strongly-curved slowly-varying cylindrical and annular lined ducts with flow

In this paper we consider the propagation of acoustic waves along a curved hollow or annular duct with lined walls. The curvature of the duct centreline and the wall radii vary slowly along the duct, allowing application of an asymptotic multiple scales analysis. This generalises Rienstra's analysis of a straight duct of varying cross-sectional radius. The result of the analysis is that the modal wavenumbers and mode shapes are determined locally as modes of a torus with the same local curvature, while the amplitude of the modes evolves as the mode propagates along the duct. The duct modes are found numerically at each axial location using a pseudo-spectral method. Unlike the case of a straight duct, there is a fundamental asymmetry between upstream and downstream propagating modes, with some mode shapes tending to be concentrated on either the inside or outside of the bend depending on the direction of propagation. The interaction between the presence of wall lining and curvature is investigated in particular; for instance, in a representative case it is found that the curvature causes the first few acoustic modes to be more heavily damped by the duct boundary than would be expected for a straight duct. Analytical progress can be made in the limit of very high mode order, in which case well-known 'whispering gallery' modes, localised close to the wall, can be identified.

Analytically-based approach to rotor-stator interaction noise in mean swirling flow

A method for modelling and predicting the noise generated by the interaction between the unsteady wake shed from the rotor and a downstream row of stators in a modern ultra-high bypass ducted turbofan engine is described. An analytically-based model is developed to account for three main features of the problem. First, the way in which a typical unsteady wake disturbance from the rotor interacts and is distorted by the mean swirling flow as it propagates downstream. The analysis allows for the inclusion of mean entropy gradients and entropy perturbations. Second, the effects of real stator-blade geometry and proper representation of the genuinely three-dimensional nature of the problem. Third, to model the propagation of the resulting noise back upstream in mean swirling flow. The analytical nature of the problem allows for the inclusion of all wake harmonics and enables the response at all blade passing frequencies to be determined. Example results are presented for an initial wake distribution corresponding to a genuine rotor configuration. Comparisons between numerical data and the asymptotic model for the wake evolution are made. Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Mesofracture mechanics: a necessary link

Classical fracture mechanics is based on the premise that small scale features could be averaged to give a larger scale property such that the assumption of material homogeneity would hold. Involvement of the material microstructure, however, necessitates different characteristic lengths for describing different geometric features. Macroscopic parameters could not be freely exchanged with those at the microscopic scale level. Such a practice could cause misinterpretation of test data. Ambiguities arising from the lack of a more precise range of limitations for the definitions of physical parameters are discussed in connection with material length scales. Physical events overlooked between the macroscopic and microscopic scale could be the link that is needed to bridge the gap. The classical models for the creation of free surface for a liquid and solid are oversimplified. They consider only the translational motion of individual atoms. Movements of groups or clusters of molecules deserve attention. Multiscale cracking behavior also requires the distinction of material damage involving at least two different scales in a single simulation. In this connection, special attention should be given to the use of asymptotic solution in contrast to the full field solution when applying fracture criteria. The former may leave out detail features that would have otherwise been included by the latter. Illustrations are provided for predicting the crack initiation sites of piezoceramics. No definite conclusions can be drawn from the atomistic simulation models such as those used in molecular dynamics until the non-equilibrium boundary conditions can be better understood. The specification of strain rates and temperatures should be synchronized as the specimen size is reduced to microns. Many of the results obtained at the atomic scale should be first identified with those at the mesoscale before they are assumed to be connected with macroscopic observations. Hopefully, "mesofracture mechanics" could serve as the link to bring macrofracture mechanics closer to microfracture mechanics.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

A Molecular Dynamics Simulation: the Effect of Finite Size on the Thermal Conductivity in a Single Crystal Silicon

Non-equilibrium molecular dynamics (NEMD) simulations are performed to calculate thermal conductivity. The environment-dependent interatomic potential (EDIP) potential on crystal silicon is adopted as a model system. The issues are related to nonlinear response, local thermal equilibrium and statistical averaging. The simulation results by non-equilibrium molecular dynamics show that the calculated thermal conductivity decreases almost linearly as the film thickness reduced at the nanometre scale. The effect of size on the thermal conductivity is also obtained by a theoretic analysis of the kinetic theory and formulas of the heat capacity. The analysis reveals that the contributions of phonon mean free path (MFP) and phonon number in a finite cell to thermal conductivity are very important.

Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood-based ABC procedures.

La exégesis de la realidad social en los Padres de la Iglesia

Resumen: Una teología desafiada en estos tiempos no puede retrotraerse simplemente a la reedición mecánica de ideas o frases sin analizar profundamente el aparato epistemológico que da coherencia a un mensaje y que permita que el mismo pueda dialogar maduramente con su entorno. El pensamiento y la praxis de los Padres de la Iglesia permiten descubrir elementos claves de una lectura particular de la historia que protagonizaron. El presente artículo intenta señalar la exégesis de los dos textos leídos por los autores patrísticos: la Sagrada escritura y la realidad social. No se busca repetir fórmulas, sino encontrar principios inspiradores y llaves que abran a una interpretación actual de la realidad socio-cultural del mundo contemporáneo. La lectura social que los Padres hacen desde la Escritura compromete una antropología, una cosmología y una eclesiología. La integralidad de su pensamiento pone en evidencia una unidad de vida, de concebir el mundo, el hombre, y la Iglesia, con relación a Dios.

Forward Smoothing Using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an on-line or "forward only" implementation of a forward filtering backward smoothing SMC algorithm proposed by Doucet, Godsill and Andrieu (2000). Compared to the standard \emph{path space} SMC estimator whose asymptotic variance increases quadratically with time even under favorable mixing assumptions, the non asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation using an SMC implementation of an on-line version of the Expectation-Maximization algorithm which does not suffer from the particle path degeneracy problem.

Crack propagation in the power-law nonlinear viscoelastic material

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The creep incompressilility assumption is used. To simulate fracture behavior of craze region, it is assumed that in the fracture process zone near the crack tip, the cohesive stress sigma(f) acts upon the crack surfaces and resists crack opening. Through a perturbation method, i. e., by superposing the Mode-I applied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelastic problem is reduced to linear problem. For weak nonlinear materials, for which the power-law index n similar or equal to 1, the expressions of stress and crack surface displacement are derived. Then, the fracture process zone local energy criterion is proposed and based on which the formulas of cracking incubation time t

Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given. (C) 2002 Published by Elsevier Science Ltd.

Variation of added mass and its application to the calculation of amplitude response for a circular cylinder

In the present study, analyzed are the variation of added mass for a circular cylinder in the lock-in ( synchronization) range of vortex-induced vibration (VIV) and the relationship between added mass and natural frequency. A theoretical minimum value of the added mass coefficient for a circular cylinder at lock-in is given. Developed are semi-empirical formulas for the added mass of a circular cylinder at lock-in as a function of flow speed and mass ratio. A comparison between experiments and numerical simulations shows that the semi-empirical formulas describing the variation of the added mass for a circular cylinder at lock-in are better than the ideal added mass. In addition, computation models such as the wake oscillator model using the present formulas can predict the amplitude response of a circular cylinder at lock-in more accurately than those using the ideal added mass.

Attractor crisis and bursting in a fluid flow with two no-slip directions

Characteristic burtsing behavior is observed in a driven, two-dimensional viscous flow, confined to a square domain and subject to no-slip boundaries. Passing a critical parameter value, an existing chaotic attractor undergoes a crisis, after which the flow initially enters a transient bursting regime. Bursting is caused by ejections from and return to a limited subdomain of the phase space, whereas the precrisis chaotic set forms the asymptotic attractor of the flow. For increasing values of the control parameter the length of the bursting regime increases progressively. Passing another critical parameter value, a second crisis leads to the appearance of a secondary type of bursting, of very large dynamical range. Within the bursting regime the flow then switches in irregular intervals from the primary to the secondary type of bursting. Peak enstrophy levels for both types of bursting are associated to the collapse of a primary vortex into a quadrupolar state.

Efecto de la fertilización foliar complementaria sobre el rendimiento de grano en sorgo (Sorghum vulgare pers.) variedad dekalb E-56-A

Con el objeto de determinar cual es la formula de fertilizantes al suelo, que complementada con un determinado numero de aplicaciones foliares, son mas adecuadas para obtener los mayores rendimientos de grano en sorgo, se llevo a cabo un experimento en el que se probaron 4 diferentes formulas de fertilizante al suelo completados con diferente numero de aplicaciones de un fertilizante foliar, usando una semilla híbrida; Dekalb E-56-A, en las condiciones de La Calera. Se observaron los siguientes caracteres: Días de floración, altura de planta, ahijamiento en la base del tallo, cantidad de forraje y rendimiento de grano. De los resultados obtenidos por el análisis de varianza se puede deducir lo siguiente: No existen diferencias significativas en ninguno de los caracteres observados; en cuanto a rendimiento del grano el tratamiento que mayor producción dio fue el testigo. Los resultados obtenidos de este experimento pueden ser de mucho valor para agricultores que siembran sorgo en condiciones similares a las de "La Calera" y para aquellos que pueden hacer un uso inapropiado de los fertilizantes foliares, sin conocer la acción de estos debido a falta de experimentación.

Efecto de la fertilización en la producción de materia verde en dos variedades en sorgo forrajero

En lotes de los terrenos conocidos como Santa Rosa de la Estación Experimental Agropecuaria "La Calera", y "Las Delicias" propiedad del señor Humberto Vigil, localizadas en el departamento de Managua se sembro de primera en 1966 dos ensayos similares para medir el efecto de la fertilización en la producción de materia verde en dos variedades de sorgos forrajeros. El diseño experimental usado fue el de bloques al azar con tres repeticiones. Las fuentes de los elementos fertilizantes fueron: Sulfato de Amonio al 21% de N. Triple supe fosfato al 46% de P205 y Cloruro potásico al 60% de K20. Los tratamientos señalados se aplicaron cuando las plantas tenían de cuatro a seis pulgadas de altura. Después de cada corte y cuando los brotes tenían unas seis pulgadas se aplico solo la dosis de nitrógeno que señala cada tratamiento. Las variedades de sorgos forrajeros usadas fueron: Trudan 2 y Sudax SX-11. No fue visible el efecto de la fertilización en el color, vigor y altura de planta en los diferentes tratamiento exceptuando los dos que no llevaban nitrógeno. Los dos caracteres medidos fueron: altura de planta y producción de materia verde. El primer corte ni se realizo a los cuarenta días a partir de la siembra sino que seis días después; los otros dos cortes se efectuaron cada cuarenta y seis días. En las dos variedades el carácter altura de planta sometido al análisis estadístico no exhibió diferencia significativa al nivel de 5% de probabilidades en los tres cortes. El carácter rendimiento de materia verde sometido al análisis estadístico dio significancia en cada uno de los tres cortes de la variedad trudan 2 y solamente en el primer corte de la variedad Sudaz SX-11. Se observo una tendencia de los rendimientos a aumentar cuando se incrementa la dosis de nitrógeno, pero las diferencias aparentes en rendimiento no fueron significativas al nivel del 5% de probabilidades en ambos ensayos. Las parcelas tratadas con la formula 0- 38.8 - 38.8 y la testigo 0-0-0- rindieron significativamente menos que los demás tratamientos con fertilizantes en los tres cortes del Trudan 2 y en el primero corte del Sudax SX-11. Entre los tratamientos con fertilizantes la formula que económicamente seria la mas conveniente fue 38.8-0-0 ya que esta permitió un rendimiento de materia verde similar a los obtenidos con las otras formulas con cantidades mayores de nitrógeno, fósforo y potasio. Se sugiere que los resultados obtenidos en estos ensayos por ser solo los primeros y preliminares, no pueden usarse aun como base para recomendaciones a los agricultores sobre la fertilización de sorgos forrajeros.