Modelling the mechanical response of the Reed-mouthpiece-lip system of a clarinet. Part I. A one-dimensional distributed model

The motion of a clarinet reed that is clamped to a mouthpiece and supported by a lip is simulated in the time-domain using finite difference methods. The reed is modelled as a bar with non-uniform cross section, and is described using a one-dimensional, fourth-order partial differential equation. The interactions with the mouthpiece Jay and the player's lip are taken into account by incorporating conditional contact forces in the bar equation. The model is completed by clamped-free boundary conditions for the reed. An implicit finite difference method is used for discretising the system, and values for the physical parameters are chosen both from laboratory measurements and by accurate tuning of the numerical simulations. The accuracy of the numerical system is assessed through analysis of frequency warping effects and of resonance estimation. Finally, the mechanical properties of the system are studied by analysing its response to external driving forces. In particular, the effects of reed curling are investigated.

Lagrangian transport of particles in Ria de Aveiro lagoon, Portugal

A two-dimensional vertically integrated hydrodynamic model coupled to a particle tracking model is applied to study the dispersion processes and residence time in Ria de Aveiro lagoon (Portugal). The only dispersion process that is considered in this study is the advection, according to the main characteristics of the local hydrodynamic. The particle tracking model computes the particles position at each time step, using a fourth-order Runge-Kutta integration method. The dispersion of passive particles released along the lagoon and in critical areas are studied in this work. The residence time is also determined for the entire lagoon. The results show that the mixture between particles coming from different channels of the lagoon is negligible in a time scale higher than 2 tidal cycles. The residence time for the lagoon central area is about 2 days, revealing a strong marine influence in this area. At the upper reaches of the channels were found values higher than 2 weeks.

Third order elastic constants of bcc Cu-Al-Ni

We have measured the changes in the ultrasonic wave velocity, induced by the application of uniaxial stresses in a Cu-Al-Ni single crystal. From these measurements, the complete set of third-order elastic constants has been obtained. The comparison of results for Cu-Al-Ni with available data for other Cu-based alloys has shown that all these alloys exhibit similar anharmonic behavior. By using the measured elastic constants in a Landau expansion for elastic phase transitions, we have been able to give an estimation of the value of a fourth-order elastic constants combination. The experiments have also shown that the application of a stress in the [001] direction, reduces the material resistance to a (110)[110] shear and thus favors the martensitic transition.

Computeralgebraische Herleitung und Auswertung atomarer Störungsreihen und deren Anwendung auf geschlossenschalige und einfache offenschalige Systeme

In der vorliegenden Arbeit wurde gezeigt, wie mit Hilfe der atomaren Vielteilchenstörungstheorie totale Energien und auch Anregungsenergien von Atomen und Ionen berechnet werden können. Dabei war es zunächst erforderlich, die Störungsreihen mit Hilfe computeralgebraischer Methoden herzuleiten. Mit Hilfe des hierbei entwickelten Maple-Programmpaketes APEX wurde dies für geschlossenschalige Systeme und Systeme mit einem aktiven Elektron bzw. Loch bis zur vierten Ordnung durchgeführt, wobei die entsprechenden Terme aufgrund ihrer großen Anzahl hier nicht wiedergegeben werden konnten. Als nächster Schritt erfolgte die analytische Winkelreduktion unter Anwendung des Maple-Programmpaketes RACAH, was zu diesem Zwecke entsprechend angepasst und weiterentwickelt wurde. Erst hier wurde von der Kugelsymmetrie des atomaren Referenzzustandes Gebrauch gemacht. Eine erhebliche Vereinfachung der Störungsterme war die Folge. Der zweite Teil dieser Arbeit befasst sich mit der numerischen Auswertung der bisher rein analytisch behandelten Störungsreihen. Dazu wurde, aufbauend auf dem Fortran-Programmpaket Ratip, ein Dirac-Fock-Programm für geschlossenschalige Systeme entwickelt, welches auf der in Kapitel 3 dargestellen Matrix-Dirac-Fock-Methode beruht. Innerhalb dieser Umgebung war es nun möglich, die Störungsterme numerisch auszuwerten. Dabei zeigte sich schnell, dass dies nur dann in einem angemessenen Zeitrahmen stattfinden kann, wenn die entsprechenden Radialintegrale im Hauptspeicher des Computers gehalten werden. Wegen der sehr hohen Anzahl dieser Integrale stellte dies auch hohe Ansprüche an die verwendete Hardware. Das war auch insbesondere der Grund dafür, dass die Korrekturen dritter Ordnung nur teilweise und die vierter Ordnung gar nicht berechnet werden konnten. Schließlich wurden die Korrelationsenergien He-artiger Systeme sowie von Neon, Argon und Quecksilber berechnet und mit Literaturwerten verglichen. Außerdem wurden noch Li-artige Systeme, Natrium, Kalium und Thallium untersucht, wobei hier die niedrigsten Zustände des Valenzelektrons betrachtet wurden. Die Ionisierungsenergien der superschweren Elemente 113 und 119 bilden den Abschluss dieser Arbeit.

Fast approximate calculation of multiply scattered lidar returns

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance, of photon direction and position. The result is that for an N-point profile the calculation is O(N-2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(N-m/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude. (C) 2006 Optical Society of America.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Numerical study of the atmospheric flow over a coastal cliff

This work presents a numerical method suitable for the study of the development of internal boundary layers (IBL) and their characteristics for flows over various types of coastal cliffs. The IBL is an important meteorological occurrence for flows with surface roughness and topographical step changes. A two-dimensional flow program was used for this study. The governing equations were written using the vorticity-velocity formulation. The spatial derivatives were discretized by high-order compact finite differences schemes. The time integration was performed with a low storage fourth-order Runge-Kutta scheme. The coastal cliff (step) was specified through an immersed boundary method. The validation of the code was done by comparison of the results with experimental and observational data. The numerical simulations were carried out for different coastal cliff heights and inclinations. The results show that the predominant factors for the height of the IBL and its characteristics are the upstream velocity, and the height and form (inclination) of the coastal cliff. Copyright (C) 2010 John Wiley & Sons, Ltd.

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which is based on Weyl symmetrically ordered operator products. By using a polydifferential representation for the deformed coordinates, xj we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth-order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.

Estimativa do comportamento de máquinas assíncronas sujeitas a afundamentos de tensão

Os afundamentos de tensão são reduções de curta duração entre o 10% a 90% da magnitude de tensão eficaz. Usualmente, estes afundamentos são associados com falhas no sistema de energia elétrica, mas podem ser causados pela elevada corrente de partida de motores de indução ou energização de transformadores. Apesar de sua curta duração, tais eventos podem causar sérios problemas para alguns equipamentos. As conseqüências dos afundamentos de tensão sobre a máquina assíncrona são: perda de velocidade durante o afundamento e picos de corrente e de conjugado que aparecem na queda de tensão e no instante de restabelecimento. Este estudo visa analisar o comportamento da máquina assíncrona diante de afundamentos de tensão e as características destes, devido à influência do motor assíncrono como carga. Enfocando-se neste ponto, é que foram considerados diferentes tipos de afundamentos devido a diferentes falhas, que produziram quedas de tensão nos terminais da máquina assíncrona com variações na magnitude e no argumento de tensão. As simulações foram realizadas aplicando um método numérico tradicional e um método simplificado, o método simplificado lineariza as equações diferenciais elétricas da máquina assíncrona considerando a velocidade mecânica constante, para o cálculo dos transitórios elétricos no início da queda de tensão e no restabelecimento da mesma. Os transitórios obtidos pelo método numérico tradicional (Runge Kutta quarta ordem) e o método simplificado foram comparados, para verificar a precisão deste método com respeito ao numérico tradicional, concluindo-se, que o método simplificado poderá aplicar-se em máquinas de baixo escorregamento e elevada constante de inércia. Além disso, foram realizados experimentos, submetendo o sistema a diferentes quedas de tensão, considerando diferentes magnitudes e durações no afundamento.

Persistência na lactação para vacas da raça Holandesa criadas no Estado do Rio Grande do Sul via modelos de regressão aleatória

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

Tm and Tm-Tb-doped germanate glasses for S-band amplifiers

The mechanism involved in the Tm(3+)((3)F(4)) -> Tb(3+)((7)F(0,1,2)) energy transfer as a function of the Tb concentration was investigated in Tm:Tb-doped germanate (GLKZ) glass. The experimental transfer rate was determined from the best fit of the (3)F(4) luminescence decay due to the Tm -> Tb energy transfer using the Burshtein model. The result showed that the 1700 nm emission from (3)F(4) can be completely quenched by 0.8 mol% of Tb(3+). As a consequence, the (7)F(3) state of Tb(3+) interacts with the (3)H(4) upper excited state of TM(3+) slighting decreasing its population. The effective amplification coefficient beta(cm(-1)) that depends on the population density difference Delta n = n((3)H(4))-n((3)F(4)) involved in the optical transition of Tm(3+) (S-band) was calculated by solving the rate equations of the system for continuous pumping with laser at 792 nm, using the Runge-Kutta numerical method including terms of fourth order. The population density inversion An as a function of Tb(3+) concentration was calculated by computational simulation for three pumping intensities, 0.2, 2.2 and 4.4 kWcm(-2). These calculations were performed using the experimental Tm -> Tb transfer rates and the optical constants of the Tm (0.1 mol%) system. It was demonstrated that 0.2 mol% of Tb(3+) propitiates best population density inversion of Tin(3+) maximizing the amplification coefficient of Tm-doped (0.1 mol%) GLKZ glass when operating as laser intensity amplification at 1.47 mu m. (C) 2007 Elsevier B.V. All rights reserved.

Solução numérica das equações de Navier-Stokes em um canal-tipo estenose usando métodos compactos e não compacos de alta ordem

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)