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

Numerical simulation of g-jitter effects on half floating zone convection under microgravity environment

The g-jitter effects on the thermocapillary convection in liquid bridge of floating half zone were studied by numerical simulation for unsteady and axi-symmetric model in the cylindrical coordinate system. The g-jitter field was given by a steady microgravity field in addition to an oscillatory low-gravity field, and the effects on the flow field, temperature distribution and free surface deformation were analyzed numerically.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

Tools for the study of dynamical spacetimes

This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

Neutron slowing down with inelastic scattering

The emphasis in reactor physics research has shifted toward investigations of fast reactors. The effects of high energy neutron processes have thus become fundamental to our understanding, and one of the most important of these processes is nuclear inelastic scattering. In this research we include inelastic scattering as a primary energy transfer mechanism, and study the resultant neutron energy spectrum in an infinite medium. We assume that the moderator material has a high mass number, so that in a laboratory coordinate system the energy loss of an inelastically scattered neutron may be taken as discrete. It is then consistent to treat elastic scattering with an age theory expansion. Mathematically these assumptions lead to balance equations of the differential-difference type.

The steady state problem is explored first by way of Laplace transformation of the energy variable. We then develop another steady state technique, valid for multiple inelastic level excitations, which depends on the level structure satisfying a physically reasonable constraint. In all cases the solutions we generate are compared with results obtained by modeling inelastic scattering with a separable, evaporative kernel.

The time dependent problem presents some new difficulties. By modeling the elastic scattering cross section in a particular way, we generate solutions to this more interesting problem. We conjecture the method of characteristics may be useful in analyzing time dependent problems with general cross sections. These ideas are briefly explored.

Theoretical investigation of turbulent boundary layer over a wavy surface

The important features of the two-dimensional incompressible turbulent flow over a wavy surface of wavelength comparable with the boundary layer thickness are analyzed.

A turbulent field method using model equation for turbulent shear stress similar to the scheme of Bradshaw, Ferriss and Atwell (1967) is employed with suitable modification to cover the viscous sublayer. The governing differential equations are linearized based on the small but finite amplitude to wavelength ratio. An orthogonal wavy coordinate system, accurate to the second order in the amplitude ratio, is adopted to avoid the severe restriction to the validity of linearization due to the large mean velocity gradient near the wall. Analytic solution up to the second order is obtained by using the method of matched-asymptotic-expansion based on the large Reynolds number and hence the small skin friction coefficient.

In the outer part of the layer, the perturbed flow is practically "inviscid." Solutions for the velocity, Reynolds stress and also the wall pressure distributions agree well with the experimental measurement. In the wall region where the perturbed Reynolds stress plays an important role in the process of momentum transport, only a qualitative agreement is obtained. The results also show that the nonlinear second-order effect is negligible for amplitude ratio of 0.03. The discrepancies in the detailed structure of the velocity, shear stress, and skin friction distributions near the wall suggest modifications to the model are required to describe the present problem.

A scaling technique for the design of idealized electromagnetic lenses

A technique is developed for the design of lenses for transitioning TEM waves between conical and/or cylindrical transmission lines, ideally with no reflection or distortion of the waves. These lenses utilize isotropic but inhomogeneous media and are based on a solution of Maxwell's equations instead of just geometrical optics. The technique employs the expression of the constitutive parameters, ɛ and μ, plus Maxwell's equations, in a general orthogonal curvilinear coordinate system in tensor form, giving what we term as formal quantities. Solving the problem for certain types of formal constitutive parameters, these are transformed to give ɛ and μ as functions of position. Several examples of such lenses are considered in detail.

热容型板条激光器的感应折射率计算

高平均功率固体激光器的增益介质由于受热而容易发生畸变,如常用材料YAG,波前畸变和去偏振现象会同时发生,高热负载固体激光介质的热效应已成为制约激光器输出功率进一步提高的严重障碍。给出一种计算热容型板条激光器热感生折射率的方法。把YAG晶体的四阶压光张量从晶胞坐标系转换到实验室坐标系,采用经过坐标转换后的新的张量,可以分析在YAG激光器中任意应力分布引起的热感应双折射。进一步的计算表明,在zigzag板条激光器中,应力双折射率与板条从晶体毛胚上切割成材的角度有关。同时也对热容板条激光器的热效应和应力特性进行了二维的理论性概述。

Control de almacén automatizado con dos ejes lineales.

[ES]El objetivo principal de este Trabajo Fin de Grado es automatizar un almacén con dos ejes lineales con la meta final de programar un panel de operador para que, ya sea un usuario u operario pueda introducir si desea depositar o recoger un palé, indicando la posición mediante un sistema de coordenadas las cuales dividen a las estanterías del almacén en filas y columnas. Para ello se cambiará parte del hardware de control, el cual incluye el antiguo módulo de posicionamiento (IP 246) que hasta ahora, controlaba el almacén. Esta tarjeta está limitada a un software ya desfasado, sin posibilidad de implementar un panel de operador con los requisitos demandados en la industria de hoy en día. También se ha utilizado una CPU S7-300, a diferencia de la SIMATIC S5 que se utilizaba con la antigua tarjeta.

Efeitos de regimes de sobreclareamento associados a produtos clareadores caseiros sobre o conteúdo mineral e a rugosidade do esmalte dentário humano

O clareamento dental se tornou um dos tratamentos estéticos mais realizados nos consultórios odontológicos, devido à simplicidade técnica e popularização através da mídia. Consiste na utilização de géis à base de peróxido de carbamida, peróxido de hidrogénio e, em uma menor escala, de perborato de sódio, com intuito de oxidar moléculas responsáveis pela pigmentação da estrutura dentária. Apesar da grande quantidade de estudos sobre o tema, não se sabe os efeitos do uso excessivo desses agentes sobre a estrutura dentária. O objetivo deste estudo foi avaliar os efeitos sobre a rugosidade superficial e conteúdo mineral do esmalte dental humano submetido a regimes de sobreclareamento associados ao uso de géis clareadores caseiros: peróxido de carbamida 10% (Opalescence PF Regular 10%, Ultradent do Brasil Produtos Odontológicos Ltda., Indaiatuba, São Paulo), peróxido de hidrogênio 9,5% (DayWhite 9,5%, Discus, LLC Culver City, EUA), bem como tiras clareadoras (Oral-B WhiteStrips, Anderson Packaging, Rockford, Estados Unidos). Quatro fragmentos de esmalte obtidos a partir de cinco dentes foram submetidos a um diferente tratamento: Grupo I - armazenamento em saliva artificial por oito semanas; Grupo 2 oito semanas de tratamento com gel de peróxido de carbamida 10% por 6 horas diárias; Grupo 3 oito semanas de tratamento com gel de peróxido de hidrogênio 9,5% com duas aplicações diárias de 30 minutos; Grupo 4 oito semanas de tratamento com tiras clareadoras duas aplicações diárias de 30 minutos. A alteração no conteúdo mineral foi avaliada semanalmente em seis pontos de cada fragmento devidamente identificados através de um sistema de coordenadas (X, Y e Z) utilizando-se a técnica de fluorescência de raios X (Artax 200). Alterações na rugosidade superficial das amostras também foram avaliadas através de um rugosímetro 3D (FormTalysurf 60, Taylor Leicester, Reino Unido). Apenas o grupo 3 apresentou diferenças estatísticas significativas com relação aos níveis de rugosidade (p<0,05), porém não consideradas como clinicamente significativos. Para os demais tratamentos e intervalos propostos, não foram encontradas diferenças estatisticamente significativas (p>0,05). Desse modo, não houve alterações compatíveis com um processo de desmineralização ou aumento real da rugosidade da superfície. Nas condições desse estudo in vitro os géis clareadores caseiros foram considerados seguros. São necessários novos estudos in situ e in vitro que analisem os efeitos de regimes de sobreclareamento quando em condições de somatório de desafios intra-orais.

Elementos finitos em fluidos dominados pelo fenômeno de advecção: um método semi-Lagrangeano.

Os escoamentos altamente convectivos representam um desafio na simulação pelo método de elementos finitos. Com a solução de elementos finitos de Galerkin para escoamentos incompressíveis, a matriz associada ao termo convectivo é não simétrica, e portanto, a propiedade de aproximação ótima é perdida. Na prática as soluções apresentam oscilações espúrias. Muitos métodos foram desenvolvidos com o fim de resolver esse problema. Neste trabalho apresentamos um método semi- Lagrangeano, o qual é implicitamente um método do tipo upwind, que portanto resolve o problema anterior, e comparamos o desempenho do método na solução das equações de convecção-difusão e Navier-Stokes incompressível com o Streamline Upwind Petrov Galerkin (SUPG), um método estabilizador de reconhecido desempenho. No SUPG, as funções de forma e de teste são tomadas em espaços diferentes, criando um efeito tal que as oscilações espúrias são drasticamente atenuadas. O método semi-Lagrangeano é um método de fator de integração, no qual o fator é um operador de convecção que se desloca para um sistema de coordenadas móveis no fluido, mas restabelece o sistema de coordenadas Lagrangeanas depois de cada passo de tempo. Isto prevê estabilidade e a possibilidade de utilizar passos de tempo maiores.Existem muitos trabalhos na literatura analisando métodos estabilizadores, mas não assim com o método semi-Lagrangeano, o que representa a contribuição principal deste trabalho: reconhecer as virtudes e as fraquezas do método semi-Lagrangeano em escoamentos dominados pelo fenômeno de convecção.

大射电望远镜精调Stewart平台工作空间分析

针对大射电望远镜精调Stewart平台的五自由度运动特性,采用快速极坐标搜索法确定了五自由度大射电望远镜精调Stewart平台的工作空间.通过实例分析验证了所提出的工作空间分析方法的有效性.为大射电望远镜馈源轨迹跟踪实现和精调Stewart平台的设计奠定了坚实的基础.

估计从UUV航行参数的混合坐标系下的EKF算法

在主从式UUV 协作系统中，由于定位和导航的需要，要求尽快估计出从UUV 的航行参数，但通常所用的递推最小二乘（RLS）算法，其初始方位测量对滤波结果影响大且存在收敛速度慢、计算精度低的缺点，难以满足应用需求，而推广卡尔曼滤波（EKF）算法能较好地克服上述问题。在直角坐标系下（CEKF），方位信息与距离信息相互耦合导致初始振荡剧烈，改为混合坐标系（MEKF）后问题得到了极大的改善。最后，通过仿真及现场试验验证了此改进方法的有效性。

遥控作业移动机器人环境建模方法研究

本文介绍了用于遥控机器人作业虚拟环境生成的建模方法．重点研究了基于人机交互的双目立体视觉和多视点建模方法，以克服视觉自动建模方法计算复杂、鲁棒性差的缺点．给出了环境建模的实验系统和实验结果。

用光学反射传感器的机器人初始定位系统

本文叙述一种用光学反射传感器自动确定机器人在工作坐标中的起始参考位置的方法。装在机器人手爪边上的光学反射传感器与工作面上的T形目标相配合,用自动反复循环定位法确定机器人在工作坐标中的期望起始点。实践和理论分析表明,虽然开机时的机器人手爪的原始位置基本上是随机的,但手爪都能自动精确地收敛到期望的起始点上。