This thesis considers linear perturbations to the steady flow of a compressible inviscid perfect gas along a cylindrical or annular duct. Particular consideration is given to the model of the duct boundary, and to the effect of curvature of the duct centreline. For a duct with a straight centreline and a locally-reacting boundary, the acoustic duct modes can be segregated into ordinary duct modes and surface modes. Previously-known asymptotics for the surface modes are generalized, and the generalization is shown to provide a distinctly better approximation in aeroacoustically relevant situations. The stability of the surface modes is considered, and previous stability analyses are shown to be incorrect, as their boundary model is illposed. By considering a metal thin-shell boundary, this illposedness is explained, and stability analysed using the Briggs-Bers criterion. The stability of a cylindrical thin shell containing compressible fluid is shown to differ significantly from the stability for an incompressible fluid, even for parameters for which the fluid would otherwise be expected to behave incompressibly. The scattering of sound by a sudden hard-wall to thin-shell boundary change is considered, using the Wiener-Hopf technique. The causal acoustic field is derived analytically, without the need to apply a Kutta-like condition or to include an instability wave, as had previously been necessary. Attention is then turned to a cylindrical duct with a curved centreline and either hard or locally-reacting walls. The centreline curvature (which is not assumed small) and wall radii vary slowly along the duct, enabling an asymptotic multiple scales analysis. The duct modes are found numerically at each axial location, and interesting characteristics are explained using ray theory. This analysis is applied to a hard-walled RAE 2129 duct, and frequency-domain solutions are convolved to give a time-domain example of a pulse propagating along this duct. Finally, some numerical work on the nonlinear propagation of a large-amplitude pulse along a curved duct is presented. This is aimed at modelling a surge event in an aeroengine with a convoluted intake.

The photoactive component of a polymeric organic solar cell can be produced by drying a mixture consisting of a volatile solvent and non-volatile polymers. As the solvent evaporates, the polymers demix and self-assemble into microscale structures, the morphology of which plays a pivotal role in determining the efficiency of the resulting device. Thus, a detailed understanding of the physical mechanisms that drive and influence structure formation in evaporating solvent-polymer mixtures is of high scientific and industrial value. This thesis explores several problems that aim to produce novel insights into the dynamics of evaporating solvent-polymer mixtures. First, the role of compositional Marangoni instabilities in slowly evaporating binary mixtures is studied using the framework of linear stability theory. The analysis is non-trivial because evaporative mass loss naturally leads to a time-dependent base state. In the limit of slow evaporation compared to diffusion, a separation of time scales emerges in the linear stability problem, allowing asymptotic methods to be applied. In particular, an asymptotic solution to linear stability problems that have slowly evolving base states is derived. Using this solution, regions of parameter space where an oscillatory instability occurs are identified and used to formulate appropriate conditions for observing this phenomenon in future experiments. The second topic of this thesis is the use of multiphase fluid models to study the dynamics of evaporating solvent-polymer mixtures. A two-phase model is used to assess the role of compositional buoyancy and to examine the formation of a polymer-rich skin at the free surface. Then, a three-phase model is used to conduct a preliminary investigation of the link between evaporation and phase separation. Finally, this thesis explores the dynamics of a binary mixture that is confined between two horizontal walls using a diffusive phase-field model and its sharp-interface and thin-film approximations. We first determine the conditions under which a homogeneous mixture undergoes phase separation to form a metastable bilayer. We then present a novel mechanism for generating a repeating lateral sequence of alternating A-rich and B-rich domains from this bilayer.

Made available in DSpace on 2017-07-21T19:25:48Z (GMT). No. of bitstreams: 1 lucas stori.pdf: 1232711 bytes, checksum: 264a44f2f6fc6eda1fa61e3d9e1d62f2 (MD5) Previous issue date: 2007-11-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The problem of so-called "quantum teleportation", or a transfer of the state of some quantum system to another quantum system has attracted attention of many authors. The aim of our study is to consider the effect of the quantum parametric excitation on the quantum information exchange between two modes of the electromagnetic field modeled by coupled quantum oscillators, where one of the oscillators has a time dependent frequency, as an extension of the case of two coupled modes considered. In the quantum case, the oscillators exchange not only energies, but also their quantum states and such an exchange can be interpreted as an ideal information transfer. We see that the possibility of quantum state exchange or information transfer can be detected in the most direct way by analyzing the Schrödinger propagator features in the coordinate representation. There are many different schemes of calculating the propagators of coupled oscillators, but the simplest one is that based on the theory of linear time dependent quantum invariants. Considering that the system in study models the coupled modes of the electromagnetic field, the interaction occurs in the domain of the weak interactions; the intensity of the coupling constants are small. Then we can consider the systems of differential equations for the dynamic behavior in the case of weak coupling limit. Starting with this argument, we can reduce the differential equations of first order to the only two groups of second order differential equations for all that ¸’s matrices. With the ¸’s matrices well determined, we can calculate the measured of entanglement, squeezing, purity and other quantum state properties of each mode in a particular case of Gaussian initial states. / O problema conhecido como "teletransporte quântico", ou transferência de estados quânticos, tem atraído a atenção de muitos autores. O objetivo de nosso estudo é considerar o efeito da excitação paramétrica quântica na troca de informação quântica entre dois modos do campo eletromagnético modelados por osciladores quânticos acoplados, onde um dos osciladores tem uma frequência dependente do tempo, sendo considerada o caso de dois modos acoplados. No caso quântico, os osciladores não trocam somente energias, mas também seus estados quânticos e tal troca pode ser interpretada como uma transferência de informação. Vemos que a possibilidade de troca de estados quânticos ou informação quântica pode ser verificadas de muitas maneiras pela análise direta do propagador de Schrödinger na representação das coordenadas. Existem várias maneiras diferentes de calcular o propagador de osciladores acoplados, mas uma maneira simples é baseada na teoria de invariantes quânticos dependentes linearmente do tempo. Considerando que o sistema em estudo é modelado por modos acoplados do campo eletromagnético, a interação ocorre nos domínios das interações fracas; a intensidade das constantes de acoplamentos são pequenas. Então, podemos considerar um sistema de equações diferenciais onde o seu comportameto dinâmico é dado no limite do acoplamento fraco. Iniciando com este argumento, nos reduzimos as equações diferenciais de primeira ordem em um conjunto de equações diferenciais de segunda ordem para as matrizes 0s. Com as matrizes ¸0s determinadas, nos podemos calcular medidadas de emaranhamento, compressão, pureza e outras propriedades de estados quânticos de cada modo em particular no caso de estados Gaussianos iniciais.

Made available in DSpace on 2017-07-21T19:25:59Z (GMT). No. of bitstreams: 1 CarlosEduardoKrassinskiSoares.pdf: 1234525 bytes, checksum: 758cda42769aa4bdf65a24c3f1cca4ed (MD5) Previous issue date: 2010-12-17 / In this dissertation, we study the physical properties of an open system, composed of two interacting bosonic modes (quantum harmonic oscillators) of different frequencies, with a explicitly time dependent coupling. It is assumed that each of the bosonic modes is under the effect of a thermal reservoir and the dynamics of their quantum properties is studied. In the case of quadratic systems and Gaussian initial states, the quantum properties of the coupled modes evolve in time according to the time evolution of the non-symmetrized second order moment which is described in the framework of the non-unitary evolution of quantum quadratic systems. The dynamical properties are determined by solving systems of differential equations for the second moments. These systems of differential equations have time-dependent coefficients and in the limit of weak coupling, the Method of Multiple Scales for constructing and solving differential equations is applied. This approach determines the differential equations solutions in a perturbative series of an appropriate parameter associated with orders of magnitude of the couplings. In this way it is obtained a description of the temporal behavior of the squeezing and the purity for each mode in the particular cases of parametric amplification and conversion. In this context, it is also considered the problem of the quantitative measure of entanglement, analyzing its dynamical behavior for different values of the system parameters and Gaussian initial states configurations. / Nesta dissertação, estudam-se propriedades físicas de um sistema aberto, composto por dois modos bosˆonicos interagentes (osciladores harmônicos quânticos) de frequências distintas, com o acoplamento explicitamente dependente do tempo. Assume-se cada um dos modos bosônicos sob efeito de reservatórios téermicos e analisa-se a dinâmica de suas propriedades quânticas. Em se tratando de sistemas quadraticos e estados iniciais Gaussianos, determina-se a evolução ao temporal das propriedades dos modos acoplados a partir da evolução ao temporal dos momentos de segunda ordem não o simetrizados na formulação de sistemas quadraticos de evolucção não unitária. As propriedades dinamicas são o determinadas solucionando-se sistemas de equacões diferenciais para os segundos momentos não simetrizados. Sendo sistemas de equções diferenciais com coeficientes dependentes do tempo, no limite do acoplamento fraco, aplica-se o Método das Escalas Múltiplas para a construção e a resolução das equações diferenciais, determinando-se suas soluções em séries perturbativas em um parâmetro adequado, associado as ordens de grandeza dos acoplamentos. Dessa maneira, analisa-se a dinâmica da medida de compressão e da pureza para os casos da amplificação e conversão paramétrica para diferentes valores de parâmetros de estados iniciais. Neste contexto, considera-se também o problema da medida quantitativa do emaranhamento, analisando seu comportamento para diferentes conjuntos de parˆametros do sistema e configurações de estados iniciais Gaussianos.

L'objectif de ce travail de thèse est d'étudier analytiquement et numériquement le comportementdynamique non-linéaire des rotors, en prenant en compte des effets significatifs comme les grandesdéformations en flexion, les non-linéarités géométriques et le cisaillement. Le manuscrit est diviséen trois parties principales. Dans la première partie, le principe de Hamilton est utilisé pour formulerles équations du mouvement qui prennent en compte un ensemble d’effets non-linéaires comme desdéformations d'ordre supérieur en flexion et le cisaillement. De plus, si les supports du rotor nepermettent pas à l'arbre de se déplacer dans la direction axiale, il y a alors une force dynamiqueharmonique agissant axialement sur le rotor en fonctionnement. Ces modèles se composentd’équations différentielles non-linéaires du deuxième et du quatrième ordre.Les deux parties suivantes sont consacrées à la résolution des différents modèles non-linéairesdéveloppés dans la première partie. Des méthodes analytiques et numériques sont appliquées afin detraiter les équations non-linéaires du mouvement. Une méthode basée sur des développementsasymptotiques, la méthode des échelles multiples (MEM) est utilisée. Les courbes de réponse sonttracées pour différentes résonances possibles et l'effet de la non-linéarité est discuté par rapport àl'analyse linéaire. La réponse forcée du système provoquée par un balourd est également présentéepour plusieurs configurations du rotor. Lorsque les déformations de cisaillement sont prises encompte, l'analyse est effectuée pour différents élancements afin de mettre en évidence cet effet sur ladynamique d’un système arbre-disque / The objective of the present work is to investigate the nonlinear dynamic behavior of the rotorsystems analytically and numerically, taking into account the significant effects, for example, higherorder large deformations in bending, geometric nonlinearity and shear effects.This thesis is dividedinto two major parts. In the first part, Hamilton’s principle is used to derive the equations of motionwhich take into account various effects, for example, nonlinearity due to higher order largedeformations in bending and shear effects. In addition, if the supports of the rotor do not allow theshaft to move in the axial direction, then there will be a dynamical force acting axially on the rotoras it operates. The mathematical models are composed of coupled nonlinear differential equations ofthe 2nd and the 4th order.In the second part, the resolution of various nonlinear models developed in the first part isaddressed. Analytical and numerical methods are applied for treating the nonlinear equations ofmotion. A method based on asymptotic developments, the method of multiple scales (MMS) is used.The response curves are plotted for different possible resonance conditions and the effect ofnonlinearity is discussed with respect to the linear analysis. The forced response of the system due toa mass unbalance is also presented for various configurations of the rotor. When shear deformationsare taken into account, the analysis is performed for various slenderness ratios to highlight sheareffects on the dynamics of the shaft-disk rotor systems

Orientador: Masayoshi Tsuchida / Banca: José Manoel Balthalzar / Banca: Adalberto Spezamiglio / Resumo: Osciladores eletromecânicos podem ser modelados matematicamente através da equação de Duffing ou equação de Van der Pol, mesmo que sejam sistemas de escala nanomética. Nesta dissertação analisamos um oscilador forçado sujeito a um amortecimento não-linear, que é representado pela equação de Duffing - Van der Pol. Em geral, não é fácil obter solução analítica exata para esta equação, então a análise é feita utilizando a teoria de perturbações para obter uma solução analítica aproximada. Para isso consideramos certos parâmetros do problema como sendo pequenos parâmetros, e obtemos a solução na forma de expansão direta. Devido o fato da frequência natural do sistema dinâmico depender do pequeno parâmetro, essa expansão é não uniforme, ou seja, apresenta termos seculares mistos (termos de Poisson), e além disso possui pequenos divisores. Essas inconveniências são eliminadas aplicando o método das múltiplas escalas e o método da média. Inicialmente os pequenos parâmetros são escolhidos de modo que o problema não perturbado se reduz a um oscilador harmônico forçado, e na escolha posterior o problema não perturbado é um oscilador linear amortecido e forçado. / Abstract: Electromechanical oscillators can be mathematically modeled by a Du±ng equation or a Van der Pol equation, even if they are nanometric systems. In this work we studied a forced oscillator having nonlinear damping, that is represented by a Du±ng - Van der Pol equation. In general, it is not easy to get the exact analytical solution for this equation, then the analysis is done using the perturbation theory to get an approximate analytical solution. For this reason we considered that certain parameters of the problem are small parameters and we obtain the solution in the form of straightforward expansion. Due to the fact that natural frequency of the dynamic system depends on the small parameter, this expansion is not uniform, i.e. presents secular terms (Poisson terms) and also small-divisors. These inconveniences are eliminated using the method of multiple scales and the aver- aging method. Initially the small parameters are chosen so that the unperturbed problem is reduced to a forced harmonic oscillator, and in the subsequent choice the unperturbed is a forced oscillator having linear damping. / Mestre

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-21T19:02:46Z No. of bitstreams: 2 Dissertação - Alcione Borges Purcina - 2016.pdf: 4973424 bytes, checksum: b35ba030a2a1888c5554daaa45f886e4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2017-07-07T20:22:01Z (GMT) No. of bitstreams: 2 Dissertação - Alcione Borges Purcina - 2016.pdf: 4973424 bytes, checksum: b35ba030a2a1888c5554daaa45f886e4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-07-07T20:22:01Z (GMT). No. of bitstreams: 2 Dissertação - Alcione Borges Purcina - 2016.pdf: 4973424 bytes, checksum: b35ba030a2a1888c5554daaa45f886e4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-09 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / In the last years, there is a growing interest in the study of nonlinear phenomena that because with the modernization of the structures and employment of innovative and more flexible materials, the nonlinearities become more evident. In that sense, this work aims to study the behavior of a mechanical system with two degrees of freedom with non-linear characteristics in primary resonance. The structure consists of the main system connected to a secondary system to act as a Nonlinear Dynamic Vibration Absorber, which partially or fully absorbs the vibrational energy of the system. The numerical solutions of the problem are obtained using the Runge-Kutta methods of 4th order and approximate analytical solutions are obtained using the Multiple Scales Method, and then it turns out how close can be closer to the numerical solutions. Through the mentioned disturbance method, too, it is determined the answers for the ordinary differential equations of the first order, which describe the modulation amplitudes and phases. Thus, the solution in steady state and the stability are studied using the frequency response. Furthermore, the behavior of the main system and the absorber are investigated through numerical simulations, such as responses in the time domain, phase planes and Poincaré map; which show that the system displays periodic movements, quasi-periodic and chaotic. / Nos últimos anos, é crescente o interesse pelo estudo dos fenômenos não lineares, isso porque com a modernização das estruturas e o emprego de materiais inovadores e mais flexíveis, as não linearidades tornaram-se mais evidentes. Nesse sentido, este trabalho tem por objetivo estudar o comportamento de um sistema mecânico de 2 graus de liberdade com características não lineares, em ressonância primária. A estrutura consiste do sistema principal conectado a um sistema secundário que atuará como um Absorvedor Dinâmico de Vibração não linear que, por sua vez, absorve parcial ou totalmente a energia vibratória do sistema. As soluções numéricas do problema são obtidas utilizando o Método de Runge-Kutta de 4ª ordem e as soluções analíticas aproximadas, são obtidas utilizando o Método das Múltiplas Escalas, para então verificar o quão próximas tais soluções conseguem aproximar-se das soluções numéricas. Através do Método de Perturbação mencionado, também, são determinadas as respostas para as equações diferenciais ordinárias de primeira ordem, que descrevem a modulação das amplitudes e fases. Sendo assim, a solução em regime permanente e sua estabilidade são estudadas utilizando a curva resposta de frequência. Além disso, o comportamento do sistema principal e do absorvedor são investigados através de simulações numéricas, tais como: respostas no domínio do tempo, os planos de fase e os seções de Poincaré; as quais evidenciam que o sistema exibe movimentos periódicos, quase-periódicos e caótico.

No description available.

Local Light Alignment is a new shading based technique in the field of shape depiction, a field which concerns itself with techniques to represent and enhance the three-dimensional (3D) shape of objects in two-dimensional (2D) visual media. The main idea of Local Light Alignment is to locally adjust the incoming direction of light to create contrast in a way that enhances the perception of shape and surface detail. It is aimed at visual artists and uses a multiple scale approach, where the user can tune the enhancement of geometric shapes of different sizes. Local Light Alignment was published together with a new objective metric for measuring shape depiction called the congruence score. This thesis strives to increase knowledge about both these new techniques by investigating how varying several parameters for Local Light Alignment affect the congruence score at different scales and strengths of enhancement. The parameters investigated are the range and spatial parameters for the bilateral filter in the scale space construction as well as the enhancement strength parameter of the main Local Light Alignment algorithm. The thesis also tries to identify any common visual characteristics for images that score high, to give a better intuition of what the congruence score represents. The tests are performed using four models, each representing a different field of application. For each model, several viewpoints are tested, and for every viewpoint, 244 differently parameterized renders are produced and scored. The results notably show that the spatial and range parameters both affect controllability of the algorithm by shifting the scores toward the finer end of the scale space with higher values, without affecting the total score. The enhancement strength parameter is shown to affect the congruence score positively, but with diminishing returns as values approach 1. It is also shown by example that the images showing the largest improvement in congruence score tend to exhibit such high degrees of exaggeration that they would probably not be considered good examples of shape depiction by human standards. This is identified as an interesting area to perform subjective evaluations in future research. These investigations will be valuable to those who will create application software that features Local Light Alignment, as well as those wanting to employ the congruence score metric. / Local Light Alignment är en ny skuggningsbaserad teknik inom området formskildring, ett område som är befattar sig med olika tekniker för att förbättra den tredimensionella formåtergivningen av objekt i tvådimensionella medier. Huvudidén bakom Local Light Alignment är att lokalt justera riktningen av inkommande ljus på ett sätt som skapar ytterligare kontrast och förstärker uppfattningen av form och ytdetaljer. Tekniken riktar sig mot designers och använder sig av en flerskalig approach, där användaren kan justera förbättringen av geometriska former av olika storlekar. Local Light Alignment publicerades tillsammans med en kvantitativ metrik för att mäta formskildring, kallad ”congruence score”, eller kongruenspoängtal på svenska. Denna uppsats eftersträvar att öka kunskapen kring båda dessa nya tekniker genom att undersöka hur parameterrymden för Local Light Alignment påverkar kongruenspoängtalet vid olika skalor och förbättringsstyrkor. De undersökta parametrarna är omfångs- och spatialparametrarna som tillhör det bilaterala filtret som används i konstruktionen av skal-rymden, samt parametern för förbättringsstyrka tillhörandes den centrala delen av Local Light Alignment algoritmen. Upptatsen försöker också att identifiera gemensamma visuella uttryck för bilder som visar stor förbättring i kongruenspängtalet, för att kunna ge en intuition om vad kongruenspoängtalet representerar som modell. Studien är genomförd med 4 olika 3D-modeller, där varje modell representerar ett separat område där Local Light Alignment skulle kunna användas. För varje modell så undersöks flera åskådningsvinklar, och för varje åskådningsvinkel så produceras 244 olika parameteriserade renderingar som sedan utvärderas med kongruenspoängtal. Resultaten visar att omfångs- och spatialparametrarna båda påverkar kontrollerbarheten hos algoritmen genom att skifta massan av poäng från den grövre delen av skal-rymden, mot den finare. Detta utan att nämnvärt påverka totalpoängen. Förbättrinsstyrkeparametern visas påverkar kongruenspoängtalet positivt, men med avtagande effect då värdet närmar sig 1. Det demonstreras också visuellt hur de bilder som visar störst förbättring i kongruenspoängtal också uppvisar så höga nivåer av överdriftseffekter att de knappast kan anses vara goda exempel av förbättrad formskildring. Detta identifieras som en intressant riktning för framtida forskning med stöd av subjektiva utvärderingar.

Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of the normal form.