Analysis of dry friction by friction test bench

A test of a device equivalent to a Girling duo-servo brake mechanism has been made. The main result is the characterization of a series of frequency associated to the system. The frequency in the spectrum that matches with the belt’s turn frequency is the clearest relation response excitation. The excitation source is related to two small notches on the surface of the belt. A frequency bandwidth with a main frequency, which has no relation to the natural frequencies of the system, is present in each spectrum and is related to non-linear friction phenomenon. Several probes have been studied to find the best solution, which is obtained with the laser distance sensor. Even using this sensor, the block’s displacement in the workbench is greater than the probe’s measure threshold in some assemblies. Several belts have been tested and the belt with smoother notches has been selected. Another source of instability comes from the necessary velocities used in the test. These force the electric motor to run at very low velocity that produces instabilities that has been considered in the analysis results. Amid the recommendations, it would be suitable get a belt without notches and another driver. In the present work the following tests has been developed with three springs set. With a set of 0.14 N/mm stiffness springs, tests have been completed at 20, 15 and 10 rpm. With a set of 0.34 N/mm stiffness springs, tests have been completed at 20, 15, 10 and 5 rpm. With a set of 0.14 and 0.34 N/mm, a test has been completed at 5 rpm. For measures related to the set of 0.14 N/mm stiffness springs, the lower angular velocity is, the more chaotic the system’s behaviour is. For measures related to the set of 0.34 N/mm stiffness springs, the higher angular velocity is, the more chaotic the system’s behaviour is. For the measure related to the set of hybrid springs, the phase’s plane space shows an area which has not relation to stick phenomenon owing to a negative slope, instead of the positive slope associated to the stick. A comparison of the results at 10 rpm for both kinds of springs sets, 0.14 and 0.34 N/mm, shows the stiffer springs are, the more chaotic behaviour is.Escuela Técnica Superior de Ingeniería IndustrialUniversidad Politécnica de Cartagen

Complex extreme nonlinear waves: classical and quantum theory for new computing models

The historical role of nonlinear waves in developing the science of complexity, and also their physical feature of being a widespread paradigm in optics, establishes a bridge between two diverse and fundamental fields that can open an immeasurable number of new routes. In what follows, we present our most important results on nonlinear waves in classical and quantum nonlinear optics. About classical phenomenology, we lay the groundwork for establishing one uniform theory of dispersive shock waves, and for controlling complex nonlinear regimes through simple integer topological invariants. The second quantized field theory of optical propagation in nonlinear dispersive media allows us to perform numerical simulations of quantum solitons and the quantum nonlinear box problem. The complexity of light propagation in nonlinear media is here examined from all the main points of view: extreme phenomena, recurrence, control, modulation instability, and so forth. Such an analysis has a major, significant goal: answering the question can nonlinear waves do computation? For this purpose, our study towards the realization of an all-optical computer, able to do computation by implementing machine learning algorithms, is illustrated. The first all-optical realization of the Ising machine and the theoretical foundations of the random optical machine are here reported. We believe that this treatise is a fundamental study for the application of nonlinear waves to new computational techniques, disclosing new procedures to the control of extreme waves, and to the design of new quantum sources and non-classical state generators for future quantum technologies, also giving incredible insights about all-optical reservoir computing. Can nonlinear waves do computation? Our random optical machine draws the route for a positive answer to this question, substituting the randomness either with the uncertainty of quantum noise effects on light propagation or with the arbitrariness of classical, extremely nonlinear regimes, as similarly done by random projection methods and extreme learning machines

Análise estatística dos parâmetros modais de sistemas randômicos

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2011A confecção de um sistema mecânico está sempre sujeita às imperfeições e incertezas oriundas do seu processo de fabricação que podem eventualmente estabelecer diferenças significativas entre o desempenho desejado inicialmente em projeto e aquele efetivamente apresentado pelo sistema real. Como conseqüência deste fato, uma variação aleatória das respostas dinâmicas é certamente esperada ao longo de um ensemble composto de sistemas similares, dificultando de forma considerável as análises de engenharia nas regiões de médias e altas frequências. Assim, com o objetivo de garantir que os requisitos de projeto e certificação sejam devidamente cumpridos, um engenheiro projetista deve considerar os principais efeitos decorrentes destas incertezas na elaboração dos seus modelos matemáticos. Neste sentido, intensos esforços têm sido realizados pela comunidade acadêmica para o desenvolvimento de metodologias eficazes e otimizadas para a descrição estatística das respostas oriundas de sistemas randômicos (i.e. sistemas com propriedades não-determinísticas). Atualmente, a Análise Estatística de Energia (SEA) é uma das principais metodologias para análise vibroacústica nas regiões de médias e altas frequências, visto que seus resultados predizem o comportamento médio esperado de um ensemble composto de sistemas similares, como por exemplo: carros que saem de uma linha de montagem ou aviões produzidos em série. Recentemente, as formulações analíticas de SEA foram estendidas para predizer a variância da resposta energética. Nestas formulações, as estatísticas dos parâmetros modais (freqüências naturais e formas modais) foram descritas pelas estatísticas dos auto-valores e auto-vetores de uma matriz do tipo GOE (Gaussian Orthogonal Ensemble) oriunda da Teoria da Matriz Randômica. Diversos trabalhos experimentais e numéricos têm confirmado um estabelecimento satisfatório da estatística GOE para as frequências naturais de sistemas suficientemente randômicos. Entretanto, alguns desvios significativos em relação ao modelo GOE têm sido identificados para as formas modais correspondentes afetando sensivelmente o desempenho das predições da variância de SEA. Neste trabalho de doutorado, as estatísticas dos parâmetros modais de sistemas randômicos foram sistematicamente investigadas com o auxílio dos resultados dos observadores estatísticos oriundos da Teoria da Matriz Randômica. Duas classes de problemas foram analisadas: ondas longitudinais em barras e ondas de flexão em placas. Para as estatísticas de cada um dos parâmetros modais, os níveis de concordância com o modelo GOE (ou de Poisson) foram prontamente avaliados. Além disso, os valores da média e da variância relativa da densidade de energia cinética foram calculados e comparados com as predições analíticas de SEA baseadas nos modelos GOE e de Poisson. Os possíveis impactos, ou degradações, no desempenho das predições da variância de SEA baseadas no modelo GOE foram investigados para os casos em que as estatísticas dos parâmetros modais não concordam plenamente com a estatística descrita pelo modelo GOE. Dentre as principais contribuições deste trabalho de doutorado destacam-se o estabelecimento de métricas eficientes para a verificação do nível de concordância de cada um dos parâmetros modais com as estatísticas descritas pelos modelos GOE e de Poisson, bem como a obtenção de uma melhor compreensão das relações existentes entre as estatísticas do modelo GOE (ou de Poisson) e as estatísticas esperadas para os parâmetros modais de sistemas vibroacústicos de engenharia

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Light beam propagation in complex crystals

Tesi per compendi de publicacions.Versió amb diverses seccions encriptades, per drets a'autorRecent advancement in Photonics have brought about a new era of miniaturisation. Along came a need for technology to allow the manipulation of light at the micrometer scale, with precise control over beam propagation. The past decades have seen numerous studies devoted to periodic nanophotonic structures, Photonic Crystals (PhCs), which brought out different temporal and spatial functionalities such as frequency bandgaps, waveguiding, or managing diffractive properties of the beam. More recently, attention was paid to equally accessible artificial nanophotonic structures, where gain and losses are modulated on the wavelength scale: Gain Loss Modulated Materials (GLMMs). Therefore, the aim of my PhD was providing a deep analysis on beam propagation in GLMMs, identifying the spatial propagation effects they held and proposing realistic scenarios in which they could be implemented, in existing and evolving technology and devices. We built our studies from a solid understanding of GLMMs of prior works performed, however, using a paraxial approximation, which reduces the predictions accuracy by excluding propagation at large angles. The methodology adopted is a combination of analytical predictions and numerical confirmation of the predicted effects. We initially investigated the high anisotropy of beam amplification/attenuation within GLMMs. As predicted by the plane wave expansion method, the propagation of light beams within such structures is sensitive to the propagation direction. We provided a numerical proof in 2D periodic Loss Modulated Materials (LMM) with square and rhombic lattice symmetry, by solving the full set of Maxwell¿s equations, using the finite difference time domain method, which entails no approximation. Anisotropy of amplification/attenuation leads to the narrowing of the angular spectrum of beams with wavevectors close to the edges of the first Brillouin Zone. The effect provides a novel tool to filter out high spatial harmonics from noisy beams, while being amplified. A later study lead us to analyse the focalisation performance of a flat LMM slab. Flat lensing was analytically predicted by the dispersion curves obtained from a coupled mode expansion of Maxwell¿s equations, and then numerically confirmed. For a range of frequencies coinciding with a high transmission window at resonant Bragg frequencies (bandgap frequencies for PhCs), light beams undergo negative (anomalous) diffraction through LMMs. The phase shifts accumulated within the structure are then compensated by normal diffraction in free space, leading to a substantial focalization beyond it. The predicted phenomena are generic for spatially modulated materials and other kinds of waves. Thus, we also discussed, for the first time, propagation in LMM acoustic crystals, predicting high angular transmission bands. While these initial studies assumed hypothetical LMM materials, in a realistic scenario, loss modulations are always accompanied by refractive index modulations, as predicted by Kramers-Kronig relations. During the final phase of my PhD, we focused on more realistic structures exhibiting both index and loss modulations, namely metallic photonic crystals (MPhCs), made of 2D rhombic arrays of metallic cylinders embedded in air. We explored their ability to tailor the spatial propagation of light beams. Indeed, MPhCs support self-collimated propagation and negative diffraction. In this later case, flat lensing was demonstrated, leading to the focalization of beams behind MPhCs slabs. Also, the anisotropic attenuation of light within MPhCs enables spatial filtering. Finally, we initiated studies towards the implementation of GLMMs as an intrinsic mechanism to improve the beam quality from Broad Area Semiconductor (BAS) amplifiers. Along the development of my PhD, we proposed, analysed and established spatial beam propagation effects in GLMM, from purely ideal LMM structures to more realistic structure as MPhCs or BAS amplifiers.Els avenços recents en Fotònica han començat una nova era de miniaturització, apareixent la necessitat tecnològica de manipular la llum a l'escala micromètrica, amb un control precís de la propagació del feixos. Les darreres dècades han estat testimoni de nombrosos estudis dedicats a estructures periòdiques nanofotòniques, Cristalls Fotònics (PhC), amb propietats temporals i espacials, com ara bandes prohibides de freqüència, guies d'ones, o el control sobre la difracció dels feixos de llum. Més recentment, s'han considerat altres estructures artificials nanofotòniques igualment accessibles, amb guanys i pèrdues modulades a l'escala de la longitud d'ona, Materials Modulats amb Guanys i Pèrdues (GLMMs). Així, l'objectiu de la meva tesi doctoral és proporcionar una anàlisi profunda sobre la propagació dels feixos de llum en GLMMs, identificant efectes espacials i proposant escenaris reals per implementar-los, en tecnologies i dispositius ja existents o en desenvolupament. Els treball parteix d'estudis previs que proporcionen una comprensió sòlida dels GLMMs, malgrat que es basen en l'aproximació paraxial, reduint la precisió de les prediccions ja que s'exclou la propagació a angles grans. La metodologia adoptada és una combinació de prediccions analítiques i confirmació numèrica dels efectes predits. Inicialment, s'investiga l'alta anisotropia d'amplificació/atenuació de feixos dins GLMMs. Tal com es prediu amb el mètode d'expansió en ones planes, la propagació del feixos en aquestes estructures és molt sensible a la direcció; proporcionant la prova numèrica en Materials 2D amb Pèrdues Modulades (LMM) amb simetria de xarxa quadrada i romboïdal, resolent el conjunt complet de les equacions de Maxwell (mètode de diferències finites en domini temporal), sense cap aproximació. L'anisotropia de l'amplificació/atenuació redueix l'espectre angular dels feixos amb vectors d'ona propers als límits de la primera zona de Brillouin; efecte que proporciona una nova eina per filtrar harmònics espacials de feixos amb soroll, mentre s'amplifiquen. Un estudi posterior duu a analitzar la possibilitat de focalitzar amb una làmina plana LMM. L'efecte es prediu analíticament amb les corbes de dispersió (expansió en modes acoblats de les equacions de Maxwell) i es confirma numèricament. Per a un rang de freqüències dins la finestra d'alta transmissió de les freqüències ressonants de Bragg (banda prohibida per a PhC), la difracció és negativa (anòmala) a través de l'LMM. La difracció normal de l'espai lliure compensa la fase negativa acumulada en l'estructura i el feix focalitza després de la làmina. Els fenòmens predits són genèrics pels materials modulats espacialment i altres tipus d'ones. També s'estudia, per primera vegada, la propagació en cristalls acústics LMM, predient bandes angulars d'alta transmissió. Malgrat inicialment es consideren materials LMM ideals, en un escenari més realista, les modulacions de pèrdues van sempre acompanyades de modulacions d'índex de refracció segons les relacions de Kramers-Kronig. La fase final de la meva Tesi se centra en estructures més realistes tant amb modulacions d'índex com de pèrdues: cristalls fotònics metàl·lics (MPhCs), formats per distribucions periòdiques ròmbiques de cilindres metàl·lics en aire, explorant-ne la capacitat per controlar la propagació de feixos de llum. En MPhCs és possible tant la propagació col·limada com la difracció negativa. En aquest últim cas, es demostra la focalització per làmines planes de MPhCs. A més, l'atenuació anisòtropa de la llum permet el filtratge espacial. Finalment, s'explora l'aplicació dels GLMMs com a mecanisme intrínsec per millorar la qualitat dels feixos emesos per amplificadors de semiconductors (BAS). Al llarg de la meva tesi doctoral, s’han proposat, analitzat i establert mecanismes de control de la difracció de feixos de llum en GLMM, des d'estructures purament ideals LMM a més realistes com MPhCs o amplificadors BAS.Postprint (published version

Symmetry and Mesoscopic Physics

Symmetry is one of the most important notions in natural science; it lies at the heart of fundamental laws of nature and serves as an important tool for understanding the properties of complex systems, both classical and quantum. Another trend, which has in recent years undergone intensive development, is mesoscopic physics. This branch of physics also combines classical and quantum ideas and methods. Two main directions can be distinguished in mesoscopic physics. One is the study of finite quantum systems of mesoscopic sizes. Such systems, which are between the atomic and macroscopic scales, exhibit a variety of novel phenomena and find numerous applications in creating modern electronic and spintronic devices. At the same time, the behavior of large systems can be influenced by mesoscopic effects, which provides another direction within the framework of mesoscopic physics. The aim of the present book is to emphasize the phenomena that lie at the crossroads between the concept of symmetry and mesoscopic physics