Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Real-time hand tracking for rehabilitation and character animation

Hand and finger tracking has a major importance in healthcare, for rehabilitation of hand function required due to a neurological disorder, and in virtual environment applications, like characters animation for on-line games or movies. Current solutions consist mostly of motion tracking gloves with embedded resistive bend sensors that most often suffer from signal drift, sensor saturation, sensor displacement and complex calibration procedures. More advanced solutions provide better tracking stability, but at the expense of a higher cost. The proposed solution aims to provide the required precision, stability and feasibility through the combination of eleven inertial measurements units (IMUs). Each unit captures the spatial orientation of the attached body. To fully capture the hand movement, each finger encompasses two units (at the proximal and distal phalanges), plus one unit at the back of the hand. The proposed glove was validated in two distinct steps: a) evaluation of the sensors’ accuracy and stability over time; b) evaluation of the bending trajectories during usual finger flexion tasks based on the intra-class correlation coefficient (ICC). Results revealed that the glove was sensitive mainly to magnetic field distortions and sensors tuning. The inclusion of a hard and soft iron correction algorithm and accelerometer and gyro drift and temperature compensation methods provided increased stability and precision. Finger trajectories evaluation yielded high ICC values with an overall reliability within application’s satisfying limits. The developed low cost system provides a straightforward calibration and usability, qualifying the device for hand and finger tracking in healthcare and animation industries.

Deteção e acompanhamento de movimento através de uma câmara de vídeo

A deteção e seguimento de pessoas tem uma grande variedade de aplicações em visão computacional. Embora tenha sido alvo de anos de investigação, continua a ser um tópico em aberto, e ainda hoje, um grande desafio a obtenção de uma abordagem que inclua simultaneamente exibilidade e precisão. O trabalho apresentado nesta dissertação desenvolve um caso de estudo sobre deteção e seguimento automático de faces humanas, em ambiente de sala de reuniões, concretizado num sistema flexível de baixo custo. O sistema proposto é baseado no sistema operativo GNU's Not Unix (GNU) linux, e é dividido em quatro etapas, a aquisição de vídeo, a deteção da face, o tracking e reorientação da posição da câmara. A aquisição consiste na captura de frames de vídeo das três câmaras Internet Protocol (IP) Sony SNC-RZ25P, instaladas na sala, através de uma rede Local Area Network (LAN) também ele já existente. Esta etapa fornece os frames de vídeo para processamento à detecção e tracking. A deteção usa o algoritmo proposto por Viola e Jones, para a identificação de objetos, baseando-se nas suas principais características, que permite efetuar a deteção de qualquer tipo de objeto (neste caso faces humanas) de uma forma genérica e em tempo real. As saídas da deteção, quando é identificado com sucesso uma face, são as coordenadas do posicionamento da face, no frame de vídeo. As coordenadas da face detetada são usadas pelo algoritmo de tracking, para a partir desse ponto seguir a face pelos frames de vídeo subsequentes. A etapa de tracking implementa o algoritmo Continuously Adaptive Mean-SHIFT (Camshift) que baseia o seu funcionamento na pesquisa num mapa de densidade de probabilidade, do seu valor máximo, através de iterações sucessivas. O retorno do algoritmo são as coordenadas da posição e orientação da face. Estas coordenadas permitem orientar o posicionamento da câmara de forma que a face esteja sempre o mais próximo possível do centro do campo de visão da câmara. Os resultados obtidos mostraram que o sistema de tracking proposto é capaz de reconhecer e seguir faces em movimento em sequências de frames de vídeo, mostrando adequabilidade para aplicação de monotorização em tempo real.

Exploratory geospatial data analysis using self-organizing maps

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Ciência e Sistemas de Informação Geográfica

Estudi dinàmic i manipulació de fluxos en monocapes de Langmuir de molècules fotosensibles

Durant el període de gaudiment de la beca, des del dia 9 de març del 2007 fins el dia 8 de març del 2010, s’han dut a terme diferents tipus d’experiments amb sistemes bidimensionals com són les monocapes de Langmuir. Inicialment es va començar per l’estudi i la caracterització d’aquests sistemes experimentals, tant en repòs com en dinàmic, com és l’estudi de la reposta col•lectiva molecular de dominis d’un azoderivat fotosensible al rotar el pla de polarització mentre es mante sota il•luminació constant i els estudis de sistemes bidimensionals al collapse que es poden relacionar a les propietats viscoplàstiques dels sòlids. Una altra via d’estudi és la reologia d’aquests sistemes bidimensionals quan flueixen a través de canals. Arrel del sistema experimental més simple, una monocapa fluint per un canal, s’ha observat i estudiat l’efecte coll d’ampolla. Un cop assolit i estudiat el sistema més senzill, s’han aplicat tècniques més complexes de fabricació per fotolitografia per fer fluir monocapes de Langmuir per circuits on hi ha un gran contrast de mullat. Un cop aquests circuits es van implementar satisfactòriament en un sistema pel control de fluxos bidimensionals, es posen de manifest les possibles aplicacions futures d’aquests sistemes per l’estudi i el desenvolupament de la microfluídica bidimensional.

The Standard Biplot

Biplots are graphical displays of data matrices based on the decomposition of a matrix as the product of two matrices. Elements of these two matrices are used as coordinates for the rows and columns of the data matrix, with an interpretation of the joint presentation that relies on the properties of the scalar product. Because the decomposition is not unique, there are several alternative ways to scale the row and column points of the biplot, which can cause confusion amongst users, especially when software packages are not united in their approach to this issue. We propose a new scaling of the solution, called the standard biplot, which applies equally well to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. The standard biplot also handles data matrices with widely different levels of inherent variance. Two concepts taken from correspondence analysis are important to this idea: the weighting of row and column points, and the contributions made by the points to the solution. In the standard biplot one set of points, usually the rows of the data matrix, optimally represent the positions of the cases or sample units, which are weighted and usually standardized in some way unless the matrix contains values that are comparable in their raw form. The other set of points, usually the columns, is represented in accordance with their contributions to the low-dimensional solution. As for any biplot, the projections of the row points onto vectors defined by the column points approximate the centred and (optionally) standardized data. The method is illustrated with several examples to demonstrate how the standard biplot copes in different situations to give a joint map which needs only one common scale on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot readable. The proposal also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important.

Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

Contribution biplots

In order to interpret the biplot it is necessary to know which points usually variables are the ones that are important contributors to the solution, and this information is available separately as part of the biplot s numerical results. We propose a new scaling of the display, called the contribution biplot, which incorporates this diagnostic directly into the graphical display, showing visually the important contributors and thus facilitating the biplot interpretation and often simplifying the graphical representation considerably. The contribution biplot can be applied to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. In the contribution biplot one set of points, usually the rows of the data matrix, optimally represent the spatial positions of the cases or sample units, according to some distance measure that usually incorporates some form of standardization unless all data are comparable in scale. The other set of points, usually the columns, is represented by vectors that are related to their contributions to the low-dimensional solution. A fringe benefit is that usually only one common scale for row and column points is needed on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot legible. Furthermore, this version of the biplot also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important, when they are in fact contributing minimally to the solution.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Bistability driven by Gaussian colored noise: First-passage times

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ¿c. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D¿c.

Evidence of aging in spin glass mean-field models

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

Experimental evidence of localized oscillations in the photosensitive chlorine dioxide-iodine-malonic acid reaction

The interaction between Hopf and Turing modes has been the subject of active research in recent years. We present here experimental evidence of the existence of mixed Turing-Hopf modes in a two-dimensional system. Using the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) and external constant background illumination as a control parameter, standing spots oscillating in amplitude and with hexagonal ordering were observed. Numerical simulations in the Lengyel-Epstein model for the CDIMA reaction confirmed the results.

Eye movements in the blind

Objectives : Eye movements are necessary to stabilize the retinal picture and to find a new object. This seems useless for blind people, so why do they nevertheless have them. We report on an EOG study on 29 blind volunteers and 5 volunteers with closed eyes. Material and methods: We recorded eye movements by EOG and let the volunteers fulfill different exercises by following an acoustic running point by gaze, pointing, imagining in the room, listing words that begin with the vocal U and a finger labyrinth. Results: We found slow eye movements as well as pathological eye movements in the blind subjects. We found that blind subjects have a horizontal preferency.The duration of fixation of pictures is shorter in the blind subjects. The blind could even modulate saccade amplitudes . Discussion: Eye movements seem to be structural properties of the brain which prepare the organism for certain situations-even if they do not take place. We think that eye movements are partially independent of the experience of view. We did not expect that the blind subjects could modify gaze according to the subject. This leads to the hypothesis of a preformed dimensional system.

Analysis of Existing Work-Zone Devices with MASH Safety Performance Criteria, TPF-5(018), 2009

Crashworthy, work-zone, portable sign support systems accepted under NCHRP Report No. 350 were analyzed to predict their safety peformance according to the TL-3 MASH evaluation criteria. An analysis was conducted to determine which hardware parameters of sign support systems would likely contribute to the safety performance with MASH. The acuracy of the method was evaluated through full-scale crash testing. Four full-scale crash tests were conducted with a pickup truck. Two tall-mounted, sign support systems with aluminum sign panels failed the MASH criteria due to windshield penetration. One low-mounted system with a vinyl, roll-up sign panel failed the MASH criteria due to windshield and floorboard penetration. Another low-mounted system with an aluminum sign panel successfully met the MASH criteria. Four full-scale crash tests were conducted with a small passenger car. The low-mounted tripod system with an aluminum sign panel failed the MASH criteria due to windshield penetration. One low-mounted system with aluminum sign panel failed the MASH criteria due to excessive windshield deformation, and another similar system passed the MASH criteria. The low-mounted system with a vinyl, roll-up sign panel successfully met the MASH criteria. Hardware parameters of work-zone sign support systems that were determined to be important for failure with MASH include sign panel material, the height to the top of the mast, the presence of flags, sign-locking mechanism, base layout and system orientation. Flowcharts were provided to assist manufacturers when designing new sign support systems.