A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

A non-aqueous solution synthesis of boron carbide by control of in-situ carbon

Synthesis of high quality boron carbide (B4C) powder is achieved by carbothermal reduction of boron oxide (B2O3) from a condensed boric acid (H3BO3) / polyvinyl acetate (PVAc) product. Precursor solutions are prepared via polymerisation of vinyl acetate (VA) in methanol in the presence of dissolved H3BO3. With excess VA monomer being removed during evaporation of the solvent, the polymerisation time is then used to manage availability of carbon for reaction.

In-situ carbon control in the preparation of precursors to boron carbide by a non-aqueous solution technique

Synthesis of high quality boron carbide (B4C) powders is achieved by carbothermal reduction of boron oxide (B2O3) from a condensed boric acid (H3BO3)/polyvinyl acetate (PVAc) product. Precursor solutions are prepared via free radical polymerisation of vinyl acetate (VA) monomer in methanol in the presence of dissolved H3BO3. A condensed product is then formed by flash evaporation under vacuum. As excess VA monomer is removed at the evaporation step, the polymerisation time is used to manage availability of carbon for reaction. This control of carbon facilitates dispersion of H3BO3 in solution due to the presence of residual VA monomer. B4C powders with very low residual carbon are formed at temperatures as low as 1,250 °C with a 4 hour residence time.

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

Introduction of a non-conventional solution for Amazon transmission system: Analysis of the electric aspects

This article shows an analysis of the longitudinal electric parameters of a three-phase transmission line/section using a 280-meter high steel tower. This characteristic, the height of the line conductors and distance between them, are intrinsic related to the longitudinal and transversal parameters of the line. By this means, an accurate study was carried out in order to show the electric variations between a transmission line using the new technology and a three-phase conventional 440 kV line for a wide range of frequencies and a variable soil resistivity. In addition, by using a digital line model, simulations are carried out in time domain to analyze critical overvoltage transients on the studied line. © 2011 IEEE.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Beta-structure of polypeptides in non-aqueous solutions. I. Spectral characteristics of the polypeptide backbone

The optical rotatory features of the beta-structure of the polypeptides in non-aqueous solutions and films cast from these solutions have been investigated. The beta-structure of poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-O-carbo-bands of their films. The optical rotatory dispersion (ORD) and circular dichroism (CD) spectra of these polypeptides are found to be very similar in both film and solution. In solvents promoting the beta-structure, the polypeptides are characterized by CD troughs in the n-pi* transition region of the peptide chromophore. The ORD spectra are found to be positive in sign throughout the visible and accessible ultraviolet regions and are interpreted in terms of the possible existence of a relatively much larger positive pi-pi* CD bands as compared with the negative n-pi* band. The rotatory data obtained in the non-aqueous solution are compared with those obtained for other poly peptides in aqueous solutions, with respect to the type and extent of beta-structure present.

Séries universelles dans CN et sur les surfaces de Riemann non compactes

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-linear boundary element analysis of floor slabs reinforced with rectangular beams

In this work, a numerical model to perform non-linear analysis of building floor structures is proposed. The presented model is derived from the Kirchhoff-s plate bending formulation of the boundary element method (BENI) for zoned domains, in which the plate stiffness is modified by the presence of membrane effects. In this model, no approximation of the generalized forces along the interface is required and the compatibility and equilibrium conditions along interfaces are imposed at the integral equation level. In order to reduce the number of degrees of freedom, the Navier Bernoulli hypothesis is assumed to simplify the strain field for the thin sub-regions (rectangular beams). The non-linear formulation is obtained from the linear formulation by incorporating initial internal force fields, which are approximated by using the well-known cell sub-division. Then, the non-linear solution of algebraic equations is obtained by using the concept of the consistent tangent operator. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness and along the rectangular beam element axes. The numerical representations are accurately obtained by either computing analytically the element integrals or performing the numerical integration accurately using an appropriate sub-elementation scheme. (C) 2007 Elsevier Ltd. All rights reserved.

Non-invasive user monitoring in daily tasks for cognitive rehabilitation

El uso de técnicas para la monitorización del movimiento humano generalmente permite a los investigadores analizar la cinemática y especialmente las capacidades motoras en aquellas actividades de la vida cotidiana que persiguen un objetivo concreto como pueden ser la preparación de bebidas y comida, e incluso en tareas de aseo. Adicionalmente, la evaluación del movimiento y el comportamiento humanos en el campo de la rehabilitación cognitiva es esencial para profundizar en las dificultades que algunas personas encuentran en la ejecución de actividades diarias después de accidentes cerebro-vasculares. Estas dificultades están principalmente asociadas a la realización de pasos secuenciales y al reconocimiento del uso de herramientas y objetos. La interpretación de los datos sobre la actitud de este tipo de pacientes para reconocer y determinar el nivel de éxito en la ejecución de las acciones, y para ampliar el conocimiento en las enfermedades cerebrales, sus consecuencias y severidad, depende totalmente de los dispositivos usados para la captura de esos datos y de la calidad de los mismos. Más aún, existe una necesidad real de mejorar las técnicas actuales de rehabilitación cognitiva contribuyendo al diseño de sistemas automáticos para crear una especie de terapeuta virtual que asegure una vida más independiente de estos pacientes y reduzca la carga de trabajo de los terapeutas. Con este objetivo, el uso de sensores y dispositivos para obtener datos en tiempo real de la ejecución y estado de la tarea de rehabilitación es esencial para también contribuir al diseño y entrenamiento de futuros algoritmos que pudieran reconocer errores automáticamente para informar al paciente acerca de ellos mediante distintos tipos de pistas como pueden ser imágenes, mensajes auditivos o incluso videos. La tecnología y soluciones existentes en este campo no ofrecen una manera totalmente robusta y efectiva para obtener datos en tiempo real, por un lado, porque pueden influir en el movimiento del propio paciente en caso de las plataformas basadas en el uso de marcadores que necesitan sensores pegados en la piel; y por otro lado, debido a la complejidad o alto coste de implantación lo que hace difícil pensar en la idea de instalar un sistema en el hospital o incluso en la casa del paciente. Esta tesis presenta la investigación realizada en el campo de la monitorización del movimiento de pacientes para proporcionar un paso adelante en términos de detección, seguimiento y reconocimiento del comportamiento de manos, gestos y cara mediante una manera no invasiva la cual puede mejorar la técnicas actuales de rehabilitación cognitiva para la adquisición en tiempo real de datos sobre el comportamiento del paciente y la ejecución de la tarea. Para entender la importancia del marco de esta tesis, inicialmente se presenta un resumen de las principales enfermedades cognitivas y se introducen las consecuencias que tienen en la ejecución de tareas de la vida diaria. Más aún, se investiga sobre las metodologías actuales de rehabilitación cognitiva. Teniendo en cuenta que las manos son la principal parte del cuerpo para la ejecución de tareas manuales de la vida cotidiana, también se resumen las tecnologías existentes para la captura de movimiento de manos. Una de las principales contribuciones de esta tesis está relacionada con el diseño y evaluación de una solución no invasiva para detectar y seguir las manos durante la ejecución de tareas manuales de la vida cotidiana que a su vez involucran la manipulación de objetos. Esta solución la cual no necesita marcadores adicionales y está basada en una cámara de profundidad de bajo coste, es robusta, precisa y fácil de instalar. Otra contribución presentada se centra en el reconocimiento de gestos para detectar el agarre de objetos basado en un sensor infrarrojo de última generación, y también complementado con una cámara de profundidad. Esta nueva técnica, y también no invasiva, sincroniza ambos sensores para seguir objetos específicos además de reconocer eventos concretos relacionados con tareas de aseo. Más aún, se realiza una evaluación preliminar del reconocimiento de expresiones faciales para analizar si es adecuado para el reconocimiento del estado de ánimo durante la tarea. Por su parte, todos los componentes y algoritmos desarrollados son integrados en un prototipo simple para ser usado como plataforma de monitorización. Se realiza una evaluación técnica del funcionamiento de cada dispositivo para analizar si es adecuada para adquirir datos en tiempo real durante la ejecución de tareas cotidianas reales. Finalmente, se estudia la interacción con pacientes reales para obtener información del nivel de usabilidad del prototipo. Dicha información es esencial y útil para considerar una rehabilitación cognitiva basada en la idea de instalación del sistema en la propia casa del paciente al igual que en el hospital correspondiente. ABSTRACT The use of human motion monitoring techniques usually let researchers to analyse kinematics, especially in motor strategies for goal-oriented activities of daily living, such as the preparation of drinks and food, and even grooming tasks. Additionally, the evaluation of human movements and behaviour in the field of cognitive rehabilitation is essential to deep into the difficulties some people find in common activities after stroke. This difficulties are mainly associated with sequence actions and the recognition of tools usage. The interpretation of attitude data of this kind of patients in order to recognize and determine the level of success of the execution of actions, and to broaden the knowledge in brain diseases, consequences and severity, depends totally on the devices used for the capture of that data and the quality of it. Moreover, there is a real need of improving the current cognitive rehabilitation techniques by contributing to the design of automatic systems to create a kind of virtual therapist for the improvement of the independent life of these stroke patients and to reduce the workload of the occupational therapists currently in charge of them. For this purpose, the use of sensors and devices to obtain real time data of the execution and state of the rehabilitation task is essential to also contribute to the design and training of future smart algorithms which may recognise errors to automatically provide multimodal feedback through different types of cues such as still images, auditory messages or even videos. The technology and solutions currently adopted in the field don't offer a totally robust and effective way for obtaining real time data, on the one hand, because they may influence the patient's movement in case of marker-based platforms which need sensors attached to the skin; and on the other hand, because of the complexity or high cost of implementation, which make difficult the idea of installing a system at the hospital or even patient's home. This thesis presents the research done in the field of user monitoring to provide a step forward in terms of detection, tracking and recognition of hand movements, gestures and face via a non-invasive way which could improve current techniques for cognitive rehabilitation for real time data acquisition of patient's behaviour and execution of the task. In order to understand the importance of the scope of the thesis, initially, a summary of the main cognitive diseases that require for rehabilitation and an introduction of the consequences on the execution of daily tasks are presented. Moreover, research is done about the actual methodology to provide cognitive rehabilitation. Considering that the main body members involved in the completion of a handmade daily task are the hands, the current technologies for human hands movements capture are also highlighted. One of the main contributions of this thesis is related to the design and evaluation of a non-invasive approach to detect and track user's hands during the execution of handmade activities of daily living which involve the manipulation of objects. This approach does not need the inclusion of any additional markers. In addition, it is only based on a low-cost depth camera, it is robust, accurate and easy to install. Another contribution presented is focused on the hand gesture recognition for detecting object grasping based on a brand new infrared sensor, and also complemented with a depth camera. This new, and also non-invasive, solution which synchronizes both sensors to track specific tools as well as recognize specific events related to grooming is evaluated. Moreover, a preliminary assessment of the recognition of facial expressions is carried out to analyse if it is adequate for recognizing mood during the execution of task. Meanwhile, all the corresponding hardware and software developed are integrated in a simple prototype with the purpose of being used as a platform for monitoring the execution of the rehabilitation task. Technical evaluation of the performance of each device is carried out in order to analyze its suitability to acquire real time data during the execution of real daily tasks. Finally, a kind of healthcare evaluation is also presented to obtain feedback about the usability of the system proposed paying special attention to the interaction with real users and stroke patients. This feedback is quite useful to consider the idea of a home-based cognitive rehabilitation as well as a possible hospital installation of the prototype.