Nodal domains of the equilateral triangle billiard

We characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula. We believe that the results belong generically to non-separable systems, thus extending the previous works which are concentrated on separable and chaotic systems.

Estudo da incorporação de diferentes tipos de argilas hidrofílicas em dispersões aquosas de poliuretanos para formação de nanocompósitos

Neste trabalho foram sintetizados nanocompósitos à base de poliuretanos em dispersão aquosa (NWPUs) e argilas hidrofílicas do tipo montimorilonita (MMT) de natureza sódica e cálcica. Os monômeros empregados na síntese foram: poli(glicol propilênico) (PPG); copolímero em bloco à base de poli(glicol etilênico) e poli(glicol propilênico) (EG-b-PG), com teor de 7% de EG; ácido dimetilolpropiônico (DMPA) e diisocianato de isoforona (IPDI). Os NWPUs tiveram as argilas, previamente deslaminadas em água e incorporadas à formulação no momento da dispersão do prepolímero. Dispersões aquosas (WPUs), sem a presença de argila, foram sintetizadas como base, nas quais foram variadas a razão NCO/OH e a proporção de copolímero em relação ao PPG. Nas formulações NWPUs, foram variados também o teor de argila em relação à massa de prepolímero e o tipo de argila sódica e cálcica. As dispersões foram avaliadas, quanto ao teor de sólidos totais, tamanho médio de partícula e viscosidade. Os filmes vazados a partir das dispersões foram caracterizados por espectrometria na região do infravermelho (FTIR), difração de raios-x (XRD) e microscopia eletrônica de varredura (SEM). A resistência térmica dos filmes foi determinada por termogravimetria (TG) e a resistência mecânica dos filmes foi avaliada por ensaios mecânicos em dinamômetro. O grau de absorção de água dos filmes também foi determinado. A formação de nanocompósitos à base de água foi confirmada pela ausência do pico de XRD, característico das argilas empregadas na maioria dos filmes analisados. As micrografias obtidas por SEM confirmam uma dispersão homogênea das argilas na matriz poliuretânica. Os filmes à base de nanocompósitos (NWPUs) apresentaram propriedades superiores às apresentadas por aqueles obtidos a partir das dispersões sem argilas (WPUs). Os revestimentos formados a partir da aplicação das dispersões aderiram à maioria dos substratos testados (metal, vidro, madeira e papel) formando superfícies homogêneas

Síntese e caracterização de nanocompósitos à base de poliuretano dispersos em água com argilas hidrofílica e organofílica

A área de pesquisa de materiais nanoestruturados tem recebido destacada atenção nos últimos anos por parte da comunidade científica, ressaltando-se os nanocompósitos à base de polímero e argila. Nesta Dissertação foram sintetizados nanocompósitos à base de poliuretano (NWPUs) com argilas do tipo montmorilonita (MMT), hidrofóbicas (organofílicas) e hidrofílica. Os monômeros empregados na síntese foram poli(glicol propilênico) (PPG); polibutadieno líquido hidroxilado (HTPB); ácido dimetilolpropiônico (DMPA), diisocianato de isoforona (IPDI) e hidrazina (HYD), como extensor de cadeia. Nas formulações, foram variadas as proporções de HTPB e o teor das argilas. As argilas organofílica Cloisite 30B e hidrofílica Cloisite Na+ foram incorporadas em 1, 3 e 5 %, enquanto que a organofílica Cloisite 15A foi incorporada no teor de 1%. As dispersões foram caracterizadas quanto ao teor de sólidos totais, tamanho médio de partículas e viscosidade. Os filmes vazados a partir das dispersões foram caracterizados por espectroscopia na região do infravermelho (FTIR), difração de raios-x (XDR), microscopia eletrônica de varredura (SEM) e microscopia de força atômica (AFM). A resistência térmica e a transição vítrea dos materiais foram determinadas por termogravimetria (TG) e calorimetria diferencial de varredura (DSC), respectivamente. O teor de absorção de água e o comportamento mecânico dos filmes foram avaliados. Foi verificada, por XRD, a ausência do pico de cristalinidade, característico das argilas puras e não-deslaminadas. As micrografias obtidas por SEM confirmam uma dispersão homogênea das argilas na matriz poliuretânica. Os filmes à base de nanocompósitos (NWPUs) apresentaram propriedades mecânicas superiores às apresentadas por aqueles obtidos a partir das dispersões sem a presença de argila (WPUs). A adesão dos revestimentos formados, pela aplicação das dispersões em diversos substratos, também foi verificada visualmente. Os resultados das análises mostraram que houve a formação de nanocompósitos à base de água, formados tanto a partir da argila hidrofílica quanto das organofílicas

The predicting power of models for eutrophication

Restoration of water-bodies from eutrophication has proved to be extremely difficult. Mathematical models have been used extensively to provide guidance for management decisions. The aim of this paper is to elucidate important problems of using models for predicting environmental changes. First, the necessity for a proper uncertainty assessment of the model, upon calibration, has not been widely recognized. Predictions must not be a single time trajectory; they should be a band, expressing system uncertainty and natural variability. Availability of this information may alter the decision to be taken. Second, even with well-calibrated models, there is no guarantee they will give correct projections in situations where the model is used to predict the effects of measures designed to bring the system into an entirely different ”operating point”, as is typically the case in eutrophication abatement. The concept of educated speculation is introduced to partially overcome this difficulty. Lake Veluwe is used as a case to illustrate the point. Third, as questions become more detailed, such as ”what about expected algal composition”, there is a greater probability of running into fundamental problems that are associated with predicting the behaviour of complex non-linear systems. Some of these systems show extreme initial condition sensitivity and even, perhaps, chaotic behaviour, and are therefore fundamentally unpredictable.

Estudo do comportamento caótico e determinação de dimensão fractal em modelos pré-inflacionários não compactos

O caos determinístico é um dos aspectos mais interessantes no que diz respeito à teoria moderna dos sistemas dinâmicos, e está intrinsecamente associado a pequenas variações nas condições iniciais de um dado modelo. Neste trabalho, é feito um estudo acerca do comportamento caótico em dois casos específicos. Primeiramente, estudam-se modelos préinflacionários não-compactos de Friedmann-Robertson-Walker com campo escalar minimamente acoplado e, em seguida, modelos anisotrópicos de Bianchi IX. Em ambos os casos, o componente material é um fluido perfeito. Tais modelos possuem constante cosmológica e podem ser estudados através de uma descrição unificada, a partir de transformações de variáveis convenientes. Estes sistemas possuem estruturas similares no espaço de fases, denominadas centros-sela, que fazem com que as soluções estejam contidas em hipersuperfícies cuja topologia é cilíndrica. Estas estruturas dominam a relação entre colapso e escape para a inflação, que podem ser tratadas como bacias cuja fronteira pode ser fractal, e que podem ser associadas a uma estrutura denominada repulsor estranho. Utilizando o método de contagem de caixas, são calculadas as dimensões características das fronteiras nos modelos, o que envolve técnicas e algoritmos de computação numérica, e tal método permite estudar o escape caótico para a inflação.

Teoria de controle ótimo com aplicações a sistemas biológicos

Neste trabalho apresentamos as etapas para a utilização do método da Programação Dinâmica, ou Princípio de Otimização de Bellman, para aplicações de controle ótimo. Investigamos a noção de funções de controle de Lyapunov (FCL) e sua relação com a estabilidade de sistemas autônomos com controle. Uma função de controle de Lyapunov deverá satisfazer a equação de Hamilton-Jacobi-Bellman (H-J-B). Usando esse fato, se uma função de controle de Lyapunov é conhecida, será então possível determinar a lei de realimentação ótima; isto é, a lei de controle que torna o sistema globalmente assintóticamente controlável a um estado de equilíbrio. Como aplicação, apresentamos uma modelagem matemática adequada a um problema de controle ótimo de certos sistemas biológicos. Este trabalho conta também com um breve histórico sobre o desenvolvimento da Teoria de Controle de forma a ilustrar a importância, o progresso e a aplicação das técnicas de controle em diferentes áreas ao longo do tempo.

Observation of locked phase dynamics and enhanced frequency stability in synchronized micromechanical oscillators

Even though synchronization in autonomous systems has been observed for over three centuries, reports of systematic experimental studies on synchronized oscillators are limited. Here, we report on observations of internal synchronization in coupled silicon micromechanical oscillators associated with a reduction in the relative phase random walk that is modulated by the magnitude of the reactive coupling force between the oscillators. Additionally, for the first time, a significant improvement in the frequency stability of synchronized micromechanical oscillators is reported. The concept presented here is scalable and could be suitably engineered to establish the basis for a new class of highly precise miniaturized clocks and frequency references. © 2013 American Physical Society.

What is the weakest topology in which feedback stability is robust?

Mathematical theorems in control theory are only of interest in so far as their assumptions relate to practical situations. The space of systems with transfer functions in ℋ∞, for example, has many advantages mathematically, but includes large classes of non-physical systems, and one must be careful in drawing inferences from results in that setting. Similarly, the graph topology has long been known to be the weakest, or coarsest, topology in which (1) feedback stability is a robust property (i.e. preserved in small neighbourhoods) and (2) the map from open-to-closed-loop transfer functions is continuous. However, it is not known whether continuity is a necessary part of this statement, or only required for the existing proofs. It is entirely possible that the answer depends on the underlying classes of systems used. The class of systems we concern ourselves with here is the set of systems that can be approximated, in the graph topology, by real rational transfer function matrices. That is, lumped parameter models, or those distributed systems for which it makes sense to use finite element methods. This is precisely the set of systems that have continuous frequency responses in the extended complex plane. For this class, we show that there is indeed a weaker topology; in which feedback stability is robust but for which the maps from open-to-closed-loop transfer functions are not necessarily continuous. © 2013 Copyright Taylor and Francis Group, LLC.

Identification of the steering control behaviour of five test subjects following a randomly curving path in a driving simulator

The paper is concerned with the identification of theoretical preview steering controllers using data obtained from five test subjects in a fixed-base driving simulator. An understanding of human steering control behaviour is relevant to the design of autonomous and semi-autonomous vehicle controls. The driving task involved steering a linear vehicle along a randomly curving path. The theoretical steering controllers identified from the data were based on optimal linear preview control. A direct-identification method was used, and the steering controllers were identified so that the predicted steering angle matched as closely as possible the measured steering angle of the test subjects. It was found that identification of the driver's time delay and noise is necessary to avoid bias in identification of the controller parameters. Most subjects' steering behaviour was predicted well by a theoretical controller based on the lateral/yaw dynamics of the vehicle. There was some evidence that an inexperienced driver's steering action was better represented by a controller based on a simpler model of the vehicle dynamics, perhaps reflecting incomplete learning by the driver. Copyright © 2014 Inderscience Enterprises Ltd.

Toward a human-like biped robot with compliant legs

Conventional models of bipedal walking generally assume rigid body structures, while elastic material properties seem to play an essential role in nature. On the basis of a novel theoretical model of bipedal walking, this paper investigates a model of biped robot which makes use of minimum control and elastic passive joints inspired from the structures of biological systems. The model is evaluated in simulation and a physical robotic platform by analyzing the kinematics and ground reaction force. The experimental results show that, with a proper leg design of passive dynamics and elasticity, an attractor state of human-like walking gait patterns can be achieved through extremely simple control without sensory feedback. The detailed analysis also explains how the dynamic human-like gait can contribute to adaptive biped walking. © 2007 Elsevier B.V. All rights reserved.

A miniature insertion element transposable in Microcystis sp FACHB 854

A 186-bp sequence with imperfect terminal inverted repeats and target direct repeats but without any transposase-encoding capacity was found to be transposable in an isolate derived from Microcystis sp. FACHB 854. This miniature insertion element, designated as ISM854-1, and with its homologues present at least 10 copies in the genome of Microcystis FACHB 854, is inserted into the 8-bp long and AT-rich target sequences, but none or few in other Microcystis strains. A variant of ISM854-1, denoted ISM854-1A, has perfect inverted repeat sequences and may transpose in pairs in a structure like a composite transposon. This is the first report of non-autonomous transposition of a mini-IS in a cyanobacterium.

Modeling of cyanobacterial blooms in hypereutrophic Lake Dianchi, China

Compared with other approaches for modeling and predicting, artificial neural networks are more effective in describing complex and non-linear systems. The occurrence of cyanobacterial blooms has been a continuous and serious problem over the past decades in hypereutrophic Lake Dianchi. Yet, the main factor(s) initiating these blooms remain(s) unclear. During 2001-2002 at 40 sampling sites in Lake Dianchi, physicochemical parameters possibly relating to the blooms were measured. Parameters directly or indirectly relating to the cyanobacterial blooms were used as driving factors in a back-propagation network to model the concentration of chlorophyll a. According to sensitivity analysis, chemical oxygen demand was identified as a very significant environmental factor for algal growth in Lake Dianchi.

Design and control of a climbing robot based on hot melt adhesion

Robust climbing in unstructured environments has been one of the long-standing challenges in robotics research. Among others, the control of large adhesion forces is still an important problem that significantly restricts the locomotion performance of climbing robots. The main contribution of this paper is to propose a novel approach to autonomous robot climbing which makes use of hot melt adhesion (HMA). The HMA material is known as an economical solution to achieve large adhesion forces, which can be varied by controlling the material temperature. For locomotion on both inclined and vertical walls, this paper investigates the basic characteristics of HMA material, and proposes a design and control of a climbing robot that uses the HMA material for attaching and detaching its body to the environment. The robot is equipped with servomotors and thermal control units to actively vary the temperature of the material, and the coordination of these components enables the robot to walk against the gravitational forces even with a relatively large body weight. A real-world platform is used to demonstrate locomotion on a vertical wall, and the experimental result shows the feasibility and overall performances of this approach. © 2013 Elsevier B.V. All rights reserved.

Sensing through body dynamics

It has been shown that sensory morphology and sensory-motor coordination enhance the capabilities of sensing in robotic systems. The tasks of categorization and category learning, for example, can be significantly simplified by exploiting the morphological constraints, sensory-motor couplings and the interaction with the environment. This paper argues that, in the context of sensory-motor control, it is essential to consider body dynamics derived from morphological properties and the interaction with the environment in order to gain additional insight into the underlying mechanisms of sensory-motor coordination, and more generally the nature of perception. A locomotion model of a four-legged robot is used for the case studies in both simulation and real world. The locomotion model demonstrates how attractor states derived from body dynamics influence the sensory information, which can then be used for the recognition of stable behavioral patterns and of physical properties in the environment. A comprehensive analysis of behavior and sensory information leads to a deeper understanding of the underlying mechanisms by which body dynamics can be exploited for category learning of autonomous robotic systems. © 2006 Elsevier Ltd. All rights reserved.