Analog methods of nonlinear vibration analysis

This thesis presents methods by which electrical analogies can be obtained for nonlinear systems. The accuracy of these methods is investigated and several specific types of nonlinear equations are studied in detail.

In Part I a general method is given for obtaining electrical analogs of nonlinear systems with one degree of freedom. Loop and node methods are compared and the stability of the loop analogy is briefly considered.

Parts II and III give a description of the equipment and a discussion of its accuracy. Comparisons are made between experimental and analytic solutions of linear systems.

Part IV is concerned with systems having a nonlinear restoring force. In particular, solutions of Duffing's equation are obtained, both by using the electrical analogy and also by approximate analytical methods.

Systems with nonlinear damping are considered in Part V. Two specific examples are chosen: (1) forced oscillations and (2) self-excited oscillations (van der Pol’s equation). Comparisons are made with approximate analytic solutions.

Part VI gives experimental data for a system obeying Mathieu's equation. Regions of stability are obtained. Examples of subharmonic, ultraharmonic, and ultrasubharmonic oscillat1ons are shown.

Tendência temporal do índice de massa corporal em alistados do Brasil (1980-2005)

Apesar da crescente prevalência da obesidade em países desenvolvidos e em desenvolvimento, há pouca evidência da associação com fatores ambientais. Objetivos: Investigar a evolução temporal do IMC em jovens alistados do sexo masculino de 18 anos no Brasil entre 1980 e 2005; identificar pontos específicos de maior variância na série temporal e comparar pontos específicos no tempo, a evolução temporal do IMC com as mudanças socioeconômicas no Brasil. Métodos: O presente estudo explorou uma série temporal de 26 anos em homens brasileiros que se alistaram no período de 1980 a 2005. A amostra compreendeu cerca de 35-40% de todos os jovens brasileiros de 18 anos de idade. O peso corporal e a estatura foram obtidos no momento do exame médico durante o alistamento militar. Todas as mensurações antropométricas foram realizadas por pessoal especializado e treinado. As prevalências do sobrepeso e da obesidade foram calculadas com intervalos de confiança de 95%. Com a finalidade de testar a presença de heterocedasticidade na série do IMC, realizou-se o teste de Multiplicador de Lagrange (LM). Para os pontos no tempo, com oscilações acima da média do IMC, variáveis dummies foram testadas utilizando-se o modelo ARCH (Autoregressivo de Heterocedasticidade Condicionada), com um nível de significância de p <0,05. Para aqueles pontos no tempo com oscilações acima da média do IMC (anos de 1985, 1994 e 2000), variáveis dummy foram incluídos sob a hipótese foi de que a taxa de crescimento do IMC não fosse a mesma ao longo da série temporal. Para as possíveis explicações para os aumentos bruscos na curva do IMC, foram consideradas as alterações nos principais indicadores econômicos do Brasil (Instituto Brasileiro de Geografia e Estatística e Instituto de Pesquisa Econômica Aplicada). Os fatores econômicos analisados foram: taxa de inflação anual, produção de alimentos, pobreza (%), o consumo de refrigerantes e o rendimento médio anual. Resultados: A prevalência de sobrepeso também passou de 4,5%, em 1980, para 12,5%, em 2005, um aumento de 2,6 vezes, enquanto a prevalência de obesidade aumentou de 0,5%, em 1980, para 1,9%, em 2005, um aumento de quase 300%, mas por comparação internacional estão abaixo da média. Particularmente em 1985-6 e 1994-5, houve um aumento acentuado e significativo do IMC. Em 1985-6, a média do IMC aumentou de 21,4 kg/m2 para 21,5 kg/m2 e, em 1994-5, a média do IMC médio aumentou de 21,7 kg/m2 para 21,9 kg/m2. Nesses dois pontos (1985-1986 e 1994-1995) ocorreram logo após duas grandes mudanças políticas econômicas que aumentaram o poder de compra da população. Em 1985-6, as mudanças foram principalmente relacionadas a fatores econômicos, tais como: a redução do nível de desigualdade social; aumento da renda familiar; redução da pobreza; o controle da inflação; aumento do tempo assistindo televisão e aumento do consumo de alimentos. Em 1994-5, além das mudanças no poder de compra, houve uma modificação na atividade física obrigatória nas escolas. Conclusão: O presente estudo mostrou um aumento abrupto da obesidade na população de homens jovens no Brasil em duas ocasiões durante esta série temporal (anos de 1985-6 e 1994-5), quando uma possível redução no gasto calórico e aumento do consumo de alimentos da população foram observados.

From the individual to the community and beyond: water quality, stress indicators and key species in coastal waters

This review examines water quality and stress indicators at levels of organisation from the individual to the community and beyond by means of three case studies concentrating on rocky shores within the north-east Atlantic. Responses of dogwhelks (Nucella) to tributyltin pollution from antifouling paints is examined as the main case study. There are effects at the individual level (development of male sexual characteristics in the female leading to effective sterility) and population level (reduction in juveniles, few females and eventual population disappearance of dogwhelks in badly contaminated areas) but information on community level effects of dogwhelk demise is sparse. Such effects were simulated by dogwhelk removal experiments on well studied, moderately exposed ledges on shores on the Isle of Man. The removal of dogwhelks reduced the size and longevity of newly established Fucus clumps that had escaped grazing. Removal of dogwhelks also increased the likelihood of algal escapes. In a factorial experiment dogwhelks were shown to be less important than limpets \{Patella) in structuring communities but still had a significant modifying effect by increasing the probability of algal escapes. Community level responses to stress on rocky shores are then explored by reference to catastrophic impacts such as oil spills, using the Torrey Canyon as a case study. Recovery of the system in response to this major perturbation took between 10-15 years through a series of damped oscillations. The final case study is that of indicators of ecosystem level change in response to climate fluctuations, using ratios of northern \{Semibalanus balanoides) and southern (Chthamalus spp.) barnacles. Indices derived from counts on the shore show good correlations with inshore sea-water temperatures after a 2-year lag phase. The use of barnacles to measure offshore changes is reviewed. The discussion considers the use of bioindicators at various levels of organisation.

Classical and Quantum Effects in Plasmonic Metals

The field of plasmonics exploits the unique optical properties of metallic nanostructures to concentrate and manipulate light at subwavelength length scales. Metallic nanostructures get their unique properties from their ability to support surface plasmons– coherent wave-like oscillations of the free electrons at the interface between a conductive and dielectric medium. Recent advancements in the ability to fabricate metallic nanostructures with subwavelength length scales have created new possibilities in technology and research in a broad range of applications.

In the first part of this thesis, we present two investigations of the relationship between the charge state and optical state of plasmonic metal nanoparticles. Using experimental bias-dependent extinction measurements, we derive a potential- dependent dielectric function for Au nanoparticles that accounts for changes in the physical properties due to an applied bias that contribute to the optical extinction. We also present theory and experiment for the reverse effect– the manipulation of the carrier density of Au nanoparticles via controlled optical excitation. This plasmoelectric effect takes advantage of the strong resonant properties of plasmonic materials and the relationship between charge state and optical properties to eluci- date a new avenue for conversion of optical power to electrical potential.

The second topic of this thesis is the non-radiative decay of plasmons to a hot-carrier distribution, and the distribution’s subsequent relaxation. We present first-principles calculations that capture all of the significant microscopic mechanisms underlying surface plasmon decay and predict the initial excited carrier distributions so generated. We also preform ab initio calculations of the electron-temperature dependent heat capacities and electron-phonon coupling coefficients of plasmonic metals. We extend these first-principle methods to calculate the electron-temperature dependent dielectric response of hot electrons in plasmonic metals, including direct interband and phonon-assisted intraband transitions. Finally, we combine these first-principles calculations of carrier dynamics and optical response to produce a complete theoretical description of ultrafast pump-probe measurements, free of any fitting parameters that are typical in previous analyses.

The ionic basis of frequency selectivity in hair cells of the bullfrog's sacculus

Hair cells from the bull frog's sacculus, a vestibular organ responding to substrate-borne vibration, possess electrically resonant membrane properties which maximize the sensitivity of each cell to a particular frequency of mechanical input. The electrical resonance of these cells and its underlying ionic basis were studied by applying gigohm-seal recording techniques to solitary hair cells enzymatically dissociated from the sacculus. The contribution of electrical resonance to frequency selectivity was assessed from microelectrode recordings from hair cells in an excised preparation of the sacculus.

Electrical resonance in the hair cell is demonstrated by damped membrane-potential oscillations in response to extrinsic current pulses applied through the recording pipette. This response is analyzed as that of a damped harmonic oscillator. Oscillation frequency rises with membrane depolarization, from 80-160 Hz at resting potential to asymptotic values of 200-250 Hz. The sharpness of electrical tuning, denoted by the electrical quality factor, Q_e, is a bell-shaped function of membrane voltage, reaching a maximum value around eight at a membrane potential slightly positive to the resting potential.

In whole cells, three time-variant ionic currents are activated at voltages more positive than -60 to -50 mV; these are identified as a voltage-dependent, non-inactivating Ca current (I_ca), a voltage-dependent, transient K current (I_a), and a Ca-dependent K current (I_c). The C channel is identified in excised, inside-out membrane patches on the basis of its large conductance (130-200 pS), its selective permeability to Kover Na or Cl, and its activation by internal Ca ions and membrane depolarization. Analysis of open- and closed-lifetime distributions suggests that the C channel can assume at least two open and three closed kinetic states.

Exposing hair cells to external solutions that inhibit the Ca or C conductances degrades the electrical resonance properties measured under current-clamp conditions, while blocking the A conductance has no significant effect, providing evidence that only the Ca and C conductances participate in the resonance mechanism. To test the sufficiency of these two conductances to account for electrical resonance, a mathematical model is developed that describes I_ca, I_c, and intracellular Ca concentration during voltage-clamp steps. I_ca activation is approximated by a third-order Hodgkin-Huxley kinetic scheme. Ca entering the cell is assumed to be confined to a small submembrane compartment which contains an excess of Ca buffer; Ca leaves this space with first-order kinetics. The Ca- and voltage-dependent activation of C channels is described by a five-state kinetic scheme suggested by the results of single-channel observations. Parameter values in the model are adjusted to fit the waveforms of I_ca and I_c evoked by a series of voltage-clamp steps in a single cell. Having been thus constrained, the model correctly predicts the character of voltage oscillations produced by current-clamp steps, including the dependencies of oscillation frequency and Q_e on membrane voltage. The model shows quantitatively how the Ca and C conductances interact, via changes in intracellular Ca concentration, to produce electrical resonance in a vertebrate hair cell.

Stability analysis of RF amplifiers based on MIMO pole-zero identification

Spurious oscillations are one of the principal issues faced by microwave and RF circuit designers. The rigorous detection of instabilities or the characterization of measured spurious oscillations is still an ongoing challenge. This project aims to create a new stability analysis CAD program that tackles this chal- lenge. Multiple Input Multiple Output (MIMO) pole-zero identification analysis is introduced on the program as a way to create new methods to automate the stability analysis process and to help designers comprehend the obtained results and prevent incorrect interpretations. The MIMO nature of the analysis contributes to eliminate possible controllability and observability losses and helps differentiate mathematical and physical quasi-cancellations, products of overmodeling. The created program reads Single Input Single Output (SISO) or MIMO frequency response data, and determines the corresponding continuous transfer functions with Vector Fitting. Once the transfer function is calculated, the corresponding pole/zero diagram is mapped enabling the designers to analyze the stability of an amplifier. Three data processing methods are introduced, two of which consist of pole/zero elimina- tions and the latter one on determining the critical nodes of an amplifier. The first pole/zero elimination method is based on eliminating non resonant poles, whilst the second method eliminates the poles with small residue by assuming that their effect on the dynamics of a system is small or non-existent. The critical node detection is also based on the residues; the node at which the effect of a pole on the dynamics is highest is defined as the critical node. In order to evaluate and check the efficiency of the created program, it is compared via examples with another existing commercial stability analysis tool (STAN tool). In this report, the newly created tool is proved to be as rigorous as STAN for detecting instabilities. Additionally, it is determined that the MIMO analysis is a very profitable addition to stability analysis, since it helps to eliminate possible problems of loss of controllability, observability and overmodeling.

Estimating the underwater shape of tuna longlines with micro-bathythermographs

An estimation method for the three-dimensional underwater shape of tuna longlines is developed, using measurements of depth obtained from micro-bathythermographs (BTs) attached to the main line at equally spaced intervals. The shape of the main line is approximated by a model which consists of a chain of unit length lines (folding-rule model), where the junction points are placed at the observed depths. Among the infinite number of possible shapes, the most likely shape is considered to be the smoothest one that can be obtained with a numerical optimization algorithm. To validate the method, a series of experimental longline operations were conducted in the equatorial region of the eastern Pacific Ocean, using 13 or 14 micro-BTs per basket of main line. Concurrent observations of oceanographic conditions (currents and temperature structure) were obtained. The shape of the main line can be calculated at arbitrary times during operations. Shapes were consistent with the current structure. On the equator, the line was elevated significantly by the Equatorial Undercurrent. It is shown that the shape of main line depends primarily upon the vertical shear and direction of the current relative to the gear. Time sequences of calculated shapes reveals that observed periodic (1-2 hours) oscillations in depth of the gear was caused by swinging movements of the main line. The shortening rate of the main line is an important parameter for formulating the shape of the longline, and its precise measurement is desirable.

Contribución al conocimiento de la biología del surel (Trachurus picturatus australis) del área de Mar del Plata (Pisces, Carangidae)

The individuals studied came from commercial catches on the coastal area off Mar del Plata. The monthly distribution of sizes shows that the juvenile stay in coastal waters, while the adult individuals leave those waters during winter season to return there in the spring during the season of sexual maturation and spawning, when the water reaches temperature of 10-11°C. The jack mackerel is a relatively small fish, compared with other species of its genus, and has a total length of scarcely 25 cm. The comparison of indexes and mesurements does not reveal any marked difference between sexes, except for the total length, which is greater in the females. Sexually nature individuals at a lenth of 13 cm have been found. Spawning takes place in coastal waters. A great part of the population spawns from December to January. There are oscillations ranging from November to March. On this latter month mature individuals of smaller size have veen found. The jack mackerel feeds usually on copepods and other planktonic organims, but it can feed also on juveniles of other fishes. This fish is caught throghout the whole year. The catches show their greater peak during winter; one other non-constant peak occurs during the spring (October-November) and declines shoraply during the summer months. It follows from this that the time of greates catch does not coincide with spawning season, or with the appearence of the greatest mean sizes. This happens because the interests of the fishermen are attracted during those months by others species of greater commercial value.

On the Dynamics of the Adenylate Energy System: Homeorhesis vs Homeostasis

Biochemical energy is the fundamental element that maintains both the adequate turnover of the biomolecular structures and the functional metabolic viability of unicellular organisms. The levels of ATP, ADP and AMP reflect roughly the energetic status of the cell, and a precise ratio relating them was proposed by Atkinson as the adenylate energy charge (AEC). Under growth-phase conditions, cells maintain the AEC within narrow physiological values, despite extremely large fluctuations in the adenine nucleotides concentration. Intensive experimental studies have shown that these AEC values are preserved in a wide variety of organisms, both eukaryotes and prokaryotes. Here, to understand some of the functional elements involved in the cellular energy status, we present a computational model conformed by some key essential parts of the adenylate energy system. Specifically, we have considered (I) the main synthesis process of ATP from ADP, (II) the main catalyzed phosphotransfer reaction for interconversion of ATP, ADP and AMP, (III) the enzymatic hydrolysis of ATP yielding ADP, and (IV) the enzymatic hydrolysis of ATP providing AMP. This leads to a dynamic metabolic model (with the form of a delayed differential system) in which the enzymatic rate equations and all the physiological kinetic parameters have been explicitly considered and experimentally tested in vitro. Our central hypothesis is that cells are characterized by changing energy dynamics (homeorhesis). The results show that the AEC presents stable transitions between steady states and periodic oscillations and, in agreement with experimental data these oscillations range within the narrow AEC window. Furthermore, the model shows sustained oscillations in the Gibbs free energy and in the total nucleotide pool. The present study provides a step forward towards the understanding of the fundamental principles and quantitative laws governing the adenylate energy system, which is a fundamental element for unveiling the dynamics of cellular life.

板条激光放大器中寄生振荡的研究

寄生振荡的存在使得放大器在信号光到达之前消耗了大量的反转粒子数,降低了放大器的激光增益和储能效率,严重地影响了激光放大器的性能,尤其对高功率激光放大器。在理论分析和实验研究的基础上,以Nd∶YAG晶体板条为例,用8条半导体激光阵列对晶体进行双侧抽运,研究了高功率激光放大器的寄生振荡现象,分析了板条晶体寄生振荡产生的原因,并详细比较了晶体在不同的抽运功率和表面处理下的放大效果,得到了2倍的单程放大,当输入能量为140 mJ时,获得了278 mJ的激光输出。

Variabilidade espacial e temporal da distribuição do material particulado em suspensão nas proximidades do canal de navegação da baía de Sepetiba (RJ)

Este estudo teve como objetivo principal caracterizar os padrões de distribuição do material particulado em suspensão ao longo da baía de Sepetiba, associando as variabilidades espaciais e temporais com ciclos de maré. Além disso, o estudo também avalia a utilização de equipamentos acústicos como ferramentas à estimativa das concentrações de material particulado em suspensão. A aquisição de dados foi realizada num total de sete campanhas realizadas entre novembro de 2010 e dezembro de 2011. Sete estações foram posicionadas nas proximidades do canal principal de acesso à baía, ao longo de um transecto que se estende do seu interior até sua desembocadura. As sete campanhas amostrais se distribuem em duas séries longas, de 13 e 25 horas, de aquisição em um ponto fixo, e cinco amostragens ao longo das estações. A aquisição de dados envolve: coleta de amostras de água, utilizadas nas estimativas das concentrações de material particulado; coleta de sedimentos de fundo para caracterização granulométrica das estações amostradas; perfis de parâmetros físico-químicos; dados de correntômetria adquiridos junto ao fundo. O processamento das amostras de água e sedimentos foi realizado no laboratório de Geologia Marinha da Faculdade de Oceanografia da Universidade do Estado do Rio de Janeiro. As concentrações de material particulado em suspensão foram utilizadas na calibração de sensores acústicos e óticos, permitindo uma avaliação espaço-temporal mais detalhada dos padrões de distribuição junto ao fundo e ao longo da coluna dágua. Os dados observados permitiram identificar que as maiores concentrações de material particulado em suspensão ocorrem em condições de maré enchente, e estão associadas à assimetria de maré. A baía pode ser dividida em dois setores: um na porção mais interna, onde se observou maior influência do aporte fluvial, onde as concentrações de material particulado em suspensão respondem à propagação da pluma do canal de São Francisco; e outro que se estende da porção central até sua desembocadura, onde predomina o domínio marinho, com influência de eventos oriundos da plataforma continental. Também pode ser identificada a influência do fenômeno La Niña, que provavelmente foi responsável por: altas salinidades encontradas no interior da baía e ocorrência da Água Central do Atlântico Sul à baixas profundidades. Quanto à utilização de equipamentos acústicos nas estimativas das concentrações de material particulado, os dados se demonstraram ricos em detalhes, que permitiram avaliar o comportamento do material particulado junto ao fundo frente a diferentes condições de maré, turbulência e incidência de oscilações.

Self-Organized Criticality, Plasticity and Sensorimotor Coupling. Explorations with a Neurorobotic Model in a Behavioural Preference Task

During the last two decades, analysis of 1/f noise in cognitive science has led to a considerable progress in the way we understand the organization of our mental life. However, there is still a lack of specific models providing explanations of how 1/f noise is generated in coupled brain-body-environment systems, since existing models and experiments typically target either externally observable behaviour or isolated neuronal systems but do not address the interplay between neuronal mechanisms and sensorimotor dynamics. We present a conceptual model of a minimal neurorobotic agent solving a behavioural task that makes it possible to relate mechanistic (neurodynamic) and behavioural levels of description. The model consists of a simulated robot controlled by a network of Kuramoto oscillators with homeostatic plasticity and the ability to develop behavioural preferences mediated by sensorimotor patterns. With only three oscillators, this simple model displays self-organized criticality in the form of robust 1/f noise and a wide multifractal spectrum. We show that the emergence of self-organized criticality and 1/f noise in our model is the result of three simultaneous conditions: a) non-linear interaction dynamics capable of generating stable collective patterns, b) internal plastic mechanisms modulating the sensorimotor flows, and c) strong sensorimotor coupling with the environment that induces transient metastable neurodynamic regimes. We carry out a number of experiments to show that both synaptic plasticity and strong sensorimotor coupling play a necessary role, as constituents of self-organized criticality, in the generation of 1/f noise. The experiments also shown to be useful to test the robustness of 1/f scaling comparing the results of different techniques. We finally discuss the role of conceptual models as mediators between nomothetic and mechanistic models and how they can inform future experimental research where self-organized critically includes sensorimotor coupling among the essential interaction-dominant process giving rise to 1/f noise.

Variabilidade ventilatória durante exercício dinâmico em indivíduos saudáveis e com insuficiência cardíaca

A presença de ventilação periódica durante o exercício confere pior prognóstico a pacientes com insuficiência cardíaca. Existem divergências quanto aos critérios para identificação deste fenômeno. Além disso, a interpretação dicotômica (presença ou ausência) quanto a este fenômeno dificulta a estratificação de risco mais detalhada dos pacientes com insuficiência cardíaca. Desta forma, esta tese avalia a utilização de técnicas estabelecidas para análise de variabilidade de sinais para quantificar as oscilações ventilatórias que ocorrem durante o teste cardiopulmonar de exercício, em indivíduos saudáveis, atletas e com insuficiência cardíaca. Um protocolo mais curto para realização de teste cardiopulmonar de exercício em cicloergômetro de braço foi proposto e validado. Tal protocolo foi utilizado em estudo posterior, onde se comprovou que, apesar dos tempos respiratórios não serem influenciados pelo tipo de exercício realizado, a variabilidade ventilatória é maior durante a realização de exercício dinâmico com membros superiores do que com membros inferiores. A capacidade aeróbica de indivíduos sadios também influencia a variabilidade ventilatória durante o teste cardiopulmonar de exercício. Isto foi comprovado pela menor variabilidade ventilatória no domínio do tempo em atletas do que sedentários durante exercício. A análise destes voluntários com o método da análise dos componentes principais revelou que em atletas a variabilidade do volume corrente é a principal responsável pela variabilidade da ventilação-minuto durante o exercício, ao passo que em sedentários a variabilidade da freqüência respiratória apresenta-se como principal responsável por tais variações. Em estudo randomizado e controlado comprovamos que, mesmo indivíduos sadios apresentam redução da variabilidade ventilatória ao exercício após 12 semanas de treinamento físico. Comprovamos que a reabilitação cardíaca reverteu a ocorrência de ventilação periódica em um paciente com insuficiência cardíaca e, finalmente, encontramos que a variabilidade ventilatória correlaciona-se inversamente com a fração de ejeção ventricular esquerda em pacientes com insuficiência cardíaca. Estudos futuros deverão analisar o poder prognóstico da variabilidade ventilatória nestes pacientes.