Computational research making use of molecular dynamics (MD) simulations has begun to expand the paradigm of structural biology to include dynamics as the mediator between structure and function. This work aims to expand the utility of MD simulations by developing Principal Component Analysis (PCA) techniques to extract the biologically relevant information in these increasingly complex data sets. Gramicidin is a simple protein with a very clear functional role and a long history of experimental, theoretical and computational study, making it an ideal candidate for detailed quantitative study and the development of new analysis techniques. First we quantify the convergence of our PCA results to underwrite the scope and validity of three 64 ns simulations of gA and two covalently linked analogs (SS and RR) solvated in a glycerol mono-oleate (GMO) membrane. Next we introduce a number of statistical measures for identifying regions of anharmonicity on the free energy landscape and highlight the utility of PCA in identifying functional modes of motion at both long and short wavelengths. We then introduce a simple ansatz for extracting physically meaningful modes of collective dynamics from the results of PCA, through a weighted superposition of eigenvectors. Applied to the gA, SS and RR backbone, this analysis results in a small number of collective modes which relate structural differences among the three analogs to dynamic properties with functional interpretations. Finally, we apply elements of our analysis to the GMO membrane, yielding two simple modes of motion from a large number of noisy and complex eigenvectors. Our results demonstrate that PCA can be used to isolate covariant motions on a number of different length and time scales, and highlight the need for an adequate structural and dynamical account of many more PCs than have been conventionally examined in the analysis of protein motion.

Nuestro trabajo se ha concentrado en la simulación y el análisis de modelos no-lineales aplicados a las curvas de luz ópticas de estrellas variables de largo periodo. Cuando las estrellas de masa pequeña o intermedia (de 1 a 11 masas solares) llegan a las fases finales de su evolución, tales como la Rama Asintótica de las (Super-)Gigantes, presentan oscilaciones regulares e irregulares de larga duración (i.e. estrellas Miras). Las pulsaciones regulares e irregulares facilitan los episodios de pérdida de masa y hacen que estas estrellas jueguen un papel crucial en la evolución química de las galaxias. Los modelos hidrodinámicos detallados existentes en la literatura proporcionan resultados muy completos, pero a menudo son difíciles de interpretar. Por lo tanto se ha creado la necesidad de entender, a un nivel más básico, los procesos que llevan a pulsaciones irregulares o comportamientos en contradicción con las observaciones. En este sentido, hemos considerado la estrella variable como constituida por un nucleo compacto y una envoltura cuyo movimiento forzado está dado por las ondas de presión originadas en el interior de la estrella. En el presente enfoque, aproximamos la envoltura mediante una sola capa y por lo tanto, los modelos basados en esta aproximación llevan el nombre de modelos de una capa. Entre ellos,los que hemos estudiado a lo largo de los últimos tres años dan cuenta de dichas irregularidades a través de un sistema de ecuaciones diferenciales que incluye, en las versiones más sencillas, la ecuación del movimiento y la conservación de masa, a las cuales hemos añadido a lo largo del estudio, la ecuación de la variación y transporte de energia en la envoltura estelar. En la presente tesis presentamos los resultados obtenidos, asi como una discusión sobre el estado de la modelización de estrellas variables en el contexto de los modelos de una capa. En el primer capítulo hemos introducido los tipos de estrellas variables y los mecanismos que llevan a su variabilidad, mientras que en el segundo capítulo hemos hecho un breve repaso de los modelos de una capa existentes en la literatura. Los modelos mencionados han sido seleccionados por su relación con los modelos que proponemos. En el primer estudio realizado que describimos en el tercer capítulo, hemos utilizado como punto de partida los resultados obtenidos por Icke et al., 1992, A&A, 258, 341, sobre un oscilador forzado que contiene la mínima dinámica necesaria para describir las oscilaciones estelares: la ecuación del movimiento y la conservación de masa. Aunque ideado para la variabilidad de estrellas de masa pequeña, nosotros hemos extendido el modelo para describir también las estrellas variables más masivas, en la fase de la Rama Asintótica de las Super-Gigantes. Hemos llevado a cabo un estudio paramétrico concienzudo a fin de investigar los tipos de com portamiento proporcionados por el modelo, identificando las bifurcaciones que producen dichos comportamientos y los rangos de los parámetros asociados a ellas. Para ello, hemos integrado en nuestro análisis los métodos característicos de la teoria de las bifurcaciones y del análisis tiempo-frecuencia, con el objetivo de determinar los posibles escenarios de transición al caos. Desde un punto de vista matemático, el análisis ha supuesto el estudio del mapa de Poincaré asociado a nuestro sistema, que, como se ha mencionado, está caracterizado por una perturbación periódica. Los resultados incluyen una serie de bifurcaciones locales y globales, entre las cuales la más importante es una triplicación. Entre las consecuencias de esta bifurcación mencionamos la adquisición por parte del mapa de Poincaré de la propiedad de nontwist que conlleva unas características del mapa de Poincaré típicas de los mapas nontwist (e.g. reconexión, meandros). Debido a la particular forma de la perturbación, la dinámica del sistema se diferencia de la del mapa cubico de Hénon, que se considera el prototipo de los mapas nontwist, y hacen del sistema investigado un ejemplo de dinámica prevista teóricamente, pero para la cual no se conocía ningún ejemplo. Desde un punto de vista astrofísico, la comparación con los resultados obtenidos por Icke et al. (1992) nos ha llevado a concluir que las estrellas variables más masivas presentan pulsaciones más irregulares que las estrella de masa pequeña, en acuerdo con las observaciones. El comportamiento irregular lleva a una pronunciada pérdida de masa, resultado comprobado por los datos observacionales. En el cuarto capítulo hemos extendido el modelo descrito anteriormente, añadiendole la ecuación del transporte de energia que permite una mejor comparación con las observaciones. Los resultados proporcionados por el modelo ampliado, entre los cuales destacamos las series temporales asociadas a la fluctuación de la luminosidad estelar, presentan sorprendentes similitudes con algunas de las más estudiadas y peculiares estrellas variables de largo periodo (las estrellas Miras). Adicionalmente, la dinámica encontrada conduce a series temporales en forma de pulsos energéticos a intervalos de tiempo del orden de mil años, que se pueden relacionar con las periodicidades encontradas en las capas circumestelares que rodean a ciertas nebulosas planetarias. En el quinto capítulo de la presente tesis hemos introducido el acoplamiento entre la convección y la pulsación estelar, proceso que se considera en la literatura como indispensable para una correcta modelización de la evolución de estas estrellas. Para ello hemos utilizado el modelo convectivo de una capa introducido en Stellingwerf, R.F., 1986, ApJ, 303, 119. Los resultados de dicho artículo nos han llamado la atención por algunas discrepancias relacionadas con el análisis de la morfologia de las curvas de luz y velocidad para casos en los cuales no existían ciclos límite. Por consiguiente, nuestra investigación se ha concentrado en el estudio parametrico del sistema con la intención de identificar las condiciones necesarias para la existencia de ciclos límite. Una vez identificadas la regiones de ciclos límite en el espacio parametrico, la morfologia de las curvas de luz asociadas ha revelado la existencia de una banda de inestabilidad semejante a la banda de inestabilidad de las variables Cefeidas. Adicionalmente, hemos ampliado el modelo considerando una forma más realista para los factores geometricos que describen el estado evolutivo de la estrella. Los resultados de esta ampliación indican una progresión de las curvas de luz - o para ser más exacto, de sus amplitudes y periodos - que recuerda la llamada Progresión Hertzsprung de las Cefeidas de tipo Bump. Hemos identificado también los tipos de contrapartidas observacionales que son susceptibles de ajustarse al modelo estudiado. Aunque existen muchos trabajos en la literatura basados en el modelo de Stellingwerf et al. (1986), consideramos que todavía muchas facetas e ideas quedan por aclarar y desarrollar.Para concluir, hemos comentado las implicaciones de nuestros resultados y estudios en el contexto de los modelos no lineales de una capa evidenciando sus capacidades y sus límites.

An objective in the design of high performance machinery is to minimize weight so magnetic bearings are often designed to operate slightly lower than the magnetic material saturation. Further weight reduction in the bearings requires operation in the nonlinear portion of the B-H curve. This necessitates a more sophisticated analysis at the bearing and rotordynamic system levels during the design stage. This dissertation addresses this problem in a unique manner by developing a fully nonlinear homopolar magnetic bearing model. The nonlinear dynamics of permanent magnet-biased homopolar magnetic bearing (PMB HoMB) system with 2-dof rigid and 4-dof flexible rotor is analyzed. The dynamic behavior of the rotor-bearing system is examined in the feedback control loop that includes low pass filter effects. An analytical magnetization curve model is proposed to predict the nonlinear magnetic force under the influence of the magnetic flux saturation more accurately. The modified Langmuir method with the novel correction terms for the weak flux region is used to curve-fit the experimental magnetization data of Hiperco 50. A new curve fit model of the B-H curve is shown to have significantly better agreement with the measured counterpart than conventional piecewise linear and other models. PMB HoMB characteristics with flux saturation, such as forces depending on the rotor position and bearing stiffness, are compared with these other models. Frequency response curve, bifurcation diagram, Poincare plot, and orbit plot are utilized to demonstrate the effects of the nonlinearities included in the 2-dof rotorbearing system. Due to heavy static loads applied to the rotor, it operates within the magnetic flux saturation region at the bearing clearance. The voltage saturation in the power amplifier of the magnetic bearing introduces lag in the control loop and the response of the heavily loaded 4-dof rotor-bearing system shows that limit cycle stability can be achieved due to the magnetic flux saturation or current saturation in the amplifier; otherwise the system would experience a destructive instability. These simulation results provide the first explanation of this commonly observed limit cycle which is referred to as ‘virtual catcher bearings’.

In this research we consider synchronization of oscillators. We use mechanical metronomes that are coupled through a mechanical medium. We investigate the problem for three different cases: 1) In passive coupling of two oscillators, the coupling medium is a one degree of freedom passive mechanical basis. The analysis of the system is supported by simulations of the proposed model and experimental results. 2) In another case, the oscillator is forced by an external input while the input is also affected by the oscillator. This feedback loop introduces dynamics to the whole system. For realization, we place the mechanical metronome on a one degree of freedom moving base. The movements of the base are a function of a feedback from the phase of the metronome. We study a family of functions for the reactions of the base and their impact on the behavior of the metronome. 3) We consider two metronomes located on a moving base. In this case the two metronomes oscillate and as the base is not freely moving, they are not directly coupled to each other. Now based on the feedbacks from the vision system, the base moves and hence the phases of the metronomes are affected by these movements. We study the space of possibilities for the movements of the base and consider impacts of the base movement on the synchronization of metronomes. We also show how such a system evolves in time.

This work investigates the use of shape memory alloys (SMAs) for vibration isolation and damping of mechanical systems. The first part of this work evaluates the nonlinear dynamics of a passive vibration isolation and damping (PVID) device through numerical simulations and experimental correlations. The device, a mass connected to a frame through two SMA wires, is subjected to a series of continuous acceleration functions in the form of a sine sweep. Frequency responses and transmissibility of the device as well as temperature variations of the SMA wires are analyzed for the case where the SMA wires are pre-strained at 4.0% of their original length. Numerical simulations of a one-degree of freedom (1-DOF) SMA oscillator are also conducted to corroborate the experimental results. The configuration of the SMA oscillator is based on the PVID device. A modified version of the constitutive model proposed by Boyd and Lagoudas, which considers the thermomechanical coupling, is used to predict the behavior of the SMA elements of the oscillator. The second part of this work numerically investigates chaotic responses of a 1- DOF SMA oscillator composed of a mass and a SMA element. The restitution force of the oscillator is provided by an SMA element described by a rate-independent, hysteretic, thermomechanical constitutive model. This model, which is a new version of the model presented in the first part of this work, allows smooth transitions between the austenitic and the martensitic phases. Chaotic responses of the SMA oscillator are evaluated through the estimation of the Lyapunov exponents. The Lyapunov exponent estimation of the SMA system is done by adapting the algorithm by Wolf and co-workers. The main issue of using this algorithm for nonlinear, rateindependent, hysteretic systems is related to the procedure of linearization of the equations of motion. The present work establishes a procedure of linearization that allows the use of the classical algorithm. Two different modeling cases are considered for isothermal and non-isothermal heat transfer conditions. The evaluation of the Lyapunov exponents shows that the proposed procedure is capable of quantifying chaos in rate-independent, hysteretic dynamical systems.

A Hamiltonian model for the radial and translational dynamics of clusters of coupled bubbles in an incompressible liquid developed by Ilinskii, Hamilton, and Zabolotskaya [J. Acoust. Soc. Am. 121, 786-795 (2007)] is extended to included the effects of compressibility in the host liquid. The bubbles are assumed to remain spherical and translation is allowed. The two principal effects of liquid compressibility are time delay in bubble interaction due to the finite sound speed and radiation damping due to energy lost to acoustic radiation. The incorporation of time delays produces a system of delay differential equations of motion instead of the system of ordinary differential equations in models of bubble interaction in an incompressible medium. The form of the Hamiltonian equations of motion is significantly different from the commonly used models based on Rayleigh-Plesset equations for coupled bubble dynamics, and it provides certain advantages in numerical integration of the time-delayed equations of motion. Corrections for radiation damping in clusters of interacting bubbles are developed in the form of a time-delayed expression for bubble self-action following the method of Ilinskii and Zabolotskaya [J. Acoust. Soc. Am. 92, 2837-2841 (1992)]. A set of approximate series expansions of this delayed expression is calculated to first order in the ratio of bubble radius to the characteristic wavelength of acoustic radiation from the bubble, and to varying orders in the ratio of bubble radius to characteristic bubble separation distance. Stability of the delay differential equations of motion is analyzed with four successive levels of approximation for the effects of radiation damping and time delay. The stability is analyzed with and without the effects of viscous and thermal damping. The effect of time delay and radiation damping on the pressure radiated by small systems of bubbles is considered. An approximate method to account for the delays in bubble interaction in a weakly compressible liquid is presented. This method converts the system of delay differential equations into an approximate system of ordinary differential equations, which may simplify numerical integration. Several sets of model equations incorporating propagation time delay in bubble interactions are solved numerically with existing algorithms specialized for delay differential equations. Numerical simulations of the dynamics of single bubbles, pairs of bubbles, and clusters of bubbles are used to compare the different levels of approximation for compressibility effects for low- and high-amplitude radial motion in systems of bubbles under free response and pulsed excitation by an external pressure source. / text

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第18991号 / 工博第4033号 / 新制||工||1621 / 31942 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 引原 隆士, 教授 土居 伸二, 教授 小林 哲生 / 学位規則第4条第1項該当

In this thesis we describe two instances of the nonlinear interaction between a fluid and an elastic solid to mimic or explain some phenomenon seen in nature. We focus on the phenomena of singing of small song birds and swimming of small fish. Song birds show a versatile range of tones and compositions that have highly complex spectral structure, while fish cut through water with amazing ease. The complexity of the Navier Stokes Equations that describe the fluid coupled with large deformation elasticity equations, makes analytic attempts intractable. Hence experiments were carried out with simple physical models to explain these observations. In the first case a cylindrical elastic tube (2.5cm long, 2.5mm diameter) was used to model the vocal organ, the syrinx, of a song bird. Muscle action was mimicked using a linear motor that implemented a squeezing action and the action of the lungs was modeled by a constant source of air flow. The combined fluid-elastic system behaved like a nonlinear dynamical system and produced sound under certain conditions of external parameters. Moreover the structure of the sound created depended sensitively on the control parameters, which in this case was dominated by the position of the linear motor. The motor was dynamically controlled to produce a range of songs from simple tonal ones of the Vireo to the complex chaotic songs of the Zebra Finch. In the second instance, a cantilever (5cm long, 1cm wide)suspended between and driven by magnetic coils arranged in an anti-Helmholtz configuration, was used to mimic the dynamics of the caudal fin of a small fish. Three different gaits were observed as a function of the control parameter, the drive frequency. One of these gaits maximized thrust and hydrodynamic efficiency, and velocities unto 6 body lengths per second were measured. / Engineering and Applied Sciences

Balance control is important for biped standing. Due to the time-varying control bounds induced by the foot constraints, and the lack of tools for analyzing stability of highly nonlinear systems, it is extremely difficult to design balance control strategies for a standing biped with a rigorous stability analysis in spite of large efforts. In this thesis, three important issues are fully considered for a standing biped: maintaining the postural stability, minimizing the energy consumption and satisfying the constraints between the biped feet and the ground. Both the theoretical and the experimental studies on the constrained and energy-efficient control are carried out systematically using the genetic algorithm (GA). The stability for the proposed balancing system is thoroughly investigated using the concept of Lyapunov exponents. On the other hand, the controlled standing biped is characterized by high nonlinearity and great complexity. For systems with such features, in general the Lyapunov exponents are hard to be estimated using the model-based method. Meanwhile the biped is supposed to be stabilized at the upright posture, indicating that the system should possess negative Lyapunov exponents only. However the accuracy of negative exponents is usually poor if following the traditional time-series-based methods. As it is nontrivial to examine the system stability for bipedal robots, the numerical accuracy of the estimated Lyapunov exponents is extremely demanding. In this research, two novel approaches are proposed based upon system approximation using different types of Radial-Basis-Function (RBF) networks. Both the proposed methods can estimate the exponents reliably with straightforward algorithms, yet no mathematical model is required in any newly developed method. The efficacies of both methods are demonstrated through a linear quadratic regulator (LQR) balancing system for a standing biped, as well as several other dynamical systems. The thesis as a whole, has set up a framework for developing more sophisticated controllers in more complex movement for robot models with less conservative assumptions. The systematic stability analysis shown in this thesis has a great potential for many other engineering systems.

The Atomic Force Microscope (AFM) is a tool for imaging surfaces at the microand nano meter scale. The microscope senses the force acting between a surfaceand a tip positioned at the end of a micro-cantilever, forming an image of the surface topography. Image contrast however, arises not only from surface topography, but also from variation in material composition. Improved material contrast, and improved interpretation of that contrast are two issues central to the further development of AFM. This thesis studies dynamic AFM where the cantilever is driven at multiple frequencies simultaneously. Due to the nonlinear dependence of the tip-surface force on the tip’s position, the cantilever will oscillate not only at the driven frequencies, but also at harmonics and at mixing frequencies of the drives, so-called intermodulation products. A mode of AFM called Intermodulation AFM (ImAFM) is primarily studied, which aims to make use of intermodulation products centered around the resonance frequency of the cantilever. With proper excitation many intermodulation products are generated near resonance where they can be measured with large signal-to-noise ratio. ImAFM is performed on samples containing two distinct domains of different material composition and a contrast metric is introduced to quantitatively evaluate images obtained at each response frequency. Although force sensitivity is highest on resonance, we found that weak intermodulation response off resonance can show larger material contrast. This result shows that the intermodulation images can be used to improve discrimination of materials. We develop a method to obtain material parameters from multifrequency AFM spectra by fitting a tip-surface force model. Together with ImAFM, this method allows high resolution imaging of material parameters. The method is very generalas it is not limited to a specific force model or particular mode of multifrequency AFM. Several models are discussed and applied to different samples. The parameter images have a direct physical interpretation and, if the model is appropriate, they can be used to relate the measurement to material properties such as the Young’s modulus. Force reconstruction is tested with simulations and on measured data. We use the reconstructed force to define the location of the surface so that we can address the issue of separating topographic contrast and material contrast. / Svepkraftmikroskop (eller atomkraftmikroskop från engelskans atomic forcemicroscope, AFM) är ett instrument för att avbilda ytor på mikro- och nanometer skalan. Mikroskopet känner av kraften som verkar mellan en yta och en spetsplacerad längst ut på ett mikrometerstort fjäderblad och kan därigenom skapa en topografisk bild av ytans form. Bildkontrast uppstår dock inte bara från ytans form utan även från variation i material. Förbättrad materialkontrast och förbättrad tolkning av denna kontrast är två centrala mål i vidareutvecklingen av AFM. Denna avhandling berör dynamisk AFM där fjädern drivs med flera frekvensersamtidigt. På grund av det ickelinjära förhållandet i yt-spets-kraften som funktion av spetsens position så kommer fjädern inte bara att svänga på de drivna frekvenserna utan också på övertoner och blandfrekvenser, så kallade intermodulationsprodukter. Vi undersöker primärt Intermodulation AFM (ImAFM) som ämnar att utnyttja intermodulationsprodukter nära fjäderns resonansfrekvens. Med en lämplig drivsignal genereras många intermodulationsprodukter nära resonansen, där de kan mätas med bra signal till brus förhållande. ImAFM utförs på ytor bestående av två distinkta domäner av olika material ochen kontrastmetrik introduceras för att kvantitativt utvärdera bilderna som skapas vid varje frekvens. Trots att känsligheten för kraftmätningen är högst på resonans-frekvensen, så fann vi att svaga intermodulationsprodukter bortanför resonansen kan visa hög materialkontrast. Detta resultat visar att intermodulationsbilderna kan användas för att bättre särskilja olika material. Vi har utvecklat en metod för att rekonstruera yt-spets-kraften från multifrekventa AFM spektra genom modellanpassning i frekvensrymden. Tillsammans med ImAFM leder detta till högupplösta bilder av materialparametrar. Metoden är generell och är applicerbar för olika kraftmodeller och AFM-varianter. Parametrarna har en direkt fysikalisk tolkning och, om lämpliga modeller används, kan egenskaper så som materialets elasticitetsmodul mätas. Metoden har testats på simulerat såvälsom experimentellt data, och den har också används för att särskilja topografisk kontrast från materialkontrast. / <p>QC 20150209</p>