The Hamiltonian of a stably stratified incompressible fluid in an internal water wave in a deep ocean is constructed. Studying the ocean internal wave field with its full dynamics is formidable (or unsolvable) so we consider a test-wave Hamiltonian to study the dynamical and statistical properties of the internal water wave field in a deep ocean. Chaos is present in the internal test-wave dynamics using actual coupling coefficients. Moreover, there exists a certain separatrix net that fills the phase space and is covered by a thin stochastic layer for a two-triad pure resonant interaction. The stochastic web implies the existence of diffusion of the Arnold type for the minimum dimension of a non-integrable autonomous system. For non-resonant case, stochastic layer is formed where the separatrix from KAM theory is disrupted. However, the stochasticity does not increase monotonically with increasing energy. Also, the problem of relaxation process is studied via microscopic Hamiltonian model of the test-wave interacting nonlinearly with ambient waves. Using the Mori projection technique, the projected trajectory of the test-wave is transformed to a form which corresponds to a generalized Langevin equation. The mean action of the test-wave grows ballistically for a short time regime, and quenches back to the normal diffusion for a intermediate time regime and regresses linearly to a state of statistical equilibrium. Applying the Nakajima-Zwanzig technique on the test-wave system, we get the generalized master equation on the test-wave system which is non-Markovian in nature. From our numerical study, the distribution of the test-wave has non-Gaussian statistics.

A fundamental question in Complexity Science is how numerous dynamic processes coordinate with each other on multiple levels of description to form a complex whole - a multiscale coordinative structure (e.g. a community of interacting people, organs, cells, molecules etc.). This dissertation includes a series of empirical, theoretical and methodological studies of rhythmic coordination between multiple agents to uncover dynamic principles underlying multiscale coordinative structures. First, a new experimental paradigm was developed for studying coordination at multiple levels of description in intermediate-sized (N = 8) ensembles of humans. Based on this paradigm, coordination dynamics in 15 ensembles was examined experimentally, where the diversity of subjects movement frequency was manipulated to induce di erent grouping behavior. Phase coordination between subjects was found to be metastable with inphase and antiphase tendencies. Higher frequency diversity led to segregation between frequency groups, reduced intragroup coordination, and dispersion of dyadic phase relations (i.e. relations at di erent levels of description). Subsequently, a model was developed, successfully capturing these observations. The model reconciles the Kuramoto and the extended Haken-Kelso-Bunz model (for large- and small-scale coordination respectively) by adding the second-order coupling from the latter to the former. The second order coupling is indispensable in capturing experimental observations and connects behavioral complexity (i.e. multistability) of coordinative structures across scales. Both the experimental and theoretical studies revealed multiagent metastable coordination as a powerful mechanism for generating complex spatiotemporal patterns. Coexistence of multiple phase relations gives rise to many topologically distinct metastable patterns with di erent degrees of complexity. Finally, a new data-analytic tool was developed to quantify complex metastable patterns based on their topological features. The recurrence of topological features revealed important structures and transitions in high-dimensional dynamic patterns that eluded its non-topological counterparts. Taken together, the work has paved the way for a deeper understanding of multiscale coordinative structures. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

Stability against capsizing is one of the most fundamental requirements to design a ship. In this research, for the first time, CFD is performed to predict main modes of capsizing. CFD first is conducted to predict parametric rolling for a naval ship. Then CFD study of parametric rolling is extended for prediction of broaching both by using CFD as input to NDA model of broaching in replacement of EFD inputs or by using CFD for complete simulation of broaching. The CFD resistance, static heel and drift in calm water and static heel in following wave simulations are conducted to estimate inputs for NDA and 6DOF simulation in following waves are conducted for complete modeling of broaching. CFD parametric rolling simulations show remarkably close agreement with EFD. The CFD stabilized roll angle is very close to those of EFD but CFD predicts larger instability zones. The CFD and EFD results are analyzed with consideration ship theory and compared with NDA. NDA predictions are in qualitative agreement with CFD and EFD. CFD and EFD full Fr curve resistance, static heel and drift in calm water, and static heel in following waves results show fairly close agreement. CFD shows reasonable agreement for static heel and drift linear maneuvering derivatives, whereas large errors are indicated for nonlinear derivatives. The CFD and EFD results are analyzed with consideration ship theory and compared with NDA models. The surge force in following wave is also estimated from Potential Theory and compared with CFD and EFD. It is shown that CFD reproduces the decrease of the surge force near the Fr of 0.2 whereas Potential Theory fails. The CFD broaching simulations are performed for series of heading and Fr and results are compared with the predictions of NDA based on CFD, EFD, and Potential Theory inputs. CFD free model simulations show promising results predicting the instability boundary accurately. CFD calculation of wave and rudders yaw moment explains the processes of surf-riding, broaching, and periodic motion. The NDA simulation using CFD and Potential Flow inputs suggests that CFD/ Potential Flow can be considered as replacement for EFD inputs.

Different theoretical models have tried to investigate the feasibility of recurrent neural mechanisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. Our mathematical analysis shows that such networks have form-stable stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. Our analysis shows also that the stability of such solutions can break down giving raise to a different class of solutions ("lurching activity waves") that are characterized by a specific spatio-temporal periodicity. These solutions cannot arise in models for direction selectivity with purely linear spatio-temporal filtering.

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.

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.

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