No description available.

Mixing in Stokes flows is notoriously difficult to achieve. With characteristic scales of the flows being too small for the turbulence to be present, and too large for the molecular diffusion to be significant, the chaotic advection presents almost the only mechanism that can lead to mixing. Unfortunately for mixing, the intrinsic symmetries of the flow create invariant surfaces that act as barriers to mixing. Thus, a key to efficient mixing is to add to the original (symmetric) flow a certain kind of perturbation that destroys those symmetries. In this dissertation, two ways of obtaining mixing in 3D near-integrable bounded time -dependent Stoke Flows are studied: resonances and separatrix crossings. First, I illustrate that the resonances between different components of the original flow and the perturbation may break the invariant surfaces, paving a way to the large-scale mixing. Theoretical estimations are compared against the results of numerical simulations, as well as 3D particle tracking velocimetry (3D-PTV) experimental results. Second, chaotic advection and mixing due to quasi-random jumps of the adiabatic invariant (AI) occurring when a streamline crosses the separatrix surfaces is studied. Analytical expressions for the change in the AI near the separatrix surfaces are derived and compared with numerical simulations. / Mechanical Engineering

Since it is difficult or impossible to generate turbulent flow in a highly viscous fluid or a microfluidic system, efficient mixing becomes a challenge. However, it is possible in a laminar flow to generate chaotic particle trajectories (well-known as chaotic advection), that can lead to effective mixing. This dissertation studies mixing in flows with the limiting case of zero Reynolds numbers that are called Stokes flows and illustrates the practical use of different theories, namely the topological chaos theory, the set-oriented analysis and lobe dynamics in the analysis, design and optimization of different laminar-flow mixing systems. In a recent development, the topological chaos theory has been used to explain the chaos built in the flow only based on the topology of boundary motions. Without considering any details of the fluid dynamics, this novel method uses the Thurston-Nielsen (TN) classification theorem to predict and describe the stretching of material lines both qualitatively and quantitatively. The practical application of this theory toward design and optimization of a viscous-flow mixer and the important role of periodic orbits as "ghost rods" are studied. The relationship between stretching of material lines (chaos) and the homogenization of a scalar (mixing) in chaotic Stokes flows is examined in this work. This study helps determining the extent to which the stretching can represent real mixing. Using a set-oriented approach to describe the stirring in the flow, invariance or leakiness of the Almost Invariant Sets (AIS) playing the role of ghost rods is found to be in a direct relationship with the rate of homogenization of a scalar. The mixing caused by these AIS and the variations of their structure are explained from the point of view of geometric mechanics using transport through lobes. These lobes are made of segments of invariant manifolds of the periodic points that are generators of the ghost rods. A variety of the concentration-based measures, the important parameters of their calculation, and the implicit effect of diffusion are described. The studies, measures and methods of this dissertation help in the evaluation and understanding of chaotic mixing systems in nature and in industrial applications. They provide theoretical and numerical grounds for selection of the appropriate mixing protocol and design and optimization of mixing systems, examples of which can be seen throughout the dissertation. / Ph. D.

Modern robotics and automation systems require high-level reasoning capability in representing, identifying, and interpreting the three-dimensional data of the real world. Understanding the world's geometric structure by visual data is known as 3D perception. The necessity of analyzing irregular and complex 3D data has led to the development of high-dimensional frameworks for data learning. Here, we design several sparse learning-based approaches for high-dimensional data that effectively tackle multiple perception problems, including data filtering, data recovery, and data retrieval. The frameworks offer generative solutions for analyzing complex and irregular data structures without prior knowledge of data. The first part of the dissertation proposes a novel method that simultaneously filters point cloud noise and outliers as well as completing missing data by utilizing a unified framework consisting of a novel tensor data representation, an adaptive feature encoder, and a generative Bayesian network. In the next section, a novel multi-level generative chaotic Recurrent Neural Network (RNN) has been proposed using a sparse tensor structure for image restoration. In the last part of the dissertation, we discuss the detection followed by localization, where we discuss extracting features from sparse tensors for data retrieval. / Doctor of Philosophy / The development of automation systems and robotics brought the modern world unrivaled affluence and convenience. However, the current automated tasks are mainly simple repetitive motions. Tasks that require more artificial capability with advanced visual cognition are still an unsolved problem for automation. Many of the high-level cognition-based tasks require the accurate visual perception of the environment and dynamic objects from the data received from the optical sensor. The capability to represent, identify and interpret complex visual data for understanding the geometric structure of the world is 3D perception. To better tackle the existing 3D perception challenges, this dissertation proposed a set of generative learning-based frameworks on sparse tensor data for various high-dimensional robotics perception applications: underwater point cloud filtering, image restoration, deformation detection, and localization. Underwater point cloud data is relevant for many applications such as environmental monitoring or geological exploration. The data collected with sonar sensors are however subjected to different types of noise, including holes, noise measurements, and outliers. In the first chapter, we propose a generative model for point cloud data recovery using Variational Bayesian (VB) based sparse tensor factorization methods to tackle these three defects simultaneously. In the second part of the dissertation, we propose an image restoration technique to tackle missing data, which is essential for many perception applications. An efficient generative chaotic RNN framework has been introduced for recovering the sparse tensor from a single corrupted image for various types of missing data. In the last chapter, a multi-level CNN for high-dimension tensor feature extraction for underwater vehicle localization has been proposed.

The design implications of chaos theory are explored. What does this theory mean, if anything, to landscape architecture or architecture? In order to investigate these questions, the research was divided into four components relevant to design. First, philosophical- chaos offers a nonlinear understanding about place and nature. Second, aesthetical-fractals describe a deep beauty and order in nature. Thirdly, modeling-it is a qualitative method of modeling natural processes. Lastly, managing- concepts of chaos theory can be exploited to mimic processes found in nature. These components draw from applications and selected literature of chaos theory. From these research components, design implications were organized and concluded. Philosophical implications, offer a different, nonlinear realization about nature for designers. Aesthetic conclusions, argue that fractal geometry can articulate an innate beauty (a scaling phenomenon) in nature. Modeling, discusses ways of using chaos theory to visualize the design process, a process which may be most resilient when it is nonlinear. The last research chapter, managing, applications of chaos theory are used to illustrate how complex form, like that in nature, can be created by designers. / Master of Landscape Architecture

In this dissertation, the extended Melnikov's method has been applied to several nonlinear ship dynamics models, which are related to the new generation of stability criteria in the International Maritime Organization (IMO). The advantage of this extended Melnikov's method is it overcomes the limitation of small damping that is intrinsic to the implementation of the standard Melnikov's method. The extended Melnikv's method is first applied to two published roll motion models. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is a model with a biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of the extended Melnikov's method is demonstrated. Then this method is used to predict more accurately the threshold of global surf-riding for a ship operating in steep following seas. A reference ITTC ship is used here by way of example and the result is compared to that obtained from previously published standard analysis as well as numerical simulations. Because the primary drawback of the extended Melnikov's method is the inability to arrive at a closed form equation, a 'best fit'approximation is given for the extended Melnikov numerically predicted result. The extended Melnikov's method for slowly varying system is applied to a roll-heave-sway coupled ship model. The Melnikov's functions are calculated based on a fishing boat model. And the results are compared with those from standard Melnikov's method. This work is a preliminary research on the application of Melnikov's method to multi-degree-of-freedom ship dynamics. In the last part of the dissertation, the method of manufactured solution is applied to systems with chaotic behavior. The purpose is to identify points with potential numerical discrepancies, and to improve computational efficiency. The numerical discrepancies may be due to the selection of error tolerances, precisions, etc. Two classical chaotic models and two ship capsize models are examined. The current approach overlaps entrainment in chaotic control theory. Here entrainment means two dynamical systems have the same period, phase and amplitude. The convergent region from control theory is used to give a rough guideline on identifying numerical discrepancies for the classical chaotic models. The effectiveness of this method in improving computational efficiency is demonstrated for the ship capsize models. / Ph. D.

No description available.

The purpose of this project was to expand the applications of time series prediction and action recognition for use with motion capture data and football plays. Both the motion capture data and football play trajectories were represented in the form of multidimensional time series. Each point of interest on the human body or football players path, was represented in two or three time series, one for each dimension of motion recorded in the data. By formulating a phase space reconstruction of the data, the remainder of each input time series was predicted utilizing kernel regression. This process was applied to the first portion of a play. Utilizing features from the theory of chaotic systems and specialized geometric features, the specific type of motion for the motion capture data or the type of play for the football data was identified by using the features with various classifiers. The chaotic features used included the maximum Lyapunov exponent, the correlation integral, and the correlation dimension. The variance and mean were also utilized in conjunction with the chaotic features. The geometric features used were the minimum, maximum, mean, and median of the x, y, and z axis time series, as well as various angles and measures of the trajectory as a whole. The accuracy of the features and classifiers was compared and combinations of features were analyzed. The novelty of this work lies in the method to recognize types of actions from a prediction made from only a short, initial portion of an action utilizing various sets of features and classifiers.

De façon générale, cette thèse porte sur l'estimation de l'état et des entrées inconnues pour une classe de systèmes non linéaires. De façon plus particulière, le problème est abordé sous l'angle de la conception d'un système de transmission sécurisée d'informations exploitant les propriétés des systèmes chaotiques et leur capacité de synchronisation. Les travaux présentés traitent trois points principaux, à savoir le choix de l'émetteur, le développement du récepteur, et la mise au point du processus de transmission de l'information ou du message. L'émetteur retenu est un système non linéaire chaotique dont la dynamique comporte un retard, ce qui lui confère un comportement particulièrement complexe. La conception du récepteur repose sur la synthèse d'un observateur non linéaire, dont la stabilité et la convergence garantissent la synchronisation avec l'émetteur. L'insertion du message est réalisée par modulation de la phase d'un signal porteur chaotique. Le décryptage de l'information s'apparente à une restauration d'entrée inconnue au niveau du récepteur. Une étude de la sécurité du processus de cryptage/décryptage a été menée, reposant sur des techniques standard de cryptanalyse. Des multimodèles chaotiques ont été proposés pour renforcer la sécurité du processus de synchronisation / In a general way, this thesis deals with state and unknown input estimation for a class of nonlinear systems. In a more particular way, the problem is addressed from a secure communication system design point of view, based on chaotic systems properties and synchronization ability. Our work deals with three main points: selection of the transmitter, design of the receiver, and development of the information (or message) transmission process. The chosen transmitter is a time-delay nonlinear chaotic system: the main reason is that a very complex behavior is brought about by the delayed state feedback. The receiver design relies on a nonlinear observer synthesis, whose stability and convergence ensure synchronization with the transmitter. The message insertion is realized through a chaotic carrier phase modulation. The decryption process is similar to an unknown input recovery, at the receiver side. The security of the proposed encryption/decryption process is studied using standard cryptanalysis techniques. Chaotic multimodels are defined to tighten up the synchronization process security

[EN] The purpose of the Ph.D. Thesis "Dynamics of strongly continuous semigroups associated to certain differential equations'' is to analyse, from the point of view of functional analysis, the dynamics of solutions of linear evolution equations. These solutions can be represented by a strongly continuous semigroup on an infinite-dimensional Banach space. The aim of our research is to provide global conditions for chaos, in the sense of Devaney, and stability properties of strongly continuous semigroups which are solutions of linear evolution equations. This work is composed of three principal chapters. Chapter 0 is introductory and defines basic terminology and notation used, besides presenting the basic results that we will use throughout this thesis. Chapters 1 and 2 describe, in general way, a strongly continuous semigroup induced by a semiflow in Lebesgue and Sobolev spaces which is a solution of a linear first order partial differential equation. Moreover, some characterizations of the main dynamical properties, including hypercyclicity, mixing, weakly mixing, chaos and stability are given along these chapters. Chapter 3 describes the dynamical properties of a difference equation based on the so-called birth-and-death model and analyses the conditions previously proven for this model improving them by employing a different strategy. The goal of this thesis is to characterize dynamical properties of these kind of strongly continuous semigroups in a general way, whenever possible, and to extend these results to another spaces. Along this memory, these findings are compared with the previous ones given by many authors in recent years. / [ES] La presente memoria "Dinámica de semigrupos fuertemente continuos asociadas a ciertas ecuaciones diferenciales'' es analizar, desde el punto de vista del análisis funcional, la dinámica de las soluciones de ecuaciones de evolución lineales. Estas soluciones pueden ser representadas por semigrupos fuertemente continuos en espacios de Banach de dimensión infinita. El objetivo de nuestra investigación es proporcionar condiciones globales para obtener caos, en el sentido de Devaney, y propiedades de estabilidad de semigrupos fuertemente continuos, los cuales son soluciones de ecuaciones de evolución lineales. Este trabajo está compuesto de tres capítulos principales. El Capítulo 0 es introductorio y define la terminología básica y notación usada, además de presentar los resultados básicos que usaremos a lo largo de esta tesis. Los Capítulos 1 y 2 describen, de forma general, un semigrupo fuertemente continuo inducido por un semiflujo en espacios de Lebesgue y en espacios de Sobolev, los cuales son solución de una ecuación diferencial lineal en derivadas parciales de primer orden. Además, algunas caracterizaciones de las principales propiedades dinámicas, incluyendo hiperciclicidad, mezclante, débil mezclante, caos y estabilidad, se obtienen a lo largo de estos capítulos. El Capítulo 3 describe las propiedades dinámicas de una ecuación en diferencias basada en el llamado modelo de nacimiento-muerte y analiza las condiciones previamente probadas para este modelo, mejorándolas empleando una estrategia diferente. La finalidad de esta tesis es caracterizar propiedades dinámicas para este tipo de semigrupos fuertemente continuos de forma general, cuando sea posible, y extender estos resultados a otros espacios. A lo largo de esta memoria, estos resultados son comparados con los resultados previos dados por varios autores en años recientes. / [CA] La present memòria "Dinàmica de semigrups fortament continus associats a certes equacions diferencials'' és analitzar, des del punt de vista de l'anàlisi funcional, la dinàmica de les solucions d'equacions d'evolució lineals. Aquestes solucions poden ser representades per semigrups fortament continus en espais de Banach de dimensió infinita. L'objectiu de la nostra investigació es proporcionar condicions globals per obtenir caos, en el sentit de Devaney, i propietats d'estabilitat de semigrups fortament continus, els quals són solucions d'equacions d'evolució lineals. Aquest treball està compost de tres capítols principals. El Capítol 0 és introductori i defineix la terminologia bàsica i notació utilitzada, a més de presentar els resultats bàsics que utilitzarem al llarg d'aquesta tesi. Els Capítols 1 i 2 descriuen, de forma general, un semigrup fortament continu induït per un semiflux en espais de Lebesgue i en espais de Sobolev, els quals són solució d'una equació diferencial lineal en derivades parcials de primer ordre. A més, algunes caracteritzacions de les principals propietats dinàmiques, incloent-hi hiperciclicitat, mesclant, dèbil mesclant, caos i estabilitat, s'obtenen al llarg d'aquests capítols. El Capítol 3 descrivís les propietats dinàmiques d'una equació en diferències basada en el model de naixement-mort i analitza les condicions prèviament provades per aquest model, millorant-les utilitzant una estratègia diferent. La finalitat d'aquesta tesi és caracteritzar propietats dinàmiques d'aquest tipus de semigrups fortament continus de forma general, quan siga possible, i estendre aquests resultats a altres espais. Al llarg d'aquesta memòria, aquests resultats són comparats amb els resultats previs obtinguts per diversos autors en anys recents. / Aroza Benlloch, J. (2015). Dynamics of strongly continuous semigroups associated to certain differential equations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/57186