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- Title
- FORMATION, EVOLUTION, AND BREAKDOWN OF INVARIANT TORI IN DISSIPATIVE SYSTEMS: FROM VISUALIZATION TO COMPUTER ASSISTED PROOFS.
- Creator
- Fleurantin, Emmanuel, Mireles-James, Jason, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
The goal of this work is to study smooth invariant sets using high order approximation schemes. Whenever possible, existence of invariant sets are established using computer-assisted proofs. This provides a new set of tools for mathematically rigorous analysis of the invariant objects. The dissertation focuses on application of these tools to a family of three dimensional dissipative vector fields, derived from the normal form of a cusp-Hopf bifurcation. The vector field displays a Neimark...
Show moreThe goal of this work is to study smooth invariant sets using high order approximation schemes. Whenever possible, existence of invariant sets are established using computer-assisted proofs. This provides a new set of tools for mathematically rigorous analysis of the invariant objects. The dissertation focuses on application of these tools to a family of three dimensional dissipative vector fields, derived from the normal form of a cusp-Hopf bifurcation. The vector field displays a Neimark-Sacker bifurcation giving rise to an attracting invariant torus. We examine the torus via parameter continuation from its appearance to its breakdown, scrutinizing its dynamics between these events. We also study the embeddings of the stable/unstable manifolds of the hyperbolic equilibrium solutions over this parameter range. We focus on the role of the invariant manifolds as transport barriers and their participation in global bifurcations. We then study the existence and regularity properties for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations and lay out a constructive method of computer assisted proof which pertains to explicit problems in non-perturbative regimes. We get verifiable lower bounds on the regularity of the attractor in terms of the ratio of the expansion rate on the torus with the contraction rate near the torus. We look at two important cases of rotational and resonant tori. Finally, we study the related problem of approximating two dimensional subcenter manifolds of conservative systems. As an application, we compare two methods for computing the Taylor series expansion of the graph of the subcenter manifold near a saddle-center equilibrium solution of a Hamiltonian system.
Show less - Date Issued
- 2021
- PURL
- http://purl.flvc.org/fau/fd/FA00013812
- Subject Headings
- Invariants, Manifolds (Mathematics), Dynamical systems
- Format
- Document (PDF)
- Title
- The Coordination Dynamics of Multiple Agents.
- Creator
- Zhang, Mengsen, Tognoli, Emmanuelle, Kelso, J. A. Scott, Florida Atlantic University, Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
- Abstract/Description
-
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,...
Show moreA 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.
Show less - Date Issued
- 2018
- PURL
- http://purl.flvc.org/fau/fd/FA00013111
- Subject Headings
- Complexity science, Coordination dynamics, Nonlinear Dynamics, Nonlinear systems and complexity
- Format
- Document (PDF)
- Title
- A UNIFIED SOFT SENSING FRAMEWORK FOR COMPLEX DYNAMICAL SYSTEMS.
- Creator
- Huang, Yu, Tang, Yufei, Florida Atlantic University, Department of Computer and Electrical Engineering and Computer Science, College of Engineering and Computer Science
- Abstract/Description
-
In the past few years, the development of complex dynamical networks or systems has stimulated great interest in the study of the principles and mechanisms underlying the Internet of things (IoT). IoT is envisioned as an intelligent network infrastructure with a vast number of ubiquitous smart devices present in diverse application domains and have already improved many aspects of daily life. Many overtly futuristic IoT applications acquire data gathered via distributed sensors that can be...
Show moreIn the past few years, the development of complex dynamical networks or systems has stimulated great interest in the study of the principles and mechanisms underlying the Internet of things (IoT). IoT is envisioned as an intelligent network infrastructure with a vast number of ubiquitous smart devices present in diverse application domains and have already improved many aspects of daily life. Many overtly futuristic IoT applications acquire data gathered via distributed sensors that can be uniquely identified, localized, and communicated with, i.e., the support of sensor networks. Soft-sensing models are in demand to support IoT applications to achieve the maximal exploitation of transforming the information of measurements into more useful knowledge, which plays essential roles in condition monitoring, quality prediction, smooth control, and many other essential aspects of complex dynamical systems. This in turn calls for innovative soft-sensing models that account for scalability, heterogeneity, adaptivity, and robustness to unpredictable uncertainties. The advent of big data, the advantages of ever-evolving deep learning (DL) techniques (where models use multiple layers to extract multi-levels of feature representations progressively), as well as ever-increasing processing power in hardware, has triggered a proliferation of research that applies DL to soft-sensing models. However, many critical questions need to be further investigated in the deep learning-based soft-sensing.
Show less - Date Issued
- 2022
- PURL
- http://purl.flvc.org/fau/fd/FA00013993
- Subject Headings
- Dynamical systems, Dynamics, Sensor networks, Deep learning (Machine learning)
- Format
- Document (PDF)
- Title
- Structured flows on manifolds: distributed functional architectures.
- Creator
- Pillai, Ajay S., Florida Atlantic University, Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
- Abstract/Description
-
Despite the high-dimensional nature of the nervous system, humans produce low-dimensional cognitive and behavioral dynamics. How high-dimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a...
Show moreDespite the high-dimensional nature of the nervous system, humans produce low-dimensional cognitive and behavioral dynamics. How high-dimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a general theoretical framework entitled 'Structured Flows on Manifolds' and its underlying mathematical basis. The framework is based on the principles of non-linear dynamical systems and Synergetics and can be used to understand how high-dimensional systems that exhibit multiple time-scale behavior can produce low-dimensional dynamics. Low-dimensional functional dynamics arises as a result of the timescale separation of the systems component's dynamics. The low-dimensional space in which the functi onal dynamics occurs is regarded as a manifold onto which the entire systems dynamics collapses. For the duration of the function the system will stay on the manifold and evolve along the manifold. From a network perspective the manifold is viewed as the product of the interactions of the network nodes. The subsequent flows on the manifold are a result of the asymmetries of network's interactions. A distributed functional architecture based on this perspective is presented. Within this distributed functional architecture, issues related to networks such as flexibility, redundancy and robustness of the network's dynamics are addressed. Flexibility in networks is demonstrated by showing how the same network can produce different types of dynamics as a function of the asymmetrical coupling between nodes. Redundancy can be achieved by systematically creating different networks that exhibit the same dynamics. The framework is also used to systematically probe the effects of lesion, (removal of nodes) on network dynamics. It is also shown how low-dimensional functional dynamics can be obtained from firing-rate neuron models by placing biologically realistic constraints on the coupling. Finally the theoretical framework is applied to real data. Using the structured flows on manifolds approach we quantify team performance and team coordination and develop objective measures of team performance based on skill level.
Show less - Date Issued
- 2008
- PURL
- http://purl.flvc.org/FAU/77649
- Subject Headings
- Manifolds (Mathematics), Differentiable dynamical systems, Mathematical physics
- Format
- Document (PDF)
- Title
- IDENTIFIABILITY ANALYSIS AND OPTIMAL CONTROL OF INFECTIOUS DISEASES EPIDEMICS AND PARAMETERIZATION METHOD FOR (UN)STABLE MANIFOLDS OF IMPLICITLY DEFINED DYNAMICAL SYSTEMS.
- Creator
- Neupane Timsina, Archana, Tuncer, Necibe, Mireles James, Jason D., Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
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This dissertation is a study about applied dynamical systems on two concentrations. First, on the basis of the growing association between opioid addiction and HIV infection, a compartmental model is developed to study dynamics and optimal control of two epidemics; opioid addiction and HIV infection. We show that the disease-free-equilibrium is locally asymptotically stable when the basic reproduction number R0 = max(Ru0; Rv0) 1 and it is locally asymptotically stable when the invasion...
Show moreThis dissertation is a study about applied dynamical systems on two concentrations. First, on the basis of the growing association between opioid addiction and HIV infection, a compartmental model is developed to study dynamics and optimal control of two epidemics; opioid addiction and HIV infection. We show that the disease-free-equilibrium is locally asymptotically stable when the basic reproduction number R0 = max(Ru0; Rv0) < 1; here Rv0 is the reproduction number of the HIV infection, and Ru0 is the reproduction number of the opioid addiction. The addiction-only boundary equilibrium exists when Ru0 > 1 and it is locally asymptotically stable when the invasion number of the opioid addiction is Ruinv < 1: Similarly, HIV-only boundary equilibrium exists when Rv0 > 1 and it is locally asymptotically stable when the invasion number of the HIV infection is Rvinv < 1. We study structural identifiability of the parameters, estimate parameters employing yearly reported data from Central for Disease Control and Prevention (CDC), and study practical identifiability of estimated parameters. We observe the basic reproduction number R0 using the parameters. Next, we introduce four distinct controls in the model for the sake of control approach, including treatment for addictions, health care education about not sharing syringes, highly active anti-retroviral therapy (HAART), and rehab treatment for opiate addicts who are HIV infected. US population using CDC data, first applying a single control in the model and observing the results, we better understand the influence of individual control. After completing each of the four applications, we apply them together at the same time in the model and compare the outcomes using different control bounds and state variable weights. We conclude the results by presenting several graphs.
Show less - Date Issued
- 2022
- PURL
- http://purl.flvc.org/fau/fd/FA00013970
- Subject Headings
- Dynamical systems, Infectious diseases, Parameter estimation
- Format
- Document (PDF)
- Title
- DATA-DRIVEN ATTRACTOR IDENTIFICATION VIA COMPUTATIONAL HOMOLOGY AND MACHINE LEARNING.
- Creator
- Tatasciore, Paul, Wille, Luc T., Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
- Abstract/Description
-
Dynamical systems play a pivotal role across various scientific domains, encompassing disciplines from physics to biology and engineering. The long-term behavior of these systems hinges on the structure of their attractors, with many exhibiting multistability characterized by multiple minimal attractors. Understanding the structure of these attractors and their corresponding basins is a central theme in dynamical systems theory. In recent years, machine learning algorithms have emerged as...
Show moreDynamical systems play a pivotal role across various scientific domains, encompassing disciplines from physics to biology and engineering. The long-term behavior of these systems hinges on the structure of their attractors, with many exhibiting multistability characterized by multiple minimal attractors. Understanding the structure of these attractors and their corresponding basins is a central theme in dynamical systems theory. In recent years, machine learning algorithms have emerged as potent tools for clustering, prediction, and modeling complex data. By harnessing the capabilities of neural networks along with techniques from topological data analysis, in particular persistence homology, we can construct surrogate models of system asymptotics. This approach also allows for the decomposition of phase space into polygonal regions and the identification of plausible attracting neighborhoods, facilitating homological Conley index computation at reduced computational expense compared to current methods. Through various illustrative examples, we demonstrate that sufficiently low training loss yields constructed neighborhoods whose homological Conley indices aligns with a priori knowledge of the dynamics.
Show less - Date Issued
- 2024
- PURL
- http://purl.flvc.org/fau/fd/FA00014475
- Subject Headings
- Dynamical systems, Computational physics, Machine learning
- Format
- Document (PDF)
- Title
- PARAMETERIZATION OF INVARIANT CIRCLES IN MAPS.
- Creator
- Blessing, David Charles, James, J. D. James, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
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We explore a novel method of approximating contractible invariant circles in maps. The process begins by leveraging improvements on Birkhoff's Ergodic Theorem via Weighted Birkhoff Averages to compute high precision estimates on several Fourier modes. We then set up a Newton-like iteration scheme to further improve the estimation and extend the approximation out to a sufficient number of modes to yield a significant decay in the magnitude of the coefficients of high order. With this...
Show moreWe explore a novel method of approximating contractible invariant circles in maps. The process begins by leveraging improvements on Birkhoff's Ergodic Theorem via Weighted Birkhoff Averages to compute high precision estimates on several Fourier modes. We then set up a Newton-like iteration scheme to further improve the estimation and extend the approximation out to a sufficient number of modes to yield a significant decay in the magnitude of the coefficients of high order. With this approximation in hand, we explore the phase space near the approximate invariant circle with a form numerical continuation where the rotation number is perturbed and the process is repeated. Then, we turn our attention to a completely different problem which can be approached in a similar way to the numerical continuation, finding a Siegel disk boundary in a holomorphic map. Given a holomorphic map which leads to a formally solvable cohomological equation near the origin, we use a numerical continuation style process to approximate an invariant circle in the Siegel disk near the origin. Using an iterative scheme, we then enlarge the invariant circle so that it approximates the boundary of the Siegel disk.
Show less - Date Issued
- 2024
- PURL
- http://purl.flvc.org/fau/fd/FA00014464
- Subject Headings
- Dynamical systems, Nonlinearity (Mathematics), Numerical analysis, Parameterization
- Format
- Document (PDF)
- Title
- Very high frequency MIMO underwater acoustic communications in ports and shallow waters.
- Creator
- Real, Gaultier., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
- Abstract/Description
-
This thesis presents the development of a Multiple-Input Multiple-Output (MIMO) capable high bit rate acoustic modem operating at high frequencies. A MIMO channel estimation technique based on Least-Squares (LS) estimation is developed here. Channel deconvolution is completed using a Minimum Mean-Square Error (MMSE) Linear Equalizer (LE). An Interference Cancellation Linear Equalizer (ICLE) is used to provide the theoretical limit of the MIMO deconvolution process. The RMSE of the channel...
Show moreThis thesis presents the development of a Multiple-Input Multiple-Output (MIMO) capable high bit rate acoustic modem operating at high frequencies. A MIMO channel estimation technique based on Least-Squares (LS) estimation is developed here. Channel deconvolution is completed using a Minimum Mean-Square Error (MMSE) Linear Equalizer (LE). An Interference Cancellation Linear Equalizer (ICLE) is used to provide the theoretical limit of the MIMO deconvolution process. The RMSE of the channel estimation process was 1.83 % and 6.1810 %, respectively for simulated and experimental data. Using experimental data, the RMSE before MIMO deconvolution process was 141.3 % and dropped down to 60.224 % and to 4.4545 %, respectively after LE and ICLE. At raw reception, the RMSE was 101.83 % and dropped down to 9.36 % and to 1.86 % using respectively LE and ICLE with simulated data.
Show less - Date Issued
- 2011
- PURL
- http://purl.flvc.org/FAU/3333309
- Subject Headings
- MIMO systems, Wireless communication systems, Underwater acoustics, Fluid dynamics
- Format
- Document (PDF)
- Title
- Dynamics and Control of Autonomous Underwater Vehicles with Internal Actuators.
- Creator
- Li, Bo, Su, Tsung-Chow, Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
- Abstract/Description
-
This dissertation concerns the dynamics and control of an autonomous underwater vehicle (AUV) which uses internal actuators to stabilize its horizontalplane motion. The demand for high-performance AUVs are growing in the field of ocean engineering due to increasing activities in ocean exploration and research. New generations of AUVs are expected to operate in harsh and complex ocean environments. We propose a hybrid design of an underwater vehicle which uses internal actuators instead of...
Show moreThis dissertation concerns the dynamics and control of an autonomous underwater vehicle (AUV) which uses internal actuators to stabilize its horizontalplane motion. The demand for high-performance AUVs are growing in the field of ocean engineering due to increasing activities in ocean exploration and research. New generations of AUVs are expected to operate in harsh and complex ocean environments. We propose a hybrid design of an underwater vehicle which uses internal actuators instead of control surfaces to steer. When operating at low speeds or in relatively strong ocean currents, the performances of control surfaces will degrade. Internal actuators work independent of the relative ows, thus improving the maneuvering performance of the vehicle. We develop the mathematical model which describes the motion of an underwater vehicle in ocean currents from first principles. The equations of motion of a body-fluid dynamical system in an ideal fluid are derived using both Newton-Euler and Lagrangian formulations. The viscous effects of a real fluid are considered separately. We use a REMUS 100 AUV as the research model, and conduct CFD simulations to compute the viscous hydrodynamic coe cients with ANSYS Fluent. The simulation results show that the horizontal-plane motion of the vehicle is inherently unstable. The yaw moment exerted by the relative flow is destabilizing. The open-loop stabilities of the horizontal-plane motion of the vehicle in both ideal and real fluid are analyzed. In particular, the effects of a roll torque and a moving mass on the horizontal-plane motion are studied. The results illustrate that both the position and number of equilibrium points of the dynamical system are prone to the magnitude of the roll torque and the lateral position of the moving mass. We propose the design of using an internal moving mass to stabilize the horizontal-plane motion of the REMUS 100 AUV. A linear quadratic regulator (LQR) is designed to take advantage of both the linear momentum and lateral position of the internal moving mass to stabilize the heading angle of the vehicle. Alternatively, we introduce a tunnel thruster to the design, and use backstepping and Lyapunov redesign techniques to derive a nonlinear feedback control law to achieve autopilot. The coupling e ects between the closed-loop horizontal-plane and vertical-plane motions are also analyzed.
Show less - Date Issued
- 2016
- PURL
- http://purl.flvc.org/fau/fd/FA00004738, http://purl.flvc.org/fau/fd/FA00004738
- Subject Headings
- Dynamics., Remote submersibles--Design and construction., Ocean engineering., Fluid dynamics., Nonlinear control theory., Differentiable dynamical systems.
- Format
- Document (PDF)
- Title
- An Algorithmic Approach to The Lattice Structures of Attractors and Lyapunov functions.
- Creator
- Kasti, Dinesh, Kalies, William D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Ban and Kalies [3] proposed an algorithmic approach to compute attractor- repeller pairs and weak Lyapunov functions based on a combinatorial multivalued mapping derived from an underlying dynamical system generated by a continuous map. We propose a more e cient way of computing a Lyapunov function for a Morse decomposition. This combined work with other authors, including Shaun Harker, Arnoud Goulet, and Konstantin Mischaikow, implements a few techniques that makes the process of nding a...
Show moreBan and Kalies [3] proposed an algorithmic approach to compute attractor- repeller pairs and weak Lyapunov functions based on a combinatorial multivalued mapping derived from an underlying dynamical system generated by a continuous map. We propose a more e cient way of computing a Lyapunov function for a Morse decomposition. This combined work with other authors, including Shaun Harker, Arnoud Goulet, and Konstantin Mischaikow, implements a few techniques that makes the process of nding a global Lyapunov function for Morse decomposition very e - cient. One of the them is to utilize highly memory-e cient data structures: succinct grid data structure and pointer grid data structures. Another technique is to utilize Dijkstra algorithm and Manhattan distance to calculate a distance potential, which is an essential step to compute a Lyapunov function. Finally, another major technique in achieving a signi cant improvement in e ciency is the utilization of the lattice structures of the attractors and attracting neighborhoods, as explained in [32]. The lattice structures have made it possible to let us incorporate only the join-irreducible attractor-repeller pairs in computing a Lyapunov function, rather than having to use all possible attractor-repeller pairs as was originally done in [3]. The distributive lattice structures of attractors and repellers in a dynamical system allow for general algebraic treatment of global gradient-like dynamics. The separation of these algebraic structures from underlying topological structure is the basis for the development of algorithms to manipulate those structures, [32, 31]. There has been much recent work on developing and implementing general compu- tational algorithms for global dynamics which are capable of computing attracting neighborhoods e ciently. We describe the lifting of sublattices of attractors, which are computationally less accessible, to lattices of forward invariant sets and attract- ing neighborhoods, which are computationally accessible. We provide necessary and su cient conditions for such a lift to exist, in a general setting. We also provide the algorithms to check whether such conditions are met or not and to construct the lift when they met. We illustrate the algorithms with some examples. For this, we have checked and veri ed these algorithms by implementing on some non-invertible dynamical systems including a nonlinear Leslie model.
Show less - Date Issued
- 2016
- PURL
- http://purl.flvc.org/fau/fd/FA00004668
- Subject Headings
- Differential equations -- Numerical solutions., Differentiable dynamical systems., Algorithms.
- Format
- Document (PDF)
- Title
- The Circular Restricted Four Body Problem is Non-Integrable: A Computer Assisted Proof.
- Creator
- Kepley, Shane, Kalies, William D., Mireles-James, Jason D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Gravitational N-body problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important...
Show moreGravitational N-body problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important role in the discussion. In the last fty years the study of numerical methods for computing invariant objects has matured into a thriving sub-discipline. This growth is driven at least in part by the needs of the world's space programs. Recent work on validated numerical methods has begun to unify the computational and analytical perspectives, enriching both aspects of the subject. Many of these results use computer assisted proofs, a tool which has become increasingly popular in recent years. This thesis presents a proof that the circular restricted four body problem is non-integrable. The proof of this result is obtained as an application of more general rigorous numerical methods in nonlinear analysis.
Show less - Date Issued
- 2017
- PURL
- http://purl.flvc.org/fau/fd/FA00004997
- Subject Headings
- Dissertations, Academic -- Florida Atlantic University, Mathematical physics., Invariants., Dynamical systems
- Format
- Document (PDF)
- Title
- Computing Global Decompositions of Dynamical Systems.
- Creator
- Ban, Hyunju, Kalies, William D., Florida Atlantic University
- Abstract/Description
-
In this dissertation we present a computational approach to Conley's Decomposition Theorem, which gives a global decomposition of dynamical systems, and introduce an explicit numerical algorithm with computational complexity bounds for computing global dynamical structures of a continous map including attractorrepeller pairs and Conley's Lyapunov function. The approach is based on finite spatial discretizations and combinatorial multivalued maps. The method is successful in exhibiting...
Show moreIn this dissertation we present a computational approach to Conley's Decomposition Theorem, which gives a global decomposition of dynamical systems, and introduce an explicit numerical algorithm with computational complexity bounds for computing global dynamical structures of a continous map including attractorrepeller pairs and Conley's Lyapunov function. The approach is based on finite spatial discretizations and combinatorial multivalued maps. The method is successful in exhibiting approximations of attractor-repeller pairs, invariant sets, and Conley's Lyapunov function. We used the C++ language to code the algorithm.
Show less - Date Issued
- 2006
- PURL
- http://purl.flvc.org/fau/fd/FA00000848
- Subject Headings
- Lyapunov functions, Control theory, Mathematical optimization, Differentiable dynamical systems
- Format
- Document (PDF)
- Title
- MODELING, PATH PLANNING, AND CONTROL CO-DESIGN OF MARINE CURRENT TURBINES.
- Creator
- Hasankhani, Arezoo, Tang, Yufei, VanZwieten, James, Florida Atlantic University, Department of Computer and Electrical Engineering and Computer Science, College of Engineering and Computer Science
- Abstract/Description
-
Marine and hydrokinetic (MHK) energy systems, including marine current turbines and wave energy converters, could contribute significantly to reducing reliance on fossil fuels and improving energy security while accelerating progress in the blue economy. However, technologies to capture them are nascent in development due to several technical and economic challenges. For example, for capturing ocean flows, the fluid velocity is low but density is high, resulting in early boundary layer...
Show moreMarine and hydrokinetic (MHK) energy systems, including marine current turbines and wave energy converters, could contribute significantly to reducing reliance on fossil fuels and improving energy security while accelerating progress in the blue economy. However, technologies to capture them are nascent in development due to several technical and economic challenges. For example, for capturing ocean flows, the fluid velocity is low but density is high, resulting in early boundary layer separation and high torque. This dissertation addresses critical challenges in modeling, optimization, and control co-design of MHK energy systems, with specific case studies of a variable buoyancy-controlled marine current turbine (MCT). Specifically, this dissertation presents (a) comprehensive dynamic modeling of the MCT, where data recorded by an acoustic Doppler current profiler will be used as the real ocean environment; (b) vertical path planning of the MCT, where the problem is formulated as a novel spatial-temporal optimization problem to maximize the total harvested power of the system in an uncertain oceanic environment; (c) control co-design of the MCT, where the physical device geometry and turbine path control are optimized simultaneously. In a nutshell, the contributions are summarized as follows:
Show less - Date Issued
- 2022
- PURL
- http://purl.flvc.org/fau/fd/FA00013991
- Subject Headings
- Marine turbines, Modeling dynamic systems, Ocean wave power
- Format
- Document (PDF)
- Title
- CFD Study of Pectoral Fins of Larval Zebrafish: Effect of Reynolds Number, Swimming Kinematics and Fin Bending on Fluid Structures and Transport.
- Creator
- Islam, Toukir, Curet, Oscar M., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
- Abstract/Description
-
Flow Structure and fluid transport via advection around pectoral fin of larval ZebraFish are studied numerically using Immersed Boundary Method, Lagrangian Coherent Structure, passive particle tracing, vortex core evolution and four statistically defined mixing numbers. Experimental fish kinematics for nominal swimming case are obtained from previous researchers and numerically manipulated to analyze the role of different body motion kinematics, Reynolds number and fin morphology on flow...
Show moreFlow Structure and fluid transport via advection around pectoral fin of larval ZebraFish are studied numerically using Immersed Boundary Method, Lagrangian Coherent Structure, passive particle tracing, vortex core evolution and four statistically defined mixing numbers. Experimental fish kinematics for nominal swimming case are obtained from previous researchers and numerically manipulated to analyze the role of different body motion kinematics, Reynolds number and fin morphology on flow structure and transport. Hyperbolic strain field and vortex cores are found to be effective particle transporter and their relative strength are driving force of varying flow structure and fluid transport. Translation and lateral undulation of fish; as a combination or individual entity, has coherent advantages and drawbacks significant enough to alter the nature of fluid advection. Reynolds number increase enhances overall fluid transport and mixing in varying order for different kinematics and nominal bending position of fin has average transport capability of other artificially induced fin morphology.
Show less - Date Issued
- 2016
- PURL
- http://purl.flvc.org/fau/fd/FA00004606, http://purl.flvc.org/fau/fd/FA00004606
- Subject Headings
- Reynolds number., Aquatic animals (Physiology), Transport theory., Computational fluid dynamics., Dynamical systems., Continuum physics., Turbulence--Mathematical models.
- Format
- Document (PDF)
- Title
- Science fiction girlfriends transgender politics and US science fiction television, 1990–present.
- Creator
- Cava, Peter, Scodari, Christine, Florida Atlantic University, Dorothy F. Schmidt College of Arts and Letters, School of Communication and Multimedia Studies
- Abstract/Description
-
The 1990s ushered in what historian Susan Stryker describes as “a tremendous burst of new transgender activism” in the United States. Concomitantly, the success of Star Trek: The Next Generation led to a renaissance of US science fiction television. This dissertation asks, what is the relation between transgender (trans) politics and US science fiction (sf) television from 1990 to the present? The theoretical framework is Trans/Elemental feminism, a new paradigm developed in the dissertation....
Show moreThe 1990s ushered in what historian Susan Stryker describes as “a tremendous burst of new transgender activism” in the United States. Concomitantly, the success of Star Trek: The Next Generation led to a renaissance of US science fiction television. This dissertation asks, what is the relation between transgender (trans) politics and US science fiction (sf) television from 1990 to the present? The theoretical framework is Trans/Elemental feminism, a new paradigm developed in the dissertation. The method is multiperspectival cultural studies, which considers how the production, content, and reception of media texts and their metatexts collectively determine the texts’ meaning. The data include trade articles about the television industry; published interviews with producers; 3,175 hours of televisual content; commercial advertisements for television programs; films, novels, and webisodes (Web episodes) in selected media franchises; professional reviews; online discussion boards; fan fiction; and fan videos.
Show less - Date Issued
- 2015
- PURL
- http://purl.flvc.org/fau/fd/FA00004435, http://purl.flvc.org/fau/fd/FA00004435
- Subject Headings
- Computer science., Computers., Artificial intelligence., Applied mathematics., Engineering mathematics., Statistical physics., Dynamical systems., Vibration., Dynamics., Computer Science.
- Format
- Document (PDF)
- Title
- Self-organizing dynamics of coupled map systems.
- Creator
- Liebovitch, Larry S., Zochowski, Michal
- Date Issued
- 1999-03
- PURL
- http://purl.flvc.org/fau/165481
- Subject Headings
- Dynamics--Mathematical models, Chaotic behavior in systems, Self-organizing maps, Self-organizing systems-Mathematical models
- Format
- Document (PDF)
- Title
- Dynamic positioning and motion mitigation of a scaled sea basing platform.
- Creator
- Marikle, Sean P., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
- Abstract/Description
-
A 6-Degree Of Freedom (DOF) numeric model and computer simulation along with the 1/10th scale physical model of the Rapidly Deployable Stable Platform (RDSP) are being developed at Florida Atlantic University in response to military needs for ocean platforms with improved sea keeping characteristics. The RDSP is a self deployable spar platform with two distinct modes of operation enabling long distance transit and superior seakeeping. The focus of this research is the development of a Dynamic...
Show moreA 6-Degree Of Freedom (DOF) numeric model and computer simulation along with the 1/10th scale physical model of the Rapidly Deployable Stable Platform (RDSP) are being developed at Florida Atlantic University in response to military needs for ocean platforms with improved sea keeping characteristics. The RDSP is a self deployable spar platform with two distinct modes of operation enabling long distance transit and superior seakeeping. The focus of this research is the development of a Dynamic Position (DP) and motion mitigation system for the RDSP. This will be accomplished though the validation of the mathematical simulation, development of a novel propulsion system, and implementation of a PID controller. The result of this research is an assessment of the response characteristics of the RDSP that quantifies the performance of the propulsion system coupled with active control providing a solid basis for further controller development and operational testing.
Show less - Date Issued
- 2009
- PURL
- http://purl.flvc.org/FAU/228767
- Subject Headings
- Inertial navigation systems, Mobile offshore structures, Design and construction, Wave motion, Theory of, Offshore structures, Dynamics, Feedback control systems
- Format
- Document (PDF)
- Title
- A Study on Random Sum Statistics: Application to Wireless Network Performance Analysis.
- Creator
- Pattaramalai, Suwat, Aalo, Valentine A., Florida Atlantic University, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
- Abstract/Description
-
The statistics of random sum is studied and used to evaluate performance metrics in wireless networks. Pertinent wireless network performance measures such as call completion/dropping probabilities and the average number of handovers usually require the probability distributions of the cell dwell time and call holding time; and are therefore not easy to evaluate. The proposed performance evaluation technique requires the moments of the cell dwell time and is given in terms of the Laplace...
Show moreThe statistics of random sum is studied and used to evaluate performance metrics in wireless networks. Pertinent wireless network performance measures such as call completion/dropping probabilities and the average number of handovers usually require the probability distributions of the cell dwell time and call holding time; and are therefore not easy to evaluate. The proposed performance evaluation technique requires the moments of the cell dwell time and is given in terms of the Laplace transform function of the call holding time. Multimedia services that have Weibull and generalized gamma distributed call holding times are investigated. The proposed approximation method uses the compound geometric random sum distribution and requires that the geometric parameter be very small. For applications in which this parameter is not sufficiently small, a result is derived that improves the accuracy (to order of the geometric parameter) of the performance measures evaluated.
Show less - Date Issued
- 2007
- PURL
- http://purl.flvc.org/fau/fd/FA00012575
- Subject Headings
- Mobile communication systems--Technological innovations, Computer network protocols, Local area networks (Computer networks), Differentiable dynamical systems
- Format
- Document (PDF)
- Title
- Developing combinatorial multi-component therapies (CMCT) of drugs that are more specific and have fewer side effects than traditional one drug therapies.
- Creator
- Liebovitch, Larry S., Tsinoremas, Nicholas, Pandya, Abhijit S.
- Date Issued
- 2007-08-30
- PURL
- http://purl.flvc.org/fau/165790
- Subject Headings
- Drug Therapy, Biomathematics, Combinatorial dynamics, Drugs--Research, Medicine-Mathematics, Biophysics--Research, Nonlinear systems
- Format
- Document (PDF)
- Title
- Fractal methods to analyze ion channel kinetics.
- Creator
- Liebovitch, Larry S., Scheurle, Daniela, Rusek, Marian, Zochowskis, Michal
- Date Issued
- 2001-08
- PURL
- http://purl.flvc.org/FAU/165246
- Subject Headings
- Fractals, Ion Channels-Mathematical models, Ion flow dynamics, Biomathematics, Chaotic behavior in systems
- Format
- Document (PDF)