Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item How Far Does the Grid Go?(2019) Pantelis, Irene Noemi; Richardson, William C; Art; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)My artwork probes the connection between daily life and what I perceive as the larger grid out there—a mesh that entangles all peoples, beings and things, cuts across all time, and is always in flux. Drawing from my everyday life and experiences as a Latin American immigrant, I incorporate materials from my suburban home environment in my multidisciplinary approach. I create organic forms and grids that abstract, excavate, ground and find universal truths in the quotidian. They also serve as platforms for engaging obliquely with history, science, archeology, philosophy, and magic realism. My artwork invites viewers to reach interpretations based on their own associations, experiences, and feelings. It thus brings attention to the power of our imagination to infuse the material world, particularly nature, with fluid possibilities of meaning and subjectivity.Item DATA-DRIVEN STUDIES OF TRANSIENT EVENTS AND APERIODIC MOTIONS(2019) Wang, Rui; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The era of big data, high-performance computing, and machine learning has witnessed a paradigm shift from physics-based modeling to data-driven modeling across many scientific fields. In this dissertation work, transient events and aperiodic motions of complex nonlinear dynamical system are studied with the aid of a data- driven modeling approach. The goal of the work has been to further the ability for future behavior prediction, state estimation, and control of related behaviors. It is shown that data on extreme waves can be used to carry out stability analysis and ascertain the nature of the transient phenomenon. In addition, it is demonstrated that a low number of soliton elements can be used to realize a rogue wave on the basis of nonlinear interactions amongst the basic elements. The pro- posed nonlinear phase interference model provides an appealing explanation for the formation of ocean extreme wave and related statistics, and a superior reconstruction of the Draupner wave event than that obtained on the basis of linear superposition. Chaotic data, another manifestation of aperiodic motions, which are obtained from prototypical ordinary differential and partial differential systems are considered and a neural machine is realized to predict the corresponding responses based on a limited training set as well to forecast the system behavior. A specific neural architecture, called the inhibitor mechanism, has been designed to enable chaotic time series forecasting. Without this mechanism, even the short-term predictions would be intractable. Both autonomous and non-autonomous dynamical systems have been studied to demonstrate the long-term forecasting possibilities with the de- veloped neural machine. For each dynamical system considered in this dissertation, a long forecasting horizon is achieved with a short historical data set. Furthermore, with the developed neural machine, one can relax the requirement of continuous historical data measurements, thus, providing for a more pragmatic approach than the previous approaches available in the literature. It is expected that the efforts of this dissertation work will lead to a better understanding of the underlying mechanism of transient and aperiodic events in complex systems and useful techniques for forecasting their future occurrences.Item Quasiperiodicity and Chaos(2015) Das, Suddhasattwa; Yorke, James A; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this work, we investigate a property called ``multi-chaos'' is which a chaotic set has densely many hyperbolic periodic points of unstable dimension $k$ embedded in it, for at least 2 different values of $k$. We construct a family of maps on the torus having this property. They serve as a paradigm for multi-chaos occurring in higher dimensional systems. One of the factors that leads to this strong form of chaos is the occurrence of a quasiperiodic orbit transverse to an expanding sub-bundle of the tangent bundle. Hence, a key step towards identifying multi-chaos numerically is finding quasiperiodic orbits in high dimensional systems. To analyze quasiperiodic orbits, we develop a method of weighted ergodic averages and prove that these averages have super-polynomial convergence to the Birkhoff average. We also show how this accelerated convergence of the ergodic averages over quasiperiodic trajectories enable us to compute the rotation number, Fourier series and Lyapunov exponents of quasiperiodic orbits with a high degree of precision ($\approx 10^{-30}$).Item ROBUSTNESS OF ATTRACTING ORBITS(2014) Joglekar, Madhura R.; Yorke, James A; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Understanding the transition to turbulence is a long-lasting problem in fluid dynamics, particularly in the case of simple flows in which the base laminar flow does not become linearly unstable. For flows at a low Reynolds number, all initial conditions decay to the laminar profile. At higher Reynolds numbers, above a critical value, turbulence is observed, often in the form of a chaotic saddle. The magnitude of the perturbation that disrupts the laminar flow into the turbulent region depends on the Reynolds number and on the direction of the perturbation. In Chapter 2, we investigate the robustness of the laminar attractor to perturbations in a 9-dimensional sinusoidal shear flow model. We examine the geometry of the `edge of chaos', where the edge denotes the boundary of the chaotic saddle, which is embedded in the basin of attraction of the laminar state, and is accessible from that state. For a smooth dynamical system $x_{n+1} = F(C, x_n)$ (depending on a parameter C), there may be infinitely many periodic windows, that is, intervals in C having a region of stable periodic behavior. However, the smaller of these windows are easily destroyed with tiny perturbations, so that only finitely many of the windows can be detected for a given level of noise. For a fixed perturbation size $\epsilon$, we consider the system behavior in the presence of noise. In this Chapter, we look at the ``$\epsilon$-robust windows'', that is, those periodic windows such that for the superstable parameter value C in that window, the general periodic behavior persists despite noise of amplitude $\le \epsilon$. We focus on the quadratic map, and numerically compute the number of periodic windows that are $\epsilon$-robust. In Chapter 3, we obtain a robustness-exponent $\alpha \approx .51 \pm .03$, which characterizes the robustness of periodic windows in the presence of noise. The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$ can convert an attractor from chaotic to non-chaotic or vice-versa. We call a parameter value where this can happen $\epsilon$-uncertain. The probability that a random choice of the parameter is $\epsilon$-uncertain commonly scales like a power law in $\epsilon$. Surprisingly, two seemingly similar ways of defining this scaling, both of physical interest, yield different numerical values for the scaling exponent. In Chapter 4, we show why this happens and present a quantitative analysis of this phenomenon. Many dynamical systems reach a level of maximum topological entropy as the system parameter is increased followed by a decrease to zero entropy. In Chapter 5, we give an example such that the number of cascades continues to increase for arbitrarily large values of the parameter. We investigate the map $S_{\mu}:[0,1] \rightarrow [0,1)$ defined by $S_{\mu}(x) := \mu \sin(2\pi x) \bmod{1}.$ For this map, the entropy increases without bound as $\mu \rightarrow \infty$, and the system has an ever-increasing number of solitary cascades for $\mu \in [0,m]$ as $m$ is increased to higher and higher integer values. Specifically, we calculate the number of period-$k$ cascades of the map, for $k>1$, for positive integer values of $\mu \in [0,m]$, where $m \in \mathbb{N}$.Item Scattering from chaotic cavities: Exploring the random coupling model in the time and frequency domains(2009) Hart, James Aamodt; Ott, Edward; Antonsen, Thomas M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Scattering waves off resonant structures, with the waves coupling into and out of the structure at a finite number of locations (`ports'), is an extremely common problem both in theory and in real-world applications. In practice, solving for the scattering properties of a particular complex structure is extremely difficult and, in real-world applications, often impractical. In particular, if the wavelength of the incident wave is short compared to the structure size, and the dynamics of the ray trajectories within the scattering region are chaotic, the scattering properties of the cavity will be extremely sensitive to small perturbations. Thus, mathematical models have been developed which attempt to determine the statistical, rather than specific, properties of such systems. One such model is the Random Coupling Model. The Random Coupling Model was developed primarily in the frequency domain. In the first part of this dissertation, we explore the implications of the Random Coupling Model in the time domain, with emphasis on the time-domain behavior of the power radiated from a single-port lossless cavity after the cavity has been excited by a short initial external pulse. In particular, we find that for times much larger than the cavity's Heisenberg time (the inverse of the average spacing between cavity resonant frequencies), the power from a single cavity decays as a power law in time, following the decay rate of the ensemble average, but eventually transitions into an exponential decay as a single mode in the cavity dominates the decay. We find that this transition from power-law to exponential decay depends only on the shape of the incident pulse and a normalized time. In the second part of this dissertation, we extend the Random Coupling Model to include a broader range of situations. Previously, the Random Coupling Model applied only to ensembles of scattering data obtained over a sufficiently large spread in frequency or sufficiently different ensemble of configurations. We find that by using the Poisson Kernel, it is possible to obtain meaningful results applicable to situations which vary much less radically in configuration and frequency. We find that it is possible to obtain universal statistics by redefining the radiation impedance parameter of the previously developed Random Coupling Model to include the average effects of certain classical trajectories within the resonant structure. We test these results numerically and find good agreement between theory and simulation.Item Transport in Poygonal Billiard Systems(2009) Reames, Matthew Lee; Dorfman, J. R.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The aim of this work is to explore the connections between chaos and diffusion by examining the properties of particle motion in non-chaotic systems. To this end, particle transport and diffusion are studied for point particles moving in systems with fixed polygonal scatterers of four types: (i) a periodic lattice containing many-sided polygonal scatterers; (ii) a periodic lattice containing few-sided polygonal scatterers; (iii) a periodic lattice containing randomly oriented polygonal scatterers; and (iv) a periodic lattice containing polygonal scatterers with irrational angles. The motion of a point particle in each of these system is non-chaotic, with Lyapunov exponents strictly equal to zero.Item Role of feed protocol in achieving chaotic mixing of highly filled flow systems during filling the empty cavity(2006-03-27) Huang, Yue; Bigio, David I; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Chaotic mixing of highly filled viscous fluids is desired but hardly achieved in the electronic packaging industries. The demand for high reliability found in electronic package attracts more and more researchers to study the properties and distribution of binders and filler particles. These will affect properties such as coefficient of thermal expansion and stiffness. Both of these contribute strongly to reliability. The filler concentration, size distribution and spatial distribution must be examined in a structured manner to understand their effects on final properties. However, most studies deal with filler concentration and size distribution, while very few studies have tied the particle spatial distribution to the properties. It is not enough to just properly control the filler concentration and size distribution. The more uniform filler distribution, the more uniform are local properties, and this can be achieved by well-designed mixing processes. Mixing is very important and in many cases the goodness of the mixing of fillers will affect or determine the properties of the products. In this thesis, the local properties of electronic package and their relations with filler particle distribution are quantified. For the first time, a new feed protocol that can generate chaotic mixing during filling cavity by implementing periodic and aperiodic filling process is presented. Instead of using single gate in the molding process, we have developed a two-gate feeding protocol. A numerical simulation experiment is conducted on a 2-D square cavity to examine the mixing of polymer fluid in low Reynolds number flows. Since there are a vast number of geometries in electronic packages, only cavities with 46 and 49 bumps, which can be treated as solder balls or leadframe, is investigated. Periodic and aperiodic feed protocols resulted in exponential growth of the distance between two adjacent particles, an indication of chaotic mixing. Entropic study shows that the global mixing has been improved 858% compared to single gate feeding. The improved properties and reliability could be foreseen in electronic package.Item Private Communications with Chaotic Code Division Multiple Access: Performance Analysis and System Design(2004-08-04) Hwang, Yeong-Sun; Papadopoulos, Haralabos C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation we develop a class of pseudochaotic direct-sequence code division multiple access (DS/CDMA) systems that can provide private and reliable communication over wireless channels. These systems exploit the sensitive dependence of chaotic sequences on initial conditions together with the presence of channel noise to provide a substantial gap between the bit error probabilities achievable by intended and unintended receivers. We illustrate how a desired level of private communication can be achieved with a systematic selection of the system parameters. This type of privacy can be readily combined with traditional encryption methods to further ensure the protection of information against eavesdroppers. The systems we propose employ linear modulation of each user's symbol stream on a spreading sequence generated by iterating a distinct initial condition through a pseudochaotic map. We evaluate and compare the uncoded probability of error (Pr(e)) achievable by intended receivers that know the initial condition used to generate the spreading sequence to the associated Pr(e) of unintended receivers that know the modulation scheme but not the initial condition. We identify the map attributes that affect privacy, and construct algorithmic design methods for generating pseudochaotic spreading sequences that successively and substantially degrade the unintended user performance, while yielding intended user performance similar to that of conventional DS/CDMA systems. We develop efficient metrics for quantifying the unintended receiver Pr(e) and prove that it decays at a constant rate of 1/sqrt(SNR) in AWGN and fading channels. In addition, we show that this decaying rate is independent of the available degrees of diversity in fading channels, showing in the process that only intended receivers can harvest the available diversity benefits. Moreover, we illustrate that the pseudochaotic DS/CDMA systems can provide reliable multiuser communication that is inherently resilient to eavesdropping, even in the worst-case scenarios where all receivers in a network except the intended one collude to better eavesdrop on the targeted transmission. We also develop optimized digital implementation methods for generating practical pseudochaotic spreading sequences that preserve the privacy characteristics associated with the underlying chaotic spreading sequences.