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
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Item Towards a Classification of Almost Complex and Spin^h Manifolds(2024) Mills, Keith; Rosenberg, Jonathan; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We show that all homotopy CP^ns, smooth closed manifolds with the oriented homotopy type of CP^n, admit almost complex structures for 3 ≤ n ≤ 6, and classify these structures by their Chern classes for n=4, 6. Our methods provide a new proof of a result of Libgober and Wood on the classification of almost complex structures on homotopy CP^4s. We also show that all homotopy RP^(2k+1)s admit stably almost complex structures. Spin^h manifolds are the quaternionic analogue to spin^c manifolds. At the prime 2 we compute the spin^h bordism groups by proving a structure theorem for the cohomology of the spin^h bordism spectrum MSpin^h as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting of MSpin^h as a wedge sum of familiar spectra. We also compute the decomposition of H^*(MSpin^h; Z/2Z) explicitly in degrees up through 30 via a counting process.Item CHARGE ORDER AND STRUCTURAL TRANSITION IN TOPOLOGICAL SEMIMETAL FAMILY AAL4(2023) Saraf, Prathum; Paglione, Johnpierre; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The BaAl$_4$-type structure hosts a variety of interesting and exotic properties, with descendant crystal structure resulting numerous interesting ground states of matter including magnetic, super-conducting and strongly correlated electron phenomena. BaAl$_4$ itself has recently been shown to host a non-trivial topological band structure, but is otherwise a paramagnetic metal. However, the other members of the 1-4 family, such as SrAl$_4$ and EuAl$_4$, exhibit symmetry-breaking ground states including charge density wave (CDW) and magnetic order, respectively. SrAl$_4$ hosts a second transition at 94K that is hysteretic in temperature and is a structural transition to a monoclinic structure. Here I report on the charge density wave in SrAl$_4$ and the effect of the structural transition on the physical and electronic properties of the material. The structural transition is extremely subtle with deviation of around 0.5 degrees from the tetragonal structure but shows significant changes in resistivity, Hall and magnetic susceptibility measurements. This transition is extremely sensitive to disorder and can be suppressed completely by substituting 1$\%$ Ba nominally or using less pure Sr during crystal growth. Furthermore, magnetoresistance in this material is extremely large, and can be up to 140 times at 2K. A combination of magnetoresistance and Hall measurements are used to fit the data to a two band model to extract carrier density and mobility of the charge carriers at 2K. Finally, work was done on the evolution of the charge-ordered state in high quality single crystals of the solid solution series Ba$_{1-x}$Sr$_x$Al$_4$, using transport, thermodynamic and scattering experiments to track the 243 K CDW order in SrAl$_4$ as it is suppressed with Ba substitution until its demise at x =0.5. Neutron and x-ray diffraction measurements reveal a nearly commensurate CDW state in SrAl$_4$ with ordering vector (0,0,0.097) that evolves with Ba substitution to (0,0,0.18) and (0,0,0.21) for x=0.8 and x=0.55, respectively. DFT calculations show a softening of phonons in SrAl$_4$ hinting at electron phonon coupling strength being the source of the charge order in this material. Similar calculations are done on the Ba substitutions to investigate the nature of the charge density waves. With very little change in the lattice parameters in this series, this evolution raises important questions about the nature of the electronic structure that directs a dramatic change in charge ordering.Item Topology from Quantum Dynamics of Ultracold Atoms(2023) Reid, Graham Hair; Rolston, Steven L; Spielman, Ian B; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Ultracold atoms are a versatile platform for studying quantum physics in the lab. Usingcarefully chosen external fields, these systems can be engineered to obey a wide range of effective Hamiltonians, making them an ideal system for quantum simulation experiments studying exotic forms of matter. In this work, we describe experiments using 87Rb Bose–Einstein condensates (BECs) to study exotic topological matter based on out-of-equilibrium effects. The topological states are prepared through the quantum dynamics of the ultracold atom system subjected to a highly tunable lattice potential described by the bipartite Rice–Mele (RM) model, created by combining dressing from a radiofrequency (RF) magnetic field and laser fields driving Raman transitions. We describe a form of crystal momentum-resolved quantum state tomography, which functions by diabatically changing the lattice parameters, used to reconstruct the full pseudospin quantum state. This allows us to calculate topological invariants characterizing the system. We apply these techniques to study out-of-equilibrium states of our lattice system, described by various combinations of sublattice, time-reversal and particle-hole symmetry. Afterquenching between lattice configurations, we observe the resulting time-evolution and follow the Zak phase and winding number. Depending on the symmetry configuration, the Zak phase may evolve continuously. In contrast, the winding number may jump between integer values when sublattice symmetry is transiently present in the time-evolving state. We observe a scenario where the winding number changes by ±2, yielding values that are not present in the native RM Hamiltonian. Finally, we describe a modulation protocol in which the configuration of the bipartite latticeis periodically switched, resulting in the Floquet eigenstates of the system having pseudospin-momentum locked linear dispersion, analogous to massless particles described by the Dirac equation. We modulate our lattice configuration to experimentally realize the Floquet system and quantify the drift velocity associated with the bands at zero crystal momentum. The linear dispersion of Floquet bands derives from nontrivial topology defined over the micromotion of the system, which we measure using our pseudospin quantum state tomography, in very good agreement with theory.Item Topological Data Analysis, Dimension Reduction, and Computational Efficiency(2022) Monson, Nathaniel; Czaja, Wojciech; Brosnan, Patrick; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we present a novel stability result for the persistent homology of the Rips complex associated to a point cloud. Our theorem is narrower than the classic result of Cohen-Steiner, Edelsbrunner, and Harer in that it does not apply to Cech complexes, nor to functions which are not measuring distance to a point cloud. It is broader than the classic result in that it is “local”; if a function approximately preserves distances in some range, but is contractionary below or expansionary above that range, our result still applies. The novel stability result is paired with the Johnson-Lindenstrauss Lemma to show that, with high probability, random projection approximately preserves persistent homology. An experimental analysis is given of the computational speedup granted by this dimension reduction. This is followed by some observations suggesting that even when the theoretical bound is loose enough that we have no guarantee of homology preservation, thereis still a high chance that significant features of the dataset are preserved.Item Geometric and Topological Reconstruction(2022) Rawson, Michael G.; Balan, Radu; Robinson, Michael; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The understanding of mathematical signals is responsible for the information age. Computation, communication, and storage by computers all use signals, either implicitly or explicitly, and use mathematics to manipulate those signals. Reconstruction of a particular signal can be desirable or even necessary depending on how the signal manifests and is measured. We explore how to use mathematical ideas to manipulate and represent signals. Given measurements or samples or data, we analyze how to produce, or \emph{reconstruct}, the desired signal and the fundamental limits in doing so. We focus on reconstruction through a geometric and topological lens so that we can leverage geometric and topological constraints to solve the problems. As inaccuracies and noise are present in every computation, we adopt a statistical outlook and prove results with high probability given noise. We start off with probability and statistics and then use that for active reconstruction where the probability signal needs to be estimated statistically from sampling various sources. We prove optimal ways to doing this even in the most challenging of situations. Then we discuss functional analysis and how to reconstruct sparse rank one decompositions of operators. We prove optimality of certain matrix classes, based on geometry, and compute the worst case via sampling distributions. With the mathematical tools of functional analysis, we introduce the optimal transportation problem. Then we can use the Wasserstein metric and its geometry to provably reconstruct sparse signals with added noise. We devise an algorithm to solve this optimization problem and confirm its ability on both simulated data and real data. Heavily under-sampled data can be ill-posed which is often the case with magnetic resonance imaging data. We leverage the geometry of the motion correction problem to devise an appropriate approximation with a bound. Then we implement and confirm in simulation and on real data. Topology constraints are often present in non-obvious ways but can often be detected with persistent homology. We introduce the barcode algorithm and devise a method to parallelize it to allow analyzing large datasets. We prove the parallelization speedup and use it for natural language processing. We use topology constraints to reconstruct word-sense signals. Persistent homology is dependent on the data manifold, if it exists. And it is dependent on the manifold's reach. We calculate manifold reach and prove the instability of the formulation. We introduce the combinatorial reach to generalize reach and we prove the combinatorial reach is stable. We confirm this in simulation. Unfortunately, reach and persistent homology are not an invariant of hypergraphs. We discuss hypergraphs and how they can partially reconstruct joint distributions. We define a hypergraph and prove its ability to distinguish certain joint distributions. We give an approximation and prove its convergence. Then we confirm our results in simulation and prove its usefulness on a real dataset.Item APPLYING RELIABILITY ANALYSIS TO DESIGN ELECTRIC POWER SYSTEMS FOR MORE-ELECTRIC AIRCRAFT(2014) Zhang, Baozhu; Xu, Huan; Systems Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The More-Electric Aircraft (MEA) is a type of aircraft that replaces conventional hydraulic and pneumatic systems with electrically powered components. These changes have significantly challenged the aircraft electric power system design. This thesis investigates how reliability analysis can be applied to automatically generate system topologies for the MEA electric power system. We first use a traditional method of reliability block diagrams to analyze the reliability level on different system topologies. We next propose a new methodology in which system topologies, constrained by a set reliability level, are automatically generated. The path-set method is used for analysis. Finally, we interface these sets of system topologies with control synthesis tools to automatically create correct-by-construction control logic for the electric power system.Item IMPROVING RESILIENCE OF RAIL-BASED INTERMODAL FREIGHT TRANSPORTATION SYSTEMS(2013) Zhang, Xiaodong; Miller-Hooks, Elise; Civil Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)With the increasing natural and human-made disasters, the risk of an event with potential to cause major disruption to our transportation systems and their components also increases. It is of paramount importance that transportation systems could be effectively recovered, thus economic loss due to the disasters can be minimized. This dissertation addresses the optimization problems for transportation system performance measurement, decision-making on pre-disaster preparedness and post-event recovery actions planning and scheduling to achieve the maximum network resilience level. In assessing a network's potential performance given possible future disruptions, one must recognize the contributions of the network's inherent ability to cope with disruption via its topological and operational attributes and potential actions that can be taken in the immediate aftermath of such an event. A two-stage stochastic program is formulated to solve the problem of measuring a network's maximum resilience level and simultaneously determining the optimal set of preparedness and recovery actions necessary to achieve this level under budget and level-of-service constraints. An exact methodology, employing the integer L-shaped method and Monte Carlo simulation, is proposed for its solution. In this dissertation, a nonlinear, stochastic, time-dependent integer program is proposed, from operational perspective, to schedule short-term recovery activities to maximize transportation network resilience. Two solution methods are proposed, both employing a decomposition approach to eliminate nonlinearities of the formulation. The first is an exact decomposition with branch-and-cut methodology, and the second is a hybrid genetic algorithm that evaluates each chromosome's fitness based on optimal objective values to the time-dependent maximum flow subproblem. Algorithm performance is also assessed on a test network. Finally, this dissertation studies the role of network topology in resilience. 17 specific network topologies were selected for network resilience analysis. Simple graph structures with 9~10 nodes and larger network with 100 nodes are assessed. Resilience is measured in terms of throughput and connectivity and average reciprocal distance. The integer L-shaped method is applied again to study the performance of the network structure with respect to all three resilience measures. The relationships between resilience and average degree, diameter, and cyclicity are also investigated.Item MANIPULATION OF DNA TOPOLOGY USING AN ARTIFICIAL DNA-LOOPING PROTEIN(2012) Gowetski, Daniel; Kahn, Jason D; Biochemistry; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)DNA loop formation, mediated by protein binding, plays a broad range of roles in cellular function from gene regulation to genome compaction. While DNA flexibility has been well investigated, there has been controversy in assessing the flexibility of very small loops. We have engineered a pair of artificial coiled-coil DNA looping proteins (LZD73 and LZD87), with minimal inherent flexibility, to better understand the nature of DNA behavior in loops of less than 460 bp. Ring closure experiments (DNA cyclization) were used to observe induced topological changes in DNA upon binding to and looping around the engineered proteins. The length of DNA required to form a loop in our artificially rigid system was found to be substantially longer than loops formed with natural proteins in vivo. This suggests the inherent flexibility of natural looping proteins plays a substantial role in stabilizing small loop formation. Additionally, by incrementally varying the binding site separation between 435 bp and 458 bp, it was observed that the LZD proteins could predictably manipulate the DNA topology. At the lengths evaluated, the distribution of topological products correlates to the helical repeat of the double helix (10.5 bp). The dependence on binding site periodicity is an unequivocal demonstration of DNA looping and represents the first application of a rigid artificial protein in this capacity. By constructing these DNA looping proteins, we have created a platform for addressing DNA flexibility in regards to DNA looping. Future applications for this technology include a vigorous study of the lower limits of DNA length during loop formation and the use of these proteins in assembling protein:DNA nanostructures.