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 Dispersion Properties of Transport Equations and Applications(2020) Lin, Hsin-Yi; Jabin, Pierre-Emmanuel; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The concept of transport is fundamental and has great influence in a wide range of fields across science. This dissertation provides three topics possessing the character of transport phenomena from the perspective of partial differential equations. The three parts include: (1) Commutator method for averaging lemma: A new commutator method is introduced to prove a new type of averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. This novel approach shows a new range of assumptions that are sufficient for the velocity average to be in $L^2([0,T],H^{1/2}_x)$ and improves the regularity result for the measure-valued solutions of scalar conservation laws in space one-dimensional case. (2) Unmixing property of incompressible flows on 2d tori: The local Hamiltonian structure of a 2d torus is utilized to show that the unmixing property of incompressible flows can be preserved under a sup-norm perturbation on stream functions. With this perturbation result, a quantitative statement was provided by considering vector fields in the form of a random Fourier series. This statement offers an interesting observation for the unmixing property from the perspective of Fourier analysis. (3) Memory effect on animal migration: The goal of this work is to obtain a better understanding of the memory effect on the animals' migration patterns under periodic environments. A memory model and a corresponding memory-driven dynamic were constructed. Through simulations, it is discovered that in order to have periodic movement, the individual must be able to gather and carry sufficient information from both short-term memory and long-term memory, and possess the ability to discriminate which information is more important with appropriate time scales. Furthermore, our mathematical model is general and can be used to test the memory effect under different circumstances. Several interesting examples are demonstrated.Item Consistency of Spectral Clustering with Functional Magnetic Resonance Image Data(2018) Moon, Jessie; Slud, Eric; Chen, Shuo; Mathematical Statistics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Functional magnetic resonance imaging (fMRI) is a non-invasive technique for studying brain activity. It uses the amount of blood flowing through a brain, referred to as the blood oxygenation level dependent (BOLD) signal. However analyzing the fMRI signals is challenging because of its complicated spatio-temporal correlation structure and its massive amount of data. There are several brain atlases available but researchers observe that fMRI signals are not coherent even within the same area in a brain atlas. Therefore providing parcellation of a brain, especially based on its functional connectivity, is necessary to understand brain activities. One of the techniques that are used for a brain parcellation is spectral clustering. It is a well-used technique in many areas of studies, such as physics and engineering. However, its asymptotic behavior, whether spectral clustering will produce consistent clustering as samples grow large, is not fully clarified. In addition, there has previously been no available mathematical justification of the large-sample properties of spectral clustering when the data are dependent. Von Luxburg et al. (2008) showed the consistency of eigenfunctions of spectral clustering under the assumption that data are independent and identically distributed. Because fMRI signals are spatially dependent, applying her results to fMRI data analysis is not appropriate. In this thesis, we extend von Luxburg's work to 3-dimensional spatially dependent data satisfying strong mixing conditions, which will be the case for fMRI data. We applied the spectral clustering algorithm to simulated data to see how the algorithm can be affected by perturbation in a similarity matrix. There are two simulated data experiments. The first type of simulated data is similar to the stochastic block model, and the second is sampled independently from a Gaussian random field distribution with correlation. We applied spectral clustering to various regions of interest (ROIs) both for a single subject and for multiple subjects. We also provided methods to analyze data from multiple subjects using spectral clustering and compared these methods using several criteria.Item Experimental Modeling of Twin-Screw Extrusion Processes to Predict Properties of Extruded Composites(2016) Dryer, Benjamin; Bigio, David I; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Twin-screw extrusion is used to compound fillers into a polymer matrix in order to improve the properties of the final product. The resultant properties of the composite are determined by the operating conditions used during extrusion processing. Changes in the operating conditions affect the physics of the melt flow, inducing unique composite properties. In the following work, the Residence Stress Distribution methodology has been applied to model both the stress behavior and the property response of a twin-screw compounding process as a function of the operating conditions. The compounding of a pigment into a polymer melt has been investigated to determine the effect of stress on the degree of mixing, which will affect the properties of the composite. In addition, the pharmaceutical properties resulting from the compounding of an active pharmaceutical ingredient are modeled as a function of the operating conditions, indicating the physical behavior inducing the property responses.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 INVESTIGATION OF FUEL-AIR MIXING IN A MICRO-FLAMEHOLDER FOR MICRO-POWER AND SCRAMJET APPLICATIONS(2005-09-26) Dellimore, Kiran Hamilton; Cadou, Christopher P; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis presents a first principles model of the fuel-air mixing process in a micro-flameholder. This model is used to identify key design parameters involved in fuel-air mixing and to characterize how mixing performance scales with the Reynolds number. The results of this analysis show that fuel-air mixing in micro-flameholders occurs primarily at low Reynolds numbers (1<Re<5x103) traditionally associated with the laminar to transitional flow regime. Mixing lengths in micro-flameholders based solely on molecular diffusion are also predicted using a modified Burke-Schumann model. The predicted mixing lengths indicate that less distance is required for fuel-air mixing as micro-flameholders get smaller. Axisymmetric CFD simulations are performed to validate the predictions of the Burke-Schumann model, and to investigate the importance of axial diffusion and viscous effects. The results of these simulations suggest that viscous shear at the wall and at the fuel-air interface can significantly impact mixing lengths in micro-flameholders.Item PASSIVE SCALAR DISPERSION IN A TURBULENT MIXING LAYER(2004-08-23) Li, Ning; Wallace, James M; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Experimental and numerical studies of spatially developed turbulent mixing layers with passive scalar concentrations was performed. In the experiment, a mixing layer was created by an S-shaped splitter plate in a wind tunnel, with a velocity ratio of 2:1. A concentration field was realized by injecting incense smoke into the high-speed side of the mixing layer. Simultaneous measurements of the velocity, vorticity and concentration fields were performed. A 12-sensor hot-wire probe was used to measure the velocity field and its gradients, while the concentration field was recorded by taking digital pictures of the laser-illuminated smoke. The statistics of the velocity and vorticity fields agree well with previous research. By synchronizing the velocity and concentration measurements, concentration fluxes were determined. Octant analysis was performed on the flux data to explore the scalar transport processes. Conditional planar average of flow properties was also performed to determine their spatial distribution with respect to the large-scale vortices. A large-eddy simulation, designed to match the experimental conditions, was performed to provide three-dimensional pictures of the mixing layer. A new approach to effectively specify the inflow boundary condition was proposed. Passive particles were released and tracked to simulate the scalar concentration field. Numerical interpolation schemes were examined for performing the particle tracking tasks. The simulation statistically supported the experimental result while providing insight about the flow topology, from which scalar transport models by the rib vortices and roller vortices were proposed and examined.