UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
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 given thesis/dissertation in DRUM.
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Item Influence of Noise on Response Localizations in Mechanical Oscillator Arrays(2022) Cilenti, Lautaro Daniel; Balachandran, Balakumar; Cameron, Maria; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The dynamics of mechanical systems such as turbomachinery and vibration energy harvesting systems (VEH) consisting of one or multiple cantilever structures is often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibration steady states. Some of these steady states are localized vibrations that are characterized by high amplitude vibrations of a subset of the system, with the rest of the system being in a state of either low amplitude vibrations or no vibrations. On one hand, these localized vibrations can be detrimental to mechanical integrity of turbomachinery, while on the other hand, the vibrations can be potentially desirable for increasing energy yield in VEHs. Transitions into or out of localized vibrations may occur under the influence of random factors. A combination of experimental and numerical studies has been performed in this dissertation to study the associated transition times and probability of transitions in these mechanical systems. The developments reported here include the following: (i) a numerical methodology based on the Path Integral Method to quantify the probability of transitions due to noise, (ii) a numerical methodology based on the Action Plot Method to quantify the quasipotential and most probable transition paths in nonlinear systems with periodic external excitations, and (iii) experimental evidence and stochastic simulations of the influence of noise on response localizations of rotating macro-scale cantilever structures. The methodology and results discussed in this dissertation provide insights relevant to the stochastic nonlinear dynamics community, and more broadly, designers of mechanical systems to avoid potentially undesirable stochastic nonlinear behavior.Item Asymptotic problems for stochastic partial differential equations(2015) Salins, Michael; Cerrai, Sandra; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an $L^p$ sense. This strengthens previous results where convergence was proved in probability.Item Mechanism and Chance: Toward an Account of Stochastic Mechanism for the Life Sciences(2014) DesAutels, Lane Thomas; Darden, Lindley; Philosophy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, my aim is to develop some important new resources for explaining probabilistic phenomena in the life sciences. In short, I undertake to articulate and defend a novel account of stochastic mechanism for grounding probabilistic generalizations in the life sciences. To do this, I first offer some brief remarks on the concept of mechanism in the history of philosophical thought. I then lay out some examples of probabilistic phenomena in biology for which an account of stochastic mechanism seems explanatorily necessary and useful: synaptic transmission in the brain, protein synthesis, DNA replication, evolution by natural selection, and Mendelian inheritance. Next, I carefully examine the concept of regularity as it applies to mechanisms--building on a recent taxonomy of the ways mechanisms may (or may not) be thought to behave regularly. I then employ this taxonomy to sort out a recent debate in the philosophy of biology: is natural selection regular enough to count as a mechanism? I argue that, by paying attention to the forgoing taxonomy, natural selection can be seen to meet the regularity requirement just fine. I then turn my attention to the question of how we should understand the chance we ascribe to stochastic mechanisms. To do this, I form a list of desiderata that any account of stochastic mechanism must meet. I then explore how mechanisms fit with several of the going philosophical accounts of chance: subjectivism, frequentism (both actual and hypothetical), Lewisian best-systems, and propensity. I argue that neither subjectivism, frequentism, nor best-system-style accounts of chance will meet all of the proposed desiderata, but some version of propensity theory can. Borrowing from recent propensity accounts of biological fitness and drift, I then go on to explore the prospects for developing a propensity interpretation of stochastic mechanism (PrISM) according to which propensities are (i) metaphysically analyzable and operationally quantifiable via a function of probability-weighted ways a mechanism might fire and (ii) not causally efficacious but nonetheless explanatorily useful. By appealing to recent analyses of deterministic and emergent chance, I argue further that this analysis need not be vulnerable to the threat of metaphysical determinism.Item Scheduling under uncertainty for a Single-Hub Intermodal Freight System(2010) Markovic, Nikola; Schonfeld, Paul; Civil Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis addresses the optimization of an intermodal system with freight transfers at a single hub. It investigates the transportation processes and constraints that arise in a system's recovery after a major disruption during which backlogs have accumulated along the routes. When dealing with the backlogs, the system operator must coordinate the transportation processes and control the inflow of freight to the terminal in order to avoid overloading its storage facilities, which might reduce the throughput of the system. The coordination of transportation processes during the system's recovery can further improve the overall system performance by reducing the dwell time, increasing vehicle utilization and reducing late delivery penalties. This work focuses on the scheduling problem and develops an approach that would help the system operator reduce the overall system cost while taking into account the constraints arising in actual intermodal and intra-modal systems. Assuming that the schedule on some routes is exogenously determined and inflexible, we seek to optimize the schedules of vehicles on remaining routes. Models are developed that minimize the total cost of operating an intermodal system with freight transfers at one hub by optimizing the departure times of vehicles on the routes with flexible schedules. This model can be solved numerically without the approximations of alternative methods such as simulation. Moreover, it can be successfully applied to situations when statistical or queuing analyses are not applicable due to the small number of events (vehicle arrivals). We specifically analyze an intermodal system consisting of multiple feeder truck routes and multiple main airline routes. The specific example of two transportation modes was used to make the development and application of the model easier to understand. However, the mathematical model developed in this thesis is applicable to any other combination of transportation modes using discrete vehicles.Item Application of Stochastic Reliability Modeling to Waterfall and Feature Driven Development Software Development Lifecycles(2011) Johnson, David Michael; Modarres, Mohammed; Smidts, Carol S; Reliability Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)There are many techniques for performing software reliability modeling. In the environment of software development some models use the stochastic nature of fault introduction and fault removal to predict reliability. This thesis research analyzes a stochastic approach to software reliability modeling and its performance on two distinct software development lifecycles. The derivation of the model is applied to each lifecycle. Contrasts between the lifecycles are shown. Actual data collected from industry projects illustrate the performance of the model to the lifecycle. Actual software development fault data is used in select phases of each lifecycle for comparisons with the model predicted fault data. Various enhancements to the model are presented and evaluated, including optimization of the parameters based on partial observations.