Mathematical models

On August 5, 2010 the U.S. Department of Energy (DOE) has designated the Center for Ocean Energy Technology (COET) at Florida Atlantic University (FAU) as a national center for ocean energy research and development. Their focus is the research and development of open-ocean current systems and associated infrastructure needed to development and testing prototypes. The generation of power is achieved by using a specialized electric generator with a rotor called a turbine. As with all machines, the turbines will need maintenance and replacement as they near the end of their lifecycle. This prognostic health monitoring (PHM) requires data to be collected, stored, and analyzed in order to maximize the lifespan, reduce downtime and predict when failure is eminent. This thesis explores the use of a data gateway which will separate high level software with low level hardware including sensors and actuators. The gateway will v standardize and store the data collected from various sensors with different speeds, formats, and interfaces allowing an easy and uniform transition to a database system for analysis.

On August 5, 2010 the U.S. Department of Energy (DOE) has designated the Center for Ocean Energy Technology (COET) at Florida Atlantic University (FAU) as a national center for ocean energy research and development of prototypes for open-ocean power generation. Maintenance on ocean-based machinery can be very costly. To avoid unnecessary maintenance it is necessary to monitor the condition of each machine in order to predict problems. This kind of prognostic health monitoring (PHM) requires a condition-based maintenance (CBM) system that supports diagnostic and prognostic analysis of large amounts of data. Research in this field led to the creation of ISO13374 and the development of a standard open-architecture for machine condition monitoring. This thesis explores an implementation of such a system for ocean-based machinery using this framework and current open-standard technologies.

Fads models for stocks under asymmetric information in a purely continuous(GBM) market were first studied by P. Guasoni (2006), where optimal portfolios and maximum expected logarithmic utilities, including asymptotic utilities for the informed and uninformed investors, were presented. We generalized this theory to Lâevy markets, where stock prices and the process modeling the fads are allowed to include a jump component, in addition to the usual continuous component. We employ the methods of stochastic calculus and optimization to obtain analogous results to those obtained in the purely continuous market. We approximate optimal portfolios and utilities using the instantaneous centralized and quasi-centralized moments of the stocks percentage returns. We also link the random portfolios of the investors, under asymmetric information to the purely deterministic optimal portfolio, under symmetric information.

As computing technology continues to advance, it has become increasingly difficult to find businesses that do not rely, at least in part, upon the collection and analysis of data for the purpose of project management and process improvement. The cost of software tends to increase over time due to its complexity and the cost of employing humans to develop, maintain, and evolve it. To help control the costs, organizations often seek to improve the process by which software systems are developed and evolved. Improvements can be realized by discovering previously unknown or hidden relationships between the artifacts generated as a result of developing a software system. The objective of the work described in this thesis is to provide a visualization tool that helps managers and engineers better plan for future projects by discovering new knowledge gained by synthesizing and visualizing data mined from software repository records from previous projects.

With congestion, environmental Impact, and the price of oil becoming topics that influence businesses and individuals in a daily basis, measures need to be undertaken in order to accommodate the growing demand for freight transportation. By directing many of the trucks travelling along the National Highways Systems to the Marine Highway corridors developed by the U.S. Maritime Administrations, many of the problems can be addressed in the Short and Medium terms. In order to do so, Short Sea Shipping, through the use of Ro/Ro (Roll-on/Roll-off) Vessels, needs to be implemented. Although the environmental and congestion reducing benefits are considerable, the profitability of this transportation mode needs to be considered. A cost benefit analysis can determine the margin of profit, and attract investors and businesses. By developing a mathematical model that accounts the costs associated with transporting trucks along a particular corridor, the competitiveness of Short Sea Shipping can be determined.

Wireless devices in wireless networks are powered typically by small batteries that are not replaceable nor recharged in a convenient way. To prolong the operating lifetime of networks, energy efficiency is indicated as a critical issue and energy-efficient resource allocation designs have been extensively developed. We investigated energy-efficient schemes that prolong network operating lifetime in wireless sensor networks and in wireless relay networks. In Chapter 2, the energy-efficient resource allocation that minimizes a general cost function of average user powers for small- or medium-scale wireless sensor networks, where the simple time-division multiple-access (TDMA) is adopted as the multiple access scheme. A class of Ç-fair cost-functions is derived to balance the tradeoff between efficiency and fairness in energy-efficient designs. Based on such cost functions, optimal channel-adaptive resource allocation schemes are developed for both single-hop and multi-hop TDMA sensor networks. In Chapter 3, optimal power control methods to balance the tradeoff between energy efficiency and fairness for wireless cooperative networks are developed. It is important to maximize power efficiency by minimizing power consumption for a given quality of service, such as the data rate; it is also equally important to evenly or fairly distribute power consumption to all nodes to maximize the network life. The optimal power control policy proposed is derived in a quasi-closed form by solving a convex optimization problem with a properly chosen cost-function. To further optimize a wireless relay network performance, an orthogonal frequency division multiplexing (OFDM) based multi-user wireless relay network is considered in Chapter 4.

Core-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of the prime sources of gravitational waves for interferometric detectors. Gravitational waves can give us access to the electromagnetically hidden compact inner core of supernovae. They will provide valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. Detection of GW signals and analysis of the observations will require realistic signal predi ctions from the non-parameterized relativistic numerical simulations of CCSN. This dissertation presents the gravitational wave signature of core-collapse v supernovae. Previous studies have considered either parametric models or nonexploding models of CCSN. This work presents complete waveforms, through the explosion phase, based on first-principles models for the first time. We performed 2D simulations of CCSN using the CHIMERA code for 12, 15, and 25M non-rotating progenitors. CHIMERA incorporates most of the criteria for realistic core-collapse modeling, such as multi-frequency neutrino transport coupled with relativistic hydrodynamics, eective GR potential, nuclear reaction network, and an industry-standard equation of state.

The synchronization of coupled semiconductor lasers with delay is investigated by numerical simulations of the nonlinear dynamic models complemented by a stability analysis of the linearized system. The equations used in the dissertation are based on the well known "Lang-Kobayashi" model modified to include unidirectional and bidirectional coupling. Stability diagrams are calculated and supplemented by numerically integrated time series. Synchronization is determined and quantified by computing the cross-correlation function. It is found that synchronized states are achievable for a wide range of coupling constants and delay times. These findings have implications for experiment and technological applications, notably in cryptography.

A magnetometer with a sensitivity of 0.01nT will be towed through the thermocline by a 2.87 meter long, 0.533 meter diameter autonomous underwater vehicle (AUV) to measure the magnetic fluctuations generated by oceanic internal waves. At this point, no research has been found that suggests towed magnetometer measurements have been done using an AUV. Simulations of the AUV, tow cable, and towfish are performed to provide an understanding of the effects of changing different input parameters, such as towing speed (0.5-2m/s), cable length (5-15m), vehicle trajectory (circle and vertical zig zag maneuvers), and current (0.25-1.25m/s). The AUV-cabletowfish system and equations of motion needed for the simulations are described herein. Results show that a 5m tow cable provides better towfish maneuvering than the longer cable lengths. High towfish pitch angle is decreased by decreasing the distance between CG and CB. Surface currents speed of 0.25m/s change the AUV and towfish circle maneuver to a spiral trajectory, while 1.25m/s current speed cause a zig zag trajectory.

Contemporary computer vision solutions to the problem of object detection aim at incorporating contextual information into the process. This thesis proposes a systematic evaluation of the usefulness of incorporating knowledge about the geometric context of a scene into a baseline object detection algorithm based on local features. This research extends publicly available MATLABRª implementations of leading algorithms in the field and integrates them in a coherent and extensible way. Experiments are presented to compare the performance and accuracy between baseline and context-based detectors, using images from the recently published SUN09 dataset. Experimental results demonstrate that adding contextual information about the geometry of the scene improves the detector performance over the baseline case in 50% of the tested cases.