Simulations

This research consists of the numerical model development and simulation of two prototype Wave Energy Convertor designs (WECs) across three simulation types. The first design is an oscillating body WEC called the Platypus designed to capture wave energy as three paddle arms actuate over the surface of the waves. The second design is an overtopping type WEC called the ROOWaC which captures and drains entrained water to generate power. Modeling of these systems was conducted using two techniques: the Morison load approach implemented using hydrodynamic response coefficients used to model the Platypus and a boundary element method (BEM) frequency-domain approach to model both WEC designs in the time domain. The BEM models included the development of hydrodynamic response coefficients using a discretized panel mesh of the system for calculation of added mass, excitation, and radiation forces. These three model families provided both performance predictions and power output information to WEC developers that supply important data for future full-scale designs. These models were used to predict power generation estimates for both WECs as follows: the Platypus WEC was predicted to have a maximum efficiency range between 14.5-35% and the ROOWaC WEC was predicted to generate a maximum peak average power of 19 W upon preliminary results.

Marine Hydrokinetic (MHK) energy is an alternative to address the demand for cleaner energy sources. This study advanced numerical modeling tools and uses these to evaluate the performance of both a Tidal Turbine (TT) and an Ocean Current Turbine (OCT) operating in a variety of conditions. Inflow models are derived with current speeds ranging from 1.5 to 3 m/s and Turbulence Intensities (TI) of 5-15% and integrated into a TT simulation. An OCT simulation representing a commercial scale 20 m diameter turbine moored to the seafloor via underwater cable is enhanced with the capability to ingest Acoustic Doppler Current Profiler (ADCP) data and simulate fault conditions. ADCP measurements collected off the coast of Ft. Lauderdale during Hurricanes Irma and Maria were post-processed and used to characterize the OCT performance. In addition, a set of common faults were integrated into the OCT model to assess the system response in fault-induced scenarios.

The purpose of online parameter learning and modeling is to validate and restore the properties of a structure based on legitimate observations. Online parameter learning assists in determining the unidentified characteristics of a structure by offering enhanced predictions of the vibration responses of the system. From the utilization of modeling, the predicted outcomes can be produced with a minimal amount of given measurements, which can be compared to the true response of the system. In this simulation study, the Kalman filter technique is used to produce sets of predictions and to infer the stiffness parameter based on noisy measurement. From this, the performance of online parameter identification can be tested with respect to different noise levels. This research is based on simulation work showcasing how effective the Kalman filtering techniques are in dealing with analytical uncertainties of data.

Mathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived. Dynamical analysis reveals the forward bifurcation in the first model. That is when the threshold value R0 < 1, disease free-equilibrium is stable locally implying that if there is small perturbation of the system, then after some time, the system will return to the disease free equilibrium. When R0 > 1 the unique endemic equilibrium is locally asymptotically stable.
For the second model, analysis of the existence and stability of equilibria reveals the existence of backward bifurcation i.e. where the disease free equilibrium coexists with the endemic equilibrium when the reproduction number R02 is less than unity. This aspect shows that in order to control vector borne disease, it is not sufficient to have reproduction number less than unity although necessary. Thus, the infection can persist in the population even if the reproduction number is less than unity. Numerical simulation is presented to see the bifurcation behaviour in the model. By taking the reproduction number as the bifurcation parameter, we find the system undergoes backward bifurcation at R02 = 1. Thus, the model has backward bifurcation and have two positive endemic equilibrium when R02 < 1 and unique positive endemic equilibrium whenever R02 > 1. Stability analysis shows that disease free equilibrium is locally asymptotically stable when R02 < 1 and unstable when R02 > 1. When R02 < 1, lower endemic equilibrium in backward bifurcation is locally unstable.

The main purpose of this dissertation is to study the inspiral and merger of binary neutron stars. The inspiral, in such a system, is caused by the loss of energy and angular momentum that is carried away by the emitted gravitational waves. Newly-formed neutron stars, after supernova explosions, are very hot. They cool down during the hundreds of millions of years, which is needed to bring the two stars in a neutron star binary close enough together to start investigating them with numerical relativity simulations. Thus, they can be considered as fluids at zero temperature to very high accuracy, when we start numerical simulations. In this description, the stars also have a well-defined star surface, beyond which there is a true vacuum. This vacuum, outside the stars, will persist until the stars get so close that mass can be ejected due to tidal forces, and later, when they come into contact and eject streams of hot matter. To date, all current numerical relativity programs use an artificial atmosphere from the very beginning. They do this, to avoid numerical problems arising from the sharp transition of the matter region to the vacuum outside the stars. To be more precise, they take the initial data and fill all the vacuum regions with a very low-density zero velocity atmosphere. While this atmosphere is not physical and used only for numerical reasons, it can still influence the results of the simulations. For example, studies of merger dynamics, merger remnant, disk mass, ejecta mass, and kinetic energy of ejecta, are hampered by the presence of the artificial zero velocity low-density material. To avoid this problem, we have developed a new method to evolve the neutron star systems, without the need for an artificial atmosphere. We describe this method, which we call vacuum method, we present tests with it, and compare it to the conventional atmosphere method. For these tests, we first consider the evolution of stable, oscillating, and collapsing single neutron stars. We also study simulations of the inspiral and merger of binaries using both methods. We find better mass conservation in low-density regions and near refinement boundaries, as well as better ejecta material conservation for the new method. However, the gravitational wave predictions produced by our simulations are almost identical for both methods, since they are mainly due to the bulk motion of the stars which is not strongly affected by the presence or absence of an artificial atmosphere.

In finance, various stochastic models have been used to describe the price movements of financial instruments. After Merton's [38] seminal work, several jump diffusion models for option pricing and risk management have been proposed. In this dissertation, we add alpha-stable Levy motion to the process related to dynamics of log-returns in the Black-Scholes model where the volatility is assumed to be constant. We use the sample characteristic function approach in order to study parameter estimation for discretely observed stochastic differential equations driven by Levy noises. We also discuss the consistency and asymptotic properties of the proposed estimators. Simulation results of the model are also presented to show the validity of the estimators. We then propose a new model where the volatility is not a constant. We consider generalized alpha-stable geometric Levy processes where the stochastic volatility follows the Cox-Ingersoll-Ross (CIR) model in Cox et al. [9]. A number of methods have been proposed for estimating parameters for stable laws. However, a complication arises in estimation of the parameters in our model because of the presence of the unobservable stochastic volatility. To combat this complication we use the sample characteristic function method proposed by Press [48] and the conditional least squares method as mentioned in Overbeck and Ryden [47] to estimate all the parameters. We then discuss the consistency and asymptotic properties of the proposed estimators and establish a Central Limit Theorem. We perform simulations to assess the validity of the estimators. We also present several tables to show the comparison of estimators using different choices of arguments ui's. We conclude that all the estimators converge as expected regardless of the choice of ui's.

This thesis presents a preliminary study on geochemical conditions within the Snapper Creek well field in Miami-Dade County, Florida. The study investigates the background groundwater chemistry within the Biscayne aquifer in order to provide information on the geochemical processes and water-rock interactions within the study site. In conjunction with hydraulic gradient information, major ion chemistry and deuterium and oxygen-18 data were used as environmental tracers to help describe the groundwater-surface water interactions between the well field and the Snapper Creek canal. Hydrologic data show there is potential for natural groundwater recharge from the canal within the shallow flow zone of the Biscayne aquifer and chemical data show evidence of canal-groundwater mixing within this zone. The limitations for the v environmental tracers employed within the study are addressed, as well as recommendations for further research involving natural geochemical tracers and groundwater-surface water interactions near municipal well fields. This study was part of a larger effort being conducted by the U.S. Geological Survey in order to assess municipal well field pumping effects on the Snapper Creek (C-2) canal.