Studying the effects of free stream turbulence on noise, vibration, and heat transfer on structures is very important in engineering applications. The problem of the interaction of large scale turbulence with a flat-plate cascade is a model of important problems in propulsion systems. Addressing the problem of large scale turbulence interacting with a flat plate cascade requires flow simulation over a large number of plates (6-12 plates) in order to be able to represent numerically integral length scales on the order of blade-to-blade spacing. Having such a large number of solid surfaces in the simulation requires very large computational grid points to resolve the boundary layers on the plates, and that is not possible with the current computing resources. In this thesis we develop a computational technique to predict the distortion of homogeneous isotropic turbulence as it passes through a cascade of thin flat plates. We use Large-Eddy Simulation (LES) to capture the spatial development of the incident turbulence and its interaction with the plates which are assumed to be inviscid walls. The LES is conducted for a linear cascade composed of six plates. Because suppression of the normal component of velocity is the main mechanism of distortion, we neglect the presence of mean shear in the boundary layers and wakes, and allow slip velocity on the plate surfaces. We enforce the zero normal velocity condition on the plates. This boundary condition treatment is motivated by rapid distortion theory (RDT) in which viscous effects are neglected, however, the present LES approach accounts for nonlinear and turbulence diffusion effects by a sub-grid scale model. We refer to this type of turbulence-blade interaction as shear-free interaction. To validate our calculations, we computed the unsteady loading and radiated acoustic pressure field from flat plates interacting with vortical structures. We consider two fundamental problems: (1) A linear cascade of flat plates excited by a vortical wave (gust) given by a 2D Fourier mode, and (2) The parallel interaction of a finite-core vortex with a single plate. We solve the nonlinear Euler equations by a high-order finite-differece method. We use nonreflecting boundary conditions at the inflow and outflow boundaries. For the gust problem, we found that the cascade response depends sensitively on the frequency of the convicted gust. The unsteady surface pressure distribution and radiated pressure field agree very well with predictions of the linear theory for the tested range of reduced frequency. We have also investigated the effects of the incident gust frequency on the undesirable wave reflection at the inflow and outflow boundaries. For the vortex-plate interaction problem, we investigate the effects of the internal structure of the vortex on the strength and directivity of radiated sound. Then we solved the turbulence cascade interaction problem. The normal Reynolds stresses and velocity spectra are analyzed ahead, within, and downstream of the cascade. Good agreement with predictions of rapid distortion theory in the region of its validity is obtained. Also, the normal Reynolds stress profiles are found to be in qualitative agreement with available experimental data. As such, this dissertation presents a viable computational alternative to rapid distortion theory (RDT) for the prediction of noise radiation due to the interaction of free stream turbulence with structures. / Ph. D.

Molecular dynamics (MD) and computational fluid dynamics (CFD) allowresearchers to study fluid dynamics from two very different standpoints. From a microscopic standpoint, molecular dynamics uses Newton's second law of motion to simulate the interatomic behavior of individual atoms, using statistical mechanics as a tool for analysis. In contrast, CFD describes the motion of a fluid from a macroscopic level using the transport of mass, momentum, and energy of a system as a model. This thesis investigates both MD and CFD as a viable means of studying viscous flow on a nanometer scale. Specifically, we investigate a pressure-driven Poiseuille flow. The results of the MD simulations are processed using software we created to measure velocity, density, and pressure. The CFD simulations are run on numerical software that implements the MacCormack method for the Navier-Stokes equations. Additionally, the CFD simulations incorporate a local definition of viscosity, which is usually uncharacteristic of this simulation method. Based on the results of the simulations, we point out similarities and differences in the obtained steady-state solutions. / Master of Science

A one-dimensional model of a heterogeneous material consisting of a matrix with embedded separated particles is considered, and the melting or solidification of the particles is investigated. The matrix is in imperfect contact with the particles, and the lumped capacity approximation applies to each individual particle. Heat is generated inside the particles or is transferred from the matrix to the particles coupled through a contact conductance. The matrix is not allowed to change phase and energy is either generated inside the matrix or transferred from the boundaries, which is initially conducted through the matrix material. The physical model of this coupled, two-step heat transfer process is solved using the energy method. The investigation is conducted in several phases using a building block approach. First, a lumped capacity system during phase transition is studied, then a one-dimensional homogeneous material during phase change is investigated, and finally the one-dimensional heterogeneous material is analyzed. A numerical solution based on the finite difference method is used to solve the model equations. This method allows for any kind of boundary conditions, any combination of material properties, particle sizes and contact conductance. In addition, computer programs, using Mathematica, are developed for the lumped capacity system, homogeneous material, and heterogeneous material. Results show the effects of control volume thickness, time step, contact conductance, material properties, internal sources, and external sources. / Master of Science

Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters. / Master of Science

Yes / The potentially broad application area in engineering design using Genetic Algorithm (GA) has been widely adopted by many researchers due to its high consistency and accuracy. Presented here is the initial design of a wideband non-dispersive wire bow-tie antenna using GA for breast cancer detection applications. The ultimate goal of this design is to achieve minimal late-time ringing but at higher frequencies such as that located from 4 to 8 GHz, in which is desire to penetrate human tissue for near field imaging. Resistively loading method to reduce minimal ringing caused by the antenna internal reflections is implemented and discussed when the antenna is located in free space and surrounded by lossy medium. Results with optimised antenna geometry and different number of resistive loads are presented and compared with and without existence of scatterers.

Electromagnetic launchers (railguns) are set to replace traditional large caliber ship mounted cannons in the near future. The success of the railgun depends heavily upon a comprehensive understanding of beam behavior during periods of heavy dynamic loading. It is hypothesized that the combination of velocity transition effects, electromagnetic loading, and other non-linear or design specific effects contribute to areas of high stresses/strains over the length of the rail/beam during launch. This paper outlines the use of the Timoshenko beam model, a model which builds upon the traditional Bernoulli-Euler beam theory with the addition of shear deformation and rotary inertia effects, a necessity for high wave velocities. Real-world experimental setups are simplified and approximated by a series of linear springs and dampers for model prediction and validation. The Timoshenko beam model is solved using finite difference (FD) methods for the approximation of spatial derivatives and MATLAB ordinary differential equation (ODE) solvers. The model shows good convergence and precision over a large range of system parameters including load velocities, foundation stiffness values, and beam dimensions. Comparison to experimental strain data has validated model accuracy to an acceptable level. Accuracy is further enhanced with the inclusion of damping and non-linear or piecewise effects used to mimic experimental observations. The MATLAB software package presents a valid preliminary analysis tool for railgun beam and foundation design while offering advantages in ease of use, computation time, and system requirements when compared to traditional FEA tools. / Master of Science

Hyperthermia is a cancer treatment modality that raises cancerous tissue to cytotoxic temperature levels for roughly 30 to 45 minutes. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol to be used in a hyperthermia treatment. This thesis presents a method to optimize a hyperthermia treatment heating protocol. An algorithm is developed which recovers a heating protocol that will cause a desired amount of thermal damage within a region of tissue. The optimization algorithm is validated experimentally on an albumen tissue phantom. The transient temperature distribution within the region is simulated using a two-dimensional, finite-difference model of the Pennes bioheat equation. The relationship between temperature and time is integrated to produce a damage field according to two different models; Henriques'' model and the thermal dose model (Moritz and Henriques (1947)), (Sapareto and Dewey (1984)). A minimization algorithm is developed which re duces the value of an objective function based on the squared difference between an optimal and calculated damage field. Either damage model can be used in the minimization algorithm. The adjoint problem in conjunction with the conjugate gradient method is used to minimize the objective function of the control problem. The flexibility of the minimization algorithm is proven experimentally and through a variety of simulations. With regards to the validation experiment, the optimal and recovered regions of permanent thermal damage are in good agreement for each test performed. A sensitivity analysis of the finite difference and damage models shows that the experimentally-obtained extent of damage is consistently within a tolerable error range. Excellent agreement between the optimal and recovered damage fields is also found in simulations of hyperthermia treatments on perfused tissue. A simplified and complex model of the human skin were created for use within the algorithm. Minimizations using both the Henriques'' model and the thermal dose model in the objective function are performed. The Henriques'' damage model was found to be more desirable for use in the minimization algorithm than the thermal dose model because it is less computationally intensive and includes a mechanism to predict the threshold of permanent thermal damage. The performance of the minimization algorithm was not hindered by adding complexity to the skin model. The method presented here for optimizing hyperthermia treatments is shown to be robust and merits further investigation using more complicated patient models. / Master of Science

Today, heterogeneous computing has truly reshaped the way scientists think and approach high-performance computing (HPC). Hardware accelerators such as general-purpose graphics processing units (GPUs) and Intel Many Integrated Core (MIC) architecture continue to make in-roads in accelerating large-scale scientific applications. These advancements, however, introduce new sets of challenges to the scientific community such as: selection of best processor for an application, effective performance optimization strategies, maintaining performance portability across architectures etc. In this thesis, we present our techniques and approach to address some of these significant issues. Firstly, we present a fully automated approach to project the relative performance of an OpenCL program over different GPUs. Performance projections can be made within a small amount of time, and the projection overhead stays relatively constant with the input data size. As a result, the technique can help runtime tools make dynamic decisions about which GPU would run faster for a given kernel. Usage cases of this technique include scheduling or migrating GPU workloads over a heterogeneous cluster with different types of GPUs. We then present our approach to accelerate a seismology modeling application that is based on the finite difference method (FDM), using MPI and CUDA over a hybrid CPU+GPU cluster. We describe the generic computational complexities involved in porting such applications to the GPUs and present our strategy of efficient performance optimization and characterization. We also show how performance modeling can be used to reason and drive the hardware-specific optimizations on the GPU. The performance evaluation of our approach delivers a maximum speedup of 23-fold with a single GPU and 33-fold with dual GPUs per node over the serial version of the application, which in turn results in a many-fold speedup when coupled with the MPI distribution of the computation across the cluster. We also study the efficacy of GPU-integrated MPI, with MPI-ACC as an example implementation, in a seismology modeling application and discuss the lessons learned. / Master of Science

<p dir="ltr">The Alpine Fault, located in the South Island, New Zealand, is a subject of intense geological study due to its potential to trigger large earthquakes. It encompasses a complex system with the interplay of mechanics, thermodynamics, and fluid. Gaining insights into these systems not only enhances our understanding of the fault but also holds the potential to guide risk mitigation efforts.</p><p dir="ltr">The damage extent and fracture networks within the metamorphic rock mass adjacent to the fault can be effectively characterized by seismic anisotropy, an elastic property of rock, where seismic waves travel at different speeds with variation directions. This thesis presents a comprehensive exploration of seismic anisotropy in the hanging wall immediately adjacent to the principal slip zone of the Alpine Fault in New Zealand. Leveraging the borehole seismic data from a unique scientific drilling project and advanced numerical modeling techniques, the ultimate goal is to invert and parameterize the bulk seismic anisotropy.</p><p dir="ltr">Motivated by these challenges, the thesis undertakes several key initiatives: The first effort focuses on gaining a comprehensive understanding of an innovative method for seismic measurement: Distributed Acoustic Sensing (DAS) – examining its operational principles, factors influencing observed wavelets, and how it contrasts with traditional point sensors for accurate interpretation. Subsequently, the research introduces the implementation of an open-source seismic wave solver designed for modeling elastic wave propagation in complicated anisotropic media. This solver is further optimized for computational efficiency with its performance rigorously benchmarked.</p><p dir="ltr">With this preparedness, the inversion is further facilitated by high-performance computing (HPC) and a deep-learning algorithm specifically designed for automatically picking transit times. The inverted bulk elastic constants, compared to the intact rock, reveal 28% to 35% reductions in qP-wave velocity, characterizing the damage due to mesoscale fracture. Further analysis sheds light on the existence of orthogonal fracture sets and an intricate geometrical arrangement that agree with the previous borehole image log. This represents an advancement in our ability to characterize and understand the geologic processes with seismic anisotropy.</p>

For realistic predictions of vehicle performance in off-road conditions, it is critical to incorporate in the simulation accurate representations of the variability of the terrain profile. It is not practically feasible to measure the terrain at a sufficiently large number of points, or, if measured, to use such data directly in the simulation. Dedicated modeling techniques and computational methods that realistically and efficiently simulate off-road operating conditions are thus necessary. Many studies have been recently conducted to identify effective and appropriate ways to reduce experimental data in order to preserve only essential information needed to re-create the main terrain characteristics, for future use. This thesis focuses on modeling terrain profiles using the finite difference approach for solving linear second-order stochastic partial differential equations. We currently use this approach to model non-stationary terrain profiles in two dimensions (i.e., surface maps). Certain assumptions are made for the values of the model coefficients to obtain the terrain profile through the fast computational approach described, while preserving the stochastic properties of the original terrain topology. The technique developed is illustrated to recreate the stochastic properties of a sample of terrain profile measured experimentally. To further analyze off-road conditions, stochastic soil properties are incorporated into the terrain topology. Soil models can be developed empirically by measuring soil data at several points, or they can be created by using mathematical relations such as the Bekker's pressure-sinkage equation for homogeneous soils. In this thesis, based on a previously developed stochastic soil model, the polynomial chaos method is incorporated in the soil model. In a virtual proving ground, the wheel and soil interaction has to be simulated in order to analyze vehicle maneuverability over different soil types. Simulations have been created on a surface map for different case studies: stepping with a rigid plate, rigid wheel and flexible wheel, and rolling of a rigid wheel and flexible wheel. These case studies had various combinations of stochastic or deterministic terrain profile, stochastic or deterministic soil model, and an object to run across the surface (e.g., deterministic terrain profile, stochastic soil model, rolling rigid wheel). This thesis develops a comprehensive terrain and soil simulation environment for off-road mobility studies. Moreover, the technique developed to simulate stochastic terrain profile can be employed to simulate other stochastic systems modeled by PDEs. / Master of Science