Master of Science / Department of Architectural Engineering and Construction Science / Julia A. Keen / Throughout recent years, to minimize the cost of construction, a large number of multipurpose spaces have been built using lightweight, less expensive materials without considering or designing for noise control to mitigate any sound that is loud, unpleasant, unexpected, or undesired yet after construction is completed, noise issues are often evident within the space and, if severe enough, may render the intended function of the structure useless. To address this problem, this report is intended to introduce Owners and Facility Managers to some of the common solutions to resolve noise issues in multipurpose rooms. The report focuses on solutions for existing projects primarily, but it is also sensitive to budget constraints and the impact of renovation. Typical multipurpose rooms researched have a volume of 50,000-150,000 cubic feet and are expected to be used for speech activities, small music functions, and some physical sports activities. Therefore, this report will introduce the fundamentals of sound and room acoustics including interior surface materials and construction. Also included are typical noise issues from interior sources, solutions that can be taken within the building to attenuate noise, and the trade-offs associated with each solution.

Master of Science / Department of Mathematics / Nathan Albin / A new methodology is introduced for use in discrete periodic extension of non-periodic functions. The methodology is based on a band-limited step function, and utilizes the computational efficiency of FC-Gram (Fourier Continuation based on orthonormal Gram polynomial basis on the extension stage) extension database. The discrete periodic extension is a technique for augmenting a set of uniformly-spaced samples of a smooth function with auxiliary values in an extension region. If a suitable extension is constructed, the interpolating trigonometric polynomial found via an FFT(Fast Fourier Transform) will accurately approximate the original function in its original interval. The discrete periodic extension is a key construction in the FC-Gram algorithm which is successfully implemented in several recent efficient and high-order PDEs solvers. This thesis focuses on a new flexible discrete periodic extension procedure that performs at least as well as the FC-Gram method, but with somewhat simpler implementation and significantly decreased setup time.

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Liang-Wu Cai / A computational system is built for conducting deterministic simulations of three-dimensional multiple scattering of elastic waves by spherical inclusions. Based on expansion expression of elastic wave fields in terms of scalar and vector spherical harmonics, analytically exact solutions of single scattering and multiple scattering are obtained, implemented and verified. The verification is done by using continuities of displacement and surface traction at the interface between an inclusion and host medium, energy conservation and published results. The scatterer polymerization methodology is extended to three-dimensional multiple scattering solution. By using this methodology, an assemblage of actual scatterers can be treated as an abstract scatterer. This methodology is verified by using different approaches, with or without scatterer polymerization, to solve a physically the same multiple scattering problem. As an application example, band gap formation process for elastic wave propagation in cubic lattice arrangements of spherical scatterers is observed through a series of numerical simulations. Along the direction of the incident wave, scatterer arrangements are viewed as comprising layers of scatterers, within which scatterers form a square grid. Starting from one layer and by increasing the number of layers, near-field forward wave propagation spectra are computed as the number of layers increases. These simulations also demonstrates that the computational system has the capability to simulate multiple scattering solutions of elastic waves in three-dimension.

Master of Arts / Department of Geography / John A. Harrington Jr / The objective of this thesis is classify climate for the Earth’s ocean areas. The classifica-tion task is accomplished in part by using monthly average sea surface temperature and precipita-tion data from 1980-2008. Coast-to-coast coverage of the needed data were obtained from the reanalysis product produced by the National Centers for Environmental Prediction and the National Center for Atmospheric Research. Köppen’s classification scheme was implemented in the ArcGIS suite of software, which was used to analyze and display all of the classified map products. Russell’s ‘climatic years’ concept was used and separate classifications were produce for each year of available data. Findings indicate that the oceans are very different from land areas when it comes to the location and extent of varying climate types. Some main findings include the idea that A, C, and E climates dominate the geography of the oceans and that there are zero continental, or D, climates. Also, the Southern Oscillation plays an important part in tropical ocean dynamics and climate, but summarizing twenty nine years of mapped patterns into a summary product removes any major effect from yearly climate system anomalies. A key finding is an argument that supports the establishment of a unique Southern Ocean surrounding Antarctica. There are polar, ET and EF, climate subtypes surrounding both the Arctic and Antarctic poles, but only the north has the well established Arctic Ocean. Oceanic E climate areas are more pronounced in the Southern Hemisphere with circumpolar rings around the Antarctic continent. Classification results support the idea of a Southern Ocean based on the spatial pattern of climate types and in view of the fact that that the climate of the Southern Ocean area is so different from the temperate, or C, climate and its subtypes. This research is important for many reasons, the primary being that climate classification helps us better understand the world around us. It is difficult to see change in the environment without first knowing what the state of the system used to be. Classification will also help depict the changes that have happened, when these shifts in climate occurred, and with that information we can better predict what the future will hold.