Success in geotechnical analysis, design, and construction invariably requires that we have proper knowledge and understanding of (1) the strength, (2) the fluid flow properties, and (3) the stress-deformation behavior of the earth materials. These important engineering properties are primarily determined by the components and structure of a soil, which also dictate the soil's responses in an electromagnetic field. As a nondestructive technique, the electromagnetic property measurement offers a promising approach to characterize earth materials and identify the effects of changes in environments. However, despite many investigations in the last several decades, the relationship between the frequency-dependent electromagnetic properties of soils and their components and structure are still not well understood. Hence, estimation of engineering properties of a soil in a quantitative way from electromagnetic measurements can be uncertain. In this research several tasks have been accomplished: (1) Development of a physically based model that provides a means of investigating the coupled effects of important polarization mechanisms on soil electromagnetic properties, and a means of relating the electromagnetic properties of a soil to its fines content, clay mineralogy, anisotropy, degree of flocculation and pore fluid chemistry; (2) Proposal of a practically applicable method to determine the volumetric water content, specific surface area and pore fluid salt concentration simultaneously from the dielectric spectrum; (3) Deduction of the wide-frequency electromagnetic properties of a soil by measuring its responses to a step pulse voltage using time domain reflectometry (TDR); (4) Establishment of the relationships between the specific surface area and compressibility, residual shear strength and hydraulic conductivity. This study establishes a framework for quantifying soil engineering properties from their electromagnetic properties. If properly determined and interpreted, the electromagnetic properties can also provide insights into the causes of soil property changes over time and can be very useful in studying the effects of biological factors in geotechnical engineering, a field that may offer great potential for future advances. / Ph. D.

Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to

Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to

Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to

Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to