Qiu, Xin.

This thesis addresses the groundwater contamination problem from a probabilistic point of view. The objective of this study is to obtain analytical solutions for the backward type Kolmogorov equations governing certain crucial variables in the case of a two-dimensional medium. These include the rate at which pollutants enter the protected zone and the length of time that a pollutant particle takes to travel from a given location to the boundary of the protected zone. It is assumed that the groundwater flow is horizontal and uniform, and that a protected zone is located downstream. Analytical solutions are obtained by using the techniques of Laplace transform and separation of variables. Numerical results are given for two cases, one with flow coming from a boundary which is imperious to the pollutant, and another with flow coming from infinity.

Theoretical investigation is carried out into the extent to which floor accelerations of a wind-excited tall building can be reduced by increasing damping in those components in a building which are generally regarded to be non-structural elements, and by using active control. The wind loads are modeled as stochastic processes, which are correlation-stationary in time. Only the drag wind forces are considered in the analyses. The spectral densities and cross-spectral densities of two commonly used models, proposed by Davenport and by Simiu, are compared. The Davenport spectrum is used in the numerical calculation for illustration purposes. Several structural models are discussed: an ideal spatially periodic model, an ideal piece-wise spatially periodic model, a nominal spatially periodic model with random disorder in periodicity, and an ideal spatially periodic model equipped with an active mass damper control system. The problems are formulated using the transfer matrix approach in the frequency domain. Analytical solutions are obtained for the spectral densities and the mean-square values of the floor accelerations and those of the active control force. Numerical examples are given for illustration.