published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

published_or_final_version / Community Medicine / Master / Master of Public Health

published_or_final_version / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

Policy analysts designing programs to improve the efficiency and expand the use of water in the irrigation of farm lands often enlist benefit-cost analysis as a means of assessing impacts and feasibility. While on-site comparisons of costs and benefits are important factors in project assessment, other dimensions such as risk, income distribution and offsite impacts may be overlooked. In this research a more complete approach to project analysis was sought. A simulation model of a river basin was developed. Paris Creek, Idaho, an area studied recently by the U.S. Soil Conservation Service, was the representative project location analyzed. An important design goal was to provide an analytical data processing template applicable to future studies. Paris Creek farmers are directly dependent on water available from Paris Creek. However, most years the flow is insufficient to provide adequate irrigation with present methods. High pumping costs, high seepage losses in delivery systems and low on-farm irrigation efficiencies compound the problem. A proposed improvement plan is analyzed, involving piped gravity-fed delivery systems and conversion from surface to sprinkler irrigation. Installation and government consulting costs are to be shared by the farmers and S.C.S. The computer model simulated monthly stream flows, irrigated crops, measured impacts, computed production benefits, and compiled costs and benefits affecting farmers and society. A 50-year project life was assumed, and statistics were collected for 25 separate iterations. It was determined that north group farmers are almost always better off with the project when annual comparisons were made between conditions. Only in years of very low stream flow would farmers lose more money with the project. However, substantially higher variability in annual income could be expected, a condition of greater risk to farmers. Society as a whole was also found to experience an increase in net benefits, but not as great as for farmers and with greater annual variability. The model was effective in providing information about risk and income distribution. However, difficulty remains in assessing offsite impacts because there lacks an effective approach and appropriate data. / Graduation date: 1986

The principal aim of this study was the use and evaluation of dynamic modeling techniques to identify mathematical models for cereal drying rates and quality changes that best describe thin-layer malt drying data. Seven thin-layer malt drying experiments were performed at the Great Western Malting pilot facilities, Vancouver, WA. Malt moisture content, temperature, β-amylase activity, endo-barley-β-glucanase activity, and color were all monitored as the malt was dried with air at various temperature and relative humidity values. A constrained direct search optimization method was used to fit available drying, enzyme deactivation, and color formation models to the data obtained by minimizing the error between predicted and experimental values. Because the deactivation of β- amylase observed during the kiln experiments was less than the error involved in β-amylase measurement, β-amylase modeling efforts were dropped from the study. The end result is a computer simulation of the malt kilning process that can predict malt drying rates, color formation, and endo-barley-β-glucanase deactivation based on the drying air temperature, relative humidity, and time spent in the kiln. Further research is suggested towards modeling malt drying rates at high moisture contents, (above 40%) analysis of drying model applicability when drying conditions fall outside those encountered in this study, and development of assay procedures and models so that the fate of other important malt quality indicators during kiln drying can be predicted. / Graduation date: 1993

Mathematical models, that depict the dynamics of a cancer cell population growing out of the human body (in vitro) in unconstrained microenvironment conditions, are considered in this thesis. Cancer cells in vitro grow and divide much faster than cancer cells in the human body, therefore, the effects of various cancer treatments applied to them can be identified much faster. These cell populations, when not exposed to any cancer treatment, exhibit exponential growth that we refer to as the balanced exponential growth (BEG) state. This observation has led to several effective methods of estimating parameters that thereafter are not required to be determined experimentally. We present derivation of the age-structured model and its theoretical analysis of the existence of the solution. Furthermore, we have obtained the condition for BEG existence using the Perron- Frobenius theorem. Amathematical description of the cell-cycle control is shown for one-compartment and two-compartment populations, where a compartment refers to a cell population consisting of cells that exhibit similar kinetic properties. We have incorporated into our mathematical model the required growing/aging times in each phase of the cell cycle for the biological viability. Moreover, we have derived analytical formulae for vital parameters in cancer research, such as population doubling time, the average cell-cycle age, and the average removal age from all phases, which we argue is the average cell-cycle time of the population. An estimate of the average cell-cycle time is of a particular interest for biologists and clinicians, and for patient survival prognoses as it is considered that short cell-cycle times correlate with poor survival prognoses for patients. Applications of our mathematical model to experimental data have been shown. First, we have derived algebraic expressions to determine the population doubling time from single experimental observation as an alternative to empirically constructed growth curve. This result is applicable to various types of cancer cell lines. One option to extend this model would be to derive the cellcycle time from a single experimental measurement. Second, we have applied our mathematical model to interpret and derive dynamic-depicting parameters of five melanoma cell lines exposed to radiotherapy. The mathematical result suggests there are shortcomings in the experimental methods and provides an insight into the cancer cell population dynamics during post radiotherapy. Finally, a mathematical model depicting a theoretical cancer cell population that comprises two sub-populations with different kinetic properties is presented to describe the transition of a primary culture to a cell line cell population.

This dissertation presents results pertaining to the mathematical modeling of semiconductor photoconductors and includes the formulation, analysis, and solution of photoconductive device model equations. The fundamental semiconductor device equations of continuity and transport are derived for the case of a material which contains a large density of deep-level impurities. Electron and hole trapping on deep-level impurities is accounted for by trapping-kinetics rate equations. The coupling between carrier drift and the electric field is completed through Poisson's equation. Simple, nonlinear model equations are presented for bulk-material response based on the dynamics of electron and hole trapping and recombination on deep-level impurities. The characteristics of the solution to these model equations are observed to depend strongly on the excitation intensity. These model equations qualitatively reproduce observed experimental behavior of an iron-doped indium phosphide photoconductor. A theory of the effect of deep-level centers on the generation-recombination noise and responsivity of an intrinsic photoconductor is presented. It is shown that the deep-level centers can influence the generation-recombination noise and responsivity in three main ways: (i) they can shorten the bulk carrier lifetime by Schockley-Read-Hall recombination; (ii) for some values of the capture cross sections, deep-level densities, and temperature, the deep-level centers can trap a significant fraction of the photogenerated minority carriers. This trapping reduces the effective minority carrier mobility and diffusivity and thus reduces the effect of carrier sweep out on both generation noise and responsivity; (iii) the deep-level centers add a new thermal noise source, which results from fluctuations between bound and free carriers. The strength of this new noise source decreases with decreasing temperature at a slower rate than band-to-band thermal generation-recombination noise. Photoconductive device model equations based on time-dependent, convective/diffusive transport equations are presented. The system of model equations is solved numerically with boundary conditions that represent ideal ohmic contacts. Computed results are presented for different photoconductor lengths and bias voltages with spatially uniform, rectangular light-pulse illumination.

A relatively simple, yet complete analytical model for predicting the performance of illuminated or unilluminated (dark) pn diodes with arbitrary doping profiles is developed and presented in this dissertation. It can be used to calculate the saturation current, minority carrier density, short circuit current, spectral response, and effective low-high (p-p⁺) junction recombination velocities of such diodes. The model is applied to dark or illuminated n⁺-p-p⁺ diodes as a function of the front and back surface recombination velocities and the bulk doping profiles. The analysis includes heavy doping effects. The results predicted by this model are compared with those predicted by numerical simulation programs. Both results agree well with each other and with the experimental data available. The complete analytical expressions produced by the model can be reduced to simpler forms for the transparent and quasi-transparent cases. These forms agree with the special case expressions developed by others. The new model is a substantial contribution leading to improved understanding of such devices.

In this thesis we study the existence and stability of positive equilibrium of a general model for the dynamics of several interacting, age-structured population. We begin with the formulation and proof of a global existence theorem for the initial value problem. The proof of this theorem is used to develop an algorithm and a FORTRAN code for the numerical solution of initial value problems for the single species case. This computer program is used to study prototype models for the dynamics of a population whose fertility and mortality rates exhibit an "Allee effect". This is done from a bifurcation theoretic point of view, using the inherent net reproductive rate as a bifurcating parameter. An unstable "left" bifurcation is found. Multi-equilibria and various kinds of oscillations are studied as a function of r, the fertility window, and the nature of the density dependence.