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A two fluid hydrodynamical model describing the modification of a stellar wind flow due to its interaction with galactic cosmic-rays is investigated. The two fluids consist of the thermal stellar wind gas and the galactic cosmic-rays. A polytropic one fluid model is used to describe the stellar wind gas, and the cosmic-rays modify the wind via their pressure gradient. The cosmic-rays are considered to be a hot low density gas of negligible mass flux, but with a significant pressure and energy flux compared to the thermal gas. The equations used are essentially those employed in two fluid hydrodynamical models of cosmic-ray shock acceleration by the first order Fermi mechanism, but suitably modified to apply in a spherical geometry and including the effects of gravity on the flow. The stellar wind consists of a transonic flow with a termination shock, and subsonic flow outside the shock. The model shows the deceleration of the wind upstream of the shock by the positive galactic cosmic-ray pressure gradient. The dissertation first discusses the fluid polytropic stellar winds and how to insert shocks in the flow. The hydrodynamical equations governing cosmic-ray modified winds are then introduced followed by a discussion of the physics of the interaction between the thermal stellar wind and the cosmic-rays. A description of the singularities of the equations is also presented. The system of equations is first solved by a finite difference method in the test particle approximation in which the cosmic-rays do not modify the flow, with appropriate boundary conditions applied at infinity, at the wind termination shock, and at the star. A perturbation scheme to determine the modification of the wind by the cosmic-rays is then developed. This scheme applies when the modification of the wind by the cosmic-rays is sufficiently small. Finally a numerical iteration is employed to exactly solve the equations. This latter method has the advantage that it can be applied when there is a considerable modification of the wind by the cosmic-rays.

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.

Two numerical models, described in detail herein, have been constructed and used to investigate the formation of secondary vortices in axisymmetrically-forced rotating flows. The particular type of vortex flow examined is that developed in a laboratory vortex simulator where secondary vortices have been produced and extensively studied. The first numerical model generated a collection of steady state, axisymmetric vortex flows based on a range of swirl ratios. The second model tested those flows for instability by simulating the behavior of small amplitude, axially asymmetric, linear perturbations superimposed on the flows: amplification of the perturbations indicated instability whereas damping indicated stability. For those flows found to be unstable, the linear perturbations of various azimuthal wavenumbers were analyzed in detail, and from the perturbation growth rates, structures, phase speeds, and energetics, the nature of the instability could be studied. The results of the instability study show that the vortex is stable for the lowest swirl ratios but that above a certain value, instability persists indefinitely. The most rapidly growing wavenumber shifts steadily with increasing swirl from 1 to around 5 in the swirl range investigated. Growth rates were found to be high enough for secondary vortices to form in the laboratory simulator in just a few seconds. Structurally, the perturbation fields were found to have a helical tilt and to be centered near the radius of maximum vertical vorticity in the axisymmetric vortex. They propagated in the same azimuthal direction as the rotation of the axisymmetric flow, but at a somewhat lower angular velocity at the surface. These linear results are all consistent with observed laboratory behavior. From this, it was concluded that linear theory is capable of explaining many important aspects of secondary vortices. An analysis of the perturbation energy equation revealed that at the higher swirl ratios, the perturbation received most of its energy from the deformation of the axisymmetric flow due to the radial distribution of azimuthal velocity, while for low swirl the primary source was from the radial distribution of the vertical velocity. No other component of the axisymmetric vortex ever contributed more than about 25% of these terms.

One result of the search for inexpensive alternative sources of protein has been the rise in interest in aquaculture, the rearing of aquatic organisms under controlled conditions. In this dissertation we examine several management approaches to the efficient rearing of aquatic animals, using mathematical modeling to discover optimal production decisions. In addition we demonstrate the feasibility of simultaneous decision and performance control, providing empirical support for a theoretical extension of traditional variance analysis techniques. The results of three studies are included. In the first we model a situation in which the manager of an aquaculture system must decide when and how many animals to stock initially, how many animals to harvest each period, and when to restock an enclosure in order to maximize contribution. We consider both limited and unlimited growing seasons, solving mixed-integer and linear programs. We examine the effects of technological improvements on production strategies. Consistent improvement in contribution is noted, along with some variation in strategy. In the second study we introduce seasonal variation in revenues and lengthen the growing season. The resulting large-scale real-world mixed-integer problem necessitates the use of a heuristic and two strategies, selective expansion and sieve, in order to achieve a near-optimal solution within a reasonable length of time. In the third study we focus on the uncertainty inherent in the aquaculture environment. We provide empirical evidence of the feasibility of a performance evaluation system which gives explicit consideration to the effects of environmental uncertainty and incorporates intraperiod adaptive behavior on behalf of the individual responsible for implementation of model-specified activities. The system we describe may be used in the simultaneous evaluation of individual and model performances, thus clarifying responsibilities for variances and improving production control.

The central goal of this dissertation is to develop a simple but powerful theory to handle a problem which arises in management situations where an optimally exploited, system at steady state is subjected to a set of continuous, persistent and unpredictable disturbances emanating from the system's environment. Such disturbances drive the system out of steady state. The question that arises in such a situation is whether there exists any additional control which can be imposed on the disturbed system in order to drive it back to the steady state and maintain it there for all future time? We show in this dissertation that such a control is possible provided bounds for the disturbances are known. We develop the additional control using concepts from reachability and the so-called Liapunov's "second method". We further develop some theory concerning certain problems which arise in generating the boundary of the reachable set, ∂R(•) using the controllability maximum principle. In generating ∂R(•) several boundary controls may be used to generate different parts of ∂R(•). We show that all the parts of ∂R(•) are polygonally connected. We also show that for a second-order system if an equilibrium point under constant control is hyperbolic and lies on ∂R(•), it is asymptotically stable. Further, in persistently disturbing a system, it is desirable to have some idea about the boundedness of the disturbed system. If the system is bounded then a boundary can be generated using controllability maximum principle. We give some theory and discussion on how to test such boundedness for linear, quasilinear and some cases of nonlinear systems. The last two chapters of this dissertation show how the theory is applied to a second-order system; in particular to a second-order grazing system.