There are very many processes in the natural and social sciences which can be represented as a set of flows of objects or people between categories of some kind. The Markov chain model has been used in the study of many of them. The basic form of the Markov chain model is, however, rarely adequate to describe social, occupational and geographical mobility processes. We shall therefore discuss a number of generalizations designed to introduce greater realism. In Chapter I we formulate and investigate a general model which results from relaxing the assumptions of sojourn-time's memorylessness and independence of origin and destination states, and of population homogeneity. The model (a mixture of semi-Markov processes) is then used in two ways. First, it provides a framework in which various special cases (which correspond to models which were used by social scientists) can be analytically compared. We pay particular attention to comparisons of rate of mobility in related versions of various models and to compatability of popular parametric forms with observed mobility patterns. Second, any result obtained for the general model can be specialized for the various cases and subcases. In Chapter II we formulate a system-model allowing interaction among individuals (components), which has been motivated by Conlisk. We define processes on this model and analyze their properties. A major effort is then devoted to establishing that when the population size becomes large, this rather complex stochastic model can be approximated by a single deterministic recursion due to Conlisk (1976). Nevertheless, we draw attention to certain aspects (particularly steady-state behavior) in which the approximation may fail. In Chapter III we address ourselves to the issue of measurement of (what we refer to as) social inheritance in intergenerational mobility processes. We distinguish between various aspects and concepts of social inheritance and outline the implications that certain "social values" may have on constructing a measure (or index). In the mathematical discussion which follows certain mechanisms for generating "families" of measures are indicated, and the properties of some particular combinations are investigated. / Business, Sauder School of / Graduate

In general, a minimum aberration criterion is used to evaluate fractional factorial designs. This dissertation begins with a comprehensive review and comparison of minimum aberration criteria definitions regarding their applications, relationships, advantages, limitations and drawbacks. A new criterion called the general balance metric, is proposed to evaluate and compare mixed-level fractional factorial designs. The general balance metric measures the degree of balance for both main effects and interaction effects. This criterion is related to, and dominates orthogonality criteria as well as traditional minimum aberration criteria. Besides, the proposed criterion provides immediate feedback and comprehensively assesses designs and has practical interpretations. The metric can also be used for the purpose of design augmentation to improve model fit. Based upon the proposed criterion, a method is proposed to identify the optimal foldover strategies for efficient mixed-level designs. The analysis of mixed-level designs involving qualitative factors can be achieved through indicator variables or contrast coefficients. A regression model is developed to include qualitative factor interactions which have been previously ignored. / A Dissertation submitted to the Department of Industrial and Manufacturing Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2006. / April 7, 2006. / Mixed-Level Designs, Augmentation, Qualitative Factor, General Balance Metric, Design Of Experiments, Foldover, Minimum Aberration Criterion / Includes bibliographical references. / James R. Simpson, Professor Directing Dissertation; Xufeng Niu, Outside Committee Member; Samuel A. Awoniyi, Committee Member; Joseph J. Pignatiello, Jr., Committee Member.

To prepare dielectric materials for High Temperature Superconductor (HTS) cables, nanocomposites consisting of Polymethylmethacrylate (PMMA) and Barium Titanate (BTA) nanoparticles have been manufactured and evaluated. The main objective of this research is to enhance the dielectric breakdown strength and reduce the dielectric losses of the nanocomposites. Polymethylmethacrylate (PMMA) with the addition of BTA (5wt.% and 10wt.% ) nanocomposites were fabricated by using two different methods. The breakdown voltage measurements have been conducted under AC, DC and lightning impulse high voltage. The measurements were conducted at both room temperature (293 K) and liquid nitrogen temperature (77 K). The results of the electrical breakdown field measurements of the nanocomposites are compared with those of the base polymer. Fracture surface analysis was carried out with SEM analysis. The difference in the breakdown area due to different modes of voltages applied and effect of the nanoparticles was studied. Mechanical characterization of the resultant nanocomposites was also carried out at both the room temperature (293K) and at cryogenic temperature (77K). The effects of nanoparticles on the electrical and mechanical properties were observed. A marginal increase in the dielectric strength of the nanocomposites was observed for AC conditions at both the temperatures. There was a decrease in the values of nanocomposites for impulse conditions. At cryogenic temperature nanocomposites showed higher dielectric strength when DC voltage was applied. For both the temperatures, dielectric losses increased as the voltage was increased for all the materials studied, except for PMMA/10wt.%BTA nanocomposites at cryogenic temperature, which showed decrease of losses by ~ 70%. An increase of ~12% in Young's modulus and ~ 65% increase in tensile strength of the nanocomposites were observed at cryogenic temperature. It also shows that more material damage was observed under AC breakdown voltage compared to the impulse and DC voltage breakdown cases. Also the material damage was more pronounced at 77 K than that at 293 K. / A Thesis submitted to the Department of Industrial and Manufacturing Engineering in partial fulfillment of the requirements for the degree of Master of Science. / Summer Semester, 2010. / July 6, 2010. / Tan Delta Losses, Impulse Breakdown, DC Breakdown, AC Breakdown, Barium Titanate, Polymethylmethacrylate (PMMA), Cryogenic Insulation, High Temperature Superconductors (HTS), Nanodielectrics, Mechanical Breakdown, Surface Fracture Analysis, Weibull Plots / Includes bibliographical references. / Zhiyong Richard Liang, Professor Directing Thesis; Horatio Rodrigo, Committee Member; Okenwa Okoli, Committee Member; Mei Zhang, Committee Member.

Carbon nanotubes (CNTs) have excellent mechanical, electrical, and thermal properties making them outstanding reinforcements in polymer matrix composites. In this research, the effect of CNT-integration in polymer matrices (two-phase) and fiber-reinforced composites (three-phase) was studied theoretically and experimentally. This work sought to enhance the mechanical properties of composites by the improving dispersion of CNTs in polymers. This was achieved by optimizing the CNT/polymer composite manufacturing process. Generally, higher sonication intensity and longer sonication time improved the mechanical properties of CNT/polymer composites through improved CNT dispersion. Simulations for CNT/polymer composites (nanocomposites) and CNT/fiber/polymer composites (multiscale composites) were successfully carried out using a new method that combines nanocomposites micromechanics and woven fiber micromechanics. With this new method, the mechanical properties, including the Young's modulus, Poisson's ratio, and shear modulus, of nanocomposites and multiscale composites were predicted in terms of CNT loading in a polymer. The relationships between the mechanical properties of the composites and aspect ratios of the CNTs were studied and, as the third part of the simulation, the mechanical properties of multiscale composites that have no CNTs in the fiber strands were compared with those of multiscale composites that have CNTs in the fiber strands. In order to compare the predicted mechanical properties obtained by the simulations, nano and multiscale composites were manufactured and characterized. Good dispersion of the CNTs and strong bonding between the CNTs and polymer matrix and fibers and matrix are necessary to improve the mechanical properties of nanocomposites and multiscale composites. / A Dissertation submitted to the Department of Industrial and Manufacturing Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester, 2009. / April 3, 2009. / Carbon Nanotubes, Design of Experiments (DOE), Nanocomposites, Multiscale Composites, Mechanical Modeling / Includes bibliographical references. / Okenwa I. Okoli, Professor Directing Dissertation; Sachin Shanbhag, Outside Committee Member; Young-Bin Park, Committee Member; Zhiyong Liang, Committee Member; David Jack, Committee Member.

Carbon nanotubes are theoretically one of the strongest and stiffest materials with a calculated tensile strength of ~200 giga Pascal and modulus of more than 1-4 tera Pascal for a single walled nanotube (SWNT). If the mechanical properties of SWNT could be effectively incorporated into a polymer matrix, composites with lightweight, exceptional strength and stiffness can be achieved. The effective utilization of nanotubes in composites for applications depends on the ability to disperse the nanotubes uniformly throughout the matrix. Carbon nanotubes are anisotropic in nature. Therefore to take advantage of the nanotubes in the axial direction, controlled tube orientation or degree of alignment of nanotubes in the polymer matrix is very important to realize their high mechanical and functional properties. The nanocomposites produced by current conventional methods using direct mixing, melt blending or solution casting have failed to yield significant improvements in composite modulus. Although tremendous progress has been made towards understanding the properties of individual carbon nanotubes, but attaining the true potential of the bulk polymeric nanocomposites have been hindered by the lack of uniform SWNT dispersion, poor interfacial bonding, inadequate tube loading and uncontrollable tube orientation or degree of alignment. This thesis work developed an innovative approach for producing nanocomposites that has uniform SWNT dispersion, high tube loading and most importantly controlled tube orientation. In this research, these properties in composites were achieved by using magnetically aligned buckypapers and resin infusion system. The aligned nanotube buckypaper and composite were characterized using AFM and SEM. The mechanical properties of these materials were experimentally determined using DMA and were theoretically verified. The electrical properties of these materials were also experimentally determined using 4-probe resistivity measurements. Significant tube alignment has been achieved in the resultant buckypaper and nanocomposites. It is shown that the developed method is an effective way for producing nanocomposites with uniform SWNT dispersion desired tube alignment and high tube loading. / A Thesis submitted to the Department of Industrial Engineering in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2003. / November 10, 2003. / Carbon, Nanotubes, SWNT Alignment, Composite, Polymer, Anisotropy, Resistivity, Nanocomposite / Includes bibliographical references. / Zhiyong Liang, Professor Directing Thesis; Ben Wang, Committee Member; Chuck Zhang, Committee Member.

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