The graph model for conflict resolution (GMCR) provides a convenient and effective means to model and analyze a strategic conflict. Standard practice is to carry out a stability analysis of a graph model, and then to follow up with a post-stability analysis, two critical components of which are status quo analysis and coalition analysis. In stability analysis, an equilibrium is a state that is stable for all decision makers (DMs) under appropriate stability definitions or solution concepts. Status quo analysis aims to determine whether a particular equilibrium is reachable from a status quo (or an initial state) and, if so, how to reach it. A coalition is any subset of a set of DMs. The coalition stability analysis within the graph model is focused on the status quo states that are equilibria and assesses whether states that are stable from individual viewpoints may be unstable for coalitions. Stability analysis began within a simple preference structure which includes a relative preference relationship and an indifference relation. Subsequently, preference uncertainty and strength of preference were introduced into GMCR but not formally integrated. In this thesis, two new preference frameworks, hybrid preference and multiple-level preference, and an integrated algebraic approach are developed for GMCR. Hybrid preference extends existing preference structures to combine preference uncertainty and strength of preference into GMCR. A multiple-level preference framework expands GMCR to handle a more general and flexible structure than any existing system representing strength of preference. An integrated algebraic approach reveals a link among traditional stability analysis, status quo analysis, and coalition stability analysis by using matrix representation of the graph model for conflict resolution. To integrate the three existing preference structures into a hybrid system, a new preference framework is proposed for graph models using a quadruple relation to express strong or mild preference of one state or scenario over another, equal preference, and an uncertain preference. In addition, a multiple-level preference framework is introduced into the graph model methodology to handle multiple-level preference information, which lies between relative and cardinal preferences in information content. The existing structure with strength of preference takes into account that if a state is stable, it may be either strongly stable or weakly stable in the context of three levels of strength. However, the three-level structure is limited in its ability to depict the intensity of relative preference. In this research, four basic solution concepts consisting of Nash stability, general metarationality, symmetric metarationality, and sequential stability, are defined at each level of preference for the graph model with the extended multiple-level preference. The development of the two new preference frameworks expands the realm of applicability of the graph model and provides new insights into strategic conflicts so that more practical and complicated problems can be analyzed at greater depth. Because a graph model of a conflict consists of several interrelated graphs, it is natural to ask whether well-known results of Algebraic Graph Theory can help analyze a graph model. Analysis of a graph model involves searching paths in a graph but an important restriction of a graph model is that no DM can move twice in succession along any path. (If a DM can move consecutively, then this DM's graph is effectively transitive. Prohibiting consecutive moves thus allows for graph models with intransitive graphs, which are sometimes useful in practice.) Therefore, a graph model must be treated as an edge-weighted, colored multidigraph in which each arc represents a legal unilateral move and distinct colors refer to different DMs. The weight of an arc could represent some preference attribute. Tracing the evolution of a conflict in status quo analysis is converted to searching all colored paths from a status quo to a particular outcome in an edge-weighted, colored multidigraph. Generally, an adjacency matrix can determine a simple digraph and all state-by-state paths between any two vertices. However, if a graph model contains multiple arcs between the same two states controlled by different DMs, the adjacency matrix would be unable to track all aspects of conflict evolution from the status quo. To bridge the gap, a conversion function using the matrix representation is designed to transform the original problem of searching edge-weighted, colored paths in a colored multidigraph to a standard problem of finding paths in a simple digraph with no color constraints. As well, several unexpected and useful links among status quo analysis, stability analysis, and coalition analysis are revealed using the conversion function. The key input of stability analysis is the reachable list of a DM, or a coalition, by a legal move (in one step) or by a legal sequence of unilateral moves, from a status quo in 2-DM or $n$-DM ($n > 2$) models. A weighted reachability matrix for a DM or a coalition along weighted colored paths is designed to construct the reachable list using the aforementioned conversion function. The weight of each edge in a graph model is defined according to the preference structure, for example, simple preference, preference with uncertainty, or preference with strength. Furthermore, a graph model and the four basic graph model solution concepts are formulated explicitly using the weighted reachability matrix for the three preference structures. The explicit matrix representation for conflict resolution (MRCR) that facilitates stability calculations in both 2-DM and $n$-DM ($n > 2$) models for three existing preference structures. In addition, the weighted reachability matrix by a coalition is used to produce matrix representation of coalition stabilities in multiple-decision-maker conflicts for the three preference frameworks. Previously, solution concepts in the graph model were traditionally defined logically, in terms of the underlying graphs and preference relations. When status quo analysis algorithms were developed, this line of thinking was retained and pseudo-codes were developed following a similar logical structure. However, as was noted in the development of the decision support system (DSS) GMCR II, the nature of logical representations makes coding difficult. The DSS GMCR II, is available for basic stability analysis and status quo analysis within simple preference, but is difficult to modify or adapt to other preference structures. Compared with existing graphical or logical representation, matrix representation for conflict resolution (MRCR) is more effective and convenient for computer implementation and for adapting to new analysis techniques. Moreover, due to an inherent link between stability analysis and post-stability analysis presented, the proposed algebraic approach establishes an integrated paradigm of matrix representation for the graph model for conflict resolution.

Shipment consolidation is a logistics strategy whereby many small shipments are combined into a few larger loads. The economies of scale achieved by shipment consolidation help in reducing the transportation costs and improving the utilization of logistics resources. The fundamental questions about shipment consolidation are i) to how large a size should the consolidated loads be allowed to accumulate? And ii) when is the best time to dispatch such loads? The answers to these questions lie in the set of decision rules known as shipment consolidation policies. A number of studies have been done in an attempt to find the optimal consolidation policy. However, these studies are restricted to only a few types of consolidation policies and are constrained by the input parameters, mainly the order arrival process and the order weight distribution. Some results on the optimal policy parameters have been obtained, but they are limited to a couple of specific types of policies. No comprehensive method has yet been developed which allows the evaluation of different types of consolidation policies in general, and permits a comparison of their performance levels. Our goal in this thesis is to develop such a method and use it to evaluate a variety of instances of shipment consolidation problem and policies. In order to achieve that goal, we will venture to use matrix-analytic methods to model and solve the shipment consolidation problem. The main advantage of applying such methods is that they can help us create a more versatile and accurate model while keeping the difficulties of computational procedures in check. More specifically, we employ a discrete batch Markovian arrival process (BMAP) to model the weight-arrival process, and for some special cases, we use phase-type (PH) distributions to represent order weights. Then we model a dispatch policy by a discrete monotonic function, and construct a discrete time Markov chain for the shipment consolidation process. Borrowing an idea from matrix-analytic methods, we develop an efficient algorithm for computing the steady state distribution of the Markov chain and various performance measures such as i) the mean accumulated weight per load, ii) the average dispatch interval and iii) the average delay per order. Lastly, after specifying the cost structures, we will compute the expected long-run cost per unit time for both the private carriage and common carriage cases.

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We revisited an empirical relationship between the integrated volume depolar- ization ratio, oacc, and the effective multiple scattering factor, -n, on the basis of Monte Carlo simulations of spaceborne lidar backscatter associated with homogeneous wa- ter clouds. The relationship is found to be sensitive to the extinction coefficient and to the particle size. The layer integrated attenuated backscatter is also obtained. Comparisons made between the simulations and statistics derived relationships of the layer integrated depolarization ratio, oacc, and the layer integrated attenuated backscatter, -n, based on the measurement by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite show that a cloud with a large effective size or a large extinction coefficient has a relatively large integrated backscatter and a cloud with a small effective size or a large extinction coefficient has a large integrated volume depolarization ratio. The present results also show that optically thin water clouds may not obey the empirical relationship derived by Y. X. Hu. and co-authors.

Marfan syndrome, affecting approximately one out of every 5,000 people, is characterized by abnormal bone growth, ectopia lentis, and often-fatal aortic dilation and dissection. The root cause is a faulty extracellular matrix protein, fibrillin-1, which associates with elastin in many tissues. Common carotids from wild-type controls and mice heterozygous for the mgR mutation, the most commonly used mouse model of Marfan syndrome, were studied in a biaxial testing device. Mechanical data in the form of pressure-diameter and force-stretch tests in both the active and passive states were collected, as well data on the functional responses to phenylephrine, carbamylcholine chloride, and sodium nitroprusside. Although little significant difference was found between the heterozygous and wild-type groups in general, the in vivo stretch for both groups was significantly different from previously studied mouse vessels. Although the two groups do not exhibit significant differences, this study comprises a control group for future work with mice homozygous for mgR, which do exhibit Marfan-like symptoms. As treatment of Marfan syndrome improves, more Marfan patients will survive and age, increasing the likelihood that they will develop many of the vascular complications affecting the normal population, including hypertension and atherosclerosis. Therefore, it is imperative to gather biomechanical data from the Marfan vasculature so that clinicians may predict the effects of vascular complications in Marfan patients and develop appropriate methods of treatment.

The objective of this dissertation is to develop a suitable statistical methodology for functional data analysis. Modern advanced technology allows researchers to collect samples as functional which means the ideal unit of samples is a curve. We consider each functional observation as the resulting of a digitized recoding or a realization from a stochastic process. Traditional statistical methodologies often fail to be applied to this functional data set due to the high dimensionality. Functional hypothesis testing is the main focus of my dissertation. We suggested a testing procedure to determine the significance of two curves with order restriction. This work was motivated by a case study involving high-dimensional and high-frequency tidal volume traces from the New York State Psychiatric Institute at Columbia University. The overall goal of the study was to create a model of the clinical panic attack, as it occurs in panic disorder (PD), in normal human subjects. We proposed a new dimension reduction technique by non-negative basis matrix factorization (NBMF) and adapted a one-degree of freedom test in the context of multivariate analysis. This is important because other dimension techniques, such as principle component analysis (PCA), cannot be applied in this context due to the order restriction. Another area that we investigated was the estimation of functions with constrained restrictions such as convexification and/or monotonicity, together with the development of computationally efficient algorithms to solve the constrained least square problem. This study, too, has potential for applications in various fields. For example, in economics the cost function of a perfectly competitive firm must be increasing and convex, and the utility function of an economic agent must be increasing and concave. We propose an estimation method for a monotone convex function that consists of two sequential shape modification stages: (i) monotone regression via solving a constrained least square problem and (ii) convexification of the monotone regression estimate via solving an associated constrained uniform approximation problem.

Nature encourages diversity in life forms (morphologies). The study of morphogenesis deals with understanding those processes that arise during the embryonic development of an organism. These processes control the organized spatial distribution of cells, which in turn gives rise to the characteristic form for the organism. Morphogenesis is a multi-scale modeling problem that can be studied at the molecular, cellular, and tissue levels. Here, we study the problem of morphogenesis at the cellular level by introducing an integrated biomechanical model of cells embedded in the extracellular matrix. The fundamental aspects of mechanobiology essential for studying morphogenesis at the cellular level are the cytoskeleton, extracellular matrix (ECM), and cell adhesion. Cells are modeled using tensegrity architecture. Our simulations demonstrate cellular events, such as differentiation, migration, and division using an extended tensegrity architecture that supports dynamic polymerization of the micro-filaments of the cell. Thus, our simulations add further support to the cellular tensegrity model. Viscoelastic behavior of extracellular matrix is modeled by extending one-dimensional mechanical models (by Maxwell and by Voigt) to three dimensions using finite element methods. The cell adhesion is modeled as a general Velcro-type model. We integrated the mechanics and dynamics of cell, ECM, and cell adhesion with a geometric model to create an integrated biomechanical model. In addition, the thesis discusses various computational issues, including generating the finite element mesh, mesh refinement, re-meshing, and solution mapping. As is known from a molecular level perspective, the genetic regulatory network of the organism controls this spatial distribution of cells along with some environmental factors modulating the process. The integrated biomechanical model presented here, besides generating interesting morphologies, can serve as a mesoscopic-scale platform upon which future work can correlate with the underlying genetic network.

Carbonates invariably have small (micron) to large (centimeter) scale heterogeneities in flow properties that may cause the effects of injected acids to differ greatly from what is predicted by a model based on a homogenous formation. To the best of our knowledge, there are neither theoretical nor experimental studies on the effect of large scale heterogeneities (vugs) on matrix acidizing. The abundance of carbonate reservoirs (60% of the world?s oil reserves) and the lack of a detailed study on the effect of multi-scale heterogeneities in carbonate acidizing are the main motivations behind this study. In this work, we first present a methodology to characterize the carbonate cores prior to the core-flood acidizing experiments. Our approach consists of characterization of the fine-scale (millimeter) heterogeneities using computerized tomography (CT) and geostatistics, and the larger-scale (millimeter to centimeter) heterogeneities using connected component labeling algorithm and numerical simulation. In order to understand the connectivity of vugs and thus their contribution to flow, a well-known 2D visualization algorithm, connected component labeling (CCL), was implemented in 3D domain. Another tool used in this study to understand the connectivity of the vugs and its effect on fluid flow is numerical simulation. A 3D finite difference numerical model is developed based on Darcy-Brinkman formulation (DBF). Using the developed simulator a flow-based inversion approach is implemented to understand the connectivity of the vugs in the samples studied. After multi-scale characterization of the cores, acid core-flood experiments are conducted. Cores measuring four inches in diameter by twenty inches in length are used to decrease the geometry effects on the wormhole path. The post acid injection porosity distribution and wormhole paths are visualized after the experiments. The experimental results demonstrate that acid follows not only the high permeability paths but also the spatially correlated ones. While the connectivity between the vugs, total amount of vuggy pore space and size of the cores are the predominant factors, spatial correlation of the petro-physical properties has less pronounced effect on wormhole propagation in acidiziation of carbonates. The fact that acid channeled through the vugular cores, following the path of the vug system, was underlined with computerized tomography scans of the cores before and after acid injection. This observation proposes that local pressure drops created by vugs are more dominant in determining the wormhole flow path than the chemical reactions occurring at the pore level. Following this idea, we present a modeling study in order to understand flow in porous media in the presence of vugs. Use of coupled Darcy and Stokes flow principles, known as Darcy-Brinkman formulation (DBF), underpins the proposed approach. Several synthetic simulation scenarios are created to study the effect of vugs on flow and transport. The results demonstrate that total injection volume to breakthrough is affected by spatial distribution, amount and connectivity of vuggy pore space. An interesting finding is that although the presence and amount of vugs does not change the effective permeability of the formation, it could highly effect fluid diversion. We think this is a very important observation for designing of multi layer stimulation.

The purpose of matrix stimulation in carbonate reservoirs is to bypass damaged zones and increase the effective wellbore area. This can be achieved by creating highly conductive flow channels known as wormholes. A further injection of acid will follow a wormhole path where the permeability has increased significantly, leaving substantial intervals untreated. Diverting materials such as surfactant-based acids plays an important role in mitigating this problem. In this study and for the first time, 20-inch long cores were used to conduct the acidizing experiments in two configurations, single coreflood and parallel coreflood. The major findings from performing single coreflood experiments can be summarized as follows: The acid injection rate was found to be a critical parameter in maximizing the efficiency of using surfactant-based acids as a diverting chemical, in addition to creating wormholes. The maximum apparent viscosity, which developed during viscoelastic surfactant acid injection, occurred over a narrow range of acid injection rates. Higher injection rates were not effective in enhancing the acidizing process, and the use of diverting material produced results similar to those of regular acids. The amount of calcium measured in the effluent samples suggests that, if the acid was injected below the optimum rate, it would allow the acid filtrate to extend further ahead of the wormhole; at some point, it would trigger the surfactant and form micelles. When the acid injection rate was lowered further to a value of 1.5 cm3/min, the fluid front developed in more progressive fashion and the calcium concentration was more significant, continuing to increase until wormhole breakthrough On the other hand, the parallel coreflood tests show several periods that can be identified from the shape of the flow rate distribution entering each core. The acid injection rate was confirmed as influencing the efficiency of the surfactant to divert acid. Acid diversion was noted to be most efficient at low rates (3 cm3/min). No significant diversion was noted at high initial permeability ratios, at least for the given core length. The use of surfactant-based acid was also found to be constrained by the scale of the initial permeability ratio. For permeability ratios greater than about 10, diversion was insufficient.

Reactive power, denoted as volt-ampere reactive (VARs), is fundamental to ac power systems and is due to the complex impedance of the loads and transmission lines. It has several undesirable consequences which include increased transmission loss, reduction of power transfer capability, and the potential for the onset of system-wide voltage instability, if not properly compensated and controlled. Reactive power compensation is a technique used to manage and control reactive power in the ac network by supplying or consuming VARs from points near the loads or along the transmission lines. Load compensation is aimed at applying power factor correction techniques directly at the loads by locally supplying VARs. Typical loads such as motors and other inductive devices operate with lagging power factor and consume VARs; compensation techniques have traditionally employed capacitor banks to supply the required VARs. However, capacitors are known to have reliability problems with both catastrophic failure modes and wear-out mechanisms. Thus, they require constant monitoring and periodic replacement, which greatly increases the cost of traditional load compensation techniques. This thesis proposes a reactive power load compensator that uses inductors (chokes) instead of capacitors to supply reactive power to support the load. Chokes are regarded as robust and rugged elements; but, they operate with lagging power factor and thus consume VARs instead of generating VARs like capacitors. A matrix converter interfaces the chokes to the ac network. The matrix converter is controlled using the Venturini modulation method which can enable the converter to exhibit a current phase reversal property. So, although the inductors draw lagging currents from the output of the converter, the converter actually draws leading currents from the ac network. Thus, with the proposed compensation technique, lagging power factor loads can be compensated without using capacitor banks. The detailed operation of the matrix converter and the Venturini modulation method are examined in the thesis. The application of the converter to the proposed load compensation technique is analyzed. Simulations of the system in the MATLAB and PSIM environments are presented that support the analysis. A digital implementation of control signals for the converter is developed which demonstrates the practical feasibility of the proposed technique. The simulation and hardware results have shown the proposed compensator to be a promising and effective solution to the reliability issues of capacitor-based load-side VAR compensation techniques.