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This thesis describes the manufacturing, structural analysis and testing of a composite cylinder for space application. This work includes the design and fabrication of a reusable multicomponent mandrel made of aluminum and steel and the manufacturing of a carbon fiber reinforced tube in an epoxy resin matrix. This structure intends to serve as the optical lens housing onboard a spacecraft. In addition, some future work needs to be done before this component is certified. The objective is to determine if the composite meets the stiffness and strength requirements for lens housing. The structural analysis is made by means of a finite element model simulating the true boundary conditions. The testing includes the design of a fixture to allow the composite cylinder to be mounted in one the testing machines at the Department of Aerospace Engineering at Texas A&M University and the preparation for the actual test. The response to the experimental analysis will be compared to the numerical simulation to verify the results.

This thesis proposes a novel synergy of the classical scenario and robust approaches used for strategic supply chain optimization under uncertainty. Two novel formulations, namely the naïve robust scenario formulation and the affinely adjustable robust scenario formulation, are developed, which can be reformulated into tractable deterministic optimization problems if the uncertainty is bounded by the infinity-norm. The two formulations are applied to a classical farm planning problem and an energy and bioproduct supply chain problem. The case study results demonstrate that, compared to the scenario formulation, the proposed formulations can achieve the optimal expected economic performance with smaller number of scenarios, and they can correctly indicate the feasibility of a problem. The results also show that the affinely adjustable robust scenario formulation can better address uncertainties than the naïve robust scenario formulation. Next, a strategic optimization problem for an industrial chemical supply chain from DuPont was studied. The supply chain involves one materials warehouse, five manufacturing plants, five regional product warehouses and five market locations. Each manufacturing plant produces up to 23 grades of final products from 55 grades of primary raw materials. The goal of the strategic optimization is to determine the capacities of the five plants to maximize the total profits of the supply chain system while satisfying uncertain customer demands at the different market locations. A mathematical model is developed to relate the material and product flows in the supply chain, based on which the classical scenario approach and the affinely adjustable robust scenario formulation were developed to address the uncertainty in the demands. The case study results show the advantages of the affinely robust scenario formulation over the scenario formulation. Using the affinely adjustable robust scenario formulation often results in problems with very large sizes, which cannot be solved by regular optimization solvers efficiently. In order to exploit the decomposable structure of the formulation, Dantzig-Wolfe decomposition is studied in the thesis. Two approaches to implement Dantzig-Wolfe decomposition are developed, and both approaches involve the solution of a sequence of linear programming (LP) and mixed-integer linear programming (MILP) subproblems. The computational study of the industrial chemical supply chain shows that a combination of the two Dantzig-Wolfe approaches can achieve an optimal or a near-optimal solution much more quickly than a state-of-the-art commercial LP/MILP solver, and the computational advantage increases with the increase of number of scenarios involved in the problem. / Thesis (Master, Chemical Engineering) -- Queen's University, 2014-03-24 20:39:42.761

This work focuses on an investigation of multi-modality in typical aerodynamic shape optimization problems and development of optimization algorithms that can find a global optimum. First, a classification of problems based on the degree of multi-modality is introduced. Then, two optimization algorithms are described that can find a global optimum in a computationally efficient manner: a gradient-based multi-start Sobol algorithm, and a hybrid optimization algorithm. Two additional algorithms are considered as well: a gradient-based optimizer and a genetic algorithm. Finally, we consider a set of typical aerodynamic shape optimization problems. In each problem, the primary objectives are to classify the problem according to the degree of multi-modality, and to select the preferred optimization algorithm for the problem. We find that typical two-dimensional airfoil shape optimization problems are unimodal. Three-dimensional shape optimization problems may contain local optima. In these problems, the gradient-based multi-start Sobol algorithm is the most efficient algorithm.

Tensors can be viewed as multilinear arrays or generalizations of the notion of matrices. Tensor decompositions have applications in various fields such as psychometrics, signal processing, numerical linear algebra and data mining. When the data are nonnegative, the nonnegative tensor factorization (NTF) better reflects the underlying structure. With NTF it is possible to extract information from a given dataset and construct lower-dimensional bases that capture the main features of the set and concisely describe the original data. Nonnegative tensor factorizations are commonly computed as the solution of a nonlinear bound-constrained optimization problem. Some inherent difficulties must be taken into consideration in order to achieve good solutions. Many existing methods for computing NTF optimize over each of the factors separately; the resulting algorithms are often slow to converge and difficult to control. We propose an all-at-once approach to computing NTF. Our method optimizes over all factors simultaneously and combines two regularization strategies to ensure that the factors in the decomposition remain bounded and equilibrated in norm. We present numerical experiments that illustrate the effectiveness of our approach. We also give an example of digital-inpainting, where our algorithm is employed to construct a basis that can be used to restore digital images.

We consider several applications in black-box quantum computation in which untrusted physical quantum devices are connected together to produce an experiment. By examining the outcome statistics of such an experiment, and comparing them against the desired experiment, we may hope to certify that the physical experiment is implementing the desired experiment. This is useful in order to verify that a calculation has been performed correctly, that measurement outcomes are secure, or that the devices are producing the desired state. First, we introduce constructions for a family of simulations, which duplicate the outcome statistics of an experiment but are not exactly the same as the desired experiment. This places limitations on how strict we may be with the requirements we place on the physical devices. We identify many simulations, and consider their implications for quantum foundations as well as security related applications. The most general application of black-box quantum computing is self-testing circuits, in which a generic physical circuit may be tested against a given circuit. Earlier results were restricted to circuits described on a real Hilbert space. We give new proofs for earlier results and begin work extending them to circuits on a complex Hilbert space with a test that verifies complex measurements. For security applications of black-box quantum computing, we consider device independent quantum key distribution (DIQKD). We may consider DIQKD as an extension of QKD (quantum key distribution) in which the model of the physical measurement devices is replaced with an adversarial model. This introduces many technical problems, such as unbounded dimension, but promises increased security since the many complexities hidden by traditional models are implicitly considered. We extend earlier work by proving security with fewer assumptions. Finally, we consider the case of black-box state characterization. Here the emphasis is placed on providing robust results with operationally meaningful measures. The goal is to certify that a black box device is producing high quality maximally entangled pairs of qubits using only untrusted measurements and a single statistic, the CHSH value, defined using correlations of outcomes from the two parts of the system. We present several measures of quality and prove bounds for them.

The design of combustion devices is very important to society today. They need to be highly efficient, while reducing emissions in order to meet strict environmental standards. These devices, however, are currently not being designed effectively. The most common method of improving them is through parametric studies, where the design parameters are altered one at a time to try and find the best operating point. While this method does work, it is not very enlightening as it neglects the non-linear interactions between the design parameters, requires a large amount of time, and does not guarantee that the best operating point is found. As the environmental standards continue to become stricter, a more robust method of optimizing combustion devices will be required. In this work a robust design optimization algorithm is presented that is capable of mathematically accounting for all of the interactions between the parameters and can find the best operating point of a combustion device. The algorithm uses response surface modeling to model the objective function, thereby reducing computational expense and time as compared to traditional optimization algorithms. The algorithm is tested on three case studies, with the goal of improving the radiant efficiency of a two stage porous radiant burner. The first case studied was one dimensional and involved adjusting the pore diameter of the second stage of the burner. The second case, also one dimensional, involved altering the second stage porosity. The third, and final, case study required that both of the above parameters be altered to improve the radiant efficiency. All three case studies resulted in statistically significantly changes in the efficiency of the burner.

This thesis intends to utilize mathematical models for testing the development of sustainable urban neighbourhoods and analyze the impact of these developments at city level using dynamic and multiobjective optimization techniques. These techniques aim to monitor and lower urban carbon emission levels, while predicting the municipality’s projected tax revenues. This study shows how multiple decision making models can operate and re- late to help analyze the implementation of a sustainable neighbourhood design in a mid-size urban area.

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