Fluorinated polymers of substantial high performance such as perfluorocyclobutyl (PFCB) and fluorinated aryl vinyl ether (FAVE) polymers can readily be synthesized by thermal [2+2] cyclopolymerization as a melt or by classical polycondensation. These fluoropolymers naturally possess high thermal and chemical resistance, low conductivity properties, and other mechanical properties. In this work, a method using 0th order kinetics is proposed and thermal degradation studies were conducted on six different aromatic ether-based polymers to gauge trends in activation energy barrier and differences in thermal stability by 0th order degradation kinetics. The activation barrier (E_a) obtained can give accurate insight into the stability of the polymer based only on structure for external applications. Activation energies ranging from 17 to 41 kcal/mol were obtained for the various polymers. Overall, this study provides an established method using TGA for thermal stability studies through 0th order kinetics that can be potentially used for future lab applications.

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Solving a sequence of high-dimensional, nonconvex, but potentially similar optimization problems poses a significant computational challenge in various engineering applications. This thesis presents the first meta-learning framework that leverages the shared structure among sequential tasks to improve the computational efficiency and sample complexity of derivative-free optimization. Based on the observation that most practical high-dimensional functions lie on a latent low-dimensional manifold, which can be further shared among problem instances, the proposed method jointly learns the meta-initialization of a search point and a meta-manifold. This novel approach enables the efficient adaptation of the optimization process to new tasks by exploiting the learned meta-knowledge. Theoretically, the benefit of meta-learning in this challenging setting is established by proving that the proposed method achieves improved convergence rates and reduced sample complexity compared to traditional derivative-free optimization techniques. Empirically, the effectiveness of the proposed algorithm is demonstrated in two high-dimensional reinforcement learning tasks, showcasing its ability to accelerate learning and improve performance across multiple domains. Furthermore, the robustness and generalization capabilities of the meta-learning framework are explored through extensive ablation studies and sensitivity analyses. The thesis highlights the potential of meta-learning in tackling complex optimization problems and opens up new avenues for future research in this area. / Master of Science / Optimization problems are ubiquitous in various fields, from engineering to finance, where the goal is to find the best solution among a vast number of possibilities. However, solving these problems can be computationally challenging, especially when the search space is high-dimensional and the problem is nonconvex, meaning that there may be multiple locally optimal solutions. This thesis introduces a novel approach to tackle these challenges by leveraging the power of meta-learning, a technique that allows algorithms to learn from previous experiences and adapt to new tasks more efficiently. The proposed framework is based on the observation that many real-world optimization problems share similar underlying structures, even though they may appear different on the surface. By exploiting this shared structure, the meta-learning algorithm can learn a low-dimensional representation of the problem space, which serves as a guide for efficiently searching for optimal solutions in new, unseen problems. This approach is particularly useful when dealing with a sequence of related optimization tasks, as it allows the algorithm to transfer knowledge from one task to another, thereby reducing the computational burden and improving the overall performance. The effectiveness of the proposed meta-learning framework is demonstrated through rigorous theoretical analysis and empirical evaluations on challenging reinforcement learning tasks. These tasks involve high-dimensional search spaces and require the algorithm to adapt to changing environments. The results show that the meta-learning approach can significantly accelerate the learning process and improve the quality of the solutions compared to traditional optimization methods.

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Electromagnetic wave propagation over random sea surfaces is a classical problem of interest for the Navy, and significant research has been done over the years. Here we make use of numerical and analytical methods to predict the propagation of microwaves over random rough surface. The numerical approach involves utilization of the direct solution (using Volterra integral equation of the second kind) to currents induced on a rough surface due to forward propagating waves to compute the scattered field. The mean scattered field is computed using the Monte-Carlo method. Since the exact solution (consisting of an infinite series) to induced current density is computationally intensive, there exists a need to predict the propagation using the closely accurate zeroth order induced current (first term of the series) for time-varying multiple realizations of a random rough surface in a computationally efficient manner. The wind-speed dependent, fully-developed, Piersen-Moskowitz sea spectrum has been considered in order to model a rough sea surface, although other partially-developed roughness spectra may also be utilized. An analytical solution based on the zeroth order current density obtained by deriving the mean scattered field as a function of the range and vertical height by directly using the Parabolic Equation (PE) approximation method and the resulting Green's function has been utilized for a comparative study. The analytical solution takes into account the diffused component of the scattered field.

In this thesis, a sliding mode controller employing a new sliding surface for antilock brake system (ABS) is proposed, its stability is proven formally and its performance is compared with existing sliding mode controllers. The new sliding mode controller uses the integral-derivative surface, which includes error, its derivative and its integral, all at the same time. This and the already existing derivative surface, which includes error and its derivative only, are named zerothorder sliding surfaces. Their stability analysis is done using first-order auxiliary surfaces. Auxiliary surfaces equal the sliding surfaces when derivative of the error becomes zero. The first-order error surface, which includes only the error, and the integral surface, which includes error and its integral, were also designed for comparison. During design, tire brake force response is modelled as an uncertainty. Controllers are simulated on a road with an abrupt change in road coefficient of adhesion. Controller parameters used are optimized, which results in comparable stopping distances while braking on a constant coefficient of adhesion road. Effect of first order actuator dynamics with varying time constants and actuator absolute time delay were considered. Reaching and sliding properties of controllers were also investigated, using results on a constant coefficient of adhesion road. It is observed that zeroth-order sliding surfaces give smoother response for both derivative and integral-derivative cases. As the controllers employing error and derivative surfaces get unstable in the presence of actuator time delay, the integral-derivative surface, proposed in this study, stands as the best controller.

We begin by studying field-theory amplitude relations such as the Kleiss-Kuijf, Bern-Carrasco-Johansson, Kawai-Lewellen-Tye and the double copy construction, which are important ingredients in this thesis. Going beyond the field-theory limit we study how the gauge-sector of the heterotic string relates to type I amplitudes through the single valued projection of multiple zeta values. At low energy and for a U(1) gauge group (a single brane) the type I amplitudes are generated by the Born-Infeld action, whereas the corresponding heterotic amplitudes vanish in this limit. As a simple exercise we study Yang-Mills theory deformed by a $F^4$ operator, which is the first correction induced by the Born-Infeld action. This exercise is then generalized by considering the four- and six-point amplitudes in Tseytlin's proposal for a non-Abelian Born-Infeld action. Comparing these amplitudes with those found in type I and heterotic string theory we attempt to gain more insight about the non-Abelian Born-Infeld action.

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The thesis deals with basic principles of metamaterials, which exhibit unusual properties in microwave applications (e.g., negative permittivity and permeability). Different type of metamaterial antennas and parameters of such antennas are described in the thesis.