RAPID SPACE TRAJECTORY GENERATION USING A FOURIER SERIES SHAPE-BASED APPROACH

With the insatiable curiosity of human beings to explore the universe and our solar system, it is essential to benefit from larger propulsion capabilities to execute efficient transfers and carry more scientific equipment. In the field of space trajectory optimization the fundamental advances in using low-thrust propulsion and exploiting the multi-body dynamics has played pivotal role in designing efficient space mission trajectories. The former provides larger cumulative momentum change in comparison with the conventional chemical propulsion whereas the latter results in almost ballistic trajectories with negligible amount of propellant. However, the problem of space trajectory design translates into an optimal control problem which is, in general, time-consuming and very difficult to solve. Therefore, the goal of the thesis is to address the above problem by developing a methodology to simplify and facilitate the process of finding initial low-thrust trajectories in both two-body and multi-body environments. This initial solution will not only provide mission designers with a better understanding of the problem and solution but also serves as a good initial guess for high-fidelity optimal control solvers and increases their convergence rate. Almost all of the high-fidelity solvers enjoy the existence of an initial guess that already satisfies the equations of motion and some of the most important constraints. Despite the nonlinear nature of the problem, it is sought to find a robust technique for a wide range of typical low-thrust transfers with reduced computational intensity. Another important aspect of our developed methodology is the representation of low-thrust trajectories by Fourier series with which the number of design variables reduces significantly. Emphasis is given on simplifying the equations of motion to the possible extent and avoid approximating the controls. These facts contribute to speeding up the solution finding procedure. Several example applications of two and three-dimensional two-body low-thrust transfers are considered. In addition, in the multi-body dynamic, and in particular the restricted-three-body dynamic, several Earth-to-Moon low-thrust transfers are investigated.

BUILDING A DISCOURSE: BRIDGING THE GAP BETWEEN NEW MEDIA'S CONVERGENCE AND RHETORIC AND COMPOSITION'S MULTIMODALITY

My dissertation emphasizes the use of narrative structuralism and narrative theories about storytelling in order to build a discourse between the fields of New Media and Rhetoric and Composition. Propp's morphological analysis and the breaking down of stories into component pieces aides in the discussion of storytelling as it appears in and is mediated by digital and computer technologies. New Media and Rhetoric and Composition are aided by shared concerns for textual production and consumption. In using the notion of "kairotic reading" (KR), I show the interconnectedness and interdisciplinarity required in the development of pedagogy utilized to teach students to develop into reflective practitioners that are aware of their rhetorical surroundings and can made sound judgments concerning their own message generation and consumption in the workplace. KR is a transferable skill that is beneficial to students and teachers alike. The dissertation research utilizes theories of New Media and New Media-influenced practitioners, including Jenkins' theory of convergence, Bourdieu's notion of taste, Gee's term "semiotic domains," and Manovich's "modification." These theoretical pieces are combined in order to show how KR can be extended by convergent narrative practices. In order to build connections with New Media, the consideration and inclusion of Kress and van Leeuwen's multimodality, Selber's "reflective practitioners," and Selfe's definition of multimodal composing allow for a greater establishment of conversation order to create a richer conversation around the implications of metacognitive development and practitioner reflexivity with scholars in New Media. My research also includes analysis of two popular media franchises Deborah Harkness' A Discovery of Witches and Fox's Bones television series to show similarities and differences among convergence-linked and multimodal narratives. Lastly, I also provide example assignments that can be taken, further developed, and utilized in classrooms engaging in multimodal composing practices. This dissertation pushes consideration of New Media into the work already being performed by those in Rhetoric and Composition.

RATE OF CONVERGENCE OF MAXIMUM LIKELIHOOD ESTIMATORS UNDER RELAXED SMOOTHNESS CONDITIONS ON THE LIKELIHOOD FUNCTION

This report reviews literature on the rate of convergence of maximum likelihood estimators and establishes a Central Limit Theorem, which yields an O(1/sqrt(n)) rate of convergence of the maximum likelihood estimator under somewhat relaxed smoothness conditions. These conditions include the existence of a one-sided derivative in θ of the pdf, compared to up to three that are classically required. A verification through simulation is included in the end of the report.