Problems in the classical calculus of variations

This dissertation concerns convergence analysis for nonparametric problems in the calculus of variations and sufficient conditions for weak local minimizer of a functional for both nonparametric and parametric problems. Newton's method in infinite-dimensional space is proved to be well-defined and converges quadratically to a weak local minimizer of a functional subject to certain boundary conditions. Sufficient conditions for global converges are proposed and a well-defined algorithm based on those conditions is presented and proved to converge. Finite element discretization is employed to achieve an implementable line-search-based quasi-Newton algorithm and a proof of convergence of the discretization of the algorithm is included. This work also proposes sufficient conditions for weak local minimizer without using the language of conjugate points. The form of new conditions is consistent with the ones in finite-dimensional case. It is believed that the new form of sufficient conditions will lead to simpler approaches to verify an extremal as local minimizer for well-known problems in calculus of variations.

IMPROVEMENTS IN SUSTAINABILITY OF GRAVITY-FED WATER SYSTEMS IN THE COMARCA NGÄBE-BUGLÉ, PANAMA: SPRING CAPTURES AND CIRCUIT RIDER MODEL

Gravity-flow aqueducts are used to bring clean water from mountain springs in the Comarca Ngäbe-Buglé, Panama, to the homes of the indigenous people who reside there. Spring captures enclose a spring to direct the flow of water into the transmission line. Seepage contact springs are most common, with water appearing above either hard basalt bedrock or a dense clay layer. Spring flows vary dramatically during wet and dry seasons, and discharge points of springs can shift, sometimes enough to impact the capture structure and its ability to properly collect all of the available water. Traditionally, spring captures are concrete boxes. The spring boxes observed by the author were dilapidated or out of alignment with the spring itself, only capturing part of the discharge. An improved design approach was developed that mimics the terrain surrounding the spring source to address these issues. Over the course of a year, three different spring sites were evaluated, and spring captures were designed and constructed based on the new approach. Spring flow data from each case study demonstrate increased flow capture in the improved structures. Rural water systems, including spring captures, can be sustainably maintained by the Circuit Rider model, a technical support system in which technical assistance is provided for the operation of the water systems. During 2012-2013, the author worked as a Circuit Rider and facilitated a water system improvement project while exploring methods of community empowerment to increase the capacity for system maintenance. Based on these experiences, recommendations are provided to expand the Circuit Rider model in the Comarca Ngäbe-Buglé under the Panamanian Ministry of Health’s Water and Sanitation Project (PASAP)

ON THE DIGITAL-POLITICAL TOPOGRAPHY OF MUSIC

The persuasive power of music is often relegated to the dimension of pathos: that which moves us emotionally. Yet, the music commodity is now situated in and around the liminal spaces of digitality. To think about how music functions, how it argues across media, and how it moves us, we must examine its material and immaterial realities as they present themselves to us and as we so create them. This dissertation rethinks the relationship between rhetoric and music by examining the creation, performance, and distribution of music in its material and immaterial forms to demonstrate its persuasive power. While both Plato and Aristotle understood music as a means to move men toward virtue, Aristotle tells us in his Laws, through the Athenian Stranger, that the very best kinds of music can help guide us to truth. From this starting point, I assess the historical problem of understanding the rhetorical potential of music as merely that which directs or imitates the emotions: that which “Soothes the savage breast,” as William Congreve writes. By furthering work by Vickers and Farnsworth, who suggest that the Baroque fascination with applying rhetorical figures to musical figures is an insufficient framework for assessing the rhetorical potential of music, I demonstrate the gravity of musical persuasion in its political weight, in its violence—the subjective violence of musical torture at Guantanamo and the objective, ideological violence of music—and in what Jacques Attali calls the prophetic nature of music. I argue that music has a significant function, and as a non-discursive form of argumentation, works on us beyond affect. Moreover, with the emergence of digital music distribution and domestic digital recording technologies, the digital music commodity in its material and immaterial forms allows for ruptures in the former methods of musical composition, production, and distribution and in the political potential of music which Jacques Attali describes as being able to foresee new political realities. I thus suggest a new theoretical framework for thinking about rhetoric and music by expanding on Lloyd Bitzer’s rhetorical situation, by offering the idea of “openings” to the existing exigence, audience, and constraints. The prophetic and rhetorical power of music in the aleatoric moment can help provide openings from which new exigencies can be conceived. We must, therefore, reconsider the role of rhetorical-musical composition for the citizen, not merely as a tool for entertainment or emotional persuasion, but as an arena for engaging with the political.