TRADITION AND INNOVATION: ANALYSIS AND PERFORMANCE OF SELECTED COMPOSITIONS FOR VIOLONCELLO BY HEITOR VILLA-LOBOS

Brazilian composer Heitor Villa-Lobos (1887-1959) began his musical career as a cellist. When he was only twelve years old, it became imperativeupon the sudden and untimely death of his fatherthat the young Villa-Lobos earn money as a cellist to provide financial support for his mother and sisters. Villa-Lobos's intimate relationship with the cello eventually inspired him to compose great music for this instrument. This dissertation explores both the diversity of compositional technique and the evolution of style found in the music for cello written by Villa-Lobos. The project consists of two recorded recital performances and a written document exploring and analyzing those pieces. In the study of the music of Villa-Lobos, it is of great interest to consider the music's traditional European elements in combination (or even juxtaposition) with its imaginative and sometimes wildly innovative Brazilian character. His early works were greatly influenced by European Romantic composers such as Robert Schumann, Frédéric Chopin, and the virtuoso cellist/composer David Popper (whom Villa-Lobos idolized). Later, Villa-Lobos flourished in a newfound compositional independence and moved away from Euro-romanticism and toward the folk music of his Brazilian homeland. It is intriguing to experience this transition through an exploration of his cello compositions. The works examined and performed in this dissertation project are chosen from among the extensive number of Villa-Lobos's cello compositions and are his most important works for cello with piano, cello with another instrument, and cello with orchestra. The chosen works demonstrate the evolving range and combination of characteristic elements found in Villa-Lobos's compositional repertoire.

Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.

DESIGN, FABRICATION, AND PERFORMANCE CHARACTERIZATION OF MULTIFUNCTIONAL STRUCTURES TO HARVEST SOLAR ENERGY FOR FLAPPING WING AERIAL VEHICLES

Flapping Wing Aerial Vehicles (FWAVs) have the capability to combine the benefits of both fixed wing vehicles and rotary vehicles. However, flight time is limited due to limited on-board energy storage capacity. For most Unmanned Aerial Vehicle (UAV) operators, frequent recharging of the batteries is not ideal due to lack of nearby electrical outlets. This imposes serious limitations on FWAV flights. The approach taken to extend the flight time of UAVs was to integrate photovoltaic solar cells onto different structures of the vehicle to harvest and use energy from the sun. Integration of the solar cells can greatly improve the energy capacity of an UAV; however, this integration does effect the performance of the UAV and especially FWAVs. The integration of solar cells affects the ability of the vehicle to produce the aerodynamic forces necessary to maintain flight. This PhD dissertation characterizes the effects of solar cell integration on the performance of a FWAV. Robo Raven, a recently developed FWAV, is used as the platform for this work. An additive manufacturing technique was developed to integrate photovoltaic solar cells into the wing and tail structures of the vehicle. An approach to characterizing the effects of solar cell integration to the wings, tail, and body of the UAV is also described. This approach includes measurement of aerodynamic forces generated by the vehicle and measurements of the wing shape during the flapping cycle using Digital Image Correlation. Various changes to wing, body, and tail design are investigated and changes in performance for each design are measured. The electrical performance from the solar cells is also characterized. A new multifunctional performance model was formulated that describes how integration of solar cells influences the flight performance. Aerodynamic models were developed to describe effects of solar cell integration force production and performance of the FWAV. Thus, performance changes can be predicted depending on changes in design. Sensing capabilities of the solar cells were also discovered and correlated to the deformation of the wing. This demonstrated that the solar cells were capable of: (1) Lightweight and flexible structure to generate aerodynamic forces, (2) Energy harvesting to extend operational time and autonomy, (3) Sensing of an aerodynamic force associated with wing deformation. Finally, different flexible photovoltaic materials with higher efficiencies are investigated, which enable the multifunctional wings to provide enough solar power to keep the FWAV aloft without batteries as long as there is enough sunlight to power the vehicle.