Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

EFFECT OF MUSIC ON THE SOUL: INTENT OR INDIFFERENCE IN THE COMPOSITION OF EWAZEN, FETTER, HIDAS, HOVHANESS, PEDERSON AND WILDER

This performance dissertation completed in 2009 by bass trombonist and Doctor of Musical Arts candidate Karl Wiederwohl consists of three live recitals and a written document which serves as a complement to the performances. The document discusses the six composers whose music is performed on the recitals. The document's six chapters respectively discuss each composer's disposition with regard to their purpose in composing music. As a complement to the performances the document gives special attention to each composer's thoughts on affecting listeners through their music. Wiederwohl creates a window into the mentality behind the artistry of Eric Ewazen, David Fetter, Frigyes Hidas, Alan Hovhaness, Tommy Pederson and Alec Wilder. The document serves to inform and enrich the experience of both performers and listeners of these six composers. This is achieved through the document's treatment of the following four questions for each composer: How did each come to be a composer? How did each come to compose in his particular style? Does the composer intend his music to serve a purpose? Does the composer intend his music to serve a purpose, and, if so, does this purpose involve reaching and/or affecting the listener at the deepest level?

A GOLDEN AGE: FRENCH AND SPANISH CELLO MUSIC FROM SAINT-SAENS TO CASSADO

Motivated by both the delicacy of French music, such as La Mer by Claude Debussy, and the exotic atmosphere of Spanish music, such as Zigeunerweisen by Pablo Sarasate, I decided to investigate the characteristics of French and Spanish cello music from Camille Saint-Saens to Gaspar Cassad6. French cello music flourished from the end ofthel9th to the middle of the 20th century because of the innovation of many unprecedented techniques and experimentation with a variety of sonorities. The Spanish were heavily influenced by the French due to the geographical connection. Cello virtuosi like Auguste Tolbecque, August Franchomme, Pierre Fournier, and Paul Tortelier inspired composers of their day, creating a "golden age" of cello music. This dissertation consisted of three recitals in Gildenhom Recital Hall. The first recital was held on May lOth, 2007 at 5:30pm with pianist David Ballena. The second recital was held on October 14th, 2007 at 2pm with collaborators Minna Han, piano and Jenny Wu, violin. The third recital was held on March 301 2008 at 5:30 with pianist Naoko Takao. Here is the program of the recitals: The first recital: Gabriel Faure(1856-1924): Sonate pour Violoncello et Piano Op.109(1917) Gaspar Cassad6 (1897-1966): Suite per Violoncello Solo (1926) Claude Debussy (1862-1918): Sonate pour Violoncelle et Piano (1915) The second recital: Manuel de Falla (1876-1946): Melodia (1897), Romanza (1898) Camille Saint-Saens (1835-1921): Concerto for Cello and Orchestra No.1 in A minor Op.33 (1873) Maurice Ravel (1875-1973): Sonata for Violin and Cello (1920-22) The third recital: Pablo Casals (1876-1973): Song of the Birds (1925) Edouard Lalo (1823-1892): Concerto for Cello and Orchestra in D Minor (1877) Franscis Poulenc (1899-1963): Sonata for Cello and Piano Op.l43(1940-48)

The Evolution of Rachmaninov's Pianistic Style from 1892 to 1941 as Seen in Selected Original Works and Transcriptions for Piano

Unlike some other major composer-pianists (Franz Liszt and Alexander Scriabin being the most notable examples), Sergei Rachmaninov did not experience any dramatic changes in his compositional style; one can, however, notice certain stylistic differences between piano works composed during different periods of his long creative life. This dissertation argues that a clear evolution of Rachmaninov's pianistic style through his three creative periods can be traced by examining a selection of his compositions, from his first significant cycle for piano, 5 Marceaux de fantaisie, Op. 3 (1892), all the way through to his last piano work, a transcription of P.I.Tchakovsky's Lullaby, Op. 16, No. 1 (1941). Rachmaninov's life as a composer can be divided into three periods. His early period was ended abruptly by the disastrous premiere ofhis First Symphony in 1897, which caused a deep psychological crisis in the life of the young composer. Piano works of this period are often characterized by relatively simple homophonic texture, when Rachmaninov was clearly influenced by some of his Russian predecessors, most notably Tchaikovsky. His second and most productive period, also known as the period of"Russian maturity," started in 1900, when he began working on the Second Suite for two pianos, Op. 17, and the Second Concerto, Op. 18; this phase ended with the Russian Bolshevik revolution of 1917. Works of this time exhibit a mature style of piano writing, with rich, virtuosic - often considered excessive by many critics - texture and ever-increasing use of chromatic harmonies. Rachmaninov's works of the third period are limited in number owing to the composer's preoccupation with a career as pianist. Original works for piano now give way to revisions of earlier compositions and transcriptions: Rachmaninov's piano writing becomes more efficient and economical without losing any of its virtuosic brilliance. This dissertation project examines in detail, over the course of three piano recitals, a variety of works composed during the "Russian maturity" period, from several Preludes from Op. 23 (1903), the first major cycle for solo piano of the period, to 9 Etudes-Tableaux, Op.39 (1917), the last one; the early period is represented by 3 of 5 Marceaux defantaisie, Op. 3 (1892), while the late period is shown through several piano transcriptions and revised versions of the remaining 2 pieces from Op. 3.