Analysis of Self-Organization

The dissertation is devoted to the study of problems in calculus of variation, free boundary problems and gradient flows with respect to the Wasserstein metric. More concretely, we consider the problem of characterizing the regularity of minimizers to a certain interaction energy. Minimizers of the interaction energy have a somewhat surprising relationship with solutions to obstacle problems. Here we prove and exploit this relationship to obtain novel regularity results. Another problem we tackle is describing the asymptotic behavior of the Cahn-Hilliard equation with degenerate mobility. By framing the Cahn-Hilliard equation with degenerate mobility as a gradient flow in Wasserstein metric, in one space dimension, we prove its convergence to a degenerate parabolic equation under the framework recently developed by Sandier-Serfaty.

Post-1945 Danish Piano Trio Literature: A Recording Dissertation

This recording dissertation surveys post-1945 literature written for piano trio (violin, violoncello and piano) by ten Danish composers. The literature was first considered for inclusion by searching a database provided by the Danish Music Information Center (www.mic.dk). Scores were rented from the publisher Edition Wilhelm Hansen AS, or purchased from the publisher Samfundet til Udgivelse af Dansk Musik. An additional score published by Viking Musikforlag was used as well. The music was then studied and evaluated for selection. During the selection process, the following criteria were considered: 1) quality of the compositions; 2) recognition of the composers at the national or international level; 3) whether the compositions had been previously recorded; and 4) variety of compositional styles. The selected works are written by Niels Viggo Bentzon, Vagn Holmboe, Anders Koppel, Herman D. Koppel, Bent Lorentzen, Anders Nordentoft, Per Norgard, Michael Nyvang, Karl Aage Rasmussen, and Poul Rovsing Olsen. The selected compositions were practiced, rehearsed, and performed under direct supervision of the composers and other expert musicians. In order to better understand the compositional style of each composer, relevant books, articles, and recordings were researched and studied. This recording dissertation is supported by a written document. A subjective preference for program balance was exercised to determine the order of recorded works. The written document is divided into chapters defined by composer, following the order of the recorded document, which include the composers' biographies and notes referring to the recorded compositions. The recording took place at the Manzius Gaarden, Birkerod, Denmark during three sessions: July 31-August 2, 2002, March 2 and 3, 2003, and June 2-4, 2003. The music for this dissertation was recorded by the members of the Jalina Trio; Line Fredens, violin, Janne Fredens, cello and Natsuki Fukasawa, piano. Aksel Trige, a well-respected recording engineer, was engaged for the recording and editing. Additionally, a Hamburg Steinway concert grand piano was rented and a Joseph Guarnerius filius Andreas Cremona violin (1706) was provided by the Augustinus Fonden, Denmark. The cellist used her own instrument, Vuillaume of Paris (c. 1850). The expense of this recording was partially paid by generous grants from the Augustinus Fonden, the Solist Foreningen af 1921, and the Dansk Musikerforbunds Kollective Rettighedsmidler. The compositions selected for this recording dissertation are assumed to be previously unrecorded, with the exception of Poul Rovsing Olsen's Trio II.

THE ART SONG OF SOUTH AMERICA: AN EXPLORATION THROUGH PERFORMANCE

The repertoire included in this dissertation was presented over the course of three recitals, The Songs of Argentina, The Songs of Brazil, Chile and Venezuela, and The Songs of Perú and Colombia. Each recital was supplemented by written program notes and English translations of the Spanish, Portuguese and Quechua texts. The selections presented in this study was chosen in an effort to pair the works of internationally renowned composers like Argentine composers Alberto Ginastera and Carlos Guastavino, and Brazilian composer Heitor Villa-Lobos, with those of lesser-known composers, including Venezuelan composer Juan Bautista Plaza, Peruvian composers Edgar Valcárcel, Theodoro Valcárcel, and Rosa Mercedes Ayarza de Morales, and Colombian composer Jaime Léon. Each composer represents a milestone in the development of art song composition in South America. All three recitals were recorded and are available on compact discs in the Digital Repository at the University of Maryland (DRUM). This dissertation was completed in May, 2011.

THE ART OF TRANSCRIBING FOR HARPSICHORD

A relatively unexplored area of the harpsichord repertoire is the group of transcriptions made by J.S. Bach (1685-1750), Jean Henry d'Anglebert (1629-1691), and Jean-Baptiste Forqueray (1699-1782). These transcriptions are valuable and worth exploring and performing. Studying them provides unique insights into their composer‘s musical thinking. By comparing transcriptions with their original sources, the transcriber's decisions and priorities can be observed. The performance component of this dissertation comprises three recitals. The first features works of Johann Sebastian Bach: two transcriptions of violin concerti by Antonio Vivaldi (1678-1741), and two transcriptions of trio sonatas by Johann Adam Reinken (1643-1722). The most salient feature of Bach‘s transcriptions is his addition of musical material: ornamenting slow movements, adding diminutions and idiomatic keyboard figurations throughout, and recomposing and expanding fugal movements. The second recital features works of Jean Henry d'Anglebert and Jean-Baptiste Forqueray, two French composer/performers. From d'Anglebert‘s many transcriptions, I assembled two key-related suites: the first comprised of lute pieces by Ennemond Gaultier (c. 1575-1651), and the second comprised of movements from operas by Jean-Baptiste Lully (1632-1687). Forqueray's transcriptions are of suites for viola da gamba and continuo, composed by his father, Antoine Forqueray (1671-1745). Creative and varied ornamentation, along with the style brisé of arpeggiated chords, are the most important features of d‘Anglebert‘s transcriptions. Forqueray‘s transcriptions are highly virtuosic and often feature the tenor and bass range of the harpsichord. The third recital features my own transcriptions: the first suite for solo cello by J.S. Bach, excerpts from the opera La Descente d’Orphée aux Enfers by Marc-Antoine Charpentier (1643-1704), and two violin pieces by Nicola Matteis (fl. c. 1670-c. 1698). In these transcriptions, I demonstrate what I have learned from studying and performing the works in the first two recitals. These recitals were performed in the Leah Smith Hall at the University of Maryland on May 4, 2010; May 11, 2010; and October 7, 2010. They were recorded on compact discs and are archived within the Digital Repository at the University of Maryland (DRUM).