Beethoven's Violinists: The Influence of Clement, Viotti, and the French School on Beethoven's Violin Compositions

Over the course of his career, Ludwig van Beethoven (1770–1827) admired and befriended many violin virtuosos. In addition to being renowned performers, many of these virtuosos were prolific composers in their own right. Through their own compositions, interpretive style and new technical contributions, they inspired some of Beethoven’s most beloved violin works. This dissertation places a selection of Beethoven’s violin compositions in historical and stylistic context through an examination of related compositions by Giovanni Battista Viotti (1755–1824), Pierre Rode (1774–1830) and Franz Clement (1780–1842). The works of these violin virtuosos have been presented along with those of Beethoven in a three-part recital series designed to reveal the compositional, technical and artistic influences of each virtuoso. Viotti’s Violin Concerto No. 2 in E major and Rode’s Violin Concerto No. 10 in B minor serve as examples from the French violin concerto genre, and demonstrate compositional and stylistic idioms that affected Beethoven’s own compositions. Through their official dedications, Beethoven’s last two violin sonatas, the Op. 47, or Kreutzer, in A major, dedicated to Rodolphe Kreutzer, and Op. 96 in G major, dedicated to Pierre Rode, show the composer’s reverence for these great artistic personalities. Beethoven originally dedicated his Violin Concerto in D major, Op. 61, to Franz Clement. This work displays striking similarities to Clement’s own Violin Concerto in D major, which suggests that the two men had a close working relationship and great respect for one another. The first recital was performed in Ulrich Recital Hall; the second and third recitals were performed in Gildenhorn Recital Hall at the University of Maryland. All three performances were collaborations with pianist, Hsiang-Ling Hsiao. A Recording of the first program can be found in the Digital Repository at the University of Maryland (DRUM). Recordings of the second and third recitals can be accessed at the University of Maryland Hornbake Library.

INVESTIGATIONS INTO MECHANISMS UNDERLYING EXTREME WAVE FORMATIONS AND COMPUTATIONALLY INTENSIVE SIMULATIONS

Various mechanisms have been proposed to explain extreme waves or rogue waves in an oceanic environment including directional focusing, dispersive focusing, wave-current interaction, and nonlinear modulational instability. The Benjamin-Feir instability (nonlinear modulational instability), however, is considered to be one of the primary mechanisms for rogue-wave occurrence. The nonlinear Schrodinger equation is a well-established approximate model based on the same assumptions as required for the derivation of the Benjamin-Feir theory. Solutions of the nonlinear Schrodinger equation, including new rogue-wave type solutions are presented in the author's dissertation work. The solutions are obtained by using a predictive eigenvalue map based predictor-corrector procedure developed by the author. Features of the predictive map are explored and the influences of certain parameter variations are investigated. The solutions are rescaled to match the length scales of waves generated in a wave tank. Based on the information provided by the map and the details of physical scaling, a framework is developed that can serve as a basis for experimental investigations into a variety of extreme waves as well localizations in wave fields. To derive further fundamental insights into the complexity of extreme wave conditions, Smoothed Particle Hydrodynamics (SPH) simulations are carried out on an advanced Graphic Processing Unit (GPU) based parallel computational platform. Free surface gravity wave simulations have successfully characterized water-wave dispersion in the SPH model while demonstrating extreme energy focusing and wave growth in both linear and nonlinear regimes. A virtual wave tank is simulated wherein wave motions can be excited from either side. Focusing of several wave trains and isolated waves has been simulated. With properly chosen parameters, dispersion effects are observed causing a chirped wave train to focus and exhibit growth. By using the insights derived from the study of the nonlinear Schrodinger equation, modulational instability or self-focusing has been induced in a numerical wave tank and studied through several numerical simulations. Due to the inherent dissipative nature of SPH models, simulating persistent progressive waves can be problematic. This issue has been addressed and an observation-based solution has been provided. The efficacy of SPH in modeling wave focusing can be critical to further our understanding and predicting extreme wave phenomena through simulations. A deeper understanding of the mechanisms underlying extreme energy localization phenomena can help facilitate energy harnessing and serve as a basis to predict and mitigate the impact of energy focusing.