Taylor, Erika A. (author), Rinaldo-Matthis, Agnes (author), Li, Lei (author), Ghanem, Mahmoud (author), Hazleton, Keith Z. (author), Cassera, María B. (author), Almo, Steven C. (author), Schramm, Vern L. (author)
Multi-mode systems, like cavities, fibers, etc, often suffer from the presence of environmental noise which causes mode mixing and subsequent interference between various modes. In many occasions, the study of the exact wave dynamics is a formidable task, due to the many degrees of freedom that have to be taken into account in the equations of motion that describe such systems. Instead, a statistical theory of wave propagation might be a best way to describe the wave transport in such frameworks. Following this way of thinking, we have utilized a Random Matrix Theory modeling which allows us to study the spreading of an initial mode excitation in the mode-space due to the environmental noise. Using this method, we have developed a systematic approach that enforces a variety of wave spreading scenarios mimicking generalized Levy-type dynamics that it is imposed from engineered noise correlations. Our theoretical predictions have been tested in realistic circumstances, like in paraxial light propagation in multimode fibers with tailored fiber cross-section modulations or in micro-cavities with time-modulated boundaries., In Copyright – Non-Commercial Use Permitted (InC-NC)
Li, Freda (Freda Li) (author), (Wai Kiu Chan) (Thesis advisor), Wesleyan University Mathematics (Degree grantor)
Let E be an imaginary quadratic field. A Hermitian lattice L is said to be regular if L globally represents all elements that are locally represented by L. It is n- regular if L globally represents all Hermitian lattices of rank n that are locally represented by L. In 2005 Rokicki proved that, for a fixed imaginary quadratic field, there exist only finitely many isometry classes of nondegenerate normalized positive definite n-regular Hermitian lattices of rank n + 1.
The notion of n-regularity can be strengthened to strict n-regularity. A sub- lattice, N, of a Hermitian lattice, L, is primitive in L if N is a direct summand of L. We say that L is strictly n-regular if L primitively represents all Hermitian lattices of rank n that are locally primitively represented by L. In this thesis, we prove an analogous result to Rokicki's for strictly n-regular Hermitian lattices, for n ≥ 2.
Another notion of regularity is almost n-regularity. A Hermitian lattice L is almost n-regular if L globally represents all but finitely many Hermitian lattices of rank n that are locally represented by L. In this thesis, we also consider almost n-regular lattices, and prove a finiteness result for almost n-regular lattices of rank n+1., In Copyright – Non-Commercial Use Permitted (InC-NC)
In the Peking opera ensemble, qinshi is the lead accompanist who plays the instrument jinghu. Historically, in addition to offering jinghu accompaniment, qinshi also served as Peking opera composers and Peking opera music teachers, contributing significantly to the artistry of Peking opera music. Since the 1980s, China has experienced tremendous social change, including economic and cultural reforms. Many traditional performance genres, including Peking opera, have encountered a survival crisis. Meanwhile, intracultural communications among different performance genres and art forms have become frequent and more intense, which have brought contemporary qinshi performance challenges as well as opportunities. In this context, many contemporary qinshi are no longer content to only play the traditional role as a lead accompanist in a Peking opera troupe. Although contemporary female qinshi¿s performances have attracted much attention in and outside of Peking opera circles, their musicality has been devalued by many Peking opera performers. In my dissertation, I will analyze the transformation of qinshi¿s performance tradition in the People¿s Republic of China (1949-present) from four perspectives: traditional jinghu accompaniment and accompaniment changes brought about by modernized Peking opera music, the institutionalization of qinshi¿s traditional training, contemporary qinshi¿s performance activities, and the impact of the all-male performance tradition on contemporary female qinshi¿s solo jinghu performance. These discussions will elaborate on how qinshi¿s performance tradition
and their musical lives have been shaped by political intervention, the market economy, mass media, and gender politics., In Copyright – Non-Commercial Use Permitted (InC-NC)