Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

This dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing the evolution of the fluid are coupled to the Smoluchowski equation for the particle density at a continuum level. First, working on fixed domains, the existence of weak solutions is established using a three-level approximation scheme and based largely on the Lions-Feireisl theory of compressible fluids. The system is then posed over a moving domain. By utilizing a Brinkman-type penalization as well as penalization of the viscosity, the existence of weak solutions of the Navier-Stokes-Smoluchowski system is proved over moving domains. As a corollary the convergence of the Brinkman penalization is proved. Finally, a suitable relative entropy is defined. This relative entropy is used to establish a weak-strong uniqueness result for the Navier-Stokes-Smoluchowski system over moving domains, ensuring that strong solutions are unique in the class of weak solutions.

W.A. Mozart's Die Zauberflöte An Arrangement and Performance Edition for Wind Instruments and Vocal Soloists

The purpose of this dissertation is to produce a new Harmonie arrangement of Mozart’s Die Zauberflöte suitable for modern performance, bringing Joseph Heidenreich’s 1782 arrangement—one of the great treasures of the wind repertoire—to life for future performers and audiences. I took advantage of the capabilities of modern wind instruments and performance techniques, and employed other instruments normally found in the modern wind ensemble to create a work in the tradition of Heidenreich’s that restored as much of Mozart’s original thinking as possible. I expanded the Harmonie band to include flute and string bass. Other instruments provide special effects, a traditional role for wind instruments in the Classical opera orchestra. This arrangement is conceived to be performed with the original vocal soloists, making it a viable option for concert performance or for smaller staged productions. It is also intended to allow the wind players to be onstage with the singers, becoming part of the dramatic action while simultaneously serving as the “opera orchestra.” This allows creative staging possibilities, and offers the wind players an opportunity to explore new aspects of performing. My arrangement also restores Mozart’s music to its original keys and retains much of his original wind scoring. This arrangement expands the possibilities for collaboration between opera studios, voice departments or community opera companies and wind ensembles. A suite for winds without voices (currently in production) will allow conductors to program this major work from the Classical era without dedicating a concert program to the complete opera. Excerpted arias and duets from this arrangement provide vocalists the option of using chamber wind accompaniment on recitals. The door is now open to arrangements of other operas by composers such as Mozart, Rossini and Weber, adding new repertoire for chamber winds and bringing great music to life in a new way.