Proof theory of quantified modal logics

We introduce labelled sequent calculi for indexed modal logics. We prove that the structural rules of weakening and contraction are height-preserving admissible, that all rules are invertible, and that cut is admissible. Then we prove that each calculus introduced is sound and complete with respect to the appropriate class of transition frames.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Development of Measurement Methods for Testing of Hydrokinetic Devices to Evaluate the Environmental Effect on Local Substrate

Modifications and upgrades to the hydraulic flume facility in the Environmental Fluid Mechanics and Hydraulics Laboratory (EFM&H) at Bucknell University are described. These changes enable small-scale testing of model marine hydrokinetic(MHK) devices. The design of the experimental platform provides a controlled environment for testing of model MHK devices to determine their effect on localsubstrate. Specifically, the effects being studied are scour and erosion around a cylindrical support structure and deposition of sediment downstream from the device.

Impact of measurement errors on the determination of the linear modulus of human meniscal attachments

For the development of meniscal substitutes and related finite element models it is necessary to know the mechanical properties of the meniscus and its attachments. Measurement errors can falsify the determination of material properties. Therefore the impact of metrological and geometrical measurement errors on the determination of the linear modulus of human meniscal attachments was investigated. After total differentiation the error of the force (+0.10%), attachment deformation (−0.16%), and fibre length (+0.11%) measurements almost annulled each other. The error of the cross-sectional area determination ranged from 0.00%, gathered from histological slides, up to 14.22%, obtained from digital calliper measurements. Hence, total measurement error ranged from +0.05% to −14.17%, predominantly affected by the cross-sectional area determination error. Further investigations revealed that the entire cross-section was significantly larger compared to the load-carrying collagen fibre area. This overestimation of the cross-section area led to an underestimation of the linear modulus of up to −36.7%. Additionally, the cross-sections of the collagen-fibre area of the attachments significantly varied up to +90% along their longitudinal axis. The resultant ratio between the collagen fibre area and the histologically determined cross-sectional area ranged between 0.61 for the posterolateral and 0.69 for the posteromedial ligament. The linear modulus of human meniscal attachments can be significantly underestimated due to the use of different methods and locations of cross-sectional area determination. Hence, it is suggested to assess the load carrying collagen fibre area histologically, or, alternatively, to use the correction factors proposed in this study.

Harry Potter and the Theory of Things

This thesis investigates the boundaries between body and object in J.K. Rowling’s Harry Potter series, seven children’s literature novels published between 1997 and 2007. Lord Voldemort, Rowling’s villain, creates Horcruxes—objects that contain fragments of his soul—in order to ensure his immortality. As vessels for human soul, these objects rupture the boundaries between body and object and become “things.” Using contemporary thing theorists including John Plotz and materialists Jean Baudrillard and Walter Benjamin, I look at Voldemort’s Horcruxes as transgressive, liminal, unclassifiable entities in the first chapter. If objects can occupy the juncture between body and object, then bodies can as well. Dementors and Inferi, dark creatures that Rowling introduces throughout the series, live devoid of soul. Voldemort, too, becomes a thing as he splits his soul and creates Horcruxes. These soulless bodies are uncanny entities, provoking fear, revulsion, nausea, and the loss of language. In the second chapter, I use Sigmund Freud’s theorization of the uncanny as well as literary critic Kelly Hurley to investigate how Dementors, Inferi, and Voldemort exist as body-turned-object things at the juncture between life and death. As Voldemort increasingly invests his immaterial soul into material objects, he physically and spiritually degenerates, transforming from the young, handsome Tom Marvolo Riddle into the snake-like villain that murdered Harry’s parents and countless others. During his quest to find and destroy Voldemort’s Horcruxes, Harry encounters a different type of object, the Deathly Hallows. Although similarly accessing boundaries between body/object, life/death, and materiality/immateriality, the three Deathly Hallows do not transgress these boundaries. Through the Deathly Hallows, Rowling provides an alternative to thingification: objects that enable boundaries to fluctuate, but not breakdown. In the third chapter, I return to thing theorists, Baudrillard, and Benjamin to study how the Deathly Hallows resist thingification by not transgressing the boundaries between body and object.