Browsing by Subject "Continuity"
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Item An application of the continuity method for an equation on line bundles(2002) Gonçalves, Alexandre Casassola; Uhlenbeck, Karen K.Item Heroes of the past, readers of the present, stories of the future : continuity, cultural memory, and historical revisionism in superhero comics(2014-05) Friedenthal, Andrew J.; Davis, Janet M.This dissertation is a study of cultural memory, exploring how superhero comic books, and their readers and creators, look back on and make sense of the past, as well as how they use that past in the creation of community and stories today. It is my contention that the superhero comics that exist as part of a long-standing "universe," particularly those published by DC and Marvel, are inextricably linked to a sense of cultural memory which defines both the organization of their fans and the history of their stories, and that cultural memory in comics takes the twinned forms of fandom and continuity. Comic book fandom, from its very inception, has been based around memories of past stories and recollections about favorite moments, creators, characters, etc. Because of this, as many of those fans have gone on to become creators themselves, the stories they have crafted reflect that continual obsession with the histories -- loosely termed "continuity" by creators, fans, and comic book scholars -- of these fictional universes. Often, this obsession translates into an engagement with actual events from the past. In many of these cases, as with much art and ephemera that is immersed in cultural memory, these fans-turned-creators combine their interest in looking at the history of the fictional universe with a working out of actual traumatic events. My case studies focus on superhero comic books that respond to such events, particularly World War II, the Vietnam War, and 9/11.Item Numerical approximation of the spectrum of a nonselfadjoint operator governing the vibrations of a nonhomogeneous damped string(Texas Tech University, 2004-08) Busse, Theresa NicoleIn my dissertation, I present the results of numerical investigations of the spectrum of the damped hyperbolic equation involving damping terms, both in the equation and in the boundary conditions. This equation describes the vibrations of a realistic string having distributed (Kevin-Voight) damping and smart material inclusions (self-straining actuators) in the string. The action of the actuators is modeled through specific boundary conditions that involve two independent parameters reflecting the strengths of smart materials. The dissertation has two distinct parts: the first part is devoted to the physical background of vibrational motion, and the second part is devoted to the formulation of a specific problem, presentation, and discussion of the main findings of research. In my dissertation I consider a non standard Strum-Liouville problem. The problem is nonstandard due to two factors, the model incorporates two energy decay mechanisms, i.e., the energy of a string dissipates through the internal friction (Kevin- Voight damping) and through the end points of the string. Many researchers have studied the Strum-Liouville problem for the string equation in the absence of any damping. My problem involves two different types of damping, which makes the problem much more difficult. My particular goals were to investigate the distribution of the eigenfrequencies for the string (in mathematical language, the distribution of the eigenvalues of some linear operator), to analyze dependence on the damping coefficient, and finally to support a well known conjecture in the mathematical community about the multiple eigenfrequencies. In the course of my work, an unexpected discovery was made. I already mentioned, my main goal originally was to support a well known idea concerning the behavior and properties of purely imaginary eigenvalues for the aforementioned Strum-Liouville problem. Since I have a string with energy dissipation, the corresponding spectrum is a countable set of complex points. These points geometrically converge to some horizontal asymptote; these points form a set symmetric with respect to the imaginary axes. It has been assumed tin the mathematical community that with a change in the damping of small steps, the two eigenvalues closest to the imaginary axes would move toward each other, and finally they merge into one double eigenvalue. A minor change in the damping instantly breaks the double eigenvalues into two different simple purely imaginary eigenvalues. A goal of this thesis was to support that idea numerically. Unexpectedly, it was observed that the actual behavior of the two eigenvalues closest to the imaginary axes is totally different from the prediction. Namely, when I change the damping by a very small step (10"^^), for the first dozen steps, the eigenvalues behave as expected: they slowly move in such a way that the distance between them decreases. However, at some moment, those two eigenvalues totally change their behavior and begin moving apart in opposite directions. The movement continues along two branches of a hyperbola like curve until the moment when both eigenvalues reach the imaginary axes. When I continue changes in the damping, the pair of eigenvalues moves along the imaginary axes. So, my calculations show that contrary to the widespread opinion, the eigenvalues never merge to create a multiple one. This interesting and important behavior had not previously been observed. It should be emphasized that in my research I have changed the values of the coefficient that stands for the first order derivative in time of the unknown function {Ut). In the dissertation of R. Plant II [9], the dependence of multiple eigenvalues upon changing the density of the string, i.e., the coefficient standing before the highest derivative in time {Uu)- The fact that R. Plant obtained similar results, validates the importance of the discovery made in this thesis. The results here create more unsolved questions, and opens a rich and exciting area for future research in this area.Item