Thesis (M.S. in Engineering Acoustics)--Naval Postgraduate School, December 2003. / Thesis advisor(s): Kevin Smith, Roy Streit. Includes bibliographical references (p. 95-100). Also available online.

In this thesis we investigate the problem of defining an extension of sutured instanton Floer homology to give an instanton invariant for a tangle. We do this in three separate steps. First, we investigate the representation variety of singular flat connections on a punctured Riemann surface \(\Sigma\). Suppose \(\Sigma\) has genus \(g\) and that there are \(n\) punctures. We give formulae for the Betti numbers of the space \(\mathcal{R}_{g,n}\) of flat \(SU(2)\)-connections on \(\Sigma\) with trace 0 holonomy around the punctures. By using a natural extension of the Atiyah-Bott generators for the cohomology ring \(H^*(\mathcal{R}_{g,n})\), we are able to write down a presentation for this ring in the case \(g=0\) of a punctured sphere. This is accomplished by studying the intersections of Poincaré dual submanifolds for the new generators and reducing the calculation to a linear algebra problem involving the symplectic volumes of the representation variety. We then study the related problem of computing the instanton Floer homology for a product link in a product 3-manifold <p>\((Y_g, K_n) := (S^1 \times \Sigma, S^1 \times \{n pts\})\).<\p> It is easy to see that the Floer homology of this pair, as a vector space, is essentially the same as the cohomology of \(\mathcal{R}_{g,n}\), and so we set ourselves to determining a presentation for the natural algebra structure on it in the case \(g = 0\). By leveraging a stable parabolic bundles calculation for \(n = 3\) and an easier version of this Floer homology, \(I _*(Y_0, K_n, u)\), we are able to write down a complete presentation for the Floer homology \(I _*(Y_0, K_n)\) as a ring. We recapitulate somewhat the techniques in \([\boldsymbol{27}]\) in order to do this. Crucially, we deduce that the eigenspace for the top eigenvalue for a natural operator \(\mu^{ orb} (\Sigma)\) on \(I_* (Y_0, K_n)\) is 1-dimensional.Finally, we leverage this 1-dimensional eigenspace to define an instanton tangle invariant THI and several variants by mimicking the de nition of sutured Floer homology SHI in \([\boldsymbol{22}]\). We then prove this invariant enjoys nice properties with respect to concatenation, and prove a nontriviality result which shows that it detects the product tangle in certain cases. / Mathematics

Thesis--Rheinische Friedrich-Wilhelms-Universität zu Bonn, 1986. / Publication date on cover: 1987. Includes bibliographical references (p. 55-58).

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2001. / Includes bibliographical references (p. 120-129).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Bibliography: leaves 60-62.

No description available.

The goal of this thesis is to present a comprehensive study of the parabolic and hyperbolic Anderson models with constant initial condition, driven by a Gaussian noise which is fractional in space with index H > 1/2 or H < 1/2, and is either white in time, or fractional in time with index H_0 > 1/2. As a preliminary step, we study the linear stochastic heat and wave equations with the same type of noise. In the case H_0 > 1/2 and H < 1/2, we present a new result, regarding the solution of the parabolic Anderson model with general initial condition given by a measure.

No description available.

This thesis continues the work started with my previous supervisor, Dr. Shaohua Chen. In [15], the authors developed some tools that showed the boundedness or blowup of solutions to a semilinear parabolic system with homogeneous Neumann boundary conditions. This system, the so called ’Activator-Inhibitor Model’, is of interest as it is used to model biological processes and pattern formation. Similar tools were later adapted to deal with the same parabolic system in [3], in which the authors prove global boundedness of solutions under homogeneous Dirichlet conditions. This new problem is of mathematical interest as the solutions may grow singular near the boundary. Shortly after, a different system was considered in [4], where the authors proved global boundedness of solutions to a system featuring similar singular reaction terms. The goal of this thesis is twofold: first, the tools developed that allow us to tackle these sorts of problems will be demonstrated in detail to showcase its utility; the second is to then use these tools to generalize some of these previous results to a larger class of singular parabolic systems. In doing so, we expand the classical literature found in [14] and other notable works, where nonsingular equations are extensively treated. The motivation for the first should be clear. While there are numerous bodies of text treating nonsingular problems, there are no collections available dealing with these types of singularities exclusively. This is of practical use to other mathematicians studying partial differential equations. The motivation for the second is, perhaps, more practical. There are a growing number of models found in physics, chemistry and biology that may be generalized to a singular type system. Through allowing those individuals to treat these problems, we may gain valuable insights into the real world and how these processes behave. / Thesis / Master of Science (MSc)

Underwater noise pollution is a significant environmental issue that can have detrimental effects on marine ecosystems. One of the main sources of underwater noise pollution is ship traffic, which has been shown to negatively impact marine animals by masking communication signals, altering their behaviors, and even causing hearing loss. In the Red Sea, ships are the main contributor to underwater noise pollution, particularly in areas with high shipping traffic. This thesis aims to understand the spatial and temporal distribution of underwater ship noise in the Red Sea using an acoustic propagation model, namely the Range-dependent Acoustic Model (RAM). RAM takes into account anthropogenic and environmental inputs including water temperature, salinity, and bathymetry to predict sound propagation in the Red Sea. By running RAM with inputs of ship traffic data, maps of underwater ship noise in the Red Sea were generated. These maps are important tools for policymakers and marine resource managers to identify areas of high noise pollution, target mitigation efforts accordingly, and guide future research on the effects of underwater noise pollution on marine life in the Red Sea.