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  1. Nonlinear Dynamics of Interacting Interfaces in Electrochemical and Biological Systems

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    Description: Interfacial phenomena play a considerable role in many physical, chemical and biological systems. Some of these systems exhibit interaction of several interfaces. This thesis contains a study of two types of systems characterized by interacting interfaces. First, a theory of the formation of nanoscale porous structures in oxides of metals...
    Keyword: Mathematics
    Subject: Applied Mathematics
    Creator: Christine Sample
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/19/2018
    Date Modified: 09/19/2018
    Date Created: 2008-09-03
    Rights: In Copyright
    Resource Type: Dissertation
  2. Resurgent analysis of the Witten Laplacian in One Dimension

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    Description: The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.
    Keyword: Mathematics
    Subject: Mathematics
    Creator: Alexander Getmaneko
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/14/2018
    Date Modified: 09/14/2018
    Date Created: 2008-08-11
    Rights: In Copyright
    Resource Type: Dissertation
  3. Index Theorems for Noncommutative Two-Tori and Hochschild Cohomology for Quantum Special Linear Groups

    Work
    Description: This paper covers three main topics. The first is addressing the question of interpolating between disparate index theorems on noncommutative two-tori. The second is to compute Hochschild cohomology for quantum special linear and special unitary groups. The third is producing an orthonormal basis for the vector space of matrix corepresentations...
    Keyword: Mathematics
    Subject: Mathematics
    Creator: Gary Clark Alexander
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/10/2018
    Date Modified: 09/10/2018
    Date Created: 2008-05-09
    Rights: In Copyright
    Resource Type: Dissertation
  4. Mathematical Modeling, Simulation, and Analysis of Two Problems in Interfacial Fluid Dynamics

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    Description: We consider two problems in low Reynolds-number, interfacial fluid mechanics: the rupture of thin liquid films on chemically patterned solid substrates, and the engulfment of foreign particles by a solidification front progressing through a binary alloy. First we investigate the stability and rupture of thin liquid films on patterned sub-...
    Keyword: Mathematics
    Subject: Applied Mathematics
    Creator: Justin Kao
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/07/2018
    Date Modified: 09/07/2018
    Date Created: 2008-05-08
    Rights: In Copyright
    Resource Type: Dissertation
  5. Group Actions via Interval Exchange Transformations

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    Description: This dissertation addresses the structure of the group of interval exchange transformations. The two primary topics considered are: a) the classification of interval exchange actions for certain groups; and b) properties of the interval exchange group which are reflected in the dynamics of interval exchange maps. In Chapter 3 a...
    Keyword: Mathematics
    Subject: Mathematics
    Creator: Christopher Novak
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/06/2018
    Date Modified: 09/06/2018
    Date Created: 2008-05-06
    Rights: In Copyright
    Resource Type: Dissertation
  6. Representing Cohomology Theories in the Triangulated Category of Motives

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    Description: Let X be a quasi-projective complex variety. It follows from the work of Voevodsky that the motivic cohomology of X, denoted as $H^{p,q}(X)$ where q and p are integers with q nonnegative, can be represented in the triangulated category of motives over the field of complex numbers, denoted as $DM^{eff,-}_{Nis}$....
    Keyword: Mathematics
    Subject: Mathematics
    Creator: Chenghao Chu
    Owner: Scholarly Digital Publishing
    Date Uploaded: 08/31/2018
    Date Modified: 08/31/2018
    Date Created: 2008-05-02
    Rights: In Copyright
    Resource Type: Dissertation
  7. Polygons, Companion Shapes and the Construction of Polyhedra

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    Description: Given any polyhedron in R3, we can cut it open along its edges, flatten it out, and obtain a polygon in the plane R2. In this project, we explored the opposite process, an open question that was first posed about 70 years ago: given a polygon in R2, what is...
    Keyword: 3D polyhedra, Geometry, Mathematics, and Dynamical system
    Creator: Yuxi Han
    Owner: Scholarly Digital Publishing
    Date Uploaded: 06/13/2018
    Date Modified: 06/13/2018
    Date Created: 2018-05-31
    Rights: In Copyright
    Resource Type: Poster
  8. Unramifiedness and Crystallinity

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    Description: This dissertation contains three results related to modular forms and Galois representations of low weight. In chapter 1, we prove that the Galois pseudo-representation valued in a Hecke algebra which acts faithfully on a space of weight one Katz modular forms of level prime to p is unramified at p....
    Keyword: Mathematics and Crystallinity
    Subject: Mathematics
    Creator: Joel Specter
    Owner: Scholarly Digital Publishing
    Date Uploaded: 03/30/2018
    Date Modified: 03/30/2018
    Date Created: 2017-01-01
    Rights: In Copyright
    Resource Type: Dissertation
  9. What Do Algebras Form?

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    Description: Algebras and their bimodules form a 2-category in which 2-morphisms are certain zero-th Hochschild cohomology groups. When we derive this structure (i.e., use Hochschild cochains instead of HH^0 for 2-morphisms), we find that algebras form a category in dg cocategories. The Hochschild-Kostant-Rosenberg theorem and non-commutative calculus give a rich algebraic...
    Keyword: Mathematics and Algebra
    Subject: Mathematics
    Creator: Ann Rebecca Wei
    Owner: Scholarly Digital Publishing
    Date Uploaded: 03/13/2018
    Date Modified: 03/13/2018
    Date Created: 2017-01-01
    Rights: In Copyright
    Resource Type: Dissertation
  10. Mixing with Piecewise Isometries

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    Description: Mixing of granular materials is an important engineering process, and a very complex problem. In this thesis, I use granular mixing in a half-full biaxial spherical tumbler (BST), a spherical container that rotates sequentially about two orthogonal axes, to motivate the study of mixing with piecewise isometries (PWIs), a rich...
    Keyword: Mathematics and Piecewise
    Subject: Engineering Sciences and Applied Mathematics
    Creator: Paul P Park
    Owner: Scholarly Digital Publishing
    Date Uploaded: 02/13/2018
    Date Modified: 02/13/2018
    Date Created: 2016-01-01
    Rights: In Copyright
    Resource Type: Dissertation