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Filtering by: Creator Eskew, Evan A. Remove constraint Creator: Eskew, Evan A. Committee Member Evans, Glenn Remove constraint Committee Member: Evans, Glenn Degree Field Mathematics Remove constraint Degree Field: Mathematics

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  • The Stokes problem of fluid mechanics, Riesz transform, and the Helmholtz-Hodge decomposition : probabilistic methods and their representations

    Creator:
    Kim, HoeWoon
    Abstract:
    The flow of incompressible, viscous fluids in R³ is governed by the non-linear Navier-Stokes equations. Two common linearizations of the Navier-Stokes equations, the Stokes equations and the Oseen equations, are studied in this thesis using probabilistic methods. The incompressibility condition presents new challenges for the well known theory relating partial...
    Resource Type:
    Dissertation
    Full Text:
    Representations Abstract approved: Enrique A. Thomann The flow of incompressible, viscous fluids in R3 is

  • Time dependent wavemaker problem for linear waves

    Creator:
    Cooper, Julia M.
    Abstract:
    The classical two-dimensional wavemaker problem is formulated for linear waves. Two conformal mappings are applied to the mathematical formulation to transform the wavemaker problem into a unit disk. It is then shown that this technique cannot produce in practice a numerical representation of the fluid motion throughout time for any...
    Resource Type:
    Masters Thesis
    Full Text:
    the wavemaker problem into a unit disk. It is then shown that this technique cannot produce in

  • The local conservation laws of the nonlinear Schrödinger equation

    Creator:
    Barrett, Johnner
    Abstract:
    The nonlinear Schrödinger equation is a well-known partial differential equation that provides a successful model in nonlinear optic theory, as well as other applications. In this dissertation, following a survey of mathematical literature, the geometric theory of differential equations is applied to the nonlinear Schrödinger equation. The main result of...
    Resource Type:
    Dissertation
    Full Text:
    Schrodinger equation is a well-known partial differential equation that provides a successful model in

  • Notions of complexity in substitution dynamical systems

    Creator:
    Wing, David Josiah
    Abstract:
    There has been a lot of work done in recent decades in the field of symbolic dynamics. Much attention has been paid to the so-called "complexity" function, which gives a sense of the rate at which the number of words in the system grow. In this paper, we explore this...
    Resource Type:
    Dissertation
    Full Text:
    in Substitution Dynamical Systems Abstract approved: Robert M. Burton There has been a lot of work

  • π-line reconstruction formulas in computed tomography

    Creator:
    Hass, Ryan Andrew
    Abstract:
    X-ray computed tomography is a noninvasive imaging modality capable of reconstructing exact density values of 3D objects. Computed tomography machines are deployed across the world to provide doctors with an image that reveals more detail than a standard x-ray image. We investigate algorithms based on exact computed tomography reconstruction formulas...
    Resource Type:
    Dissertation
    Full Text:
    tomography is a noninvasive imaging modality capable of reconstructing exact density values of 3D objects