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  • The Variable Speed Wave Equation and Perfectly Matched Layers

    Creator:
    Kim, Dojin
    Abstract:
    A perfectly matched layer (PML) is widely used to model many different types of wave propagation in different media. It has been found that a PML is often very effective and also easy to set, but still many questions remain. We introduce a new formulation from regularizing the classical Un-Split...
    Resource Type:
    Dissertation
    Full Text:
    Doctor of Philosophy in Mathematics presented on June 4, 2015. Title: The Variable Speed Wave Equation

  • A local perturbation problem of the 3D Navier-Stokes equations

    Creator:
    Zeng, Jhih-Jyun
    Abstract:
    This dissertation explores mathematical theory of the 3 dimensional incompressible Navier-Stokes equations that consists a set of partial differential equations which govern the motion of Newtonian fluids and can be seen as Newton's second law of motion for fluids. The main interest of this work focuses on how local perturbation...
    Resource Type:
    Dissertation
    Full Text:
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 A The Poisson Equation and Its Relation to the Navier-Stokes Equations 72 A.1 The Laplace

  • Construction and numerical simulation of a two-dimensional analogue to the KdV equation

    Creator:
    Black, Wendy
    Abstract:
    Arising from an investigation in Hydrodynamics, the Korteweg-de Vries equation demonstrates existence of nonlinear waves that resume their profile after interaction. In this thesis, the classical equations governing wave motion are the starting point for the development of an analogue of the KdV that describes the evolution of a wave...
    Resource Type:
    Dissertation

  • 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:
    Conservation Laws of the Nonlinear Schrodinger Equation Abstract approved: Tevian Dray The nonlinear

  • Multiscale analysis of saturated flow in a porous medium with an adjacent thin channel

    Creator:
    Morales, Fernando A.
    Abstract:
    This thesis contains three parts addressing the asymptotic analysis of fluid flow through fully saturated porous medium in the presence of an adjacent thin channel. In the first part the problem is modeled by Darcy's law in both the porous medium and in the channel. The permeability in the channel...
    Resource Type:
    Dissertation
    Full Text:
    Convergence of the Equation Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.4 The

  • Asphericity of length 6 equations over torsion free groups

    Creator:
    Kim, Seong Kun
    Resource Type:
    Dissertation

  • The galois theory of iterated binomials

    Creator:
    Danielson, Lynda Major
    Resource Type:
    Dissertation
    Full Text:
    , equation (3.1) becomes b[bn - rn 1] = +cP = (+c)P = for some c1 E R. Likewise, if p = 2, then n is even

  • Killing spinors and affine symmetry tensors in Gödel's Universe

    Creator:
    Cook, Samuel A.
    Abstract:
    The existence of generalized symmetries of Maxwell's equations in Gödel's Universe is investigated. It is shown that their existence is in turn tied to the existence of certain spinorial objects called Killing spinors. The conformal algebra, corresponding to valence (1; 1) Killing spinors, for Gödel's Universe is discussed in detail....
    Resource Type:
    Dissertation
    Full Text:
    Maxwell’s equations in Gödel’s Universe, a cosmological solution of Einstein’s equation. Due to the

  • Numerical inversion of laplace transforms by the trapezoidal-type methods

    Creator:
    Lin, FuSen F.
    Abstract:
    In this dissertation, we investigate three numerical methods for inverting the Laplace transform. These methods are all based on the trapezoidal-type approximations to the Bromwich integral. The first method is the direct integration method: It is a straightforward application of the trapezoidal rule to the Bromwich integral, followed by convergence...
    Resource Type:
    Dissertation
    Full Text:
    have s= +(_1)/c_1Lak= +R1. Again, we multiply by 22 on both sides of the equation (1.11) and then

  • Compatible Discretizations for Maxwell's Equations with General Constitutive Laws

    Creator:
    McGregor, D. A.
    Abstract:
    In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...
    Resource Type:
    Dissertation
    Full Text:
    ’ Law and Continuity Equation . . . . . . . . . . . . . . . . . . . 96 4.4 Numerical Demonstration of