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Filtering by: Creator Newton, Alfred F. Remove constraint Creator: Newton, Alfred F. Committee Member Faridani, Adel Remove constraint Committee Member: Faridani, Adel

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  • A Partial Proof of Bertrand's Theorem

    Creator:
    Musgrove, John F.
    Abstract:
    In this paper, we provide a thorough proof of most of Bertrand's Theorem. Using Arnold's book "Mathematical methods of classical mechanics" as a backbone and calculus methods demonstrated by Jovanović in his article "A note on the proof of Bertrand's theorem," we show that for masses in a central field...
    Resource Type:
    Honors College Thesis
    Full Text:
    reduced mass times the velocity. The rate of change of L is: dL dt = ṙ× µṙ + r× µr̈ = ṙ× µṙ + r× F

  • Dynamic behavior of ferromagnetic particles in a liquid-solid magnetically assisted fluidized bed (MAFB) : theory, experiment, and CFD-DPM simulation

    Creator:
    Pinto-Espinoza, Joaquin
    Abstract:
    Magnetically Assisted Fluidized Bed (MAFB) is a novel technology where an external magnetic field with constant gradient interacts with magnetically susceptible particles. The linear magnetic field creates two type of forces: external and interparticle magnetic forces. A theoretical mathematical model based on the interaction of ideal dipoles is proposed to...
    Resource Type:
    Dissertation
    Full Text:
    based on the Newton equation of particle motion. A Fortran code, AZTECA, is developed to perform the

  • Numerical Study of Convexity Splitting Scheme for Coupled Phase Field and Stefan Free Boundary Problems

    Creator:
    Bigler, Lisa A.
    Abstract:
    In this work, we consider a convexity splitting scheme for a coupled phase field and energy equation, a modification of Stefan problem. The Stefan problem is a free boundary value problem that models the temperature in a homogeneous multiphase medium. Each phase is modeled using a heat diffusion parabolic partial...
    Resource Type:
    Masters Thesis
    Full Text:
    convexity splitting method and compare the results to other 5 FIGURE 2.1: Splitting for F (u) in section

  • Finite volume method modeling of corona discharge microreactor oxidization of dibenzothiophene

    Creator:
    Fan, Xiangru
    Abstract:
    The growing need for cleaner fuels requires the development of better deep fuel desulfurization methods. The current study presents a reaction model for the mechanism of dibenzothiophene oxidization by dissolved oxygen occurring in a corona discharge microreactor. In the present work, a Finite Volume Method model of the reactor is...
    Resource Type:
    Masters Thesis
    Full Text:
    Abstract approved: ___________________________________________________________ Alexandre F. Yokochi

  • Modeling Flow and Transport at Pore Scale with Obstructions

    Creator:
    Umhoefer, Joseph G.
    Abstract:
    In this thesis we study mathematical and computational models for phenomena of flow and transport in porous media in the presence of changing pore scale geometries. The differential equations for the flow and transport models at Darcy scale involve the coefficients of permeability, porosity, and tortuosity which depend on the...
    Resource Type:
    Dissertation
    Full Text:
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.10 Flow domains D (i) f and D (ii) f , and an illustration of the flow solutions for Example

  • Virtual Element Methods for Magnetohydrodynamics on General Polygonal and Polyhedral Meshes

    Creator:
    Naranjo, Sebastián
    Abstract:
    The aim of this dissertation is to construct a virtual element method (VEM) for models in magneto-hydrodynamics (MHD), an area that studies the behavior and properties of electrically conducting fluids such as a plasma. MHD models are a coupling of the Maxwell’s equations for electromagnetics and models for fluid flow....
    Resource Type:
    Dissertation
    Full Text:
    detail will be clear from context. For a pair of sufficiently regular real-valued functions f, g : U → R

  • Coupled dynamics of bouys and mooring tethers

    Creator:
    Idris, Krisnaldi
    Abstract:
    Time-domain models were developed to predict the response of a tethered buoy subject to hydrodynamic loadings. A coupled analysis of the interaction of a buoy and its mooring is included and three-dimensional response is assumed. External loadings include hydrodynamic forces, tethers tensions, wind loadings and the weight of both cable...
    Resource Type:
    Dissertation
    Full Text:
    153 Appendix F Comparison Plots for Sphere Buoy Cases 171 Appendix G Comparison Plots for Spar

  • Evaluating Stiffness Metrics for Predicting the Cost of Chemical Kinetics Integration

    Creator:
    Alferman, Andrew Thomas
    Abstract:
    Simulations of combustion and reacting flows often encounter stiffness in the equations governing chemical kinetics. Explicit solvers for these ordinary differential equations offer low computational expense, but typically cannot efficiently handle stiff systems. In contrast, implicit methods demand greater expense but offer unconditional stability—as a result, most reactive-flow solvers rely...
    Resource Type:
    Masters Thesis
    Full Text:
    stiffness circa 1970 involved the use of Lipschitz con- stants [28], which describe how much a function f(u

  • Ruin Problems with Risky Investments

    Creator:
    Loke, Sooie-Hoe
    Abstract:
    In this dissertation, we study two risk models. First, we consider the dual risk process which models the surplus of a company that incurs expenses at a constant rate and earns random positive gains at random times. When the surplus is invested in a risky asset following a geometric Brownian...
    Resource Type:
    Dissertation
    Full Text:
    . 2.1 The model Let (Ω,F , P ) be a probability space. Define the risk process {Ut}t≥0 on this prob

  • Mathematical and Computational Considerations of a Model of Microbiologically Induced Calcite Precipitation

    Creator:
    Barry, Zachary T.
    Abstract:
    In this paper, we discuss two possible modifications to a numerical solution method for a model of microbiologically induced calcite precipitation (MICP). MICP provides a means to seal cracks in the surfaces of geological structures. From a mathematical and computational point of view MICP has very interesting features which make...
    Resource Type:
    Capstone Project
    Full Text:
    as follows. F (Un+1) = Un+1 − Un − kf(Un+1) = 0. (2.19) We seek to solve (2.19) by Newton iteration