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Filtering by: Creator Duddles, Ralph E. Remove constraint Creator: Duddles, Ralph E. Committee Member Showalter, Ralph Remove constraint Committee Member: Showalter, Ralph

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  • Existence Theory in Sobolev Spaces for an Aggregation Equation

    Creator:
    Barta, Hannah E.
    Abstract:
    Aggregation equations have been used to model phenomena such as insect swarming and chemotaxis. Previous work on aggregation equations in the area of analysis applied to PDE has proven well-posedness of certain classes of aggregation equations in Lebesgue spaces. We will prove local existence of solutions in H^1 to an...
    Resource Type:
    Capstone Project
    Full Text:
    example of such an acceptable potential is G(x) = e−|x|, which we will discuss at length, showing that it

  • A Discourse on the Gauge Integral

    Creator:
    Lilly, Jeremy
    Abstract:
    The gauge integral is a rather obscure object in mathematics. Like the Riemann integral, it is relatively simple to define, but unlike the Riemann integral, the gauge integral has the ability to integrate a very large class of functions. Here, we provide a development of the gauge integral at an...
    Resource Type:
    Honors College Thesis
    Full Text:
    theory, gauge, henstock, integral Corresponding e-mail address: lillyj@oregonstate.edu ©Copyright by

  • Explorations of Optimization Methods for Deep Learning with Examples from Various Applications

    Creator:
    Zhang, Nachuan
    Abstract:
    This paper explores some optimization methods such as the gradient descent method, Gauss-Newton method, and stochastic gradient method. Some examples of minimizing objective functions are given to validate the theories. Then we introduce a simple example of artificial neural networks, define its structure, and apply the optimization methods to it....
    Resource Type:
    Capstone Project
    Full Text:
    , 2021. The MS Committee consisted of Dr. Malgorzata Peszynska (Adviser), Dr. Robert Higdon and Dr. Ralph

  • Some results in probability from the functional analytic viewpoint

    Creator:
    Gelbaum, Zachary A.
    Abstract:
    This dissertation presents some results from various areas of probability theory, the unifying theme being the use of functional analytic intuition and techniques. We first give a result regarding the existence of certain stochastic integral representations for Banach space valued Gaussian random variables. Next we give a spectral geometric construction...
    Resource Type:
    Dissertation
    Full Text:
    elsewhere that deserve thanks. Ralph Showalter had the largest impact on me mathematically; aside from my

  • Nonlinear finite difference schemes for the Klausmeier system

    Creator:
    McClellan, Natalia A.
    Abstract:
    In this work we consider a model for pattern-producing vegetation in semi-arid regions of the world proposed by Klausmeier. It is a coupled nonlinear diffusion-advection evolutionary PDE system describing the vegetation density and water amount. The model was studied extensively by J.Sherratt who took into consideration the field data for...
    Resource Type:
    Masters Thesis
    Full Text:
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.1 Equilibrium E = (0,A

  • Nonlinear solvers for a model problem of fluid flow in the subsurface

    Creator:
    Biederman, Shannon Miriah
    Abstract:
    Water is one of the most biologically and economically important substances on Earth. A significant portion of Earth's water subsists in the subsurface. Our ability to monitor the flow and transport of water and other fluids through this unseen environment is crucial for a myriad of reasons. One difficulty we...
    Resource Type:
    Masters Thesis
    Full Text:
    ) ∈ B(δ), the Newton iterate u(κ) given by equation (4.3) satisfies ‖ eκ+1 ‖≤ K ‖ eκ ‖2 . (4.4) where

  • Analysis of domain decomposition methods for the simulation of charge transport in semiconductor structures with heterojunctions

    Creator:
    Costa, Timothy B.
    Abstract:
    Charge transport in a semiconductor structure with heterojunction is described by a multiscale partial differential equation model. This model can be used, e.g., for the design of more efficient solar cells. Phenomena at the heterojunction must be resolved at the angstrom scale while the size of the device is that...
    Resource Type:
    Masters Thesis
    Full Text:
    Emission Model in Slotboom variables is [ψ]Γ = ψ4, (2.19)[ � ∂ψ ∂ν ] Γ = 0, (2.20) JΓn = a n 2 (e ψu

  • Upscaling non-Darcy flow using mixed finite element method

    Creator:
    Garibotti, Cristiano Rodrigues
    Abstract:
    In this paper we develop an upscaling technique for non-Darcy flow in porous media. Non-Darcy model of flow applies to flow in porous media when large velocities occur. The well-posedness results for theory of quasilinear elliptic partial differential equations. To discretize the model we used lowest order Raviart-Thomas mixed finite...
    Resource Type:
    Masters Thesis

  • An experimental study of co-flow ammonia-water desorption in an oil-heated, microscale, fractal-like branching heat exchanger

    Creator:
    Mouchka, Gregory A.
    Abstract:
    An experimental study was performed in which an ammonia-water solution was desorbed within a branching fractal-like microchannel array. The solution entered in the center of a disk, and flowed out radially until discharging in to a gravity-driven separation chamber. Heat was added to the ammonia-water through a thin wall, above...
    Resource Type:
    Masters Thesis
    Full Text:
    student. Thank you to Drs. James Liburdy, Vinod Narayanan, and Ralph Showalter for serving on my

  • Two-grid a-priori and a-posteriori error analysis for coupled elliptic and parabolic systems with applications to flow and transport problems

    Creator:
    Klein, Viviane
    Abstract:
    We develop several a-priori and a-posteriori error estimates for two-grid finite element discretization of coupled elliptic and parabolic systems with a set of parameters P. We present numerical results that verify the convergence order of the numerical schemes predicted by the a-priori estimates. We present numerical results that verify the...
    Resource Type:
    Dissertation
    Full Text:
    gostaria de agradecer aos meus pais, Ivonete e Mercedo, a todo o apoio que me deram quando eu decidi