Theses and Dissertations from UMD

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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

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    MAGNETOHYDRODYNAMIC SIMULATIONS OF BLACK HOLE ACCRETION
    (2017) Avara, Mark James; Reynolds, Christopher S; McKinney, Jonathan; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Black holes embody one of the few, simple, solutions to the Einstein field equations that describe our modern understanding of gravitation. In isolation they are small, dark, and elusive. However, when a gas cloud or star wanders too close, they light up our universe in a way no other cosmic object can. The processes of magnetohydrodynamics which describe the accretion inflow and outflows of plasma around black holes are highly coupled and nonlinear and so require numerical experiments for elucidation. These processes are at the heart of astrophysics since black holes, once they somehow reach super-massive status, influence the evolution of the largest structures in the universe. It has been my goal, with the body of work comprising this thesis, to explore the ways in which the influence of black holes on their surroundings differs from the predictions of standard accretion models. I have especially focused on how magnetization of the greater black hole environment can impact accretion systems.
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    Turbulent Transport in Global Models of Magnetized Accretion Disks
    (2011) Sorathia, Kareem; Reynolds, Christopher; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    The modern theory of accretion disks is dominated by the discovery of the magnetorotational instability (MRI). While hydrodynamic disks satisfy Rayleigh's criterion and there exists no known unambiguous route to turbulence in such disks, a weakly magnetized disk of plasma is subject to the MRI and will become turbulent. This MRI-driven magnetohydrodnamic turbulence generates a strong anisotropic correlation between the radial and azimuthal magnetic fields which drives angular momentum outwards. Accretion disks perform two vital functions in various astrophysical systems: an intermediate step in the gravitational collapse of a rotating gas, where the disk transfers angular momentum outwards and allows material to fall inwards; and as a power source, where the gravitational potential energy of infalling matter can be converted to luminosity. Accretion disks are important in astrophysical processes at all scales in the universe. Studying accretion from first principles is difficult, as analytic treatments of turbulent systems have proven quite limited. As such, computer simulations are at the forefront of studying systems this far into the non-linear regime. While computational work is necessary to study accretion disks, it is no panacea. Fully three-dimensional simulations of turbulent astrophysical systems require an enormous amount of computational power that is inaccessible even to sophisticated modern supercomputers. These limitations have necessitated the use of local models, in which a small spatial region of the full disk is simulated, and constrain numerical resolution to what is feasible. These compromises, while necessary, have the potential to introduce numerical artifacts in the resulting simulations. Understanding how to disentangle these artifacts from genuine physical phenomena and to minimize their effect is vital to constructing simulations that can make reliable astrophysical predictions and is the primary concern of the work presented here. The use of local models is predicated on the assumption that these models accurately capture the dynamics of a small patch of a global astrophysical disk. This assumption is tested in detail through the study of local regions of global simulations. To reach resolutions comparable to those used in local simulations an orbital advection algorithm, a semi-Lagrangian reformulation of the fluid equations, is used which allows an order of magnitude increase in computational efficiency. It is found that the turbulence in global simulations agrees at intermediate- and small-scales with local models and that the presence of magnetic flux stimulates angular momentum transport in global simulations in a similar manner to that observed for local ones. However, the importance of this flux-stress connection is shown to cast doubt on the validity of local models due to their inability to accurately capture the temporal evolution of the magnetic flux seen in global simulations. The use of orbital advection allows the ability to probe previously-inaccessible resolutions in global simulations and is the basis for a rigorous resolution study presented here. Included are the results of a study utilizing a series of global simulations of varying resolutions and initial magnetic field topologies where a collection of proposed metrics of numerical convergence are explored. The resolution constraints necessary to establish numerical convergence of astrophysically-important measurements are presented along with evidence suggesting that the use of proper azimuthal resolution, while computationally-demanding, is vital to achieving convergence. The majority of the proposed metrics are found to be useful diagnostics of MRI-driven turbulence, however they suffer as metrics of convergence due to their dependence on the initial magnetic field topology. In contrast to this, the magnetic tilt angle, a measure of the planar anisotropy of the magnetic field, is found to be a powerful tool for diagnosing convergence independent of initial magnetic field topology.
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    A Lattice Kinetic Scheme with Grid Refinement for 3D Resistive Mangetohydrodynamics
    (2004-05-26) Osborn, Bryan Russell; Dorland, William D; Applied Mathematics and Scientific Computation
    We develop, analyze, and numerically test a 3D lattice kinetic scheme for the resistive magnetohydrodynamic (MHD) equations. This scheme is based on the square D3Q19 lattice for the fluid and the square D3Q7 lattice for the magnetic field. The scheme is shown to be consistent with the MHD equations in the low-Mach, high-beta limit. We numerically test the scheme in a pseudo-3D implementation by examining its reproduction of linear MHD eigenmodes as well as its performance on the non-linear Orszag-Tang problem. Results show that the waves are correctly reproduced and that the code has second-order convergence in time step and grid spacing. A multi-block refinement algorithm is then tested, and its convergence properties are examined for the non-linear Orszag-Tang problem. We conclude that this multi-block refinement algorithmpreviously only applied to hydrodynamic lattice kinetic schemescan be used in conjunction with MHD lattice kinetic schemes.
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    Hydromagnetic turbulent instability in liquid sodium experiments
    (2004-04-30) Sisan, Daniel R; Lathrop, Daniel P; Physics
    This dissertation describes the observation of magnetically-induced instabilities that occur from a preexisting hydrodynamically turbulent background. We claim these instabilities are the first direct observation of the magneto-rotational instability (MRI). An extensive body of theoretical and numerical research has established the MRI is important in the theory of accretion disks: magnetic fields destabilize otherwise stable astrophysical flows, causing turbulence and an increased angular momentum transport needed for accretion. Our instabilities occur in liquid sodium between differentially rotating concentric spheres (spherical Couette flow) where an external field is applied parallel to the axis of rotation. Our experiments are also the first known spherical Couette flow in an electrically conducting fluid, and only the second experiment, in any fluid, at an aspect ratio of 2, the same of the Earth's core. We describe the development of a Hall probe array that measures the field at 30 points outside the sphere and is used to perform a spherical harmonic decomposition (up to l=4) of the induced field. We present measurements taken with this array, along with measurements of torque needed to spin the inner sphere and of the flow velocity using ultrasound doppler velocimetry. Our experiment is consistent with prior theory, even though our instabilities occur in the presence of preexisting hydrodynamic turbulence (the theory starts with an initially laminar flow). This result may be particularly relevant in light of an ongoing debate on whether accretion disks are hydrodynamically unstable independent of external fields. The most important contribution of our experiments, however, may be in providing data with which to benchmark the many numerical and theoretical studies of the MRI and the codes used to simulate the Earth's core.