UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

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 given thesis/dissertation in DRUM.

More information is available at Theses and Dissertations at University of Maryland Libraries.

Browse

Filters

20141

Settings

Author: search.filters.author.Mitchell, Joe DanSubject: search.filters.subject.duality

Search Results

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Duality methods in networks, computer science models, and disordered condensed matter systems
    (2014) Mitchell, Joe Dan; Galitski, Victor M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In this thesis, I explore lattice independent duality and systems to which it can be applied. I first demonstrate classical duality on models in an external field, including the Ising, Potts, and x-y models, showing in particular how this modifies duality to be lattice independent and applicable to networks. I then present a novel application of duality on the boolean satsifiability problem, one of the most important problems in computational complexity, through mapping to a low temperature Ising model. This establishes the equivalence between boolean satisfiability and a problem of enumerating the positive solutions to a Diophantine system of equations. I continue by combining duality with a prominent tool for models on networks, belief propagation, deriving a new message passing procedure, dual belief propagation. In the final part of my thesis, I shift to propose and examine a semiclassical model, the two-component Coulomb glass model, which can explain the giant magnetoresistance peak present in disordered films near a superconductor-insulator transition as the effect of competition between single particle and localized pair transport. I numerically analyze the density of states and transport properties of this model.