University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • Theses and Dissertations from UMD
    • UMD Theses and Dissertations
    • View Item
    •   DRUM
    • Theses and Dissertations from UMD
    • UMD Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    A Modified Zwanzig-Mori Formalism

    Thumbnail
    View/Open
    Halbert_umd_0117E_10605.pdf (704.3Kb)
    No. of downloads: 791

    Date
    2009
    Author
    Halbert, James Thomas
    Advisor
    Levermore, Charles D.
    Metadata
    Show full item record
    Abstract
    Recent advances in science have led to a better understanding of physical phenomena across a vast range of time and length scales. This has given the research community access to mathematical models for most scales in a given problem. A common strategy applied to Hamiltonian systems has been to select scales of interest and remove the others through the Zwanzig-Mori formalism. As long as the scales involved are strongly separated this approach works well. However, many problems in science and engineering involve processes in which there is no clear scale separation. It is still possible to use this procedure in some such cases but it has notably failed in many others (e.g. complex fluids). This failure has been blamed on the presence of poorly understood empirical closures and much current work is dedicated to eliminating the need for these or at least quantifying the errors they introduce. I have constructed a model system that possesses many of the features present in relevant problems and have used it as a testbed for investigating a modification of the Zwanzig-Mori formalism. The modified formalism I propose is applicable beyond the standard class of Hamiltonian systems: it is designed to work with damped, noise-driven, Hamiltonian systems. This thesis describes the modest first steps in understanding the underlying functional analytic structure of the new formalism. In particular, I have placed the model into a hierarchy of systems related to one another by a map between scales. The scale connection between the hierarchy elements is made evident by the construction of an intrinsic entropy-based fluid moment system — each element of the hierarchy is realized as a formal coarsening of this fluid moment system. What is more, I have formally constructed the "infinite particle'' limit for the fluid moment system and found that it too has an associated entropy. The existence of these entropies implies an amenability of the new formalism to analysis — this is the most useful and novel aspect of the work.
    URI
    http://hdl.handle.net/1903/9571
    Collections
    • Mathematics Theses and Dissertations
    • UMD Theses and Dissertations

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility