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  • Creators(s):
    Jennifer Tank
    Description:

    This dataset contains data from 17 stream 15N-NH4 tracer addition experiments conducted globally, with data partitioned by autotrophic uptake compartments (i.e., epilithic biofilm, filamentous algae, bryophytes/macrophytes) and heterotrophic uptake compartments (i.e., leaves, small wood, and fine particles) that comprise the base of stream food webs. The dataset includes compartmental data on N biomass and uptake as well as other physiochemical variable that describe conditions in each stream.

    Date Created:
    2017-09-12
  • Creators(s):
    Margaret Regan, Jonathan Hauenstein
    Description:

    Three key aspects of applying homotopy continuation to parameterized systems of polynomial equations are investigated. First, for parameterized systems which are homogenized with solutions in projective space, we investigate options for selecting the affine patch where computations are performed. Second, for parameterized systems which are overdetermined, we investigate options for randomizing the system for improving the numerically stability of the computations. Finally, since one is typica…

    Date Created:
    2017-07-06
  • Author:
    Qian Li
    Advisory Committee:
    Michael Wiescher, Stefan Frauendorf, Ani Aprahamian, Carol Tanner
    Degree Area:
    Physics
    Degree:
    Doctor of Philosophy
    Defense Date:
    2015-05-11
  • Author:
    Xin Liu
    Advisory Committee:
    Amanda B. Hummon, Robert V Stahelin, Paul William Bohn
    Degree Area:
    Chemistry and Biochemistry
    Degree:
    Doctor of Philosophy
    Defense Date:
    2017-04-06
  • Creators(s):
    Jonathan Hauenstein
    Description:

    The Kuramoto model describes synchronization behavior among coupled oscillators and enjoys successful application in a wide variety of fields. Many of these applications seek phase-coherent solutions, i.e., equilibria of the model. Historically, research has focused on situations where the number of oscillators, n, is extremely large and can be treated as being infinite. More recently, however, applications have arisen in areas such as electrical engineering with more modest values of n. For…

    Date Created:
    2017-04-07
  • Description(s):
    A movie showing the change in the number of stable steady-state solutions as a function of the cell-to-cell communication. Software code using Matlab and Bertini is also provided which was used to generate the frames of this movie.
    Creator(s):
    Jonathan Hauenstein
  • Creators(s):
    Jonathan Hauenstein
    Description:

    Stewart-Gough platforms are mechanisms which consist of two rigid objects, a base and a platform, connected by six legs via spherical joints. For fixed leg lengths, a generic Stewart-Gough platform is rigid with 40 assembly configurations (over the complex numbers) while exceptional Stewart-Gough platforms have infinitely many assembly configurations and thus have self-motion. We define a family of exceptional Stewart-Gough platforms called Segre-dependent Stewart-Gough platforms which aris…

    Date Created:
    2017-01-17
  • Creators(s):
    Jonathan Hauenstein
    Description:

    We define tensors, most of which correspond with cubic polynomials, which have the same exponent w as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor defined on an nxn matrix A by trace(A^3). The use of polynomials enables the introduction of additional techniques from algebraic geometry in the study of the matrix multiplication exponent w.

    Date Created:
    2017-01-07
  • Author:
    Hao Wang
    Advisory Committee:
    Zachary D. Schultz
    Degree Area:
    Chemistry and Biochemistry
    Degree:
    Doctor of Philosophy
    Defense Date:
    2016-11-17
  • Author(s):
    Michael Gekhtman
    Abstract:

    This work is devoted to integration of semi-infinite and finite non-Abelian lattices of Toda-type, that is, nonlinear differential-difference equations that can be written in a Lax form

    L˙(t) = [L(t), A(t)] , where L is a tridiagonal matrix of order N ≤ ∞ whose entries are bounded operators in some Banach or Hilbert space and A is a finite band matrix of the same order whose entries depend on those of L. We develop an inverse spectral problem method for such equations that generalizes the on…

    Date Created:
    1990-06-30
    Resource Type
    Document
  • Author:
    Andrew Schmudlach
    Advisory Committee:
    Paul Huber, Norman Dovichi, Amanda Hummon
    Degree Area:
    Chemistry and Biochemistry
    Degree:
    Doctor of Philosophy
    Defense Date:
    2016-11-17
  • Author(s):
    Daniel Bates, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Numerical algebraic geometry is the area devoted to the solution and manipulation of polynomial systems by numerical methods, which are mainly based on continuation. Due to the extreme intrinsic parallelism of continuation, polynomial systems may be successfully dealt with that are much larger than is possible with other methods. Singular solutions require special numerical methods called endgames, and the endgames currently used do not take advantage of parallelism. This article gives an ove…