Browsing by Author "Deang, Jennifer M."

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    Issues related to least-squares finite element methods for the stokes equations
    Deang, Jennifer M.; Gunzburger, Max D. (Siam Publications, 1998-10)
    Least-squares finite element methods have become increasingly popular for the approximate solution of first-order systems of partial differential equations. Here, after a brief review of some existing theories, a number of issues connected with the use of such methods for the velocity-vorticity-pressure formulation of the Stokes equations in two dimensions in realistic settings are studied through a series of computational experiments. Finite element spaces that are not covered by existing theories are considered; included in these are piecewise linear approximations for the velocity. Mixed boundary conditions, which are also not covered by existing theories, are also considered, as is enhancing mass conservation. Next, problems in nonconvex polygonal regions and the resulting nonsmooth solutions are considered with a view toward seeing how accuracy can be improved. A conclusion that can be drawn from this series of computational experiments is that the use of appropriate mesh-dependent weights in the least-squares functional almost always improves the accuracy of the approximations. Concluding remarks concerning three-dimensional problems, the nonlinear Navier-Stokes equations, and the conditioning of the discrete systems are provided.
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    Nucleation of superconductivity in finite anisotropic superconductors and the evolution of surface superconductivity toward the bulk mixed state
    Kogan, V. G.; Clem, J. R.; Deang, Jennifer M.; Gunzburger, Max D. (American Physical Society, 2002-02-14)
    In anisotropic superconductors having an arbitrary orientation of the sample surface relative to the crystal principal axes, the surface critical field H-c3 is less than 1.695H(c2) unless the field is situated along one of the principal crystal planes. Below H-c3 in the vicinity of nucleation, the order parameter scales as rootH(c3)-H. Computational studies for infinite cylinders having rectangular cross sections are presented which show that, due to corners and a finite cross section, the surface superconductivity state persists for fields above the theoretically predicted value for semi-infinite samples. They also show that vortices exist within the Surface superconductivity sheath above the bulk critical field.
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    Stochastic dynamics of Ginzburg-Landau vortices in superconductors
    Deang, Jennifer M.; Du, Q.; Gunzburger, Max D. (American Physical Society, 2001-08-01)
    Thermal fluctuations and randomly distributed defects in superconductors are modeled by stochastic variants of the time-dependent Ginzburg-Landau equations. Numerical simulations are used to compare the effects of additive and multiplicative noise models.
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    A Study of Inhomogeneities and Anisotrophies In Superconductors via Ginzburg-Landau Type models
    Deang, Jennifer M. (Virginia Tech, 1997-03-14)
    Superconductivity continues to be of great theoretical and practical interest and remains a challenging area of scientific inquiry. Most superconductors of practical utility are of type-II, i.e., they allow the penetration of magnetic fields in the form of tubes of flux that are referred to as "vortices." Motion of these vortices due to, e.g., applied currents, induce a loss of perfect conductivity. Knowing how vortices move and arrange themselves in lattice structures, how their movement is suppressed by pinning mechanisms, and how their movement is affected by thermal fluctuations is critical to understanding how to maintain resistanceless current flow. We study a variety of Ginzburg-Landau type models for superconductivity that can account for inhomogeneous and isotropy materials, grain boundaries, and thermal fluctuations. We develop robust, accurate, and efficient numerical codes and apply them to numerous studies of how vortex motions are affected by the various mechanisms mentioned above. We also examine some analytical aspects of type-II superconductors under the influence of thermal fluctuations.