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Full-Text Articles in Physical Sciences and Mathematics
Nonlocal Electrostatics In Spherical Geometries, Andrew Bolanowski
Nonlocal Electrostatics In Spherical Geometries, Andrew Bolanowski
Theses and Dissertations
Nonlocal continuum electrostatic models have been used numerically in protein simulations, but analytic solutions have been absent. In this paper, two modified nonlocal continuum electrostatic models, the Lorentzian Model and a Linear Poisson-Boltzmann Model, are presented for a monatomic ion treated as a dielectric continuum ball. These models are then solved analytically using a system of differential equations for the charge distributed within the ion ball. This is done in more detail for a point charge and a charge distributed within a smaller ball. As the solutions are a series, their convergence is verified and criteria for improved convergence is …
Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, Stefan Raymond Schnake
Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, Stefan Raymond Schnake
Doctoral Dissertations
This dissertation consists of three integral parts. Part one studies discontinuous Galerkin approximations of a class of non-divergence form second order linear elliptic PDEs whose coefficients are only continuous. An interior penalty discontinuous Galerkin (IP-DG) method is developed for this class of PDEs. A complete analysis of the proposed IP-DG method is carried out, which includes proving the stability and error estimate in a discrete W2;p-norm [W^2,p-norm]. Part one also studies the convergence of the vanishing moment method for this class of PDEs. The vanishing moment method refers to a PDE technique for approximating these PDEs by a …