Date of Award

August 2017

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Lijing Sun

Committee Members

Kevin McLeod, Peter Hinow, Allen D. Bell, Chao Zhu


Associated Legendre Polynomials, Electrostatics, Lorentzian Model, Partial Differential Equations, Poisson-boltzmann Model


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 given.

Included in

Mathematics Commons