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Full-Text Articles in Physical Sciences and Mathematics
An Optimal Decay Estimation Of The Solution To The Airy Equation, Ashley Scherf
An Optimal Decay Estimation Of The Solution To The Airy Equation, Ashley Scherf
Theses and Dissertations
In this thesis, we investigate the initial value problem to the Airy equation \begin{align} \partial_t u + \partial_{x}^3 u &= 0\\ u(0,x) &= f(x). \end{align}
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 …
Mathematical Modeling Of Competition For Light And Nutrients Between Phytoplankton Species In A Poorly Mixed Water Column, Thomas George Stojsavljevic
Mathematical Modeling Of Competition For Light And Nutrients Between Phytoplankton Species In A Poorly Mixed Water Column, Thomas George Stojsavljevic
Theses and Dissertations
Phytoplankton live in a complex environment with two essential resources forming various gradients. Light supplied from above is never homogeneously distributed in a body of water due to refraction and absorption from biomass present in the ecosystem and from other sources. Nutrients in turn are typically supplied from below. In poorly mixed water columns phytoplankton can be heterogeneously distributed forming various layering patterns. The relationship between the location and the thickness of the layers is an open problem of interest. Here we present three models which study how competition for light and resources can form common layering patterns seen in …