The classical two-dimensional wavemaker problem is formulated for
linear waves. Two conformal mappings are applied to the mathematical
formulation to transform the wavemaker problem into a unit disk. It is then
shown that this technique cannot produce in practice a numerical
representation of the fluid motion throughout time for any...
This research was an attempt at gaining insight into the nature of the incompressibility conditions of the Navier-Stokes Equations on the Unit Circle. We realized the Riesz transformation is given in R^3 after taking the Fourier Transform of the Neumann Boundary Value problem, but this is not well defined on...
The main goal of this project is to implement an algorithmic music composition procedure and present all procedures and results in a reproducible fashion by creating a web application produced by R. To approach the implementation of the algorithmic composition of music, we start by exploring various models, but ultimately...
The introduction of an Magnetohydrodynamic (MHD) generator in coal or natural gas energy plants could significantly increase the efficiency by converting kinetic and thermal energy of the combustion exhaust to electrical energy by the generation of a Faraday and Hall current. The traditional MHD system was transformed into a simplified...
Within this dissertation, we develop tools and techniques to demonstrate the feasibility of real-time optimization of a magnetohydrodynamics generator. To ease computational complexity, we work on the kinematic magnetohydrodynamic system, prescribing the fluid-flow and model the material response of the system through an updated Generalized Ohm’s law. We focus on...
Generalization is a fundamental mathematical practice across all disciplines and content areas (Amit & Klass, 2005; Lannin, 2005; Pierce, 1902; Vygotsky, 1986; Ellis, Lockwood, Tillema & Moore, 2017). While a considerable amount of research has been conducted on students' generalizing activity in algebraic contexts (Amit & Klass 2005; Becker &...
Regular null curves in Regular null curves in L³ always have a time component parametrization. This fact puts the Frenet equations for regular null curves in L³ in a simple form. A fundamental existence and uniqueness theorem for regular null curves in L³ is proved, and applications to geometry are...
The problem of a general incompressible viscous fluid flow past
a flat plate with heat transfer due to forced convection is considered
in this thesis. The synthetic method developed by B. R.
Seth is applied to the Navier-Stokes equations and the equation of
energy governing the flow to obtain the...
Many geophysical phenomena exhibit complicated dynamics that, due to a variety of factors, diverge quickly from physical models. The arrival of new observations allows researchers to combine the model estimate with measurements in a statistical process called data assimilation to produce a revised estimate of the phenomenon. This assimilation of...
