The purpose of this study was to address the implementation fidelity of one part of a professional development model developed by the Northwest Regional Educational Laboratory (NWREL). Specifically, this research investigates middle school teachers’ use of a formative feedback guide developed by NWREL staff, examining the reliability with which teachers...
In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to
21st century problems. We also discuss the previous work on the numerical simulations of
Maxwell's equations. Introductions to Maxwell's equations and the Yee finite difference...
The purpose of this study was to document the development of pre-service teachers' Technology Specific Pedagogy as they learned to teach mathematics with technology during their initial licensure program. The study investigated the pre-service teachers' learning using both a social and a psychological perspective of teacher learning. Two research questions...
A fundamental question related to any Lie algebra is to know its subalgebras. This is
particularly true in the case of E6, an algebra which seems just large enough to contain the algebras which describe the fundamental forces in the Standard Model of particle physics. In this situation, the question...
The generalized variational principle of Herglotz defines the functional whose extrema are sought by a differential equation rather than an integral. It reduces to the classical variational principle under classical conditions. The Noether theorems are not applicable to functionals defined by differential equations. For a system of differential equations derivable...
This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutations e.g., transpositions and 3-cycles.
Cellular sets in the Hilbert cube are the intersection of nested sequences of normal
cubes. One way of getting cellular maps on the Hilbert cube is by decomposing the Hilbert
cube into cellular sets and using a quotient map. By using a cellular decomposition of the
Hilbert cube, an example...
This thesis contains three manuscripts addressing the application of stochastic processes to the analysis and solution of partial differential equations (PDEs) in mathematical physics.
In the first manuscript, one dimensional diffusion and Burgers equation are considered. The Fourier transform of the solution to each PDE is represented as the expected...
In this paper we develop an upscaling technique for non-Darcy flow in porous media. Non-Darcy model of flow applies to flow in porous media when large velocities occur. The well-posedness results for theory of quasilinear elliptic partial differential equations. To discretize the model we used lowest order Raviart-Thomas mixed finite...
Water is one of the most biologically and economically important substances on Earth. A significant portion of Earth's water subsists in the subsurface. Our ability to monitor the flow and transport of water and other fluids through this unseen environment is crucial for a myriad of reasons.
One difficulty we...