Related papers: Student difficulties with Boundary Conditions in e…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
We have derived general boundary conditions (BC) for the multiband envelope functions (which do not contain spurious solutions) in semiconductor heterostructures with abrupt heterointerfaces. These BC require the conservation of the…
Expanding our knowledge of student difficulties in advanced undergraduate electromagnetism is essential if we are to develop effective instructional interventions. Drawing on an analysis of course materials, in-class observations and…
The study of the laws of nature has traditionally been pursued in the limit of isolated systems, where energy is conserved. This is not always a valid approximation, however, as the inclusion of features like gain and loss, or periodic…
Standardized assessment tests that allow researchers to compare the performance of students under various curricula are highly desirable. There are several research-based conceptual tests that serve as instruments to assess and identify…
In this paper exact 1D transparent boundary conditions (TBC) for the 2D parabolic wave equation with a linear or a quadratic dependence of the dielectric permittivity on the transversal coordinate are reported. Unlike the previously derived…
The Dirac delta function is a standard mathematical tool used in multiple topical areas in the undergraduate physics curriculum. While Dirac delta functions are usually introduced in order to simplify a problem mathematically, students…
In this paper a characteristics-based open boundary condition (CBC) is proposed for the magnetohydrodynamic (MHD) system of equations. The algorithm is carefully designed and implemented in the context of a high-order flux reconstruction…
Bifurcation problems in which periodic boundary conditions (PBC) or Neumann boundary conditions (NBC) are imposed often involve partial differential equations that have Euclidean symmetry. In this case posing the bifurcation problem with…
Despite the recognition that reflection is an essential part of problem solving, it is often not emphasized in upper-division physics courses. In this paper, we discuss homework corrections (HWCs) as a pedagogical tool to motivate…
Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels.…
A class of evolutionary operator equations is studied. As an application the equations of linear acoustics are considered with complex material laws. A dynamic boundary condition is imposed which in the time-harmonic case corresponds to an…
Many physics instructors aim to support student sensemaking in their classrooms. However, this can be challenging since instances of sensemaking tend to be short-lived, with students often defaulting to approaches based on answer-making or…
At very high energies, the bremsstrahlung and pair production cross sections exhibit complex behavior due to the material in which the interactions occur. The cross sections in dense media can be dramatically different than for isolated…
We have been investigating the difficulties that students in upper-level undergraduate courses have in determining the probability distribution for measuring energy and position as a function of time when the initial wave function is…
Favorable outcomes from ongoing research at the University of Colorado Boulder on student learning in junior-level electrostatics (E&M I) have led us to extend this work to upper-division electrodynamics (E&M II). We describe here our…
We report results from a study designed to identify links between undergraduate students' views about experimental physics and their engagement in multiweek projects in lab courses. Using surveys and interviews, we explored whether students…