Related papers: Student difficulties with Boundary Conditions in e…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
Upper-division physics students spend much of their time solving problems. In addition to their basic skills and background, their epistemic framing can form an important part of their ability to learn physics from these problems.…
We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion…
We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
A general derivation is proposed for several boundary conditions arisen in the lattice Boltzmann simulations of various physical problems. Pair-wise moment conservations are proposed to enforce the boundary conditions with given macroscopic…
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…
We introduce a method for effectively identifying bound states in the continuum (BICs) - notably without computing the imaginary part of the eigenvalues - thereby simplifying the modeling and potentially reducing computation time. In real,…
In a model of a gate-patterned quantum device it is important to choose the correct electrostatic boundary conditions (BCs) in order to match experiment. In this study, we model gated-patterned devices in doped and undoped GaAs…
We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and…
This paper re-centres the discussion of student learning in physics to focus on context. In order to do so, a theoretically-motivated understanding of context is developed. Given a well-defined notion of context, data from a novel…
We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using the degenerate perturbation theory. The investigation was carried out in…
We study and develop constraint preserving boundary conditions for the Newtonian magnetohydrodynamic equations and analyze the behavior of the numerical solution upon considering different possible options.
The use of validated conceptual assessments alongside more standard course exams has become standard practice for the introductory courses in many physics departments. These assessments provide a more standard measure of certain learning…
The research reported in this article represents a systematic, multi-year investigation of student understanding of the behavior of bipolar junction transistor circuits using a variety of different tasks to isolate and probe key aspects of…
We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research,…
The persistent underrepresentation of women and other gender minorities in physical science fields has been an ongoing concern. This study investigates gender dynamics in introductory physics laboratory courses, focusing on whether students…
Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions…
Periodic boundary conditions are commonly applied in molecular dynamics simulations in the microcanonical (NVE), canonical (NVT) and isothermal-isobaric (NpT) ensembles. In their simplest application, a biological system of interest is…