Dynamic Line Integral Convolution for Visualizing Streamline Evolution
The depiction of time-dependent vector fields is a central problem in scientific visualization. This article describes a technique for generating animations of such fields where the motion of the streamlines to be visualized is given by a second “motion” vector field. Each frame of our animation is a Line Integral Convolution of the original vector field with a time-varying input texture. The texture is evolved according to the associated motion vector field via an automatically adjusted set of random particles. We demonstrate this technique with examples from electromagnetism.
How Does Technology-Enabled Active Learning Affect Undergraduate Students’ Understanding of Electromagnetism Concepts?
Educational technology supports meaningful learning and enables the presentation of spatial and dynamic images, which portray relationships among complex concepts. The Technology-Enabled Active Learning (TEAL) Project at MIT involves media-rich software for simulation and visualization in freshman physics carried out in a specially redesigned classroom to facilitate group interaction. These technology-based learning materials are especially useful in electromagnetism to help students conceptualize phenomena and processes. This study analyzes the effects of the unique learning environment of the TEAL project on students’ cognitive and affective outcomes. The assessment of the project included examining students' conceptual understanding before and after studying electromagnetism in a media-rich environment. We also investigated the effect of this environment on students' preferences regarding the various teaching methods. As part of the project, we developed pre- and posttests consisting of conceptual questions from standardized tests, as well as questions designed to assess the effect of visualizations and experiments. The research population consisted of 811 undergraduate students. It consisted of a small and a large-scale experimental groups and a control group. TEAL students improved their conceptual understanding of the subject matter to a significantly higher extent than their control group peers. A majority of the students in the small-scale experiment noted that they would recommend the TEAL course to fellow students, indicating the benefits of interactivity, visualization, and hands-on experiments, which the technology helped enable. In the large-scale implementation students expressed both positive and negative attitudes in the course survey.
Field Line Motion in Classical Electromagnetism
We consider the concept of field line motion in classical electromagnetism for crossed electromagnetic fields, and suggest definitions for this motion that are physically meaningful, but not unique. Our choice has the attractive feature that the local motion of the field lines is in the direction of the Poynting vector. The animation of the field line motion using our approach reinforces Faraday’s insights into the connection between the shape of electromagnetic field lines and their dynamical effects. We give examples of these animations, which are available on the Web. |
