Gia-Wei Chern / Physics
Computational physics has become a crucial and indispensable part of modern physics research. For example, in addition to the development of ultra-high precision interferometers, the capability of the LIGO collaboration to numerically simulate the merger of two black holes and its effects on the space-time fabric also plays a key role in the recent discovery of gravitational waves. In condensed matter physics, which is my own research area, highly sophisticated methods for computing many-body quantum states have become feasible thanks to the dramatic advances in computer technology. However, I find the current physics education at University of Virginia (UVa) does not take full advantage of this development. Moreover, while the average physics students are familiar with basic computer techniques, such as how to use the operating systems and some programing languages, they do not have the knowledge of some useful numerical algorithms and how computational techniques can be used in their study of core courses such as classical mechanics, electromagnetism, statistical and quantum physics. One of my goals as a teacher is to bridge this gap and expose students to the usage of computational methods early in their undergraduate study.
My dream idea is to invite a small group of (up to ten) undergraduate students to create a set of interactive Learning Modules that highlight how numerical techniques and computer algorithms can be used in physics education and research. Each module will be self-contained and focus on a particular topic of numerical techniques. One advantage of such modules is that they can be inserted into the syllabus of existing core courses. For example, modules about solving differential equations can be useful for courses like classical mechanics or quantum physics. Students who take these core courses can use these modules to learn the relevant numerical techniques and to improve their understanding of the topics.
For a more concrete example, consider numerical techniques for ordinary differential equations. I plan to design a module centered about the famous Fermi-Pasta-Ulam-Tsingou (FPUT) nonlinear chain model, which is one of the first problems that were studied with the aid of computers. The module will include history of the FPUT problem, the motivation, the numerical techniques (Runge-Kutta, velocity-Verlet), and clear instruction on the programming. I have given a shortened version of this as a project assignment in the two-semester courses “Computational Physics” that I taught at UVA. Interestingly, I found that with proper guidance and motivation, almost all students were able to complete the assignment and demonstrate the famous recurrence phenomenon.
Each student participating in this program will be in charge of one or two modules. Students are also encouraged to work together as a team for the same module. We will first discuss the central topic of each module. The students will then write a short report on the motivation, historical developments, and details of the numerical method for the module, sort of like a term paper. Next we will work together to design a few numerical problems to demonstrate the application of the numerical techniques. The students will also implement computer codes to solve these problems. Finally, we will put together these contents into a specialized webpage.
I will recruit undergraduate students who took my Computational Physics I and II in the past to join this project. I also plan to attend one of the weekly meetings of the Society of Physics Students, explain my idea, and personally invite these students to participate. To encourage students better understand the various computational techniques and also to help them build the modules of their choice, I will arrange weekly or biweekly meetings to discuss various topics from the famous reference book “Numerical Recipes in C/C++” or from the huge collection in “A survey of Computational Physics”. The students will also be asked to present their results in 4 or 5 seminar-style group meetings. These include work-in-progress presentation, and a presentation with demo at the end of the project.
In addition, I will also invite my collaborators who are numerical experts from Los Alamos National Lab or Oak Ridge National Lab to give seminar talks at the physics department. Students participating in this program will be invited to have lunches with the seminar speakers. The students can learn firsthand how numerical techniques and computer algorithms are used in cutting-edge physics research, and how large-scale numerical simulations are performed in super-computers or high-performance clusters.
Refreshment and food for 4~5 group meetings: ~$1000
4 Lunches with seminar speakers: ~$800
10 x books on computational physics: ~$900