A Monte Carlo study of a percolation modelThe student will investigate a basic percolation model in twodimensions, using computer simulations. A program will be developed in Vpython to simulate the model and analyze the results, by looking for spanning paths. The finite volume effects will be investigated and the critical probability for filling will be determined. The student will investigate applications of the percolation models to subjects such as: terrorist networks and the propagation of diseases. In the final part of the project, the student will explore using a 3D printer to visualize a snapshot of the model, based on the idea of "Sculplexity", introduced by Tim Evans and collaborators at Imperial College. See the more detailed notes on the project. The code below contains some hints for writing the percolation code. The code is embedded in the web page using trinket.io. It uses the following parts of Python: Visualization of a chaotic dynamical systemThe student will be taught the basics of how to program physics applications in Vpython. A particular feature of this language is theability to create 3D visualizations of objects in a simple way. The student will write computer programs to study dynamical systems with chaotic behavior, such as the double pendulum, and a ball bouncing ona vibrating platform. (The dynamics of bouncing is useful for spaceships landing on a comet.)
See the slightly more detailed notes on the project A 3D printer will be used to print a snapshot of the dynamics. The student will think about the forces and the structorial stability of the printed objects. A video of a Vpython code to show a ball bouncing between two plates. In the project you will get the ball to bounce in the vertical direction and include the force of gravity. Background readingSome curated links about topics we discussed.
