Bunimovich stadium¶
The Bunimovich stadium is a box built from straight lines and circular arcs. Implement the collision rule for this box.
Turn off the collisions between the particles and start with a large number of particles placed in the same position which are launched radially in different directions. Observe the result.
Take just a single particle in the box, every time it moves its radius mark the position with a single, small dot. Let the simulation run and interpret the results.
Launch two particles which are close in space (without collisions). Measure their separation as a function of time. Compare the curves for different starting conditions. You should probably work on a log-log scale.
This is one of the very few systems in statistical mechanics where the mathematicians are able to proove theorems. https://blogs.ams.org/visualinsight/2016/11/15/bunimovich-stadium/
The rules for valid collisions between a particle and the circular arcs are s little subtle. Talk with us, before programming. Logic involves the intercept of trajectories with the extension of the two linear segments.
