Billiards with Memories
Mathematical Billiards are the simplest form of dynamical systems. They consist of particles that move on a straight line with a constant velocity. Despite being so simple in fundamental laws, they pose some of the most challenging open problems in classical and modern physics and mathematics. Inspired by experimental observation, we have recently made a new type of mathematical billiards in which the particle has memory: it remembers where it was before and react to that “spatial memory”. This opened many new open problems for us which we would like to explore in the future.
Your Research
you will work in a team to extend the current single body billiard to multiple body problem. It is not obvious how such system evolve over time and how properties of the system depends on the way particles interact. Next we will design new “mathematical games”, exploring the properties of many-body billiards with memory. E.g., what happens when particles “forget”? what if the reaction of particles to the same memory is different? How does the system change from 2D to 3D?
Model Development will be based on the recently developed code and involves event-based programming in Python or Julia.
Supervisors: Mazi Jalaal (m.jalaal@uva.nl)