• Corpus ID: 252090226

From pinned billiard balls to partial differential equations

@inproceedings{Burdzy2022FromPB,
  title={From pinned billiard balls to partial differential equations},
  author={Krzysztof Burdzy and Jeremy G. Hoskins and Stefan Steinerberger},
  year={2022}
}

• K. Burdzy, J. Hoskins, S. Steinerberger
• Published 3 September 2022
• Physics, Mathematics

. We discuss the propagation of kinetic energy through billiard balls fixed in place along a one-dimensional segment. The number of billard balls is assumed to be large but finite and we assume kinetic energy propagates following the usual collision laws of physics. Assuming an underlying stochastic mean-field for the expectation and the variance of the kinetic energy, we derive a coupled system of nonlinear partial differential equations assuming a stochastic energy re-distribution procedure. The system of PDEs has a number of interesting dynamical properties some of which are numerically simulated.