# 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} }

. 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…

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