论文标题
从固定的台球到部分微分方程
From pinned billiard balls to partial differential equations
论文作者
论文摘要
我们讨论了动能通过沿一维段固定在适当位置的台球的传播。假定台球球的数量很大，但有限，我们假设动能在通常的物理碰撞定律之后传播。假设具有动能的期望和方差的潜在随机平均场，我们会得出一个非线性偏微分方程的耦合系统，假设随机能量重新分布过程。 PDES系统具有许多有趣的动力学属性，其中一些是数值模拟的。
We discuss the propagation of kinetic energy through billiard balls fixed in place along a one-dimensional segment. The number of billiard 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.
