随机弹跳球动力学中的记忆
Memory in random bouncing ball dynamics
摘要：
非弹性球在振动板上的弹跳是一种流行的模型，用于从颗粒气体到纳米尺寸的机械接触等各个领域。对于随机板块运动，到目前为止，该模型已被研究使用庞加莱{é}映射，其中的激励板在连续的反弹被假定为一个离散的马尔可夫（无记忆）过程。在这里，我们调查数值的行为的连续随机激发与可调相关时间的模型。我们表明，系统的动力学控制的马尔可夫平均飞行时间的球和连续的峰值之间的平均时间在运动的激励板的比率。当这个比率，这取决于激励信号的带宽，超过一定的值，马尔可夫方法是适当的;下面，前面的激励的记忆出现，导致跳跃持续时间的显着减少;在最小值的比率，发生抖动。总的来说，我们的研究结果开辟了道路，在低激发制度，这仍然是知之甚少的模型的使用。
英文摘要：
The bouncing of an inelastic ball on a vibrating plate is a popular model used in various fields, from granular gases to nanometer-sized mechanical contacts. For random plate motion, so far, the model has been studied using Poincar{é} maps in which the excitation by the plate at successive bounces is assumed to be a discrete Markovian (memoryless) process. Here, we investigate numerically the behaviour of the model for continuous random excitations with tunable correlation time. We show that the system dynamics are controlled by the ratio of the Markovian mean flight time of the ball and the mean time between successive peaks in the motion of the exciting plate. When this ratio, which depends on the bandwidth of the excitation signal, exceeds a certain value, the Markovian approach is appropriate; below, memory of preceding excitations arises, leading to a significant decrease of the jump duration; at the smallest values of the ratio, chattering occurs. Overall, our results open the way for uses of the model in the low excitation regime, which is still poorly understood.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
