Pine D J, Gollub J P, Brady J F, Leshansky A M
Department of Chemical Engineering and KITP, University of California, Santa Barbara, California 93106-5080, USA.
Nature. 2005 Dec 15;438(7070):997-1000. doi: 10.1038/nature04380.
Systems governed by time reversible equations of motion often give rise to irreversible behaviour. The transition from reversible to irreversible behaviour is fundamental to statistical physics, but has not been observed experimentally in many-body systems. The flow of a newtonian fluid at low Reynolds number can be reversible: for example, if the fluid between concentric cylinders is sheared by boundary motion that is subsequently reversed, then all fluid elements return to their starting positions. Similarly, slowly sheared suspensions of solid particles, which occur widely in nature and science, are governed by time reversible equations of motion. Here we report an experiment showing precisely how time reversibility fails for slowly sheared suspensions. We find that there is a concentration dependent threshold for the deformation or strain beyond which particles do not return to their starting configurations after one or more cycles. Instead, their displacements follow the statistics of an anisotropic random walk. By comparing the experimental results with numerical simulations, we demonstrate that the threshold strain is associated with a pronounced growth in the Lyapunov exponent (a measure of the strength of chaotic particle interactions). The comparison illuminates the connections between chaos, reversibility and predictability.
由时间可逆运动方程支配的系统常常会产生不可逆行为。从可逆行为到不可逆行为的转变是统计物理学的基础，但在多体系统中尚未通过实验观察到。低雷诺数下牛顿流体的流动可以是可逆的：例如，如果同心圆柱之间的流体通过随后反转的边界运动而受到剪切，那么所有流体元素都会回到其起始位置。同样，在自然和科学中广泛存在的固体颗粒缓慢剪切悬浮液也由时间可逆运动方程支配。在此，我们报告一项实验，精确展示了缓慢剪切悬浮液的时间可逆性是如何失效的。我们发现，对于变形或应变存在一个浓度依赖性阈值，超过该阈值，颗粒在一个或多个循环后不会回到其起始构型。相反，它们的位移遵循各向异性随机游走的统计规律。通过将实验结果与数值模拟进行比较，我们证明阈值应变与李雅普诺夫指数（衡量混沌颗粒相互作用强度的指标）的显著增长相关。这种比较阐明了混沌、可逆性和可预测性之间的联系。
