Donado F, Moctezuma R E, López-Flores L, Medina-Noyola M, Arauz-Lara J L
Instituto de Ciencias Básicas e Ingeniería de la Universidad Autónoma del Estado de Hidalgo-AAMF, Pachuca, 42184, Hgo., Mexico.
Conacyt- Instituto de Física, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000, San Luis Potosí, S.L.P., Mexico.
Sci Rep. 2017 Oct 3;7(1):12614. doi: 10.1038/s41598-017-12737-1.
The Ornstein-Uhlenbeck stochastic process is an exact mathematical model providing accurate representations of many real dynamic processes in systems in a stationary state. When applied to the description of random motion of particles such as that of Brownian particles, it provides exact predictions coinciding with those of the Langevin equation but not restricted to systems in thermal equilibrium but only conditioned to be stationary. Here, we investigate experimentally single particle motion in a two-dimensional granular system in a stationary state, consisting of 1 mm stainless balls on a plane circular surface. The motion of the particles is produced by an alternating magnetic field applied perpendicular to the surface of the container. The mean square displacement of the particles is measured for a range of low concentrations and it is found that following an appropriate scaling of length and time, the short-time experimental curves conform a master curve covering the range of particle motion from ballistic to diffusive in accordance with the description of the Ornstein-Uhlenbeck model.
奥恩斯坦-乌伦贝克随机过程是一种精确的数学模型，能为处于稳态的系统中的许多实际动态过程提供准确的表示。当应用于描述诸如布朗粒子等粒子的随机运动时，它能提供与朗之万方程一致的精确预测，但不限于热平衡系统，仅需满足处于稳态的条件。在此，我们通过实验研究处于稳态的二维颗粒系统中的单粒子运动，该系统由平面圆形表面上的1毫米不锈钢球组成。粒子的运动由垂直施加于容器表面的交变磁场产生。在一系列低浓度范围内测量了粒子的均方位移，结果发现，经过适当的长度和时间缩放后，短时实验曲线符合一条主曲线，该主曲线涵盖了从弹道运动到扩散运动的粒子运动范围，这与奥恩斯坦-乌伦贝克模型的描述一致。
