Rivas Nicolas, Thornton Anthony R, Luding Stefan, van der Meer Devaraj
Multi-Scale Mechanics (MSM), MESA +, CTW, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Mathematics of Computational Science (MaCS), MESA +, CTW, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042202. doi: 10.1103/PhysRevE.91.042202. Epub 2015 Apr 23.
Grains inside a vertically vibrated box undergo a transition from a density-inverted and horizontally homogeneous state, referred to as the granular Leidenfrost state, to a buoyancy-driven convective state. We perform a simulational study of the precursors of such a transition and quantify their dynamics as the bed of grains is progressively fluidized. The transition is preceded by transient convective states, which increase their correlation time as the transition point is approached. Increasingly correlated convective flows lead to density fluctuations, as quantified by the structure factor, that also shows critical behavior near the transition point. The amplitude of the modulations in the vertical velocity field are seen to be best described by a quintic supercritical amplitude equation with an additive noise term. The validity of such an amplitude equation, and previously observed collective semiperiodic oscillations of the bed of grains, suggests a new interpretation of the transition analogous to a coupled chain of vertically vibrated damped oscillators. Increasing the size of the container shows metastability of convective states, as well as an overall invariant critical behavior close to the transition.
在垂直振动的盒子中的颗粒会经历从一种密度反转且水平均匀的状态（称为颗粒莱顿弗罗斯特状态）到浮力驱动的对流状态的转变。我们对这种转变的前兆进行了模拟研究，并在颗粒床逐渐流化时量化其动力学。转变之前存在瞬态对流状态，随着接近转变点，其关联时间会增加。如结构因子所量化的，越来越相关的对流流动会导致密度波动，在转变点附近也表现出临界行为。垂直速度场中的调制幅度被认为最好用带有加性噪声项的五次超临界幅度方程来描述。这种幅度方程的有效性以及之前观察到的颗粒床的集体半周期振荡，为类似于垂直振动的阻尼振荡器耦合链的转变提供了一种新解释。增大容器尺寸显示出对流状态的亚稳定性，以及接近转变时整体不变的临界行为。
