Néel Baptiste, Rondini Ignacio, Turzillo Alex, Mujica Nicolás, Soto Rodrigo
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Apr;89(4):042206. doi: 10.1103/PhysRevE.89.042206. Epub 2014 Apr 23.
A granular system confined in a quasi-two-dimensional box that is vertically vibrated can transit to an absorbing state in which all particles bounce vertically in phase with the box, with no horizontal motion. In principle, this state can be reached for any density lower than the one corresponding to one complete monolayer, which is then the critical density. Below this critical value, the transition to the absorbing state is of first order, with long metastable periods, followed by rapid transitions driven by homogeneous nucleation. Molecular dynamics simulations and experiments show that there is a dramatic increase on the metastable times far below the critical density; in practice, it is impossible to observe spontaneous transitions close to the critical density. This peculiar feature is a consequence of the nonequilibrium nature of this first-order transition to the absorbing state. A Ginzburg-Landau model, with multiplicative noise, describes qualitatively the observed phenomena and explains the macroscopic size of the critical nuclei. The nuclei become of small size only close to a second critical point where the active phase becomes unstable via a saddle node bifurcation. It is only close to this second critical point that experiments and simulations can evidence spontaneous transitions to the absorbing state while the metastable times grow dramatically moving away from it.
一个被限制在垂直振动的准二维盒子中的颗粒系统可以转变为一种吸收态，在这种状态下，所有颗粒与盒子同步垂直弹跳，没有水平运动。原则上，对于任何低于对应于一个完整单层的密度，都可以达到这种状态，该密度即为临界密度。低于这个临界值时，向吸收态的转变是一级的，具有较长的亚稳期，随后是由均匀成核驱动的快速转变。分子动力学模拟和实验表明，在远低于临界密度时，亚稳时间会急剧增加；实际上，在接近临界密度时不可能观察到自发转变。这一独特特征是向吸收态的这种一级转变的非平衡性质的结果。一个具有乘性噪声的金兹堡 - 朗道模型定性地描述了所观察到的现象，并解释了临界核的宏观尺寸。只有在接近第二个临界点时，核才会变小，在该点，活跃相通过鞍结分岔变得不稳定。只有在接近这个第二个临界点时，实验和模拟才能证明向吸收态的自发转变，而随着远离该点，亚稳时间会急剧增加。
