Random loose packing and an order parameter for the parking lot model

On the Glassy Behavior of Parking Lot Model

We present a theoretical discussion of the reversible parking problem, which appears to be one of the simplest systems exhibiting glassy behavior. The existence of slow relaxation, nontrivial fluctuations, and an annealing effect can all be understood by recognizing that two different time scales are present in the problem. One of these scales corresponds to the fast filling of existing voids, the other is associated with collective processes that overcome partial ergodicity breaking. The results of the theory are in a good agreement with simulation data; they provide a simple qualitative pict…

Record Dynamics in the Parking Lot Model

We present an analytical and numerical study of the parking lot model (PLM) of granular relaxation and make a connection to the aging dynamics of dense colloids. As we argue, the PLM is a Kinetically Constrained Model which features astronomically large equilibration times and displays a characteristic aging behavior on all observable time scales. The density of parked cars displays quasi-equilibrium Gaussian fluctuations interspersed by increasingly rare intermittent events, quakes, which can lead to an increase of the density to new record values. Defining active clusters as the shortest dom…

平面硬圆盘随机堆积的几何概率方法

A geometric probabilistic approach to random packing of hard disks in a plane

本研究采用几何概率方法，建立平面等尺寸硬圆盘的随机密堆积模型，提出单分散圆盘随机松堆积的统计几何模型，推导得到配位数的闭式表达式，结果与已有实验、模拟及Rényi停车模型等结果高度吻合。