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Exit distribution function crossover in a Galton board

机译：在高尔顿板上退出分配功能交叉

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摘要

Here we present an experimental and numerical study concerning the problem of the influence of walls on a granular flow through obstacles. The system based on a Galton Board is a vertical bi-dimensional array of equally spaced obstacles arranged to form a triangular lattice. Lateral walls, whose relative separation can be varied, are set. Disks of equal diameters are launched at the top of the system. During the fall, the disks collide inelastically with the obstacles of the lattice and, eventually, with lateral walls. At the exit, at the bottom of the board, disks are collected in separate bins depending on their final horizontal positions. The aim of the present paper is to study the dependence of the exit distributions of small disks on the separa- tion between the lateral walls of the board. We found that there exists a crossover from a Gaussian-like to a uniform-like behaviour when the separation between walls is less than a critical value. A systematic study of this crossover is performed through numerical simulations and the results are also approximated by a theoretical model of the problem.
机译：在这里，我们提出了关于壁对通过障碍物的颗粒流影响问题的实验和数值研究。基于高尔顿板的系统是垂直二维阵列，其均等间隔地布置成一个三角形格子。设置了可以改变相对间距的侧壁。直径相等的磁盘在系统顶部启动。在坠落期间，圆盘与格子的障碍物以及最终与侧壁发生非弹性碰撞。在板子底部的出口处，根据磁盘的最终水平位置将其收集在单独的存储箱中。本文的目的是研究小圆盘出口分布对板侧壁之间分离的依赖性。我们发现，当壁之间的间距小于临界值时，存在从高斯型行为向均匀型行为的过渡。通过数值模拟对这种交叉进行了系统的研究，结果也通过问题的理论模型进行了近似。

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