Costello Rachel M, Cruz K L, Egnatuk Christie, Jacobs D T, Krivos Matthew C, Louis Tim Sir, Urban Rebecca J, Wagner Hanna
Department of Physics, The College of Wooster, Ohio 44691, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Apr;67(4 Pt 1):041304. doi: 10.1103/PhysRevE.67.041304. Epub 2003 Apr 25.
Self-organized criticality has been proposed to explain complex dynamical systems near their critical points. This experiment examined a monodisperse conical bead pile and how the distribution of avalanches is affected by the pattern of beads glued on a base, by the size or shape of the base, and by the height at which each bead was dropped onto the pile. By measuring the number of avalanches for a given size that occurred during the experiment, the resulting distribution could be compared to a power law description. When the beads were dropped from a small height, all data were consistent with a simple power law of exponent -1.5, which is the mean-field model value. The data showed that neither the bead pattern on the base nor the base size or shape significantly affected the power law behavior. However, when the bead is dropped from different heights, then the power law description breaks down and a power law times an exponential is more appropriate. We found a scaling relationship in the distribution of avalanches for different heights and relate the data to an energy dissipation model. We both confirm self-organized criticality and observe deviations from it.
自组织临界性被提出来解释复杂动力系统接近其临界点时的情况。本实验研究了单分散锥形珠堆，以及雪崩的分布是如何受到粘贴在基座上的珠子图案、基座的尺寸或形状，以及每个珠子落到堆上的高度的影响。通过测量实验过程中给定大小的雪崩数量，可以将所得分布与幂律描述进行比较。当珠子从较小高度落下时，所有数据都与指数为-1.5的简单幂律一致，这是平均场模型值。数据表明，基座上的珠子图案、基座尺寸或形状均未对幂律行为产生显著影响。然而，当珠子从不同高度落下时，幂律描述就不再适用，幂律乘以指数的形式更为合适。我们发现了不同高度下雪崩分布的标度关系，并将数据与能量耗散模型联系起来。我们既证实了自组织临界性，也观察到了与之的偏差。
