论文标题
空隙过渡
Lacunarity Transition
论文作者
论文摘要
研究漂浮在随机搅拌流体上的颗粒的实验显示出非常低密度的区域，这尚不清楚。我们介绍了一个简化的模型，以理解基于瘦面包师地图的扩展，以理解非自治，混乱动力学系统的相位空间的稀疏区域。我们展示了如何将空隙中空间大小的分布映射到Wiener过程的运行最大值的统计数据。我们发现该模型表现出裂解性转变，其特征是随着轨迹数量的增加，相位空间的区域保持空位。
Experiments investigating particles floating on a randomly stirred fluid show regions of very low density, which are not well understood. We introduce a simplified model for understanding sparsely occupied regions of the phase space of non-autonomous, chaotic dynamical systems, based upon an extension of the skinny bakers' map. We show how the distribution of the sizes of voids in the phase space can be mapped to the statistics of the running maximum of a Wiener process. We find that the model exhibits a lacunarity transition, which is characterised by regions of the phase space remaining empty as the number of trajectories is increased.
