The confinement properties of the diffusive running sandpile are characterized by tracking the motion of a population of marked grains of sand. It is found that, as the relative strength of the avalanching to the diffusive transport channel is varied, a point is reached at which the particle global confinement time and the probability density functions of the jump-sizes and waiting-times of the tracked grains experience a sudden change, thus revealing a dynamical transition, that is consistent with previous studies (Newman DE et al., Phys Rev Lett 2002;88(20):204304). Across this transition, the sandpile moves from a regime characterized by self-similarity and memory, where avalanches of all possible sizes dominate transport across the system, to another regime where transport is taken over by near system-size, quasi-periodic avalanches. Values for the fractional transport exponents that quantify effective transport across the sandpile prior to the transition are also obtained.

扩散运行的沙堆的约束性质是通过跟踪大量带标记的沙粒的运动来表征的。研究发现，随着雪崩相对于扩散传输通道的相对强度发生变化，到达了一个点，在该点处颗粒整体约束时间以及被跟踪晶粒的跃迁尺寸和等待时间的概率密度函数经历了突变，从而揭示出动态转变，这与先前的研究一致（Newman DE et al。，Phys Rev Lett 2002; 88（20）：204304）。在整个过渡过程中，沙堆从以自我相似和记忆为特征的状态（其中所有可能大小的雪崩主导整个系统的传输）转移到另一个状态，在该状态下，传输由接近系统大小的准周期雪崩接管。