中文摘要：

研究了斜槽中的二维颗粒流由稀疏到密集转变的临界现象,在二维颗粒槽的入口流量Q0和出口尺寸d固定的条件下，记录并统计了稀疏流转变为密集流所经历的时间．研究发现，在统计时间内转变不发生的概率C（t）随时间指数衰减，其衰减的特征时间尺度a^-1（d）可以很好地由幂律函数n（dc-d）^-r来拟合，其中dc为临界开口尺寸，此临界尺寸的存在确定了稀疏流到密集流转变的临界现象．

英文摘要：

The criticality of the dilute-to-dense transition in an inclined two-dimensional（2D） granular channel flow is investigated. The waiting time t before the transition occurs and after the flow is initiated is recorded. It is found that the probability function C（t） for the flow remaining dilute at time t decays exponentially with a characteristic time a^-1 （ d）. The characteristic time is found to be fitted well by a power law a（ dc - d）^-r, where dc is the critical opening size： as for d 〉 dc, the transition will never happen. The existence of a critical opening size at the exit confirms that the dilute-to-dense transition in 2D granular flow is a critical transition.