Collective transport of Lennard–Jones particles through one-dimensional periodic potentials
He Jian-hui, Wen Jia-le, Chen Pei-rong, Zheng Dong-qin, Zhong Wei-rong
       

(color online) (a) We use the density and velocity of each small section of the channel in the potential well. For comparing the actual flux—, the density and velocity are multiplied to obtain the other flux of each section, then the average for the entire channel is obtained. The two values of flux obtained from different ways are in agreement. Then is translated into . (b) This result also occurs in the potential barrier. Thus, we verify in the transport with external fields. Besides, in the transport channels of the potential well (c) and barrier (d), the products of density and velocity in the entire channel are still almost constants.