||We observe the dynamics of steel spheres in three kinds of asymmetric annular cells vibrated vertically. First, the annular cell is carved with asymmetric troughs in the bottom and the spheres are continuously driven to move in one direction. The average angular velocities of the spheres in different vibration frequencies and amplitudes are measured. The velocity distribution of the deviation from the average velocity is shown to follow the Gaussian distribution. According to the displacement deviation from the average velocity, the diffusion constant is obtained. When the spheres are confined in one region of the cell, we assume the potential isU=Fd Rθand fit the density distribution with Boltzmann distribution to get the driving force Fd. Using the driving force and the average velocity, we can get the ratio of the effective temperature and the drag coefficient. Comparing this ratio with the diffusion constant, the behavior fit Einstein-Smoluchowski theory. We put multiple spheres in the cell and add magnet under the cell to control the magnetic field which change the density distribution of the spheres. It is found that the collective behaviors like effective temperature change in different densities. The relation between the average angular velocity and the non-uniform density is also reported. In other experiments, the sphere is put in the asymmetrical boundary systems. The sphere transports. The relation of the vibrate amplitudes and the average velocity is brought up. When we add asymmetrical magnetic field on a symmetrical system. The behavior of the sphere change from trapped, transport, to moving randomly. The trajectories of the sphere show how the magnetic field change the sphere’s direction. This mechanism is asymmetrical in two direction which makes the sphere move in one direction. The transport velocity can’t increase infinite in these three methods.|
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