Statistical Model And The Kinetic Model Of Aggregation Of Particulate Matter

We introduce an urn model and noise activated granular dynamics to describe the granular cluster, diffusion and phase transition in shaken sand.Firstly 2-urn model which can simulate the classical experiment concerns to the spatial separation of sand is studied. From the granular temperature and master equation we obtain the three critical lines and tricritical point. One of the three is proved to be a line of continuous transition by the order parameter and susceptibility. Others are discontinuous transition lines. We also study the probability distribution and characteristic time in the four regions and on the critical lines.Secondly we study the 3-urn model and present the phase diagram. There is granular cluster which suddenly breaks down in the urn. We find that with different initial condition the dynamical behavior of the average time of the cluster near the critical line is not the same.In the end, we simulate the shaken grand with noise activated granular dynamics. We study the behavior of some particles moving in a bistable and tristable potential, colliding inelastically with each other and driven by a stochastic bath. The system has the tendency to clusterize with Gauss velocity distribution. Moreover, we compute the granular temperature and energy, and obtain the relationship between the granular temperature and restitution coefficient.