Right Type Departmental Bulletin Paper

Collisions are common phenomena in nature. For example, in the microscopic scale, atoms and molecules in gas are colliding each other. In the macroscopic scale, we often see collision of balls in sports such as the baseball and the billiard. In such collisions, the initial kinetic energy of material dissipates into internal degrees of freedom like elastic vibration, sound emission, and heat. As a result, macroscopic collisions are always inelastic. Inelastic collisions play an important role in granular materials[l]. Characteristic behaviors of granular material come from inelastic collisions among particles. By tilting or shaking the container which contains granular material, one can see the characteristic behavior of granules which is different from that of ordinary fluid. The Distinct Element Method (DEM) is awell-known simulation method for the granular materials[2]. DEM contains some phenomenological parameters such as the Coulomb’s coefficient of friction, dashpots, and so on. Nobody can determine such the viscoelastic parameter from the first principle. However, even the determination of the simplest parameter, the coefficient of normal restitution (COR) is not reliable. The coefficient of normal restitution(COR) $e $ is afamiliar parameter which is introduced in text books of the elementary physics. COR is defined by the ratio of the normal components of th