| Summary: | 碩士 === 國立中央大學 === 物理研究所 === 88 === We consider the dynamics of an ensemble of identical, inelastic, hard disks in a square
domain, with three kinds of dierent boundary conditions, (i) double periodic bound-
aries, (ii) a pair of smooth, elastic walls in the x-direction and periodic boundaries in
the y-direction, (iii) four smooth and elastic walls. Starting with the almost elastic
case, in which the coeÆcient of restitution is just a little less than 1, the homoge-
neous regime resembles a classical non-dissipative gas and there is no large structure.
When decreases, the system becomes inhomogeneous and spatial non-uniformity
occurs. Clusters appear when is even smaller, large clusters of disks form, break,
and reform. As time goes by, the cluster stays in a status of hydrodynamic shear
state, or collapse. Inelastic collapse, which is a dynamic singularity of the binary
collision model, is caused by the many-body dynamics. Numerical simulations show
that the energy decay in the homogeneous regime is proportion to t
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