We study inelastic collapse in a one-dimensional N-particle system when the system is driven from below under gravity. We investigate the hard-sphere limit of inelastic soft-sphere systems by numerical simulations to find how the collision rate per particle ncoll increases as a function of the elastic constant of the sphere k when the restitution coefficient e is kept constant. For systems with large enough Na≳320, we find three regimes in e depending on the behavior of ncoll in the hard-sphere limit: (i) an uncollapsing regime for 1≥e>ec1, where n coll converges to a finite value, (ii) a logarithmically collapsing regime for ec1>e>ec2, where ncoll diverges as ncoll∼logk, and (iii) a power-law collapsing regime for ec2>e>0, where ncoll diverges as n coll∼kα with an exponent α that depends on N. The power-law collapsing regime shrinks as N decreases and seems not to exist for the system with N=3, while, for large N, the size of the uncollapsing and the logarithmically collapsing regime decreases as ec1≃1-2.6/N and ec2≃1-3.0/N. We demonstrate that this difference between large and small systems exists already in the inelastic collapse without external drive and gravity.
|ジャーナル||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|出版ステータス||出版済み - 4 5 2013|
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