title: Inelastic collapse in one-dimensional driven systems under gravity.
abstract: 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 n(coll) 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 N>/~20, we find three regimes in e depending on the behavior of n(coll) in the hard-sphere limit: (i) an uncollapsing regime for 1≥e>e(c1), where n(coll) converges to a finite value, (ii) a logarithmically collapsing regime for e(c1)>e>e(c2), where n(coll) diverges as n(coll)~logk, and (iii) a power-law collapsing regime for e(c2)>e>0, where n(coll) diverges as n(coll)~k(α) 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 e(c1)=/~1-2.6/N and e(c2)=/~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.
authors.affiliation: Miyakonojo National College of Technology, Miyakonojo-shi, Miyazaki 885-8567, Japan. wakou@cc.miyakonojo-nct.ac.jp
authors.forename: Jun'ichi
authors.initials: J
authors.lastname: Wakou
authors.forename: Hiroyuki
authors.initials: H
authors.lastname: Kitagishi
authors.forename: Takahiro
authors.initials: T
authors.lastname: Sakaue
authors.forename: Hiizu
authors.initials: H
authors.lastname: Nakanishi