### 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 Na≳^{3}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}∼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 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.

Original language | English |
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Article number | 042201 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 87 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 5 2013 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*87*(4), [042201]. https://doi.org/10.1103/PhysRevE.87.042201

**Inelastic collapse in one-dimensional driven systems under gravity.** / Wakou, Jun'Ichi; Kitagishi, Hiroyuki; Sakaue, Takahiro; Nakanishi, Hiizu.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 87, no. 4, 042201. https://doi.org/10.1103/PhysRevE.87.042201

}

TY - JOUR

T1 - Inelastic collapse in one-dimensional driven systems under gravity

AU - Wakou, Jun'Ichi

AU - Kitagishi, Hiroyuki

AU - Sakaue, Takahiro

AU - Nakanishi, Hiizu

PY - 2013/4/5

Y1 - 2013/4/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84876737654&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevE.87.042201

DO - 10.1103/PhysRevE.87.042201

M3 - Article

AN - SCOPUS:84876737654

VL - 87

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 042201

ER -