Inelastic collapse in one-dimensional driven systems under gravity

Jun'Ichi Wakou, Hiroyuki Kitagishi, Takahiro Sakaue, Hiizu Nakanishi

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 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.

Original languageEnglish
Article number042201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume87
Issue number4
DOIs
Publication statusPublished - Apr 5 2013

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Collapsing
Gravity
gravitation
Hard Spheres
Diverge
Power Law
collision rates
Decrease
Elastic Constants
Particle System
elastic properties
exponents
Collision
Exponent
Converge
coefficients
Numerical Simulation
Coefficient
simulation
Demonstrate

All Science Journal Classification (ASJC) codes

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

Cite this

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

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 87, No. 4, 042201, 05.04.2013.

Research output: Contribution to journalArticle

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