### Abstract

The velocity distribution of inelastic granular gas is examined numerically on a two-dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with the Maxwell-Boltzmann distribution, then after several inelastic collisions per particle, the system falls in the state that the Boltzmann’s equation predicts with the stationary form of velocity distribution. It turns out, however, that due to the velocity correlation the form of the distribution function does not stay time independent, but gradually returns to the Maxwellian immediately after the initial transient till the clustering instability sets in. It shows that, even in the homogeneous cooling state (Haff state), where the energy decays exponentially as a function of collision number, the velocity correlation in the inelastic system invalidates the assumption of molecular chaos and the prediction of the Boltzmann’s equation fails.

Original language | English |
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Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 67 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)

### Cite this

**Velocity distribution of inelastic granular gas in a homogeneous cooling state.** / Nakanishi, Hiizu.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Velocity distribution of inelastic granular gas in a homogeneous cooling state

AU - Nakanishi, Hiizu

PY - 2003/1/1

Y1 - 2003/1/1

N2 - The velocity distribution of inelastic granular gas is examined numerically on a two-dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with the Maxwell-Boltzmann distribution, then after several inelastic collisions per particle, the system falls in the state that the Boltzmann’s equation predicts with the stationary form of velocity distribution. It turns out, however, that due to the velocity correlation the form of the distribution function does not stay time independent, but gradually returns to the Maxwellian immediately after the initial transient till the clustering instability sets in. It shows that, even in the homogeneous cooling state (Haff state), where the energy decays exponentially as a function of collision number, the velocity correlation in the inelastic system invalidates the assumption of molecular chaos and the prediction of the Boltzmann’s equation fails.

AB - The velocity distribution of inelastic granular gas is examined numerically on a two-dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with the Maxwell-Boltzmann distribution, then after several inelastic collisions per particle, the system falls in the state that the Boltzmann’s equation predicts with the stationary form of velocity distribution. It turns out, however, that due to the velocity correlation the form of the distribution function does not stay time independent, but gradually returns to the Maxwellian immediately after the initial transient till the clustering instability sets in. It shows that, even in the homogeneous cooling state (Haff state), where the energy decays exponentially as a function of collision number, the velocity correlation in the inelastic system invalidates the assumption of molecular chaos and the prediction of the Boltzmann’s equation fails.

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U2 - 10.1103/PhysRevE.67.010301

DO - 10.1103/PhysRevE.67.010301

M3 - Article

AN - SCOPUS:85035270736

VL - 67

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 1

ER -