### Abstract

In a cooling gas of rigid particles interacting with a constant coefficient of restitution, groups of particles within the gas may experience an infinite number of collisions in a finite time. This singularity, named inelastic collapse, is a shortcoming of the mathematical model, and it hampers the efforts of simulating a freely evolving, cooling granular system. After a brief review of previous works addressing the problem, we propose a one-dimensional model where a grain is seen as a pair of point masses joined by a massless, dissipative spring. We show that binary interactions of such grains are described as impacts with a constant restitution coefficient, whose expression is given in terms of the spring parameters. However, the impact is not instantaneous, but it requires a finite time. We show that in situations that would lead to inelastic collapse, multiple interactions among grains transfer kinetic energy into potential energy associated with the deformation of the springs, rather than dissipate it. This effectively avoids the collapse. Finally, we discuss the results of the simulations of a cooling granular system in comparison with other models.

Original language | English (US) |
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Pages (from-to) | 218-229 |

Number of pages | 12 |

Journal | Computers and Mathematics with Applications |

Volume | 55 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2008 |

### Fingerprint

### Keywords

- Granular gas
- Inelastic collapse
- Restitution coefficient

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation

### Cite this

**Absence of inelastic collapse for a 1D gas of grains with an internal degree of freedom.** / Paparella, Francesco; Passoni, Giuseppe.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 55, no. 2, pp. 218-229. https://doi.org/10.1016/j.camwa.2007.04.012

}

TY - JOUR

T1 - Absence of inelastic collapse for a 1D gas of grains with an internal degree of freedom

AU - Paparella, Francesco

AU - Passoni, Giuseppe

PY - 2008/1/1

Y1 - 2008/1/1

N2 - In a cooling gas of rigid particles interacting with a constant coefficient of restitution, groups of particles within the gas may experience an infinite number of collisions in a finite time. This singularity, named inelastic collapse, is a shortcoming of the mathematical model, and it hampers the efforts of simulating a freely evolving, cooling granular system. After a brief review of previous works addressing the problem, we propose a one-dimensional model where a grain is seen as a pair of point masses joined by a massless, dissipative spring. We show that binary interactions of such grains are described as impacts with a constant restitution coefficient, whose expression is given in terms of the spring parameters. However, the impact is not instantaneous, but it requires a finite time. We show that in situations that would lead to inelastic collapse, multiple interactions among grains transfer kinetic energy into potential energy associated with the deformation of the springs, rather than dissipate it. This effectively avoids the collapse. Finally, we discuss the results of the simulations of a cooling granular system in comparison with other models.

AB - In a cooling gas of rigid particles interacting with a constant coefficient of restitution, groups of particles within the gas may experience an infinite number of collisions in a finite time. This singularity, named inelastic collapse, is a shortcoming of the mathematical model, and it hampers the efforts of simulating a freely evolving, cooling granular system. After a brief review of previous works addressing the problem, we propose a one-dimensional model where a grain is seen as a pair of point masses joined by a massless, dissipative spring. We show that binary interactions of such grains are described as impacts with a constant restitution coefficient, whose expression is given in terms of the spring parameters. However, the impact is not instantaneous, but it requires a finite time. We show that in situations that would lead to inelastic collapse, multiple interactions among grains transfer kinetic energy into potential energy associated with the deformation of the springs, rather than dissipate it. This effectively avoids the collapse. Finally, we discuss the results of the simulations of a cooling granular system in comparison with other models.

KW - Granular gas

KW - Inelastic collapse

KW - Restitution coefficient

UR - http://www.scopus.com/inward/record.url?scp=36849008153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849008153&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2007.04.012

DO - 10.1016/j.camwa.2007.04.012

M3 - Article

VL - 55

SP - 218

EP - 229

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 2

ER -