# The coordination number of granular cylinders

From Soft-Matter

(in progress)

## Contents

## Soft Matter Keywords

#### Coordination Number,

## Summary

In a granular material, the average coordination number <math>\langle z\rangle</math> is defined as the average number of touching neighbors per particle. For hard spheres, <math>\langle z\rangle</math> has been well-studied and is widely-agreed upon. This is paper discusses <math>\langle z\rangle</math> for cylindrical grains. Using constraint equations, the authors prove the following equations:

Grain Type | <math>\langle z\rangle</math> |

10 |

× | 1 | 2 | 3 |
---|---|---|---|

1 | 1 | 2 | 3 |

2 | 2 | 4 | 6 |

3 | 3 | 6 | 9 |

4 | 4 | 8 | 12 |

5 | 5 | 10 | 15 |

First, the authors prove that frictionless cylinder grains have <math>\langle z\rangle = 10</math>, which comes right out of constraint equations.

## Relevance to Soft Matter

## References

J. Blouwolff and S. Fraden. "The coordination number of granular cylinders." *Europhys. Letters*, **76** (6), pp. 1095-1101 (2006).