# Difference between revisions of "The coordination number of granular cylinders"

From Soft-Matter

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==Soft Matter Keywords== | ==Soft Matter Keywords== | ||

+ | ====[[Coordination Number]], ==== | ||

==Summary== | ==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: | ||

+ | |||

+ | {| class="wikitable" style="text-align:center" | ||

+ | |- | ||

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

+ | |- | ||

+ | | Frictionless Cylinder| 10 | ||

+ | |} | ||

+ | |||

+ | {| class="wikitable" style="text-align:center" | ||

+ | |+Multiplication table | ||

+ | |- | ||

+ | ! × !! 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== | ==Relevance to Soft Matter== | ||

+ | |||

+ | ==References== | ||

+ | |||

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

## Revision as of 15:53, 4 November 2009

(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).