# The coordination number of granular cylinders

(in progress)

## Summary

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

 Grain Type $\langle z\rangle$ 10
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 $\langle z\rangle = 10$, which comes right out of constraint equations.

## References

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