# Coordination Number

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

### Definition

The number of touching neighbors per particle in a granular material.1

### Discussion

Often, the value of interest is the average coordination number, $\langle z \rangle$. If $n_z\,$ is the number of rods with $z\,$ touching neighbors, then we can calculate $\langle z \rangle$ as a weighted average.

$\langle z \rangle = \frac{\sum_z z n_z}{\sum_z n_z} \equiv \sum_z z \gamma_z$,

where $\gamma_z \equiv \frac{n_z}{\sum_z n_z}$ is defined as the coordination number distribution function. $\gamma_z\,$ will depend on the shape of the grains.

### References

1J. Blouwolff and S. Fraden. "The coordination number of granular cylinders." Europhys. Letters, 76 (6), pp. 1095-1101 (2006).