Coordination Number

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


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

<math>\langle z \rangle = \frac{\sum_z z n_z}{\sum_z n_z} \equiv \sum_z z \gamma_z </math>,

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


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