Granular crystal cluster

Minkowski structure metrics are well-suited to detect order in amorphous point patterns [bibcite key=mickel2013shortcomings].

For example, in this simulation of a granular gas in a shallow cell, an ordered cluster forms:

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(Data by Thomas Schindler [bibcite key=schindler2019-granularness])

In projection, the the particles of the cluster form a hexagonal lattice. This kind of order is obvious in the q_6 order parameter, because all the normals of the Voronoi cells point into directions which are multiples of 60 degrees.

In a q_6 histogram, the growth of the cluster is evidenced by a growing peak at q_6=1:

The unordered background appears as the continuous part of this “spectrum”.

The shallow cell granular gas has a few more phases with different symmetries which can be analysed using other IMT order parameters such as q_4 [bibcite key=schindler2019-granularness].