Enumeration of distinct mechanically stable disk packings in small systems

Abstract

We create mechanically stable (MS) packings of bidisperse disks using an algorithm in which we successively grow or shrink soft repulsive disks followed by energy minimization until the overlaps are vanishingly small. We focus on small systems because this enables us to enumerate nearly all distinct MS packings. We measure the probability of obtaining an MS packing at packing fraction φ and find several notable results. Firstly, the probability is highly non-uniform. When averaged over narrow packing fraction intervals, the most probable MS packing occurs at the highest φ and the probability decays exponentially with decreasing φ. Even more striking, within each packing-fraction interval, the probability can vary by many orders of magnitude. By using two different packing-generation protocols, we show that these results are robust and the packing frequencies do not change qualitatively with different protocols.

Acknowledgements

Financial support from NSF grant numbers CTS-0348175 (GG,JB), DMR-0448838 (GG,CSO), and CTS-0456703 (CSO) is gratefully acknowledged. We also thank Yale's High Performance Computing Center for generous amounts of computer time.