TY - JOUR
T1 - Enumeration of distinct mechanically stable disk packings in small systems
AU - Gao, G. J.
AU - Blawzdziewicz, J.
AU - O'Hern, C. S.
N1 - Funding Information:
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.
PY - 2007/1
Y1 - 2007/1
N2 - 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 fractionand 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 highestand the probability decays exponentially with decreasing . 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.
AB - 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 fractionand 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 highestand the probability decays exponentially with decreasing . 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.
UR - http://www.scopus.com/inward/record.url?scp=33847170939&partnerID=8YFLogxK
U2 - 10.1080/14786430600851760
DO - 10.1080/14786430600851760
M3 - Article
AN - SCOPUS:33847170939
SN - 1478-6435
VL - 87
SP - 425
EP - 431
JO - Philosophical Magazine
JF - Philosophical Magazine
IS - 3-5
ER -