scholarly journals CALCULATIONS OF HARD SPHERE PACKINGS IN LARGE CYLINDERS

1966 ◽  
Author(s):  
B.E. Clancy
Keyword(s):  
Soft Matter ◽  
2014 ◽  
Vol 10 (39) ◽  
pp. 7838-7848 ◽  
Author(s):  
Vasili Baranau ◽  
Ulrich Tallarek

2015 ◽  
Vol 91 (6) ◽  
Author(s):  
M. Hanifpour ◽  
N. Francois ◽  
V. Robins ◽  
A. Kingston ◽  
S. M. Vaez Allaei ◽  
...  

2014 ◽  
Vol 141 (4) ◽  
pp. 044510 ◽  
Author(s):  
Moumita Maiti ◽  
Srikanth Sastry

2004 ◽  
Vol 197 (1) ◽  
pp. 139-166 ◽  
Author(s):  
Aleksandar Donev ◽  
Salvatore Torquato ◽  
Frank H. Stillinger ◽  
Robert Connelly

2009 ◽  
Vol 50 (4) ◽  
pp. 761-768 ◽  
Author(s):  
A. V. Anikeenko ◽  
N. N. Medvedev
Keyword(s):  

2019 ◽  
Vol 7 ◽  
Author(s):  
MATTHEW JENSSEN ◽  
FELIX JOOS ◽  
WILL PERKINS

We prove a lower bound on the entropy of sphere packings of $\mathbb{R}^{d}$ of density $\unicode[STIX]{x1D6E9}(d\cdot 2^{-d})$. The entropy measures how plentiful such packings are, and our result is significantly stronger than the trivial lower bound that can be obtained from the mere existence of a dense packing. Our method also provides a new, statistical-physics-based proof of the $\unicode[STIX]{x1D6FA}(d\cdot 2^{-d})$ lower bound on the maximum sphere packing density by showing that the expected packing density of a random configuration from the hard sphere model is at least $(1+o_{d}(1))\log (2/\sqrt{3})d\cdot 2^{-d}$ when the ratio of the fugacity parameter to the volume covered by a single sphere is at least $3^{-d/2}$. Such a bound on the sphere packing density was first achieved by Rogers, with subsequent improvements to the leading constant by Davenport and Rogers, Ball, Vance, and Venkatesh.


Sign in / Sign up

Export Citation Format

Share Document