Hard-Sphere Packing and Icosahedral Assembly in the Formation of Mesoporous Materials

2007 ◽  
Vol 129 (29) ◽  
pp. 9044-9048 ◽  
Author(s):  
Jiawei Tang ◽  
Xufeng Zhou ◽  
Dongyuan Zhao ◽  
Gao Qing Lu ◽  
Jin Zou ◽  
...  
Keyword(s):  
Mesoporous Materials ◽  
Hard Sphere ◽  
Sphere Packing

scholarly journals ON THE HARD SPHERE MODEL AND SPHERE PACKINGS IN HIGH DIMENSIONS

2019 ◽  
Vol 7 ◽  
Author(s):  
MATTHEW JENSSEN ◽  
FELIX JOOS ◽  
WILL PERKINS
Keyword(s):  
Lower Bound ◽  
Packing Density ◽  
Hard Sphere ◽  
Statistical Physics ◽  
Sphere Packing ◽  
Hard Sphere Model ◽  
Sphere Packings ◽  
Sphere Model ◽  
Single Sphere ◽  
Mere Existence

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.

scholarly journals Fluidization of a vertically vibrated two-dimensional hard sphere packing: A granular meltdown

2006 ◽  
Vol 74 (1) ◽  
Author(s):  
Andreas Götzendorfer ◽  
Chi-Hwang Tai ◽  
Christof A. Kruelle ◽  
Ingo Rehberg ◽  
Shu-San Hsiau
Keyword(s):  
Hard Sphere ◽  
Sphere Packing ◽  
Two Dimensional
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