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Updated: Apr 12, 2026
06:35
Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
Published on: February 15, 2016
8.6K
Cluster and constraint analysis in tetrahedron packings
Weiwei Jin1, Peng Lu1, Lufeng Liu1
1Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China.
Summary
Disordered tetrahedra packings are primarily ordered by local particle clusters. This study identifies key clusters and develops an order metric, revealing a maximally random jammed packing density of 0.6337 for hard tetrahedra.
Area of Science:
- Physics
- Materials Science
- Computational Science
Background:
- Disordered tetrahedra packings lack macroscopic order, with local cluster order being dominant.
- Understanding local structures is crucial for characterizing tetrahedron packing properties.
Purpose of the Study:
- To investigate local structures and properties of tetrahedron packings using cluster analysis.
- To develop an order metric for hierarchical packing structures and identify jamming points.
Main Methods:
- Cluster analysis to determine cluster size distribution and identify key cluster types (dimer, wagon wheel).
- Correlation analysis between cluster amounts and packing density.
- Monte Carlo simulations for jamming tests and identification of maximally random jammed packing.
Main Results:
- Identified a cluster distribution with peaks at dimer and wagon wheel clusters.
- Observed linear correlations between dimer/wagon wheel amounts and packing density.
- Developed an order map and identified a maximally random jammed packing density of 0.6337.
Conclusions:
- Local cluster order, particularly dimers, serves as a robust metric for tetrahedron packing hierarchy.
- The study provides a new maximally random jammed packing configuration for hard tetrahedra.
- Constraint analysis helps delineate isostatic and hyperstatic regions within the packing order map.
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