Calculations of the percolation thresholds of a three-dimensional (icosahedral) Penrose tiling by the cubic approximant method
@article{Zakalyukin2005CalculationsOT, title={Calculations of the percolation thresholds of a three-dimensional (icosahedral) Penrose tiling by the cubic approximant method}, author={Ruslan M. Zakalyukin and Viacheslav A. Chizhikov}, journal={Crystallography Reports}, year={2005}, volume={50}, pages={938-948} }
The percolation thresholds of a three-dimensional Penrose tiling with icosahedral symmetry are determined using the cubic approximant method. The percolation thresholds of the three-dimensional Penrose tiling for the site problem and the bond problem are calculated with an accuracy of 0.001.
2 Citations
Percolation of disordered jammed sphere packings
- Physics
- 2016
We determine the site and bond percolation thresholds for a system of disordered jammed sphere packings in the maximally random jammed state, generated by the Torquato–Jiao algorithm. For the site…
Molecular jenga: the percolation phase transition (collapse) in virus capsids
- Biology, ChemistryPhysical biology
- 2018
Application of percolation theory to understanding capsid association and dissociation may prove a general approach to relating virus biology to the underlying biophysics of the virus particle.
References
SHOWING 1-10 OF 18 REFERENCES
Technical Note: Percolation Thresholds and Conductivities of a Uniaxial Anisotropic Simple-Cubic Lattice
- Physics
- 1998
We have investigated the percolation and transport behavior of uniaxial anisotropic networks, in which the bond occupation probability in one, ‘perpendicular’, direction is different from that in the…
The space groups of orthorhombic approximants to the icosahedral quasilattice
- Geology
- 1992
The space groups of the orthorhombic approximant lattices to the primitive icosahedral quasilattice are classified. There exist three Bravais classes: Pmmm, Cmmm and Immm. The basis vectors of the…
Quasicrystals: a new class of ordered structures
- Physics
- 1984
A quasicrystal is the natural extension of the notion of a crystal to structures with quasiperiodic, rather than periodic, translational order. We classify two- and three-dimensional quasicrystals by…
Quasicrystals and their approximants: dodecahedral local ordering versus canonical‐cell description
- Physics
- 1994
Two models of icosahedral quasicrystals are compared and connected. These are canonical-cell ordering (CCO) over medium-length scales (about 10 A and more) and dodecahedral local ordering (DLO),…
Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
- Materials Science
- 1984
We have observed a metallic solid (Al-14-at.%-Mn) with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations. Its diffraction…
Cubic approximants in quasicrystal structures
- Materials Science
- 1990
2014 The regular deviations from the exact icosahedral symmetry, usually observed at the diffraction patterns of quasicrystal alloys, are analyzed. It is shown that shifting, splitting and asymmetric…
On Periodic and Non-periodic Space Fillings of E
- Mathematics
- 1984
A periodic lattice in \bb En is associated with an n-grid and its dual, and with a point symmetry group G. Given a subgroup H of G, a subspace \bb Em, m < n, of \bb En, invariant under H, is chosen…
Introduction To Percolation Theory
- Physics
- 1985
Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in…