scholarly journals Random tilings with the GPU

2018 ◽  
Vol 59 (9) ◽  
pp. 091420 ◽  
Author(s):  
David Keating ◽  
Ananth Sridhar
Keyword(s):  
Random Tilings

Morphometry and structure of natural random tilings

2010 ◽  
Vol 33 (4) ◽  
pp. 369-375 ◽  
Author(s):  
A. Hočevar ◽  
S. El Shawish ◽  
P. Ziherl
Keyword(s):  
Random Tilings

scholarly journals Random tilings of spherical 3-manifolds

2008 ◽  
Vol 58 (11) ◽  
pp. 1451-1464 ◽  
Author(s):  
Juan García Escudero
Keyword(s):  
Random Tilings

CONFIGURATIONAL ENTROPY IN OCTAGONAL TILING MODELS

1993 ◽  
Vol 07 (06n07) ◽  
pp. 1427-1436 ◽  
Author(s):  
RÉMY MOSSERI ◽  
FRANCIS BAILLY
Keyword(s):  
Configurational Entropy ◽  
Upper Bounds ◽  
Partition Problem ◽  
Asymptotic Case ◽  
Random Tilings

We calculate the configurational entropy of random tilings obtained by elementary flips from a perfect octagonal tiling with an octagonal boundary. We map the problem of generating all configurations onto a partition problem. We calculate numerically the number of configurations and the associated entropy. We give some exact expressions in restricted cases and upper bounds for the entropy in the asymptotic case.

Decagonal random tilings and their quasi-unit cell cluster coverings

2021 ◽  
pp. 2150171
Author(s):  
Juan García Escudero
Keyword(s):  
Electron Microscopy ◽  
Structural Unit ◽  
Cell Cluster ◽  
Penrose Tiling ◽  
Decagonal Quasicrystals ◽  
Different Types ◽  
Complex Structural ◽  
Random Tilings ◽  
Microscopy Images ◽  
Bow Tie

Electron microscopy images of decagonal quasicrystals obtained recently have been shown to be related to cluster coverings with a Hexagon–Bow–Tie decagon as single structural unit. Most decagonal phases show more complex structural orderings than models based on deterministic tilings like the Penrose tiling. We analyze different types of decagonal random tilings and their coverings by a Hexagon–Bow–Tie decagon.

Boundary conditions, entropy and the signature of random tilings

1996 ◽  
Vol 29 (21) ◽  
pp. 6709-6716 ◽  
Author(s):  
Dieter Joseph ◽  
Michael Baake
Keyword(s):  
Boundary Conditions ◽  
Random Tilings

scholarly journals Entropy along convex shapes, random tilings and shifts of finite type

2002 ◽  
Vol 46 (3) ◽  
pp. 781-795 ◽  
Author(s):  
Paul Balister ◽  
Béla Bollobás ◽  
Anthony Quas
Keyword(s):  
Finite Type ◽  
And Shifts ◽  
Random Tilings

scholarly journals Extreme boundary conditions and random tilings

2021 ◽  
Author(s):  
Jean-Marie Stéphan
Keyword(s):  
Boundary Conditions ◽  
Quantum Particle ◽  
Condensed Matter ◽  
Two Dimensions ◽  
Basic Knowledge ◽  
Dimer Model ◽  
Long Range Correlations ◽  
Statistical Mechanical ◽  
Local Densities ◽  
Random Tilings

Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as illustrated by the famous 'arctic circle theorem' for dimer coverings in two dimensions. In these notes, I discuss such examples in the context of critical phenomena, and their relation to 1+1d quantum particle models. All those turn out to share a common feature: they are inhomogeneous, in the sense that local densities now depend on position in the bulk. I explain how such problems may be understood using variational (or hydrodynamic) arguments, how to treat long range correlations, and how non trivial edge behavior can occur. While all this is done on the example of the dimer model, the results presented here have much greater generality. In that sense the dimer model serves as an opportunity to discuss broader methods and results. [These notes require only a basic knowledge of statistical mechanics.]

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