scholarly journals The ice model and the eight-vertex model on the two-dimensional Sierpinski gasket

2013 ◽  
Vol 392 (8) ◽  
pp. 1776-1787 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen ◽  
Hsin-Yun Lee
Keyword(s):  
Sierpinski Gasket ◽  
Two Dimensional ◽  
Vertex Model ◽  
Sierpiński Gasket ◽  
Ice Model

scholarly journals ACYCLIC ORIENTATIONS ON THE SIERPINSKI GASKET

2012 ◽  
Vol 26 (24) ◽  
pp. 1250128 ◽  
Author(s):  
SHU-CHIUAN CHANG
Keyword(s):  
Sierpinski Gasket ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Sierpiński Gasket ◽  
Asymptotic Behaviors ◽  
Asymptotic Growth ◽  
Acyclic Orientations ◽  
Growth Constants

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket SG 2,b(n) at stage n with b equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants of SG 2,b and d-dimensional Sierpinski gasket SG d.

Acyclic Orientations on the Generalized Two-Dimensional Sierpinski Gasket

2011 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
Zacharias Anastassi
Keyword(s):  
Sierpinski Gasket ◽  
Two Dimensional ◽  
Sierpiński Gasket ◽  
Acyclic Orientations

scholarly journals Structure of spanning trees on the two-dimensional Sierpinski gasket

2011 ◽  
Vol Vol. 12 no. 3 (Combinatorics) ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Probability Distribution ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Sierpinski Gasket ◽  
Rational Numbers ◽  
Limiting Distribution ◽  
Two Dimensional ◽  
Sierpiński Gasket ◽  
Average Probability ◽  
International Audience

Combinatorics International audience Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage n is a non-negative integer. For any given vertex x of SG(n), we derive rigorously the probability distribution of the degree j ∈{1,2,3,4} at the vertex and its value in the infinite n limit. Adding up such probabilities of all the vertices divided by the number of vertices, we obtain the average probability distribution of the degree j. The corresponding limiting distribution φj gives the average probability that a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree configurations. They are rational numbers given as φ1=10957/40464, φ2=6626035/13636368, φ3=2943139/13636368, φ4=124895/4545456.

Ice Model

2019 ◽  
pp. 425-429
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Crystal Structure ◽  
Hydrogen Atom ◽  
The Other ◽  
Residual Entropy ◽  
Two Dimensional ◽  
Vertex Model ◽  
Mechanical Models ◽  
Statistical Mechanical ◽  
The One ◽  
Ice Model

The crystal structure of several of the phases of ice shows a peculiarity associated with a special type of disorder: the one hydrogen atom between the two oxygen atoms is closer to one or the other of the two. This peculiarity depends only on the configuration and is independent of temperature. It gives rise to a finite entropy of ice, even at zero temperature, i.e. the residual entropy. This observation is used as a physical motivation to study a certain type of two-dimensional statistical mechanical models, the so-called vertex models, the exemplary vertex model being the ice model, for which we introduce the ice rule.

scholarly journals Dimer Coverings on the Sierpinski Gasket

2008 ◽  
Vol 131 (4) ◽  
pp. 631-650 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

2021 ◽  
Vol 385 ◽  
pp. 107771
Author(s):  
Therese-Marie Landry ◽  
Michel L. Lapidus ◽  
Frédéric Latrémolière
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Spectral Triples

scholarly journals Level sets of harmonic functions on the Sierpiński gasket

2002 ◽  
Vol 40 (2) ◽  
pp. 335-362 ◽  
Author(s):  
Anders Öberg ◽  
Robert S. Strichartz ◽  
Andrew Q. Yingst
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

Design Sierpinski Gasket Antenna for WLAN Application

2007 ◽  
Author(s):  
C.Z.C. Ghani ◽  
M.H.A. Wahab ◽  
N. Abdullah ◽  
S.A Hamzah ◽  
A. Ubin ◽  
...  
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket
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