Search Results - subject:"Tilings"

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Statistical mechanics of two dimensional tilings

Kaatz, Forrest H.; Estrada, Ernesto; Bultheel, Adhemar; … - In: Physica A: Statistical Mechanics and its Applications 391 (2012) 10, pp. 2957-2963

statistical mechanics of ideal networks. The tilings have possible applications such as the 2D locations of pore sites in …-scale limit, the degree of these 2D networks approaches 3, 4, and 6, in agreement with the degree of the regular tilings. In …

Persistent link: https://www.econbiz.de/10010872137

Symmetry groups and reticulations of the hexagonal H surface

Robins, Vanessa; Ramsden, S.J.; T. Hyde, Stephen - In: Physica A: Statistical Mechanics and its Applications 339 (2004) 1, pp. 173-180

We describe a systematic approach to generate nets that arise from decorations of periodic minimal surfaces. Such surfaces are covered by the hyperbolic plane, in the same way that the euclidean plane covers a cylinder. Thus, a symmetric hyperbolic network can be wrapped onto an appropriate...

Persistent link: https://www.econbiz.de/10010589993

Susceptibility calculations in periodic and quasiperiodic planar Ising models

Au-Yang, Helen; Perk, Jacques H.H. - In: Physica A: Statistical Mechanics and its Applications 321 (2003) 1, pp. 81-89

New results are presented for the wavevector-dependent susceptibility of Z-invariant periodic and quasiperiodic Ising models in the scaling limit, generalizing old results of Tracy and McCoy for the square lattice. Explicit results are worked out for the two leading singular terms of the...

Persistent link: https://www.econbiz.de/10010590268

Tiling Groups for Wang Tiles

Moore, Cristopher; Rapaport, Ivan; Rémila, Eric - Santa Fe Institute - 2001

We apply tiling groups and height functions to tilings of regions in the plane by Wang tiles, which are squares with … efficient algorithms that tell whether a given region with colored boundary is tileable, show how to sample random tilings, and … lattice structure of the set of tilings, and study several examples with three and four colors as well. …

Persistent link: https://www.econbiz.de/10005623662

Hard Tiling Problems with Simple Tiles

Moore, Cristopher; Robson, John Michael - Santa Fe Institute - 2000

It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show tthat Monotone 1-in-3...

Persistent link: https://www.econbiz.de/10005791014

Some Polyomino Tilings of the Plane

Moore, Cristopher - Santa Fe Institute - 1999

We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino …, the L tetromino, and the T tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by each …

Persistent link: https://www.econbiz.de/10005790897