96 citations · 120 across the 8 of their papers we have counts for
8 papers
Covers of Tiling Spaces
Franz Gähler, Jianlong Liu, Lorenzo Sadun
We study the ways that one tiling space can be a finite regular cover of another. We classify all of the finite regular covers of a tiling space via its structure as an inverse lim…
Dynamical Invariants from Asymptotic Composants
Franz Gähler
Asymptotic composants and their incidence relations are powerful invariants of 1-dimensional inflation tilings spaces, which can distinguish many MLD classes of tilings. In particu…
Cohomology groups for spaces of 12-fold tilings
Nicolas Bedaride, Franz Gahler, Ana G. Lecuona
We consider tilings of the plane with 12-fold symmetry obtained by the cut and projection method. We compute their cohomology groups using the techniques introduced by the second a…
Substitution rules and topological properties of the Robinson tilings
Franz Gähler
A relatively simple substitution for the Robinson tilings is presented, which requires only 56 tiles up to translation. In this substitution, due to Joan M. Taylor, neighboring til…
Effective potentials for quasicrystals from ab-initio data
Peter Brommer, Franz Gähler
Classical effective potentials are indispensable for any large-scale atomistic simulations, and the relevance of simulation results crucially depends on the quality of the potentia…
Finite-Temperature Order-Disorder Phase Transition in a Cluster Model of Decagonal Tilings
Michael Reichert, Franz Gähler
In a recent paper ["Cluster Model of Decagonal Tilings" (to be published in Phys. Rev. B)], we have introduced a cluster model for decagonal tilings in two dimensions. This model i…