scholarly journals Maximal equicontinuous generic factors and weak model sets

2020 ◽  
Vol 40 (12) ◽  
pp. 6855-6875
Author(s):  
Gerhard Keller ◽  
Keyword(s):  
Weak Model ◽  
Model Sets

scholarly journals Periods and factors of weak model sets

2018 ◽  
Vol 229 (1) ◽  
pp. 85-132 ◽  
Author(s):  
Gerhard Keller ◽  
Christoph Richard
Keyword(s):  
Weak Model ◽  
Model Sets

scholarly journals On weak model sets of extremal density

2017 ◽  
Vol 28 (1) ◽  
pp. 3-31 ◽  
Author(s):  
Michael Baake ◽  
Christian Huck ◽  
Nicolae Strungaru
Keyword(s):  
Weak Model ◽  
Model Sets

scholarly journals Dynamics on the graph of the torus parametrization

2016 ◽  
Vol 38 (3) ◽  
pp. 1048-1085 ◽  
Author(s):  
GERHARD KELLER ◽  
CHRISTOPH RICHARD
Keyword(s):  
Uniform Distribution ◽  
Haar Measure ◽  
Pure Point ◽  
Dynamical Spectrum ◽  
Maximal Density ◽  
Weak Model ◽  
Model Sets ◽  
Push Forward ◽  
Model Set ◽  
Dynamical Properties

Model sets are projections of certain lattice subsets. It was realized by Moody [Uniform distribution in model sets. Canad. Math. Bull. 45(1) (2002), 123–130] that dynamical properties of such a set are induced from the torus associated with the lattice. We follow and extend this approach by studying dynamics on the graph of the map that associates lattice subsets to points of the torus and then we transfer the results to their projections. This not only leads to transparent proofs of known results on model sets, but we also obtain new results on so-called weak model sets. In particular, we prove pure point dynamical spectrum for the hull of a weak model set of maximal density together with the push forward of the torus Haar measure under the torus parametrization map, and we derive a formula for its pattern frequencies.

Weak Model Sets

2021 ◽  
pp. 719-721
Author(s):  
Nicolae Strungaru
Keyword(s):  
Weak Model ◽  
Model Sets

scholarly journals On Pattern Entropy of Weak Model Sets

2015 ◽  
Vol 54 (3) ◽  
pp. 741-757 ◽  
Author(s):  
Christian Huck ◽  
Christoph Richard
Keyword(s):  
Weak Model ◽  
Model Sets

Model sets with positive entropy in Euclidean cut and project schemes

2019 ◽  
Vol 52 (5) ◽  
pp. 1073-1106 ◽  
Author(s):  
Tobias JÄGER ◽  
Daniel LENZ ◽  
Christian OERTEL
Keyword(s):  
Positive Entropy ◽  
Model Sets

scholarly journals Design of a structure model set for inorganic compounds based on ping-pong balls linked with snap buttons

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ryo Horikoshi ◽  
Hiroyuki Higashino ◽  
Yoji Kobayashi ◽  
Hiroshi Kageyama
Keyword(s):  
High School Students ◽  
Coordination Compounds ◽  
Periodic Structures ◽  
Inorganic Compounds ◽  
Structure Model ◽  
School Students ◽  
Model Sets ◽  
Ping Pong ◽  
Hands On ◽  
Model Set

Abstract Structure model sets for inorganic compounds are generally expensive; their distribution to all students in a class is therefore usually impractical. We have therefore developed a structure model set to illustrate inorganic compounds. The set is constructed with inexpensive materials: ping-pong balls, and snap buttons. The structure model set can be used to illustrate isomerism in coordination compounds and periodic structures of ceramic perovskites. A hands-on activity using the structure model set was developed for high school students and was well-received by them. Despite the concepts being slightly advanced for them, the students’ retention of the knowledge gained through the activity was tested a week after they completed the activity and was found to be relatively high, demonstrating the usefulness of the activity based on the structure model set.

Efficient Dynamics Estimation With Adaptive Model Sets

2021 ◽  
Vol 6 (2) ◽  
pp. 2373-2380
Author(s):  
Ellis Ratner ◽  
Andrea Bajcsy ◽  
Terrence Fong ◽  
Claire J. Tomlin ◽  
Anca D. Dragan
Keyword(s):  
Adaptive Model ◽  
Model Sets
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