Model Sets: A Survey

By Robert V. Moody. 2000

210 citations recorded by the source corpus.

Even when reduced to its simplest form, namely that of point sets in euclidean space, the phenomenon of genuine quasi-periodicity appears extraordinary. Although it seems unfruitful to try and define the concept precisely, the following properties may be considered as representative: discreteness; extensiveness; finiteness of local complexity; repetitivity; diffractivity; aperiodicity; existence of exotic symmetry (optional).

Subfields: Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/e29809777dfe5f9bae1a42a9635a8c7ef9d26a15

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In Computational Theory and Mathematics

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Citations in the corpus

Point Sets and Dynamical Systems In the Autocorrelation Topology (2004, background): “Regular model sets are always Delone sets [5, 6] and have well-defined autocorrelations.”
On the Pisot Substitution Conjecture (2015, background): “See [19, 20, 76, 89, 101] for more on model sets.”
Geometric theory of unimodular Pisot substitutions (2006, unknown): “(See [22] for background on model sets.”
What is Aperiodic Order (2002, background): “Moody [13, 12] who recognized the connections to Meyer’s abstract concepts and championed their application in the theory of aperiodic order and their further development into the shape and form used today.”
Topological Properties of Rauzy Fractals (2010, methodology): “Mathematically, we then speak of Meyer sets and such Meyer sets are obtained by exhibiting the cut-and-project scheme [99].”
Weighted Dirac combs with pure point diffraction (2002, background): “If our original set S itself is a model set, then this property of the Pε relates to the fact that also S−S is a model set [29], which, in turn, contains the Pε for all 0 < ε < 1.”
On weak model sets of extremal density (2015, methodology): “Ĝ×H ≃ Ĝ× Ĥ, the dual CPS [30, 31] is given by”
Characterization of model sets by dynamical systems (2005, background): “Then, (S) is relatively dense if the interior of S is non-empty and it is uniformly discrete if the closure of S is compact, see [24] for details.”