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On a Family of Random Noble Means Substitutions

100%

Moll M.

Acta Physica Polonica A

2014

vol. 126

issue 2

539-542

In 1989, Godrèche and Luck introduced the concept of local mixtures of primitive substitution rules along the example of the well-known Fibonacci substitution and foreshadowed heuristic results on the topological entropy and the spectral type of the diffraction measure of associated point sets. In this contribution, we present a generalisation of this concept by regarding the so-called "noble means families", each consisting of finitely many primitive substitution rules that individually all define the same two-sided discrete dynamical hull. We report about results in the randomised case on topological entropy, ergodicity of the two-sided discrete hull, and the spectral type of the diffraction measure of related point sets.

Discrete Tomography: Magic Numbers for N-Fold Symmetry

51%

Huck C., Moll M., Nilsson J.

Acta Physica Polonica A

2014

vol. 126

issue 2

486-489

We consider the problem of distinguishing convex subsets of n-cyclotomic model sets Λ by (discrete parallel) X-rays in prescribed Λ-directions. In this context, a 'magic number' m_{Λ} has the property that any two convex subsets of Λ can be distinguished by their X-rays in any set of m_{Λ} prescribed Λ-directions. Recent calculations suggest that (with one exception in the case n=4) the least possible magic number for n-cyclotomic model sets might just be N+1, where N=lcm(n,2).

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2 Acta Physica Polonica A

2 2014

2 Moll M.

1 Huck C.

1 Nilsson J.

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On a Family of Random Noble Means Substitutions

Discrete Tomography: Magic Numbers for N-Fold Symmetry