Diffractive point sets with entropy

@article{Baake1998DiffractivePS,
  title={Diffractive point sets with entropy},
  author={Michael Baake and Robert V. Moody},
  journal={Journal of Physics A},
  year={1998},
  volume={31},
  pages={9023-9039}
}
  • M. BaakeR. Moody
  • Published 1 September 1998
  • Computer Science
  • Journal of Physics A
After a brief historical survey, this paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically… 
View PDF on arXiv
42 Citations
Background Citations
21
Methods Citations
3
Results Citations
2

42 Citations

Which distributions of matter diffract? - Some answers

This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory…

A ug 2 00 2 Diffraction and Palm measure of point processes

Using the Palm measure notion, we prove the existence of the diffraction measure of all stationary and ergodic point processes. We get precise expressions of those measures in the case of specific…

Diffraction of Stochastic Point Sets: Explicitly Computable Examples

Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases…

Diffraction of Random Tilings: Some Rigorous Results

The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction…

Dworkin’s argument revisited: Point processes, dynamics, diffraction, and correlations

A ug 2 00 0 Diffraction of random tilings : some rigorous results

The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction…

Universal bounds on the selfaveraging of random diffraction measures

Abstract. We consider diffraction at random point scatterers on general discrete point sets in ℝν, restricted to a finite volume. We allow for random amplitudes and random dislocations of the…

MATHEMATICAL DIFFRACTION THEORY IN EUCLIDEAN SPACES : AN INTRODUCTORY SURVEY

Mathematical diffraction theory is concerned with the Fourier transform of the autocorrelation of translation bounded complex measures. While the latter are meant to encapsulate the relevant order of…

Deformation of Delone Dynamical Systems and Pure Point Diffraction

AbstractThis article deals with certain dynamical systems built from point sets and, more generally, measures on locally compact Abelian groups. These systems arise in the study of quasicrystals and…

Random Fields on Model Sets with Localized Dependency and Their Diffraction

For a random field on a general discrete set, we introduce a condition that the range of the correlation from each site is within a predefined compact set D. For such a random field ω defined on the…

References

SHOWING 1-10 OF 70 REFERENCES

Diffraction from visible lattice points and kth power free integers

LIMIT-(QUASI)PERIODIC POINT SETS AS QUASICRYSTALS WITH P-ADIC INTERNAL SPACES

Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal…

Random tilings: concepts and examples

We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling…

Multi-Component Model Sets and Invariant Densities

Model sets (also called cut and project sets) are generalizations of lattices, and multi-component model sets are generalizations of lattices with colourings. In this paper, we study…

Boundary conditions, entropy and the signature of random tilings

We investigate the influence of boundary conditions on the results of Monte Carlo simulations of 2D random tilings. Looking at the fluctuations in internal space we compare fixed and periodic…

Théorie des distributions

II. Differentiation II.2. Examples of differentiation. The case of one variable (n = 1). II.2.3. Pseudofunctions. Hadamard finite part. We calculate the derivative of a function f(x) which is equal…

Dynamics of self-similar tilings

  • B. Solomyak
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1997
This paper investigates dynamical systems arising from the action by translations on the orbit closures of self-similar and self-affine tilings of ${\Bbb R}^d$. The main focus is on spectral…

The reference lattice concept and its application to the analysis of diffraction patterns

Abstract The concept of the reference lattice has been thoroughly discussed in physical and in higher-dimensional spaces. Such an approach has been applied to diffraction pattern analysis of…

Aperiodic tiles

A number of aperiodic sets which were briefly described in the recent bookTilings and Patterns, but for which no proofs of their a periodic character were given are considered.

Strictly ergodic symbolic dynamical systems

be the set of all two sided infinite sequences (2.2) x = {a"In Z}, an = A for all n E Z, where (2.3) Z = {nln = O, + 1, + 2,} is the set of all integers. For each n E Z, an is called the nth…
...