Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/wiley/robust-minimal-matching-rules-for-quasicrystals-UEgIYpFO3U
References (57)
-
Y. Meyer (1972)
Algebraic numbers and harmonic analysis -
G. Oszlányi, A. Sütő (2008)
The charge flipping algorithm.Acta crystallographica. Section A, Foundations of crystallography, 64 Pt 1
-
(2003)
225–265. Singapore: World Scientific -
K. Nagao, T. Inuzuka, K. Nishimoto, K. Edagawa (2015)
Experimental Observation of Quasicrystal Growth.Physical review letters, 115 7
-
Shaw, Elser, Henley (1991)
Long-range order in a three-dimensional random-tiling quasicrystal.Physical review. B, Condensed matter, 43 4
-
C. Henley (1991)
Random Tiling Models, 11
-
E. Spanier (1990)
Algebraic Topology -
S. Beucher, F. Meyer (2018)
The Morphological Approach to Segmentation: The Watershed TransformationMathematical Morphology in Image Processing
-
Nicolas Bédaride, Thomas Fernique (2013)
When Periodicities Enforce AperiodicityCommunications in Mathematical Physics, 335
-
J. Kellendonk, D. Lenz, J. Savinien (2015)
Mathematics of aperiodic order -
N. Bruijn (1981)
Algebraic theory of Penrose''s non-periodic tilings -
P. Kalugin (2005)
Cohomology of quasiperiodic patterns and matching rulesJournal of Physics A: Mathematical and General, 38
-
J. Harris (1995)
Algebraic Geometry: A First Course -
Robert Berger (1966)
The undecidability of the domino problemMemoirs of the American Mathematical Society
-
C. Rourke, B. Sanderson (1972)
Introduction to Piecewise-Linear Topology -
B. Durand, Andrei Romashchenko, A. Shen (2009)
Fixed-point tile sets and their applicationsJ. Comput. Syst. Sci., 78
-
L. Sadun (2014)
Cohomology of Hierarchical TilingsarXiv: Dynamical Systems
-
M. Quiquandon, D. Gratias (2006)
Unique six-dimensional structural model for Al-Pd-Mn and Al-Cu-Fe icosahedral phasesPhysical Review B, 74
-
M. Duneau, A. Katz (1985)
Quasiperiodic patterns.Physical review letters, 54 25
-
D. Joseph, V. Elser (1997)
A MODEL OF QUASICRYSTAL GROWTHPhysical Review Letters, 79
-
M. Marcolli (2006)
Number Theory in Physics -
J. Bellissard, R. Benedetti, J. Gambaudo (2001)
Spaces of Tilings, Finite Telescopic Approximations and Gap-LabelingCommunications in Mathematical Physics, 261
-
F. Kremer (1996)
Beyond QuasicrystalsZeitschrift für Physikalische Chemie, 194
-
A. Ritter (2016)
Quasicrystals The State Of The Art -
D. Du, Frank Hwang (1995)
Computing in Euclidean Geometry -
Hao Wang (1961)
Proving theorems by pattern recognition — IIBell System Technical Journal, 40
-
(1998)
Annals Math -
(2016)
Homotopical Topology. Graduate Texts in Mathematics -
J. Roerdink (1993)
Mathematical Morphology in Image Processing -
V. Elser (1985)
Indexing problems in quasicrystal diffraction.Physical review. B, Condensed matter, 32 8
-
S. Fortune (2004)
Voronoi Diagrams and Delaunay Triangulations -
James Walton (2014)
Pattern-Equivariant Homology of Finite Local Complexity PatternsarXiv: General Topology
-
J. Socolar (1990)
Weak matching rules for quasicrystalsCommunications in Mathematical Physics, 129
-
(2003)
Classical manifolds -
P. Kalugin (1989)
Density and Stoichiometry of Icosahedral Quasi-Crystals and Related Commensurate PhasesEPL, 9
-
Stefan Friedl (2020)
Algebraic topologyGraduate Studies in Mathematics
-
R. Kenyon (1992)
Rigidity of planar tilingsInventiones mathematicae, 107
-
W. Dwyer, David Fried (1987)
Homology of Free Abelian Covers, IBulletin of The London Mathematical Society, 19
-
L. Levitov (1988)
Local rules for quasicrystalsCommunications in Mathematical Physics, 119
-
C. Goodman-Strauss (1998)
MATCHING RULES AND SUBSTITUTION TILINGSAnnals of Mathematics, 147
-
H. Takakura, Cesar Gómez, A. Yamamoto, M. Boissieu, A. Tsai (2007)
Atomic structure of the binary icosahedral Yb-Cd quasicrystal.Nature materials, 6 1
-
(1981)
Kon . Ned . Akad -
S. Eilenberg, J. Zilber (1950)
SEMI-SIMPLICIAL COMPLEXES AND SINGULAR HOMOLOGYAnnals of Mathematics, 51
-
(2009)
Ergod -
M. Baake, D. Damanik, U. Grimm (2002)
What is Aperiodic OrderNotices of the American Mathematical Society, 63
-
A. Quivy, M. Quiquandon, Y. Calvayrac, F. Faudot, D. Gratias, C. Berger, R. Brand, V. Simonet, F. Hippert (1996)
A cubic approximant of the icosahedral phase in the (Al - Si) - Cu - Fe systemJournal of Physics: Condensed Matter, 8
-
Sutherland (1986)
Self-similar ground-state wave function for electrons on a two-dimensional Penrose lattice.Physical review. B, Condensed matter, 34 6
-
Peter Stricklandc (2005)
Acta Crystallographica Section A: Foundations of CrystallographyActa Crystallographica Section A, 61
-
A. Katz (1992)
A Short Introduction to Quasicrystallography -
A. Katz (1995)
Matching Rules and Quasiperiodicity: the Octagonal Tilings -
J. Savinien, J. Bellissard (2007)
A spectral sequence for the K-theory of tiling spacesErgodic Theory and Dynamical Systems, 29
-
(1985)
Al0.86Mn0.14: a six-dimensional crystal -
D. Bruijn (1990)
Updown generation of Penrose patternsIndagationes Mathematicae, 1
-
M. Bremner (2011)
Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications -
Thomas Fernique, M. Sablik (2016)
Weak colored local rules for planar tilingsErgodic Theory and Dynamical Systems, 39
-
C. Rourke, B. Sanderson (1971)
Δ-SETS I: HOMOTOPY THEORYQuarterly Journal of Mathematics, 22
-
D. Bruijn (1981)
Algebraic theory of Penrose's non-periodic tilings of the plane. II, 84
- Publisher
- Wiley
- Copyright
- Copyright © 2019 Wiley Subscription Services, Inc., A Wiley Company
- ISSN
- 0108-7673
- eISSN
- 1600-5724
- DOI
- 10.1107/S2053273319008180
- Publisher site
- See Article on Publisher Site
Abstract
A unified framework is proposed for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real‐world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching rules, directly from the phased diffraction data. The construction yields precise values for the spatial density of distinct atomic positions and tolerates the presence of defects in a robust way.
Journal
Acta Crystallographica Section A Foundations of Crystallography – Wiley
Published: Sep 1, 2019
Keywords: ; ;