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The Mathematics of Long-Range Aperiodic Order : NATO SCIENCE SERIES SERIES C: MATHEMATICAL AND PHYSICAL SCIENCES - R.V. Moody

The Mathematics of Long-Range Aperiodic Order

NATO SCIENCE SERIES SERIES C: MATHEMATICAL AND PHYSICAL SCIENCES

By: R.V. Moody (Editor)

Hardcover

Published: 31st March 1997
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THEOREM: Rotational symmetries of order greater than six, and also five-fold rotational symmetry, are impossible for a periodic pattern in the plane or in three-dimensional space. The discovery of quasicrystals shattered this fundamental 'law', not by showing it to be logically false but by showing that periodicity was not synonymous with long-range order, if by 'long-range order' we mean whatever order is necessary for a crystal to produce a diffraction pat­ tern with sharp bright spots. It suggested that we may not know what 'long-range order' means, nor what a 'crystal' is, nor how 'symmetry' should be defined. Since 1984, solid state science has been under going a veritable K uhnian revolution. -M. SENECHAL, Quasicrystals and Geometry Between total order and total disorder He the vast majority of physical structures and processes that we see around us in the natural world. On the whole our mathematics is well developed for describing the totally ordered or totally disordered worlds. But in reality the two are rarely separated and the mathematical tools required to investigate these in-between states in depth are in their infancy.

Organizers
Preface
Conference Participants
Knotted Tilingsp. 1
Solution of the Coincidence Problem in Dimensions [actual symbol not reproducible]p. 9
Self-Similar Tilings and Patterns Described by Mappingsp. 45
Delone Graphs; Some Species and Local Rulesp. 85
What is the Long Range Order in the Kolakoski Sequence?p. 115
Topics in Aperiodicity: Penrose Tiling Growth and Quantum Circuitsp. 127
The Diffraction Pattern of Self-Similar Tilingsp. 141
Pisot-Cyclotomic Integers for Quasilatticesp. 175
Aperiodic Ising Modelsp. 199
Diffraction by Aperiodic Structuresp. 239
Aperiodic Schrodinger Operatorsp. 269
Symmetry Concepts for Quasicrystals and Non-commutative Crystallographyp. 307
Local Rules for Quasiperiodic Tilingsp. 331
Almost-Periodic Sequences and Pseudo-Random Sequencesp. 367
The Symmetry of Crystalsp. 377
Meyer Sets and Their Dualsp. 403
Non-crystallographic Root Systems and Quasicrystalsp. 443
Remarks on Tiling: Details of a [actual symbol not reproducible] Setp. 467
Aperiodic Tilings, Ergodic Theory, and Rotationsp. 499
A Critique of the Projection Methodp. 521
Indexp. 549
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345060
ISBN-10: 0792345061
Series: NATO SCIENCE SERIES SERIES C: MATHEMATICAL AND PHYSICAL SCIENCES
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 556
Published: 31st March 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 17.15  x 3.81
Weight (kg): 1.18