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Beyond Quasicrystals

Les Houches, March 7–18, 1994

  • Conference proceedings
  • © 1995

Overview

Editors:
  1. Françoise Axel

    1. Université Paris VII-Denis Diderot, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Denis Gratias

    1. CECN-CNRS, Vitry, France

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Centre de Physique des Houches (LHWINTER, volume 3)

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Table of contents (19 papers)

  1. Front Matter

    Pages I-XVI
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  2. Quasicrystals…

    1. Front Matter

      Pages 1-1
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    2. Quasicrystals, Diophantine approximation and algebraic numbers

      • Yves Meyer
      Pages 3-16

    3. The pentacrystals

      • J. Patera
      Pages 17-31

    4. Elements of a multimetrical crystallography

      • A. Janner
      Pages 33-54

    5. Non-commutative Models for Quasicrystals

      • P. Kramer, J. Garcia-Escudero
      Pages 55-73

    6. From Quasiperiodic to More Complex Systems

      • T. Janssen
      Pages 75-140

    7. Matching Rules and Quasiperiodicity: the Octagonal Tilings

      • A. Katz
      Pages 141-189

    8. A mechanism for diffusion in quasicrystals

      • P. A. Kalugin
      Pages 191-201

    9. Experimental aspects of the structure analysis of aperiodic materials

      • Walter Steurer
      Pages 203-228

    10. Scattering on aperiodic superlattices

      • P. Mikulík
      Pages 229-247

    11. Defects in quasicrystals, in systems with deterministic disorder and in amorphous materials

      • Nicolas Rivier
      Pages 249-290

  3. … and Beyond

    1. Front Matter

      Pages 291-291
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    2. Automata and automatic sequences

      • J.-P. Allouche, M. Mendès France
      Pages 293-367

    3. Spectral study of automatic and substitutive sequences

      • Martine Queffelec
      Pages 369-414

    4. Random and automatic walks

      • F. M. Dekking
      Pages 415-432

    5. Singular words, invertible substitutions and local isomorphisms

      • Wen Zhi-Ying
      Pages 433-440

    6. Entropy in deterministic and random systems

      • V. Berthé
      Pages 441-463

    7. Trace maps

      • J. Peyrière
      Pages 465-480

    8. Schrödinger difference equation with deterministic ergodic potentials

      • András Sütö
      Pages 481-549
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Keywords

About this book

This book is the collection of most of the written versions of the Courses given at the Winter School "Beyond Quasicrystals" in Les Houches (March 7-18, 1994). The School gathered lecturers and participants from all over the world and was prepared in the spirit of a general effort to promote theoretical and experimental interdisciplinary communication between mathematicians, theoretical and experimental physicists on the topic of the nature of geometric order in solids beyond standard periodicity and quasi periodicity. The overall structure of the book reflects the wish of the editors to pose this fundamental question of geometric order in solids from both the experimental and theoretical point of view. The first part is devoted more specifically to quasicrystals. These materials were the common starting point of most of the audience and present a first concrete example of a non-trivial geometric order. We chose to focus on a few fundamental aspects of quasicrystals related to hidden symmetries in solids which are not easily found in standard textbooks on the topic, not to reach an exhaustive survey which is already available elsewhere.

Editors and Affiliations

  • Université Paris VII-Denis Diderot, France

    Françoise Axel

  • CECN-CNRS, Vitry, France

    Denis Gratias

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