Beyond Quasicrystals (eBook, PDF)

Les Houches, March 7-18, 1994
Redaktion: Axel, Francoise; Gratias, Denis

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 619
• Erscheinungstermin: 29. Juni 2013
• Englisch
• ISBN-13: 9783662031308
• Artikelnr.: 53392438

Inhaltsangabe

Quasicrystals ....- Course 1 Quasicrystals, diophantine approximation and algebraic numbers.- Course 2 The pentacrystals.- Course 3 Elements of a multimetrical crystallography.- Course 4 Non-commutative models for quasicrystals.- Course 5 From quasiperiodic to more complex systems.- Course 6 Matching rules and quasiperiodicity: the octagonal tilings.- Course 7 A mechanism for diffusion in quasicrystals.- Course 8 Experimental aspects of the structure analysis of aperiodic materials.- Course 9 Scattering on aperiodic superlattices.- Course 10 Defects in quasicrystals, in systems with deterministic disorder and in amorphous materials.- ...and Beyond.- Course 11 Automata and automatic sequences.- Course 12 Spectral study of automatic and substitutive sequences.- Course 13 Random and automatic walks.- Course 14 Singular words, invertible substitutions and local isomorphisms.- Course 15 Entropy in deterministic and random systems.- Course 16 Trace maps.- Course 17 Schrödinger difference equation with deterministic ergodic potentials.- Course 18 Schrödinger equation in a hierarchical potential.- Course 19 Introduction to multifractal analysis.- Appendix 1. Legendre transforms.- Appendix 2. Large deviations.- Annexes.- Current deterministic sequences.- Extra references.