The topic of this book is the nature of geometric order in solids beyond standard periodicity and quasiperiodicity. Its overall structure reflects the wish of the editors to pose this fundamental question from both the experimental and theoretical point of view. The first part is book is devoted more specifically to quasicrystals. The second part deals with deterministic aperiodic order "beyond" quasiperiodicity, as generated by automatic and substitutive sequences. This pedagogically written topical volume can be seen by experimentalists as a manual on the theoretical background of their work.…mehr
The topic of this book is the nature of geometric order in solids beyond standard periodicity and quasiperiodicity. Its overall structure reflects the wish of the editors to pose this fundamental question from both the experimental and theoretical point of view. The first part is book is devoted more specifically to quasicrystals. The second part deals with deterministic aperiodic order "beyond" quasiperiodicity, as generated by automatic and substitutive sequences. This pedagogically written topical volume can be seen by experimentalists as a manual on the theoretical background of their work.
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.
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.
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