The Mathematics of Long-Range Aperiodic Order - Couverture souple

Couverture souple

ISBN 10 : 9048148324 ISBN 13 : 9789048148325

Editeur : Springer, 2010

Synopsis

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.

A propos du livre

Présentation de l'éditeur

In this book devoted entirely to the mathematics of long-range aperiodic order the reader will find survey and research articles on the major areas of mathematics and mathematical physics that are emerging in this new field, including tilings, discrete geometry, diffraction and harmonic analysis, self-similarity and symmetry, non-crystallographic root systems, the cut and project method, number theoretical considerations, aperiodic Ising models and Schrödinger operators.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 9048148324
• ISBN 13: 9789048148325
• Reliure: Broché
• Numéro d'édition: 1
• Nombre de pages: 572
• Éditeur: Moody R.V.
• Coordonnées du fabricant: GPSR Kontakt; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Allemagne