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Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multi-volume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals, written by Peter Kramer, one of the founders of the field.

Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multi-volume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals, written by Peter Kramer, one of the founders of the field.

Paperback. Over the past several decades, aThis book deals with the characterisation of the structure, the structure determination and the study of the physical properties, especially dynamical and electronic properties of aperiodic crystals. The treatment is based on a description in a space with more dimensions than three, the so-called superspace. This allows us to generalise the standard crystallography and to look differently at the dynamics. Thethree main classes of aperiodic crystals, modulated phases, incommensurate composites and quasicrystals are treated from a unified point of view, which stresses similarities of the various systems. Thebook assumes as a prerequisite a knowledge of the fundamental techniques of crystallography and the theory of condensed matter, and covers the literature at the forefront of the field.Since the first edition of this book in 2007, the field of aperiodic crystals has developed considerably, with the discovery of new materials and new structures. Progress has been made in structure determination, in the interpretation and understanding of the structural characteristics andin the calculation of electrons and phonons. This new edition reflects these new developments, and it includes discussions of natural quasicrystals, incommensurate magnetic and multiferroic structures,photonic and mesoscopic quasicrystals. The second edition also includes a number of new exercises that give the reader an opportunityt to check their understanding of the material. This book explains aperiodic crystals, which cannot be described by the classical model of 3-dimensional periodicities. The study of these new types of material necessitates describing them in dimensions larger than three. It describes the physical and mathematical methods to solve and characterize them, and to understand their physical properties. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.

Describes the leading techniques for analyzing noise. Discusses methods that are applicable to periodic signals, aperiodic signals, or random processes over finite or infinite intervals. Provides readers with a useful reference when designing or modeling communications systems.

Describes the leading techniques for analyzing noise. Discusses methods that are applicable to periodic signals, aperiodic signals, or random processes over finite or infinite intervals. Provides readers with a useful reference when designing or modeling communications systems.