Aperiodic Order: Volume 2, Crystallography and Almost Periodicity

The second volume in a series exploring the mathematics of aperiodic order. Covers various aspects of crystallography.

Michael Baake (Edited by), Uwe Grimm (Edited by)

9780521869928, Cambridge University Press

Hardback, published 2 November 2017

404 pages, 52 b/w illus.
24.1 x 16 x 2.2 cm, 0.81 kg

'This is still an open and fascinating field that continues to develop, and is presented in a coherent manner in the book series edited by M. Baake and U. Grimm … Although most of the chapters contain an easy-to-read introduction that explains the goal and the problems to be solved, the book is clearly written for mathematicians interested by this growing field.' Marc de Boissieu, Acta Cryst

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.

Foreword Jeffrey C. Lagarias
Preface Michael Baake and Uwe Grimm
1. More inflation tilings Dirk Frettlöh
2. Discrete tomography of model sets: reconstruction and uniqueness Uwe Grimm, Peter Gritzmann and Christian Huck
3. Geometric enumeration problems for lattices and embedded Z-modules Michael Baake and Peter Zeiner
4. Almost periodic measures and their fourier transforms Robert V. Moody and Nicolae Strungaru
5. Almost periodic pure point measures Nicolae Strungaru
6. Averaging almost periodic functions along exponential sequences Michael Baake, Alan Haynes and Daniel Lenz
Epilogue. Gateways towards quasicrystals Peter Kramer
Index.

Subject Areas: Crystallography [PNT], Mathematical physics [PHU], Differential & Riemannian geometry [PBMP], Calculus & mathematical analysis [PBK]