Aperiodic Order. Volume 2: Crystallography and Almost Periodicity

Baake, Michael and Grimm, Uwe (2017). Aperiodic Order. Volume 2: Crystallography and Almost Periodicity. Encyclopedia of Mathematics and Its Applications, 166. Cambridge: Cambridge University Press.

DOI: https://doi.org/10.1017/9781139033862

Abstract

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.

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