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Mathematics of aperiodic order

What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quas...

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Detalles Bibliográficos
Autores principales: Kellendonk, Johannes, Lenz, Daniel, Savinien, Jean
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-0348-0903-0
http://cds.cern.ch/record/2032358
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author Kellendonk, Johannes
Lenz, Daniel
Savinien, Jean
author_facet Kellendonk, Johannes
Lenz, Daniel
Savinien, Jean
author_sort Kellendonk, Johannes
collection CERN
description What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.
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spelling cern-20323582021-04-21T20:10:01Zdoi:10.1007/978-3-0348-0903-0http://cds.cern.ch/record/2032358engKellendonk, JohannesLenz, DanielSavinien, JeanMathematics of aperiodic orderMathematical Physics and MathematicsWhat is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.Springeroai:cds.cern.ch:20323582015
spellingShingle Mathematical Physics and Mathematics
Kellendonk, Johannes
Lenz, Daniel
Savinien, Jean
Mathematics of aperiodic order
title Mathematics of aperiodic order
title_full Mathematics of aperiodic order
title_fullStr Mathematics of aperiodic order
title_full_unstemmed Mathematics of aperiodic order
title_short Mathematics of aperiodic order
title_sort mathematics of aperiodic order
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-0348-0903-0
http://cds.cern.ch/record/2032358
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