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MATHEMATICAL MODELS

Ted Janssen, Gervais Chapuis, and Marc de Boissieu

in Aperiodic Crystals: From Modulated Phases to Quasicrystals

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198567776
eISBN:
9780191718335
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567776.003.0003
Subject:
Physics, Crystallography

This chapter discusses mathematical models for studying the basic properties of crystals. Topics covered include model sets, introduction of tilings, aperiodic tilings, approximants, coverings, and ... More


Applications of the Frobenius number

J. L. Ramírez Alfonsín

in The Diophantine Frobenius Problem

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568209
eISBN:
9780191718229
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568209.003.0008
Subject:
Mathematics, Algebra, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents a number of applications of FP to a variety of problems. The complexity analysis of the Shellsort method was not well understood until J. Incerpi and R. Sedgewick nicely ... More


Anion-topology approach

Sergry V. Krivovichev

in Structural Crystallography of Inorganic Oxysalts

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199213207
eISBN:
9780191707117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213207.003.0004
Subject:
Physics, Crystallography

This chapter deals with description of dense 2-D topologies using the concept of anion-topology introduced by P. C. Burns and co-authors for the analysis of uranyl layered structures. Anion ... More


Crystallographic description of crystal structures

Walter Steurer and Julia Dshemuchadse

in Intermetallics: Structures, Properties, and Statistics

Published in print:
2016
Published Online:
September 2016
ISBN:
9780198714552
eISBN:
9780191782848
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198714552.003.0003
Subject:
Physics, Crystallography

Crystal structures, be they periodic or aperiodic, can be described in many different ways: as lattices, tilings, or coverings decorated by atoms or clusters on one hand, or as packings of structural ... More


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