Corona Limits of Tilings: Periodic Case View Full Text


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Article Info

DATE

2018-09-28

AUTHORS

Shigeki Akiyama, Jonathan Caalim, Katsunobu Imai, Hajime Kaneko

ABSTRACT

We study the limit shape of successive coronas of a tiling, which models the growth of crystals. We define basic terminologies and discuss the existence and uniqueness of corona limits, and then prove that corona limits are completely characterized by directional speeds. As an application, we give another proof that the corona limit of a periodic tiling is a centrally symmetric convex polyhedron [see Zhuravlev (St Petersbg Math J 13(2):201–220, 2002) and Maleev and Shutov (Layer-by-layer growth model for partitions, packings, and graphs, Tranzit-X, Vladimir, 2011)]. More... »

PAGES

626-652

References to SciGraph publications

  • 2014-11-13. Inverse problem in the layer-by-layer growth model in CRYSTALLOGRAPHY REPORTS
  • 2017-09-23. Layer-by-layer growth of vertex graph of Penrose tiling in CRYSTALLOGRAPHY REPORTS
  • 2000-01. Wulff-shape and Density Deviation in GEOMETRIAE DEDICATA
  • 1995. Classical Descriptive Set Theory in NONE
  • 2007-03. Layer-by-layer growth of quasi-periodic Rauzy tiling in CRYSTALLOGRAPHY REPORTS
  • 1982. An Introduction to Ergodic Theory in NONE
  • 2016-06-02. The Corona Limit of Penrose Tilings Is a Regular Decagon in CELLULAR AUTOMATA AND DISCRETE COMPLEX SYSTEMS
  • 2010-09-24. 2D quasi-periodic Rauzy tiling as a section of 3D periodic tiling in CRYSTALLOGRAPHY REPORTS
  • 1985. A Course in Functional Analysis in NONE
  • 1998-07. Wulff Shape for Nonperiodic Arrangements in LETTERS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00454-018-0033-x

    DOI

    http://dx.doi.org/10.1007/s00454-018-0033-x

    DIMENSIONS

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    165 grid-institutes:grid.257022.0 schema:alternateName Graduate School of Engineering, Hiroshima University, 739-8527, Higashi-Hiroshima, Japan
    166 schema:name Graduate School of Engineering, Hiroshima University, 739-8527, Higashi-Hiroshima, Japan
    167 rdf:type schema:Organization
     




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