IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v406y2014icp42-58.html
   My bibliography  Save this article

The effects of regularity on the geometrical properties of Voronoi tessellations

Author

Listed:
  • Zhu, H.X.
  • Zhang, P.
  • Balint, D.
  • Thorpe, S.M.
  • Elliott, J.A.
  • Windle, A.H.
  • Lin, J.

Abstract

This study comprehensively quantifies the effects of regularity on the geometrical properties of a random three-dimensional Voronoi tessellation (VT), where regularity was defined as the ratio of the minimum seed distance to the seed distance of the correlated body-centred cubic lattice. A scheme to generate Voronoi tessellations with controlled regularity is proposed, which was used to simulate 106 cells for a series of regularities. The results were used to derive probability distributions for the properties of the tessellation, including faces and edges per cell, vertex and dihedral cell angles, cell areas and volumes, etc. An understanding of the relation between a simple, measurable parameter characterizing the degree of regularity of a Voronoi tessellation and its geometrical properties is essential in generating virtual microstructures that are statistically representative of reality; the statistical results are also relevant to all other applications involving random Voronoi tessellations. Finally, an application is presented of the proposed Voronoi tessellation generation scheme applied to micromechanical modelling of grain structures with defined regularities for crystal plasticity finite element analysis.

Suggested Citation

  • Zhu, H.X. & Zhang, P. & Balint, D. & Thorpe, S.M. & Elliott, J.A. & Windle, A.H. & Lin, J., 2014. "The effects of regularity on the geometrical properties of Voronoi tessellations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 42-58.
    • Handle: RePEc:eee:phsmap:v:406:y:2014:i:c:p:42-58
    DOI: 10.1016/j.physa.2014.03.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114002064
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.03.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ferenc, Járai-Szabó & Néda, Zoltán, 2007. "On the size distribution of Poisson Voronoi cells," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 518-526.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hafver, Andreas & Jettestuen, Espen & Baetens, Jan M. & Malthe-Sørenssen, Anders, 2014. "Network formation by contact arrested propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 240-255.
    2. Yangyang Chen & Feng Yan & Xavier Lagrange, 2017. "Performance analysis of cellular networks with mobile relays under different modes," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 66(2), pages 217-231, October.
    3. Uhlmann, Markus, 2020. "Voronoï tessellation analysis of sets of randomly placed finite-size spheres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    4. Hiroyuki Usui, 2018. "Estimation of geometric route distance from its topological distance: application to narrow road networks in Tokyo," Journal of Geographical Systems, Springer, vol. 20(4), pages 387-412, October.
    5. Brodskii, Roman Ye., 2024. "Transparent windows in a layered medium with mosaic layers.Windows distribution by area," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    6. Hiroyuki Usui, 2018. "Statistical distribution of building lot frontage: application for Tokyo downtown districts," Journal of Geographical Systems, Springer, vol. 20(3), pages 295-316, July.
    7. Stegehuis, Clara & Weedage, Lotte, 2022. "Degree distributions in AB random geometric graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:406:y:2014:i:c:p:42-58. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.