IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v555y2020ics0378437120303010.html
   My bibliography  Save this article

Voronoï tessellation analysis of sets of randomly placed finite-size spheres

Author

Listed:
  • Uhlmann, Markus

Abstract

The purpose of this note is to clarify the effect of the finite size of spherical particles upon the characteristics of their spatial distribution through a random Poisson process (RPP). This information is of special interest when using RPP data as a reference for the analysis of the spatial structure of a given (non-RPP) particulate system, in which case ignoring finite-size effects upon the former may yield misleading conclusions. We perform Monte Carlo simulations in triply-periodic spatial domains, and then analyze the particle-centered Voronoï tessellations for solid volume fractions ranging from 10−5 to 0.3. We show that the standard-deviation of these volumes decreases with the solid volume fraction, the deviation from the value of point sets being reasonably approximated by an exponential function. As can be expected, the domain size for which the random assemblies of finite-size particles are generated has a constraining effect if the number of particles per realization is chosen too small. This effect is quantified, and recommendations are given. We have also revisited the case of random point sets (i.e. the limit of vanishing particle diameter), for which we have confirmed the accuracy of the earlier data by Tanemura (2003).

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120303010
    DOI: 10.1016/j.physa.2020.124618
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120303010
    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.2020.124618?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. 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.
    4. 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).
    5. 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.
    6. 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.
    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:555:y:2020:i:c:s0378437120303010. 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.