IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v274y1999i1p267-280.html
   My bibliography  Save this article

Application of braid statistics to particle dynamics

Author

Listed:
  • Skjeltorp, Arne T.
  • Clausen, Sigmund
  • Helgesen, Geir

Abstract

How, in a simple and forceful way, do we characterize the dynamics of systems with several moving components? The methods based on the theory of braids may provide the answer. Knot and braid theory is a subfield of mathematics known as topology. It involves classifying different ways of tracing curves in space. Knot theory originated more than a century ago and is today a very active area of mathematics. Recently, we have been able to use notions from braid theory to map the complicated trajectories of tiny magnetic beads confined between two plates and subjected to complex magnetic fields. The essentially two-dimensional motion of a bead can be represented as a curve in a three-dimensional space–time diagram, and so several beads in motion produce a set of braided curves. The topological description of these braids thus provides a simple and concise language for describing the dynamics of the system, as if the beads perform a complicated dance as they move about one another, and the braid encodes the choreography of this dance.

Suggested Citation

  • Skjeltorp, Arne T. & Clausen, Sigmund & Helgesen, Geir, 1999. "Application of braid statistics to particle dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 267-280.
    • Handle: RePEc:eee:phsmap:v:274:y:1999:i:1:p:267-280
    DOI: 10.1016/S0378-4371(99)00324-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437199003246
    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/S0378-4371(99)00324-6?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.

    More about this item

    Statistics

    Access and download statistics

    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:274:y:1999:i:1:p:267-280. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.