Braid theory and Zipf-Mandelbrot relation used in microparticle dynamics

  • K. de Lange KristiansenEmail author
  • G. Helgesen
  • A. T. Skjeltorp
Statistical and Nonlinear Physics


A study is presented of the dynamics of a few body system of microparticles by using rank-ordering statistics in order to gain insight in the magneto-rheological properties of ferrofluids. This dynamical system is made up of micrometer sized plastic spheres dispersed in a ferrofluid driven by external magnetic fields. The world lines of the microspheres are captured and the dynamical modes are described by mathematical braid theory. Rank-ordering statistics on these modes shows a wide power law region consistent with the Zipf-Mandelbrot relation. We have also performed numerical simulations of the experimental system which show results in agreement with the observations.


05.45.-a Nonlinear dynamics and chaos 83.10.Pp Particle dynamics 02.10.Kn Knot theory 75.75.+a Magnetic properties of nanostructures 


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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  • K. de Lange Kristiansen
    • 1
    • 2
    Email author
  • G. Helgesen
    • 2
  • A. T. Skjeltorp
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of OsloOsloNorway
  2. 2.Physics DepartmentInstitute for Energy TechnologyKjellerNorway

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