Eur. Phys. J. B 51, 363-371 (2006)
https://doi.org/10.1140/epjb/e2006-00241-7

Braid theory and Zipf-Mandelbrot relation used in microparticle dynamics

¹ Department of Physics, University of Oslo, Blindern, 0316 Oslo, Norway
² Physics Department, Institute for Energy Technology, 2027 Kjeller, Norway

Corresponding author: ^a kaidk@fys.uio.no

Received: 16 November 2005
Revised: 30 March 2006
Published online: 21 June 2006

Abstract

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.