Material Technology

Braid theory and Zipf-Mandelbrot relation used in microparticle dynamics

De Lange Kristiansen, K. , Helgesen, G. , Skjeltorp, A.T.
European physical journal B, Vol. 51, no. 3 (June 2006), 363-371
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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. Copyright Springer
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