Braid theory and Zipf-Mandelbrot relation used in microparticle dynamics

K. de Lange Kristiansen (), G. Helgesen and A. T. Skjeltorp

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 51, issue 3, 363-371

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 05.45.-a Nonlinear dynamics and chaos; 83.10.Pp Particle dynamics; 02.10.Kn Knot theory; 75.75.+a Magnetic properties of nanostructures (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1140/epjb/e2006-00241-7

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