Braid theory and Zipf relation used in dynamics of magnetic microparticles

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• 作者：de Lange Kristiansen ; Kai ; Helgesen ; Geir ; Skjeltorp ; Arne T.
• 关键词：05.45.&minus ; a ; 75.50.Mm ; 83.10.Pp ; 02.10.Kn ; Ferrofluid ; Microparticle dynamics ; Rank-ordering statistics ; Anomalous diffusion ; Braid theory
• 刊名：Journal of Magnetism and Magnetic Materials
• 出版年：2004
• 出版时间：May, 2004
• 年：2004
• 卷：272-276
• 期：Part 3
• 页码：2387-2388
• 全文大小：210 K

文摘

We have studied the two-dimensional dynamics of a few body system of microparticles using rank-ordering statistics. The world lines from the microspheres were captured and converted to a braid notation according to mathematical braid theory. Rank-ordering statistics of the dynamical modes in the system shows a power law region consistent with the Zipf relation. A simple numerical simulation of the experimental system shows similar behavior. To exemplify the diversity of our system a result showing anomalous diffusion is also given.