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
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.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 83.10.Pp – Particle dynamics / 02.10.Kn – Knot theory / 75.75.+a – Magnetic properties of nanostructures
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006