Ferrofluids, complex particle dynamics and braid description

Finely divided magnetic matter is important in many areas of science and te chnology. A special sub-class of systems are made up of freely moving parti cles suspended in a carrier liquid where the magnetic interactions play an important role in the actual structure formation and dynamical behaviour. T hese include ferrofluids. which arc colloids of magnetic particles disperse d in carrier fluids, magnetic micro-beads, which are micrometer sized plast ic beads loaded with iron oxide, and nonmagnetic particles dispersed in fer rofluids, forming the so-called "magnetic holes". How, in a simple and forc eful way, is it possible to characterise the dynamics of systems with sever al moving components like dispersed magnetic particles subjected to externa l magnetic fields? The methods based on the theory of braids may provide th e answer. Braid theory is a sub-field of mathematics known as topology. It involves classifying different ways of tracing curves in space. The topolog ical description of braids thus provides a simple and concise language for describing the dynamics of a system of moving particles as if they perform a complicated dance as they move about one another, and the braid encodes t he choreography of this dance. (C) 2001 Elsevier Science B.V. All rights re served.