Abstract
The aim of this review is to describe some aspects of the dynamic properties of magnetic multiparticle systems in the micrometer range. These particles include monodisperse magnetic microspheres, and magnetic holes, i.e. nonmagnetic particles dispersed in ferrofluids.
The complementary use of analogue simulations and computer simulations to explore the dynamic properties is demonstrated.
The ability to describe the complex dynamics of magnetic holes in quantitative symbolic dynamic terms using the notion of knot- and braid theory will be discussed. In particular, statistical analysis of braid words, diffusion, memory effects and correlations for the complex dynamics is illustrated.
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References
For an extensive review of the applications of experimental and numerical models to the physics of multiparticle systems, see P. Meakin and A.T. Skjeltorp (1993) Advances in Physics 42, 1–127.
Jacobs, I.S. and Bean, C.P. (1955) Phys. Rev. 100, 1060.
de Gennes, P.G., and Pincus, P.A. (1970) Phys. kondens. Mat. 11, 189.
Helgesen, G., Skjeltorp, A.T., Mors, P.M., Botet, R., and Jullien, R. (1988) Phys. Rev. Lett. 61, 1736.
Mandelbrot, B.B. (1985) Physica Scripta 32, 257.
Mandelbrot, B.B. (1986) Proceedings of the Sixth Trieste International Symposium on Fractals in Physics, ed. by L. Pietronero and E. Tosatti (North-Holland, Amsterdam, pp. 3, 17, 21.
Vicsek, T., and Family, F. (1984) Phys. Rev. Lett. 52, 1669.
Blums, E., Ozols, R., and Rosensweig, R.E. (1990) J. Magn. Magn. Mater. 85, 303.
Rosensweig, R.E. (1985) Ferrohydrodynamics (Cambridge Univ. Press).
Skjeltorp, A.T. (1983) Phys. Rev. Lett. 51, 2306.
Strandburg, K.J. (1988) Rev. Mod. Phys. 60, 161.
Skjeltorp, A.T. (1987) J. Magn. Magn. Mat. 65, 195.
Pieranski, P., Clausen, S., Helgesen, G., and Skjeltorp, A.T. (1996) Phys. Rev. Lett. 77, 1620.
Type EMG 909, produced by Ferrofluidics Corporation, 40 Simon St., Nashua, NH 03061.
Moore, C. (1993) Phys. Rev. Lett. 70, 3675.
The reference frame rotating in unison with the magnetic field is not the only one in which the N-strand structures plaited by the magnetic holes can be seen as periodic braids. In another reference frame of this kind one of the axes, x”, rotates together with the long axis of the cluster formed by the magnetic holes.
Ashley, C. (1944) The Ashley Book of Knots, (Doubleday, New York). This is an amazing book on knots from a nonmathematical point of view. Ashley collected around 3900 different kinds of knots for practical uses.
Rolfsen, D. (1976) Knots and Links, (Publish or Perish Press, Berkeley, Calif.)
Kauffman, L. (1991) Knots and Physics, (World Scientific, London).
Adams, C.C. (1994) The Knot Book, (W.H. Freeman, New York).
Skerrett, P.J. (1994) The Ties That Bind, Popular Science, May, p. 114.
Skjeltorp, A.T., Clausen, S., Helgesen, G., and Pieranski, P. (1996) in Physics of Biomaterials: Fluctuations, Selfassembly and Evolution, eds. Riste, T., and Sherrington, D. (Kluwer, Dordrecht), p. 187.
Pieranski, P., Clausen, S., Helgesen, G., and Skjeltorp, A.T. (1996) Phys. Rev. Lett. 77, 1620.
Berger, M.A. (1996) News and Views, Nature 383, 479.
Birman, J.S. (1974) Braids, Links and mapping Class Group, Annals of Math. Study, 82, (Princeton University Press).
Elrifai, E.A., and Morton, H.R. (1994) Quart. J. Math. Oxford (2) 45, 479.
Morton, H.R., and Short, H.B. (1990) Journal of Algorithms 11, 117.
Zipf, G.K. (1949) Human Behaviour and the Principle of Least Effort (Addison-Wesley Press, Cambridge, MA).
Shannon, C.E. (1948) (1951) Bell Syst. Tech. J. 27, 379
Shannon, C.E. (1948) (1951) Bell Syst. Tech. J. 30, 50.
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Skjeltorp, A.T., Clausen, S., Helgesen, G. (1998). Magnetic Multiparticle Systems and Symbolic Dynamics. In: Skjeltorp, A.T., Sherrington, D. (eds) Dynamical Properties of Unconventional Magnetic Systems. NATO ASI Series, vol 349. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4988-4_15
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