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             Magnetization and Bénard Rolls: examples of self-organization

   To make the phenomenon of [2]self-organization more concrete, it is useful to
   look at two basic examples of self-organizing systems. Perhaps the simplest such
   process that has been extensively studied is magnetization. A piece of
   potentially magnetic material, such as iron, consists of a multitude of tiny
   magnets, called "spins" (see Figure 1). Each spin has a particular orientation,
   corresponding to the direction of its magnetic field. In general, these spins
   will point in different directions, so that their magnetic fields cancel each
   other out. This disordered configuration is caused by the random movements of the
   molecules in the material. The higher the temperature, the stronger these random
   movements affecting the spins, and the more difficult it will be for any ordered
   arrangement of spins to maintain or emerge.

   [Magnetization.gif] ;

   Figure 1: two arrangement of spins: disordered (left) and ordered (right)

   However, when the temperature decreases, the spins will spontaneously align
   themselves, so that they all point in the same direction. Instead of cancelling
   each other, the different magnetic fields now add up, producing a strong overall
   field. The reason that the spins "prefer" this ordered arrangement is because
   spins pointing in opposite directions repel each other, like the North poles of
   two magnets that are brought together. Spins pointing in the same direction, on
   the other hand, attract each other, like the North pole of one magnet attracts
   the South pole of another magnet. Magnetization is a clear case of
   self-organization, which can be used as a paradigm for a whole range of similar
   phenomena, such as crystallization (where not only the orientations but also the
   positions of the molecules become evenly arranged).

   A somewhat more complex example will illustrate further characteristics of
   self-organization. In the Bénard phenomenon, a liquid is heated evenly from
   below, while cooling down evenly at its surface, like the water in an open
   container that is put on an electric hot-plate. Since warm liquid is lighter than
   cold liquid, the heated liquid tries to move upwards towards the surface.
   However, the cool liquid at the surface similarly tries to sink to the bottom.
   These two opposite movements cannot take place at the same time without some kind
   of coordination between the two flows of liquid. The liquid tends to
   self-organize into a pattern of hexagonal cells, or a series of parallel "rolls",
   with an upward flow on one side of the roll or cell and a downward flow on the
   other side. This example is similar to the magnetization in the sense that the
   molecules in the liquid were moving in random directions at first, but end up all
   moving in a coordinated way: all "hot" molecules moving upwards on one side of
   the roll, all "cool" molecules downwards on the other side (see Figure 2). The
   difference is that the resulting pattern is not static but dynamic: the liquid
   molecules remain in perpetual movement, whereas the magnetic spins are "frozen"
   in a particular direction.

   [Benard.gif]

   Figure 2: two types of movements of liquid molecules: random (left) and in the
   form of Bénard rolls (right), caused by a difference of temperature between the
   bottom and the surface of the container.
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   [3]Copyright© 1999 Principia Cybernetica - [4]Referencing this page

   Author
   F. [5]Heylighen,

   Date
   Dec 2, 1999

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References

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