Losing their marbles?
at the Max Planck Institute are puzzled-they have been playing with
marbles and talking about magic numbers. But this is no holiday-season
silliness, explains Philip Ball.
24 December 1999
Physicists at the Max Planck Institute for Molecular Physiology in
Dortmund, Germany, have been playing with marbles. With an experiment
so simple that many children will have unwittingly conducted it many
times, they have revealed an unexpected and, as yet, unexplained
phenomenon. Certain 'magic numbers' of marbles being swirled around in
a dish will form organized structures as they move.
Karsten Kötter and colleagues made their discovery by simulating the
motion of the spherical balls within a flat, circular dish on a
computer, although they say that it is confirmed by real experiments.
As the dish is swirled, the balls roll around and collide with one
another. In some cases, their motion remains disorderly as they jostle
one another. But in others a pattern emerges in which the balls
congregate in concentric rings or 'shells', and stay there. In an
intermediate situation, the balls form almost-stable shells which
exchange single balls occasionally.
The appearance of the nested shell structure from amongst a
collection of colliding balls is reminiscent of the way that a crystal
solidifies from a cooled liquid. Indeed, Kötter and colleagues regard
it as a peculiar kind of solidification. The bizarre thing is that
whether or not the balls 'solidify' is highly dependent on how many of
them there are in the dish. A dish containing 21 balls of a certain
size solidifies, whereas the same dish containing 23 balls produces a
'liquid-like' disorderly state.
The 'frozen' ring structures appear at other 'magic' numbers: 7, 8,
12, 14, 19, 30, 37, and so on. Each time they changed the number of
balls, Kötter's team altered the ball size too, so as to ensure that
they covered the same total surface area of the dish. So in every case,
the amount of free space available to the balls was the same. If this
proportion of free space was altered, the magic numbers sometimes
altered, they found, but only to form another mysterious sequence.
The researchers show that the solid-like shell structures seem to be
organized into families with shells of the same size. For instance, the
magic numbers 7, 19 and 37 correspond to shells containing one and six
balls (7), one, six and twelve balls (19) and one, six, twelve and
eighteen balls (37). Other sets of magic numbers correspond to shells
with three or four balls, rather than one, at their centre. This is
analogous to the way that the atoms of the chemical elements are built
up from shells of electrons, and can be grouped together into families
corresponding to the columns of the Periodic Table.
But where do these 'magic' shell sizes come from? No one knows. Nor
do the researchers yet understand the process by which magic numbers
lose their stability and start to exchange balls between shells. This
switching process is intermittent, and shows some similarities to the
way that other ordered systems of moving particles give way to chaos.