Losing their marbles?

PHILIP BALL

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.

© Nature News Service / Macmillan Magazines Ltd 2001