A FLOCK of thousands of birds suddenly banks, as if on cue. In smooth-flowing traffic a jam suddenly clogs the roads. In a bustling crowd, a stampede erupts, seemingly from nowhere. It may now be possible to detect the subtle precursors to such phase transitions, and so take steps to avoid the undesirable ones.
A phase transition is a transformation in a system鈥檚 organisation, such as liquid water freezing to solid ice. Such transitions are routine in nature, and reflect a sudden reorganisation of atoms or molecules, but predicting exactly when they occur was thought to require information about most of the particles involved 鈥� an incredibly onerous demand.
Now physicist Robert Wicks and colleagues at the University of Warwick in the UK have shown otherwise. Using a mathematical model of a phase transition, they attempted to detect an oncoming change by monitoring only a small fraction of the elements in the system (Physical Review E, ). They found that they could do so by focusing on the 鈥渕utual information鈥� shared by those elements. Mutual information is a quantity taken from information theory; it measures the correlation between the behaviour of different elements.
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In a disordered state, looking at a particle gives no information about what others are doing. As the system approaches a phase transition, the mutual information between particles increases, so that one particle鈥檚 behaviour does provide information about the speed and trajectory of other particles.
The team tested their idea on a model that replicates the flocking behaviour of birds. 鈥淲e detected the signs of an incipient transition,鈥� says Wicks, 鈥渂y watching only a few 鈥榩articles鈥�.鈥�
The technique may provide a means to manage phase transitions in human settings. In crowds, the precursors to a transformation from ordinary, regular movement to a dangerous, turbulent state or stampede can be detected mathematically by video analysis, but only with extensive computation on the movements of many people. The new technique could make practical detection much easier, Wicks suggests, perhaps with cameras tracking only a few individuals. The researchers鈥� simulations suggest that in a crowd of, say, 1000 people, observations on as few as five people might be sufficient.
