Synchronized behavior occurs when different elements (or oscillators) interact in a way that coordinates their movements. A new model of closely packed bearings shows that these mechanical disks act like a complex network of interacting oscillators. The work, presented in Physical Review Letters, finds that bearings tuned with a particular mass-radius relationship will have a stronger (more stable) synchronization.
Common examples of synchronization include contraction of heart muscles and the rhythmic unison of musicians. Recent interest in synchronization focuses on which interactions might enhance or reduce coordination. One prediction is that a synchronized state is most stable when the interaction strength is inversely proportional to the number of interacting partners that a particular oscillator has.
To provide a test bed for this theory, Nuno Araújo of the Swiss Federal Institute of Technology (ETH) in Zurich and his colleagues turned to complex bearing networks. They devised a model in which two-dimensional bearings of various sizes fit together to fill a given volume. This system is synchronized when all the elements have the same tangential velocity (i.e., no slipping). The team calculated how such a synchronized state responds to perturbations and found the most stable case was when the mass of each bearing was directly proportional to its radius. As such, larger bearings, which typically touch (interact with) more of their neighbors, have a larger moment of inertia and thus are less affected by these interactions. In other words, elements with more partners compensate with weaker interactions, just as predicted. – Michael Schirber