The broken symphony of swinging metronomes

June 19, 2013
For these images, fluorescent stickers were added to the metronomes‘ pendulums and the entire setup illuminated with ultraviolet light. If the pendulums are close to their reversal point, so they are slow; in the center position they move quickly. By choosing an appropriate exposure time, coexisting synchrony and disorder are clearly displayed. The synchronous subgroup can occur either on the left swing (left) or on the right swing (right). © MPIDS

An experiment with 30 metronomes reveals chimera states which combine aspects of synchrony and of disorder. Researchers had been looking for such states for ten years.

When in a concert, a music video or in synchronized swimming several people perform in unison, it can be quite annoying, if one or a few of them blunder and step out of line. The overall impression is ruined. From the point of view of a physicist this is quite different: For ten years researchers have been looking for systems comprised of several similar oscillatory units in which simultaneously some units are synchronized, while others are not. Japanese scientists had predicted these in . Only now, however, has a simple experimental proof been found. To this end, an international team of researchers led by the Max Planck Institute for Dynamics and Self-Organization (MPIDS) in Germany has developed an of 30 swinging metronomes.

When in warm summer nights swarms of try to attract partners with their signals, some species display an astonishing synchrony: all bugs flash their at the same time. Other processes occurring in systems of many similar units can also synchronize on their own – for example certain in colonies of , or electrical currents in superconducting junctions. However, apart from synchrony and utter confusion, a third state is possible: a sort of mixed state with a few units acting synchronously, but others out of step.

Researchers refer to these states as chimera states, alluding to the monster from of the same name. The chimera unites incongruent parts: it has a lion's head, a goat's head, and a serpent's tail. In the world of oscillations, this means the coexistence of the incongruent states of synchrony and asynchrony. Ten years ago, delivered the theoretical proof of these states. Since then however, a simple experimental confirmation for the mysterious mixture of order and disorder could not be found in any real-world system. Only experiments, in which a computer controlled the interaction of the system's units, kept up the hopes of the scientific community.

In the quest for these chimera states, researchers from the MPIDS, the Technical University of Denmark, and the Princeton University have now achieved a breakthrough with a surprisingly simple experimental design. "More than 300 years ago, the Dutch physicist Christiaan Huygens observed that two pendulum clocks suspended on a beam would synchronize the motion of their pendula", Dr. Erik A. Martens from the MPIDS describes the historical experiment which inspired the new study. "We drew inspiration from this classic experiment; but we took it quite a few steps further: we built an experiment out of swings, springs, and metronomes", he adds. 30 commercially available metronomes were placed on two swings which were connected with a mechanical spring.

The experimental setup is surprisingly simple: Metronomes are placed on two swings connected by a metal spring. © MPIDS

"The calculations performed by the Japanese colleagues indicated that the way in which the metronomes interact with each other is decisive", says Dr. Shashi Thutupalli from the MPIDS. Metronomes running at identical frequencies and interacting equally strongly with every other metronomes, can only achieve one of two states: either they all lock-step and synchronize, or they beat incoherently. But a mixed state of partial is not possible. The same holds true for setups where only neighboring metronomes interact. "Our objective here was to go beyond these two possibilities and construct a system where distant metronomes couple weakly, but close ones interact strongly", says Thutupalli.

"In our experiment, we implement this by employing two different kinds of interaction", he adds. Metronomes placed on the same swing interact strongly via the moving swing underneath them. Metronomes on different swings, however, can only interact via the spring between the swings. The interaction via the spring is then the weaker of the two.

The key to finding the elusive chimeras was finding the appropriate coupling between the swings. "The spring between the swings must be neither too rigid, nor too soft", says Martens. When the spring stiffness is just right, the metronomes on one swing tick in perfect unison, while their twins on the second swing oscillate in a disordered way. The elusive chimera thus comes to life. This broken symmetry between the left and right sides is confirmed with a mathematical model of the swings and metronomes using computer simulations.

"This odd symmetry breaking was carefully tested by making sure that losses due to friction from left and the right swings are exactly the same", stresses Thutupalli. "This is a key test for chimeras: ensuring that small sources of unevenness do not make the setup prefer any one swing over the other." Otherwise, the results could be due to an inaccurate, asymmetrical setup.

Despite these experimental difficulties, the experiment is surprisingly simple. "Researchers from all over the world have been looking for a system displaying this behavior for ten years. It's almost a small sensation, that it can be constructed from such every-day articles as swings, springs, and metronomes", says Martens. Another essential ingredient are earplugs. "With time, the constant ticking can be really unnerving", Dr. Antoine Fourrière from the MPDS remembers with a smile.

"Though at first it may seem that metronomes have little to do with the real-world, the system captures basic elements, such as inertia and friction, common to numerous natural systems", says research group leader Dr. Oskar Hallatschek from the MPIDS. "Therefore chimeras can be expected to also occur in other real systems, for example in electronics, chemistry or opto-mechanics", says Martens.

Explore further: Is there an invisible tug-of-war behind bad hearts and power outages?

More information: Erik A. Martens, Shashi Thutupalli, Antoine Fourrière & Oskar Hallatschek, Chimera states in mechanical oscillator networks, Proceedings of the National Academy of Sciences (PNAS), 13 June 2013; doi: 10.1073/pnas.1302880110

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