Rockettes dancing at the Alabama Theater in 2016 (Image: CurtisPalmer/Vimeo)

Fireflies, heart cells, clocks, and power grids all do it — they can spontaneously sync up, sending signals out in unison. For centuries, scientists have been perplexed by this self-organizing behavior, coming up with theories and experiments that make up the science of sync. But despite progress being made in the field, mysteries still persist — in particular how networks of completely identical elements can fall out of sync.

Now, in a study published March 8 in the journal Science, a cross-institutional team of researchers has shown experimentally how a simple network of identical synchronized nanomachines can give rise to out-of-sync, complex states. Imagine a line of Rockette dancers: When they are all kicking at the same time, they are in sync. One of the complex states observed to arise from the simple network would be akin to the Rockette dancers kicking their legs "out of phase" with each other, where every other dancer is kicking a leg up, while the dancers in between have just finished a kick. The findings experimentally demonstrate that unanticipated behaviors can emerge from even simple networks. 

“One of the amazing things about emergent properties is that we are surprised when we see them, and this drives us to develop theoretical understanding of their underlying mechanisms which can then often explain these behaviors across multiple complex systems,” says Raissa D’Souza, a professor at UC Davis and an external professor at the Santa Fe Institute. She is the Principle Investigator of the award funding this research, with the overarching project goal of controlling collective phenomena in networks across scales.

According to D’Souza, understanding emergence in basic networks, like the nanoelectromechanical (NEMS) system described in the study, could lead to understanding more complex, interacting networks that enable our modern world. This knowledge, in turn, may ultimately lead to new tools for controlling those networks. For example, by better understanding how heart cells or power grids display complexity in seemingly uniform networks, researchers may be able to develop new tools for pushing those networks back into rhythm.

"We want to learn how we can just tickle, or gently push, a system in the right direction to set it back into a synced state," says Michael L. Roukes, a physicist at Caltech and corresponding author of the new Science study. "This could perhaps engender a form of new, less harsh defibrillators, for example, for shocking the heart back into rhythm."

Synchronized oscillations were first noted as far back as the 1600s when the Dutch scientist Christiaan Huygens noted that two pendulum clocks hung from a common support would eventually come to tick in unison. Through the centuries, mathematicians and other scientists have come up with various ways to explain the strange phenomenon, seen also in heart and brain cells, fireflies, clouds of cold atoms, the circadian rhythms of animals, and many other systems.

In essence, these networks consist of two or more oscillators (the nodes of the network), which have the ability to tick on their own, sending out repeated signals. The nodes must also be connected in some way to each other (through the network edges), so that they can communicate and send out messages about their various states. In the experimental system, eight NEMS oscillator nodes are connected together in a ring, in other words, each one is connected to one neighbor to the right and one neighbor to the left.

To the team's surprise, the eight-node system spontaneously evolved into various exotic, complex states. "This is the first experimental demonstration that these many distinct, complex states can occur in the same simple system," says co-author James Crutchfield, a professor at UC Davis who is also a visiting associate at Caltech and an external professor at the Santa Fe Institute.

To return to the Rockettes metaphor, another example of one of these complex states would be if every other dancer were kicking a leg up in unison, unaffected by what stage in the kick their immediate neighbors are in. "The perplexing feature of this particular state is that the Rockettes in our metaphor can only see their nearest neighbor, yet manage to be coordinating with their neighbor's neighbor," says lead author Matthew Matheny, a research scientist at Caltech.

"We didn't know what we were going to see," says Matheny. "But what these experiments are telling us is that you can get complexity out of a very simple system. This was something that was hinted at before but not shown experimentally until now." Video illustrations of these complex states are available on Matheny's website.

"These exotic states arising from a simple system are what we call emergent," says Roukes. "The whole is greater than the sum of the parts."

The researchers hope to continue to build increasingly complex networks and observe what happens when more than eight nodes are connected. They say that the more they can understand about how the networks evolve over time, the more they can precisely control them in useful ways.

D’Souza hopes to eventually scale up their understanding to more complex, interdependent networks like modern infrastructure. She muses that the exotic synchronization patterns observed in the “toy” nanomechanical system might one day be used to enable a distributed clock for controlling a multi-scale communication network.

“Our modern society relies on this collection of interdependent networks, like the power grid, communication networks, social networks, transportation networks, and supply chains,” she explains. “Each one of those networks on its own is a complex system showing emergent behaviors. When we couple them all together, it’s pretty staggering to think what kinds of emergent behaviors we’re going to see.”

The new Science study, titled, "Exotic States in a Simple Network of Nanoelectromechanical Oscillators," was funded by a Multidisciplinary University Research Initiative grant from the U.S. Army Research Office with computing support from the Intel Corporation. D’Souza organized working groups at The Santa Fe Institute on the resilience of interdependent networks in June of 2010, and together with Crutchfield on control of interdependent networks in June 2015 that contributed to this research direction.

[Adapted from text authored by Whitney Clavin for Caltech]