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Physicists discover surprisingly complicated states that come out of simple, synchronized networks

Fireflies glowing in harmony. Credit: Radim SchreiberFireflies, heart cells, clocks and electricity networks do everything &#821 1; they can spontaneously synchronize, transmit signals in consensus. For centuries, researchers have been confused by this self-organizing behavior, and come up with theories and experiments that make up the synchronization science. But despite the progress made in the field, the mysteries continue, especially how networks of completely identical elements can fall out of synchronization. In a new study in the 8th issue of the journal Science Caltech researchers have shown experimentally how a simple network of identical synchronized nanomachines can give rise to synchronized, complex states. Imagine a series of Rockette dancers: When they all kick at the same time, they are synchronized. One of the complex states that emerges from the simple network would be like the Rockette dancers who kick the legs out of phase with each other, where all the other dancers kick one leg up, while the dancers in between have just finished a kick. The findings experimentally show that even simple networks can lead to complexity, and this knowledge can in turn lead to new tools for controlling these networks. By better understanding how heart cells or electricity networks show complexity in seemingly uniform networks, researchers can develop new tools to drive these networks back to the rhythm. "We want to learn how we can only tickle, or gently press a system in the right direction to put it back in a synchronized state," says Michael L. Roukes,…



Fireflies glowing in harmony. Credit: Radim Schreiber

Fireflies, heart cells, clocks and electricity networks do everything &#821

1; they can spontaneously synchronize, transmit signals in consensus. For centuries, researchers have been confused by this self-organizing behavior, and come up with theories and experiments that make up the synchronization science. But despite the progress made in the field, the mysteries continue, especially how networks of completely identical elements can fall out of synchronization.

In a new study in the 8th issue of the journal Science Caltech researchers have shown experimentally how a simple network of identical synchronized nanomachines can give rise to synchronized, complex states. Imagine a series of Rockette dancers: When they all kick at the same time, they are synchronized. One of the complex states that emerges from the simple network would be like the Rockette dancers who kick the legs out of phase with each other, where all the other dancers kick one leg up, while the dancers in between have just finished a kick.

The findings experimentally show that even simple networks can lead to complexity, and this knowledge can in turn lead to new tools for controlling these networks. By better understanding how heart cells or electricity networks show complexity in seemingly uniform networks, researchers can develop new tools to drive these networks back to the rhythm.

“We want to learn how we can only tickle, or gently press a system in the right direction to put it back in a synchronized state,” says Michael L. Roukes, Frank J. Roshek professor of physics, applied physics and bioengineering at Caltech and principal researcher of the new Science study, “This may create a form of new, less hard defibrillators, for example, to shock the heart back in the rhythm.”

Synchronized oscillations were first noted so far back as in the 17th century, when Dutch researcher Christiaan Huygens, known for discovering Saturnian Moon Titan, noted that two pendulum clocks were hanging from a joint support will eventually tick in consensus. Through the centuries, mathematicians and other researchers have come in different ways for to explain the strange phenomenon, also seen in the hearts and brain cells, fireflies, cold cloud clouds, animal circadian rhythms and m steam other systems

In this video, the researchers show an example of synchronization. In the beginning no clear phase order is seen at any time and the oscillators are not synchronized. This is because the oscillators are switched off. But in this system we have control over the connection. When they turn on the clutch, they observe a sharp transition to an antiphase synchronized state. Credit: Matthew H. Matheny

Essentially, these networks consist of two or more oscillators (network nodes) that are capable of crossing on their own and transmitting repeated signals. The nodes must also be connected in some way to each other (via the network edges) so that they can communicate and send messages about their different states.

But it has also been observed since the early 2000s that these networks, even though they consist of identical oscillators, can spontaneously turn out of synchronization and develop into complex patterns. To better understand what is happening, Roukes and colleagues began to develop networks of oscillating nanomechanical devices. They started by just connecting two, and now in the new study they have developed an interconnected system with eight.

To the team’s surprise, the eight node system evolved spontaneously into various exotic, complex states. “This is the first experimental demonstration that these many distinct, complex states can occur in the same simple system,” said co-author James Crutchfield, a guest physics association at Caltech and a professor of physics at UC Davis.

To return to the Rockettes metaphor, another example of one of these complex states would be if all the other dancers kicked one leg up, while the dancers in between did something completely different than waving their hats. And the examples are even more nuanced than this; With pair of dancers making the same movements between pairs of other dances does something different.

“The confusing feature of these specific states is that the rockets in our metaphor can only see their nearest neighbor, but still manage to coordinate with their neighbors’ neighbor,” said lead author Matthew Matheny, a researcher at Caltech and a member of the Kavli Nanoscience Institute .

In this video, the researchers show pattern data over oscillator phases. The pattern they discuss here arises from a uniformly synchronized state with identical oscillator phases, ie the in-phase state. The in-phase state is only stable when the network connection is large. If they suddenly shift this link down beyond where the state is stable, they extinguish the system. After extinguishing, the system shows a spread in the phase, which is not random. The phase winds up and down with a period of 8 oscillators. Credit: Matthew H. Matheny

“We didn’t know what to see,” says Matheny. “But what these experiments tell us is that you can get complexity from a very simple system. It was something that was hinted earlier but not shown experimentally until now.”

“These exotic states arising from a simple system are what we call appear,” says Roukes. “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, saying that the more they can understand how networks evolve over time, the more they can accurately control them, and eventually they can even apply what they learn to model and better understand. human brain – one of the most complex networks we know of, with not only eight nodes, but 200 billion neurons connected to each other, typically of thousands of synaptic edges.

“Ten years after the first theories of synchronization science, and we are only finally beginning to understand what is happening, “says Roukes.” It will take a while before we understand the incredibly complex network of our brain. “

The New a Science study is called “Exotic States in a Simple Network of Nanoelectromechanical Oscillators”.


Explore further:
Physicists train the oscillatory neural network to recognize images

More information:
“Exotic states in a simple network of nanoelectromechanical oscillators” Science (2019). science.sciencemag.org/cgi/doi … 1126 / science.aav7932

Journal reference:
Science

Provided by:
California Institute of Technology

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