Research by the RAIN Lab's Afshin Mesbahi, Siavash Alemzadeh, Mehran Mesbahi, and Mathias Hudoba de Badyn was published in Science in a collaborative paper with colleagues from institutions including Caltech and UC Davis.

A&A's RAIN Lab conducts research on how the structure of networks affects the dynamics of systems that evolve over them. One area of research examines how symmetric the structure of networks are. If two parts of the network can be rearranged without changing the qualitative features of their interdependence, the network has an inherent symmetry.

The RAIN Lab’s recent research with collaborators from Caltech, UC Davis, and others, published in Science, examined a simple system of eight nanoelectromechanical oscillators interconnected over a ring. Similar oscillators are found, for example, in cell phones. A chip that uses an oscillator detects the orientation of the phone as it is rotated. Results showed how each simple rearrangement of this ring of oscillators -- each network symmetry -- corresponds to an oscillation pattern. These oscillation patterns are unique: in some of them, the oscillators decouple from their direct neighbors and oscillate in sync with other oscillators in the ring.

The technique proposed in this work has a number of consequences for understanding complex dynamics exhibited by large-scale nonlinear networks, such as power grid and neuronal networks. These networks have massive amounts of nodes, and traditional analysis techniques do not computationally scale. The synchronization of groups of oscillators via symmetries offers a powerful way to group nodes together and reduce the dimensionality of the system. It also offers new insights into how to control these networks for desired behaviors, a topic that RAIN Lab focuses on.

Original paper and further reading

Exotic states in a simple network of nanoelectromechanical oscillators in Science, March 8, 2019, with A&A authors Professor Mehran Mesbahi and doctoral candidate Mathias Hudoba de Badyn.

Fireflies, Heartbeats, and the Science of Sync, March 7, 2019, by Whitney Clavin, Caltech.

Exotic Synchronization Patterns Emerge in a Simple Network, March 7, 2019, by Andy Fell, UC Davis.

Scientists Discover Exotic New Patterns of Synchronization, April 4, 2019, by Natalie Wolchover, Quantamagazine.

The Math of How Crickets, Starlings, and Neurons Sync Up, April 7, 2019, by Natalie Wolchover, in Wired.