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Paper Co-Authored by Clarkson University Professor Accepted by Prestigious Physics & Math Journal

A paper co-authored by Clarkson University Assistant Professor of Mathematics Jie Sun has recently been published by a prestigious journal in physics and mathematics.

Jie SunThe manuscript, "Optimal Synchronization of Complex Networks," was published by Physical Review Letters.

Researchers from Clarkson University, Universitat Rovira i Virgili (Catalonia, Spain), the Statistical and Applied Mathematical Sciences Institute, and University of North Carolina collaborated on the paper, which studies the collective behaviors resulting from interactions between individuals.

From the frequency of firefly flashes to power grid efficiency, the paper examines two key ingredients that determine synchronization: the network structure which dictates who interacts with whom, and the intrinsic heterogeneity among the individuals.

"We derived a mathematical formula which measures how the network structure and individuals’ heterogeneity jointly determine synchronization," Sun said. "This new result highlights the important role played by the individuals’ heterogeneity in addition to the network structure, and allows us to find and design synthetic networks -- including its structure and dynamics -- that optimize synchronization."

For example, Sun said, individual fireflies flash at different frequencies, but as a group they flash in synchronicity. While the fireflies don't have identical natural frequency, they are influenced by what they observe in a local neighborhood.

The same scenario occurs when people clap in a theater and alter the frequency of their clapping depending on what they observe from the crowd, Sun said. Synchronization is only achievable if the individual can observe other individuals.

"This is what we call coupling between the individuals. Interestingly, even modest coupling can result in a synchronized behavior among the entire population," Sun said.

Potential applications of this research include the renovation of "smart" power grids, advancement of dynamic communication channels and reprogramming of biological networks with the goal of synchronicity. Sun said synchronization can optimize the performance of the network.

"The frequencies of the generators are usually different because of things such as physical noise," Sun said. "If you don't synchronize the network efficiently, there can be a huge loss of energy when power is transported among different stations."

The paper was generously supported by a Simons Foundation grant, which encourages collaboration across institutions.

Clarkson University launches leaders into the global economy. One in five alumni already leads as a CEO, VP or equivalent senior executive of a company. Located just outside the Adirondack Park in Potsdam, N.Y., Clarkson is a nationally recognized research university for undergraduates with select graduate programs in signature areas of academic excellence directed toward the world’s pressing issues. Through 50 rigorous programs of study in engineering, business, arts, sciences and the health professions, the entire learning-living community spans boundaries across disciplines, nations and cultures to build powers of observation, challenge the status quo, and connect discovery and engineering innovation with enterprise.

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