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Network Science: A New Frontier in Theoretical Physics

(Professor Charles Duke, Physics & Astronomy)

by Daniel Linford & Lois. H. Gresh

December 27, 2006: A recent National Research Council (NRC) report called Network Science documents the profound impact of networks in our daily lives and describes how physicists can predict the behavior of these networks. According to the chairman of the NRC study, Professor Charles Duke of the University of Rochester Physics Department, who is a member of the National Academy of Sciences and the National Academy of Engineering, "This is an emerging area of interest to physicists, especially those studying complex systems."

Problems dealing with the collective behavior of humans, cells, or elements of a cell are complex because they include feedback loops, produce counter-intuitive behaviors, and exhibit behaviors that cannot be predicted from the attributes of individual components. A complex system includes all of the above features, yet also exhibits emergent collective behavior caused by the interactions among its components.

Professor Duke, a theoretical condensed matter physicist who was elected to both the National Academy of Sciences and the National Academy of Engineering, explains that complex systems exhibit phase transitions to and between collective states in systems as diverse as superfluids and superconductors; and in all sorts of interacting spin systems, resulting in collective magnetic behaviors.

A key question in network science is: how do the emergent collective behaviors depend on the connectivity of the network? Physicists have thoroughly studied this question in magnetic spin systems, for which it has long been recognized that the details of a phase diagram depend on the dimensionality of the system, the symmetries of the spin-spin interactions, and the range of these interactions.

The study of the relation between structure and the resulting dynamics (behaviors) of networks remains, however, in its infancy. This is a current frontier in theoretical physics: one of enormous practical application in a variety of biological and social networks, as well as traditional physical networks such as interacting magnetic spins or electrical and communications networks.

In the past, many scientists working in different fields were interested in what was essentially the same thing -- networks -- despite the fact that they rarely talked or collaborated with each other. The Network Science study found that network theory has applications in fields as diverse as biology, engineering, sociology, and physics. Moreover, it was also found that in most areas where network theory can be applied, it is not able to give an adequate description of the phenomena studied. We just don't know enough about networks, even though they are all around us.

Common examples of network systems include the electric power grid that provides electricity for our homes and businesses, the water and sewer systems, and the transportation system. In fact, even our internal body parts are connected in large, intricate webs, which help control the operation of our cells, the expression of our genes, our metabolism, the flow of our blood, and the operation of our minds. Most of these have been simulated using mathematical models familiar to physicists who study complex systems.

In addition to noting that we don't know enough about networks, the study urged that we explore the connections between network theory and experiments on a large enough scale to gain progress in social, biological, and physical networks. Several sample experiments of direct interest to the Defense Department's Network Centric Operations initiative are outlined in the study. These experiments are no more costly or complex than typical high-energy physics experiments. They offer, however, the promise of developing predictive models of social phenomena useful in such diverse contexts as orchestrating the response to large-scale terrorist attacks or natural disasters; and the education of inner city elementary school children.

The more physicists study network systems, the closer we'll be to protecting ourselves and improving our lives.

Additional Details

For further details, see:

Network Science, Committee on Network Science for Future Army Applications, National Research Council (The National Academies Press, 2006), available for free download at: http://www.nap.edu/catalog/11516.html

For more information, please contact:
   Professor Charles Duke
   Email: aed22cbd@frontiernet.net
   Faculty Webpage: http://spider.pas.rochester.edu/mainFrame/people/pages/Duke_Charles_B.html

This article was co-authored by Daniel Linford as part of the curriculum of PHY 396, Supervised Science Writing I, Spring 2007. Daniel is a sophomore Physics undergraduate, who serves as the Society of Physics Students' Social & Publicity Chair.

On January 4, 2007, this article was the top story in "Hot Science" on the National Website of the Society of Physics Students at http://www.spsnational.org/news/hotscience.htm.

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