EUGENE, Ore. -- (Feb. 24, 2011) -- Neither births nor deaths stop the flocking of organisms. They just keep moving, says theoretical physicist John J. Toner of the University of Oregon. The notion, he says, has implications in biology and eventually could point to new cancer therapies.
Picture any scenario in which self-propelled organisms -- animals, birds, bacteria, molecules within cells, cancer cells, fish, and even tiny plastic rods on a vibrating table -- move as a swarm or flock in the same direction. Eighteen years ago, Toner co-developed two equations that together provide a complete theory of flocking for "immortal" flocks -- those in which creatures are not being born and dying while the moving.
Now he has extended that work to include the effects of birth and death.
The new equations are as complete a description of flocks as the Navier-Stokes equation is of fluid dynamics. This equation, named after French physicist and engineer Claude-Louis Navier and British scientist George Gabriel Stokes applies equally well to all fluids; air, water, honey and the oil from the Gulf of Mexico disaster are all described by it. All of the differences between these very different fluids can be incorporated into the Navier-Stokes equation by changing the value of one number, called "the viscosity." Large values apply to sticky fluids like honey and oil, while smaller values describe air and water.
The Navier-Stokes equation has been used successfully for more than a century in the design of aircraft, automobiles, plumbing and power stations.
Toner's equations likewise work for all flocks, and contain some numbers that must be adjusted to account for differences between different kinds of flocks. The earlier work on immortal flocks has been applied to the flocking behavior of birds, particularly studies of starlings in Rome by Andrea Cavagna and Irene Giardina.
In a new paper -- "Birth, Death, and Flight: A
|Contact: Jim Barlow|
University of Oregon