U of T Study Expands Understanding of Diffusion

A new method developed by a University of Toronto mathematician gives the most precise understanding yet of diffusion, a finding with potential applications to phenomena such as the spread of heat through materials, population modeling and fluid seepage through rock or soil.

“We were able to get much more precise information than anticipated,” says Robert McCann, a professor in U of T’s Department of Mathematics and co-investigator of an article in the March 19-23 issue of the Proceedings of the National Academy of Sciences Online Early Edition.

His team’s research is based on studies that examined non-linear spreading of heat into the characteristic shape of a bell curve. The slowest factor in this process is known as the rate-determining factor. The study’s findings, which show how quickly the shape is achieved, are the first to identify the nature of changes to the rate-determining factor at certain critical events – called transition points – which depend on the nature of the process. “Our calculation illustrates how the rate-determining factors change on each side of the transition point,” says McCann. “This equation has been used as a model for a number of different phenomena, including ’avalanches’ in sand piles.”

The work was co-written with a researcher at the University of Tennessee at Knoxville, and funded by the National Science Foundation, the Natural Sciences and Engineering Research Council of Canada and an Ontario Premier’s Research Award of Excellence. CONTACT: Professor Robert McCann, Department of Mathematics, (currently in Texas) 512-232-7761 or 512-477-1246, mccann@math.utoronto.ca or Nicolle Wahl, U of T public affairs, 416-978-6974, nicolle.wahl@utoronto.ca