CORVALLIS - A lot of people think geometry is complicated and high school algebra is tough. College calculus would make them break into a cold sweat.
But a group of mathematicians at Oregon State University see those types of problems as child's play. With the help of a three-year, $500,000 "Focused Research Group" grant from the National Science Foundation, they're now tackling a group of problems that have baffled scientists for 150 years. And the results may have implications for everything from climate models to the future function of the Internet.
The task at hand is addressing "probabilistic methods in nonlinear partial differential equations of flow." More simply, it's trying to figure out "Navier-Stokes equations" about the flow of fluids.
Five mathematicians from OSU and Indiana University are hard at work on this, along with two OSU mathematics graduate students supported in part by the National Science Foundation and the College of Science. The problems are not easy.
"Let's say you take a ball, throw it at a certain initial speed and a certain direction and want to know where it will land," said Edward Waymire, an OSU professor of mathematics. "That's a simple calculus question a first year math student could figure out."
"Now take that same ball, throw it into the churning waters of Devils Punchbowl on the Oregon coast, and tell me where it will go," Waymire said. "That's a pretty complicated math problem, but in fact illustrates how complex the flows can be."
The issue is one of probability theory and methods used to solve equations relating to fluid flow, with different physical forces at work. In studying this, scientists refer to the laws of motion developed by Isaac Newton and use conceptual approaches about laws of average first developed by Albert Einstein. They wade through coefficients, sines, cosines and fourier analysis. But the fact is there's still a lot they don't know and a lot of work to do.
"Basic science such as this is what sets the stage for engineering applications," Waymire said.
In this case, some applications of the work may relate to the spread of contaminating pollutants in groundwater or climate forces relevant to global climate change. And some experts in private industry see similarities of data structure in the flow of fluids and Internet "packets" that travel electronically.
"The future function of the Internet is not at all clear, and there are a lot of people concerned that a stable Internet service may be difficult to achieve because of the volume of flowing information that we pump into it. So our work may relate to that. We certainly don't want to see the Internet turned into another Devil's Punchbowl."