This is a discussion on mathematics tricks within the Product And Services forums, part of the Miscellaneous category; For all the advances in computing in recent years, many real-world problems still defy the capability of even the most ...
- 08-20-2010, 11:01 AM #1Unregistered Guest
For all the advances in computing in recent years, many real-world problems still defy the capability of even the most advanced supercomputers and to address one such problem a team of mathematicians has been called for help.
As part of the US government's $20-million initiative to have advanced mathematics pick up where sheer computing power is inadequate, the Oregon State University recently received a $647,000 grant from the Department of Energy.
In this project, varsity mathematicians will try to model the flow of fluids through a porous medium, such as water through soil. It might sound simple but in practice this could be so extraordinarily complex that there are still more questions than answers, a university statement said.
"The use of models that are suitable for laboratory experiments to describe processes on the scale of a watershed will bring any computer to its knees," said Ralph Showalter, professor and head of the university's maths department.
"We're trying to connect information at the micro-scale to the big picture and for that we need new mathematical systems that at least give the computers a chance."
The federal initiative will cover many topics ranging from the production of energy to pollution clean-up, manufacturing smaller computer chips and making new "nano-materials".
The Oregon State University is one of 17 universities and eight Department of Energy laboratories participating in the initiative.
The programme tackles problems of "multi-scale mathematics" - questions that span time scales from fractions of a second to years, and the atomic level to whole watersheds.
The problems are so vast that they cannot easily be broken down into simpler questions that could be solved using traditional mathematical techniques and models.
Even in the study of something as basic as water moving through soil, what you see depends on what window you look through, Showalter said.
"You look through a microscope at a liquid moving for a few moments between soil particles and you observe a certain behaviour," he said.
"Study the same process at the scale of a bucket or barrel and longer time scales, and the picture is incredibly different. And for our purposes, we might need to effectively model this process on the scale of a reservoir or a polluted field of groundwater over a period of decades."
Showalter said that conceptually it is similar to trying to describe the path of a butterfly on a long migration rather than the up-and-down motion of its body with each cycle of its wings.
Existing mathematics is able to do this averaging or "upscaling" in many cases, he said, but not yet in the more complex problems the Department of Energy initiative plans to address.
Showalter and a colleague will try to create new mathematical models that are able to tackle these topics and then do analysis and simulation to study their accuracy.
With success, they said, some day the problems may be simplified enough that a supercomputer can handle them.
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