Science & Technology: MATHEMATICS
SHADES OF ISAAC NEWTON?
At the age of 69, electrical engineer Michael F. Lamorte has one big advantage over his younger cohorts: He learned his craft using a slide rule, not a computer. He had to use insight rather than brute computing power to solve problems. Along the way, he acquired an in-the-bones feeling for how equations govern the world: how oil percolates beneath the ground or how a plate of steel bends and snaps. His name is on 12 patents, from chips to solar cells.
Now, at an age when most engineers are working on their chip shots, Lamorte is trying to introduce a radically different way of using math to mimic nature. While his method requires a computer, in spirit it harks back to the precomputer era--in fact, all the way back to his hero, the English mathematician and natural philosopher Sir Isaac Newton, who died in 1727. Lamorte hopes it will vastly enhance the ability of engineers to design planes, cars, and bridges, create new drugs, and find oil.
Lamorte calls his method CLAMP, for "closed-form solutions applied to a mesh-point field." The basic idea: to transform equations that can't be solved into close approximations that can be. The "mesh-point field" is a virtual grid that's spread over the object being studied, whether a sports car or a hurricane. CLAMP helps generate predictions--"closed-form solutions"--for what happens at each point in the grid.
Lamorte does not lack ambition. He is trying to commercialize CLAMP through a company, Applied Engineering Software Inc., that operates out of his home in Durham, N.C. Newton's methods have advanced science for three centuries, Lamorte says. "Perhaps," he wrote last year, "CLAMP may serve in a similar capacity in the 21st century."
That remains to be seen. Lamorte is keeping the details of his method close to the vest, and many engineers who hear about CLAMP think he's a crackpot. When Lamorte's pitch reached General Motors Corp.'s Research Laboratories in Warren, Mich., James C. Cavendish, the principal research scientist in mathematics, said: "I had to keep my laughter down.... That's turning lead into gold." No one from GM has met with Lamorte.
On the other hand, Lamorte's results to date have intrigued people who have taken a closer look, including high-level staff at the Army Research Laboratory at Langley Research Center in Hampton, Va. Wolf Elber, director of the lab's Vehicle Structure Directorate, watched Lamorte use CLAMP to simulate the stresses on a metal plate with a hole in it. The method solved the problem on a personal computer in 0.06 seconds, vs. 30 minutes using the traditional method, finite element analysis. Says Elber: "It wasn't a world-class answer, but to do it that way at all, given what he's telling us about what he's doing, seems very, very interesting."
DIFFERENCES. Lamorte sees himself carrying on the tradition of Isaac Newton, who invented differential calculus to study such problems as the orbit of the earth around the sun. Newton broke down the orbit into infinitesimal parts, which he called differences, and then "integrated" them to produce an overall picture of the orbit's behavior.
Trouble is, most of nature, from electromagnetism to weather, is described by differential equations that are inherently nonintegrable. In the computer age, engineers have dealt with such equations using finite element analysis, in which they break a problem into a mesh of little pieces and repeatedly run separate equations on each piece. FEA, as it's called, is widely used today in design and analysis.
But FEA has some significant problems. Setting up the problem is time-consuming, and solving a big one requires a supercomputer, and there's no way to tell which of many possible solutions is correct. To be useful, the results have to be calibrated against real-world data. GM's Cavendish says the awesome computing demands of FEA "make it almost impossible to do interactive design."
LONE WOLF. Enter Lamorte. His CLAMP generates equations that describe what happens at each point in the virtual mesh covering the object that's being described. Then it knits together all those little equations into one big one that governs the whole system, something that's not done in conventional FEA. Says Lamorte: "The penalty you pay is that the equation is not simple. If you wrote it out by hand it would be about 200 feet long."
This month, Lamorte used CLAMP to simulate the output of a natural-gas field in an Energy Dept.-funded test at Montana Tech in Butte, Mont. A graduate student, Barry Browne, says CLAMP produced results more realistic and "orders of magnitude faster" than those of the conventional method, finite difference, a cousin of finite element analysis. Says Browne: "I'm really encouraged."
Michael Lamorte will need a lot more results like that before he will win over doubters. He arouses skepticism by refusing to lay out the details of his CLAMP methodology. He says he's afraid the concept will be stolen if it's made public. For now, he would prefer to take in customers' data and use CLAMP himself to generate simulations. That leads to another question--would anyone but Lamorte be capable of using CLAMP? Says the Army Research Lab's Elber: "This man has a feeling as to how higher-order differential equations behave. Where is he training his disciples? He's not."
Lamorte says CLAMP can be taught. He says he'll vanquish skeptics by sheer force of results. "My response would then be, `Who cares? It does the job!"' You can say this for Lamorte: He's putting his math where his mouth is.By Peter Coy in New York