CHEMISTRY
Joel Miller
Thanh N. Truong
Peter J. Stang
MATHEMATICS
Graeme W. Milton
Jim Carlson
PHYSICS
Charles Jui
Charles Jui
Craig Taylor
Valy Vardeny
Valy Vardeny
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The Math of Mixtures
By Lee Siegel
The Salt Lake Tribune
Sometimes Graeme Milton devises new materials by using a computer to search through millions of geometric structures. Or he works out mathematical formulas that
describe new substances and how they should behave. But often, an idea for a new, beneficial material simply pops into his head.
"You just think about it geometrically while on a beach or biking or sleeping at night," said Milton, a distinguished professor of mathematics at the University of
Utah. "Shapes come into your mind."
Milton, a native of Australia, is a physicist who works as an applied mathematician. His research is based on the principle that the properties of a material are
dictated by the material's internal structure. He finds or dreams up geometric structures, then uses complicated mathematical formulas to prove they have certain desired
properties.
"You can tailor-design materials to do things," Milton said. In the past, most new materials were made by trial-and-error experiments.
During an interview, he compared the need for new materials with "a kid with building blocks. If you give him just a few types of blocks, he won't be able to build much.
But if you give him all sorts of blocks, he'll be able to build whatever he wants."
It is difficult to predict future uses for the materials Milton devises, but he said they "could potentially revolutionize manufacturing processes."
"We need new materials for technological progress in the next century," he said. "If you look at improvements in technology, computers and the semiconductor industry
and things like that, we are trying to push the limits in the way of what is possible in creating new materials."
Milton outlined his research Wednesday during the university's quarterly Science at Breakfast lecture in Salt Lake City.
Jim Carlson, the U.'s math chairman, and Rod Lakes, an engineering professor at the University of Wisconsin, Madison, said the Utah math department
now has the best group of scientists in the nation for studying the mathematics of new materials. The group includes Milton, Ken Golden, Andrej and
Elena Cherkaev, David Eyre, Paul Fife, Sergey Serkov, Knut Solna and Sasha Balk. Colleagues are not shy about crediting Milton as the group's key player.
"He's a genius," Golden said. "In the mathematics of materials, he's the best in the world."
The materials dreamed up by Milton are called composites, which are mixtures of substances that do not react chemically with one another. That makes it easier to
design a new material with a desired physical behavior or property, Milton said.
Composites are ubiquitous. Sandstone is a composite of sand grains with air-filled voids between them. Sea ice, lung tissue and sponges also are composites of a solid material and pores filled with
air or liquid. Other composites include milk -- fat in liquid -- and chocolate-chip ice cream.
Epoxy and carbon fiber are combined in composites to make lightweight but strong airplanes, spacecraft and tennis rackets. Solid fuel for rockets is a composite of aluminum
particles in an oxidizing substance. Materials that convert sunlight to heat are composites of ceramic and metal. Wool and cotton are composites of fiber and air. Cement is
a composite of water, sand and gravel. Clouds, fog and rain are composites of air and water.
Composites can combine desirable properties of two materials "so you get the best of both worlds," Milton said.
For example, steel rods are expensive but strong. Concrete is cheap but crumbles easily under tension. A composite of concrete and steel reinforcement bars is widely used
for relatively cheap, strong building material.
"Sometimes the properties of a composite can be very different from either material in it," Milton said.
For example, certain old church windows contain gold particles in clear glass. It makes the glass look red, he said.
Learning how a composite material's microscopic structure relates to its behavior is important for helping physicists learn "the link between how things behave at atomic
scale and how things behave at larger, everyday scales," Milton said.
Milton and other materials scientists have worked on "antirubber," which, when pulled, gets fatter in the direction perpendicular to the way it is being stretched. Rubber
becomes thinner when stretched.
Antirubber may be useful for designing sensitive hydrophones to detect underwater sounds. "You might want to detect submarines, schools of fish or underwater
earthquakes," Milton said.
In 1987, Lakes constructed a foam that expanded when stretched. Lakes said Milton then showed an entire class of materials could act as antirubbers. Lakes has worked with
aircraft manufacturers to study sandwiching antirubber materials between metal layers to make the wings and fuselage more damage-resistant by spreading stress from a dent
over a wider area than where the dent happened.
Milton said he and Andrej Cherkaev used mathematical formulas to show it is possible to design materials that have every conceivable elastic behavior. One such material will be
stiff if squeezed on all sides, but soft if squeezed only on two sides. If used in machinery, such materials could "guide stress in desired directions so there is less stress on some
part and it would take longer to break down," Milton said.
He also tries to design materials with other desirable characteristics, including stiffness, strength, an ability to absorb vibrations from events such as earthquakes, low electrical
conductivity, and light absorption for solar power cells.
With U. math instructor Solna, Milton showed it is possible to construct a composite through which light travels faster than it would travel through either ingredient. Milton
and Eyre did work for General Motors, checking data on a new composite designed to reduce static on car radios.
Milton, 42, was born in Sydney, Australia, and lived there until he was 22. As a high-school student, he developed an interest in chemistry because "I was curious to try to build
better bombs." He also became enthralled with relativity.
"The problem was, I got too interested in the advanced subjects, so when I first went to Sydney University, I came close to failing because I was going to the library
to read books on quantum mechanics and general relativity, but not going to my regular classes."
Milton took a break from college, spent a year hitchhiking through New Zealand, then went back to the university, where he earned undergraduate and master's degrees in
physics.
After earning a doctorate in physics at Cornell University in upstate New York and doing postdoctoral work at the California Institute of Technology in Pasadena,
Milton was hired by New York University's math department.
In 1994, Caltech and the University of Utah fought a fierce bidding war to attract Milton. The U.'s strong group on the mathematics of materials helped him
decide onÊ Utah, but was not the only reason.
"The quality of life -- the outdoors -- was a big factor," said Milton, whose pastimes include photography, skiing, mountain biking, rafting and canoeing.
Originally published October 28, 1999, in The Salt Lake Tribune.
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