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January 23, 1997

Saturday mornings find provost relaxing with statistical physics

Some people collect coins, some people tie trout flies, others work with wood, knit or play golf. It would seem safe to say, though, that few people consider statistical physics and the role of randomness in producing complicated patterns in material systems as a hobby. In fact, Provost James Maher may be one of the only people who relaxes on Saturday mornings after a tough week in the office by exchanging views on such phenomena with a team of graduate students and post doctoral fellows.

"There are two reasons why I've kept up my current level of activity," says Maher. "One is because it is my hobby. I genuinely like it and I find it relaxing to be able to do some of it.

"Secondly," he continues, "it is a resource for the physics department. It is a working laboratory that has a certain amount of international visibility. If I can keep it operating without failing in my duties as provost, it is a resource that we should not close down." Half of the funding for Maher's "hobby" is being provided by the U.S. Department of Energy and the other half by NASA. The combined annual budget of the two grants is about $220,000. It is a sum that any University department would be more than happy to add to its budget, especially since such federal funding is becoming ever more difficult to obtain.

"The projects that we are working on in the lab are very good projects that have been identified nationally as important scientific questions," Maher says. "It is my responsibility to make sure that the work done in the lab is of high quality. But it is obvious that a lot of the work that is going to be done in the lab will be work that is published by others under my supervision." Since becoming provost in June 1994, Maher has continued his research with the help of four upper level graduate students who work in his lab during the week and meet with him to discuss what they have done and share ideas on Saturday mornings. Maher is in the process of replacing those four students, who recently graduated, with two new graduate students and two post doctoral fellows who will supervise the students during the week. The provost will continue to meet with the new team on Saturday mornings.

Of the work itself, the role of randomness in producing complicated patterns in material systems, Maher says it involves both practical questions associated with making very pure samples of materials, and impractical, but intellectually important, questions about how some natural processes can show so much sensitivity to starting conditions.

"For instance," he explains, "the latter question has been described in the popular literature as saying: 'How does New York's weather change in June if a butterfly flaps its wings near the North Pole in March?'" Over the past 20 years, work in the field of statistical physics has had profound results in terms of understanding apparently random phenomena, as well as in material processing applications, such as growing pure crystals for high tech materials that can be used in electronic and optical devices.

In the laboratory, Maher's team has been testing mathematical models by designing experiments so simple that the physical system should be closely matched to the mathematical model. Results to date have shown "considerably more richness" to even the simplest of physical systems than might have been thought.

"Most mathematical models are rather crude approximations to the physical systems that they are intended to imitate," the provost explains. "That's not so bad if you are dealing with a physical system that is not very sensitive to details of the initiation of the process. But when you are dealing with chaotic or very complicated processes, then it becomes extremely important that the physical system that is being used in the laboratory be one that is plausibly subject to the approximations in the mathematical model." Maher said it takes "quite a bit of work" to make an experiment so controllable that a person can believe with confidence that the mathematical model is applicable.

One simple case that Maher's team has done a lot of work on is called "fingering instability," which affects oil spill recovery problems and is mathematically close to the problem of dendritic growth in crystals. A simple example of a dendrite is a snowflake. Many different materials show such dendritic or snowflake-like growth, which affects their quality.

The fingering instability or dendritic growth of oil is what makes it difficult to clean up after a spill. Since oil is lighter than water, Maher points out, it floats. Because it floats, the public might assume that an oil company could simply vacuum up the oil that has spilled onto the ocean or some other waterway. "If you tried to vacuum up such oil," Maher says, "what you would find is that you would pull a finger of water right through the oil into your pump and not get much of the oil up. That instability makes controlling the flow of pairs of fluids very difficult under some circumstances." Similarly, oil companies would love to be able to force water down into porous rock and have the oil float to the surface. Because of fingering instability, though, what usually happens is that the water travels right through the oil.

Maher's group has been studying simple cases of such instability because the mathematics of such instabilities can be expressed reasonably simply. Perhaps one day the provost's Saturday morning "hobby" might actually help to clean up an oil spill or create a new type of semi conductor for a computer that hasn't even been imagined yet.

–Mike Sajna

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