"NCSU Forges Partnerships with Local Industry"

In its 70-year history, the Lord Corporation (just outside Research Triangle Park, North Carolina) has never hired an applied mathematician. Joint research projects under way with graduate students, postdocs, and faculty from the Industrial Applied Mathematics Program (IAMP) in the Center for Research in Scientific Computation (CRSC) at nearby North Carolina State University, however, are making it clear to Lord management that mathematical modeling and scientific computation can help streamline the product design process and, in at least one case, bring a sophisticated new product to market. Today, Lord is paying half of the salary of an industry/university postdoc, and its management has expressed interest in hiring applied mathematicians in the near future.

From the NCSU students' point of view, the work they do at Lord provides them not only with valuable real-world experience but also, in some cases, with help in continuing their education and with employment offers. From the perspective of CRSC director H.T. Banks, University Professor and Drexel Professor of Mathematics, the research done by first-year graduate students at Lord, or any of the several other organizations with which IAMP has created partnerships, motivates the students for the advanced courses they will be taking later in their graduate work.

Lord Corp., explains Banks, is a major player in the development of rubber-like polymer-based devices for suppressing vibrations, mainly for manufacturers of heavy-duty vehicles and aircraft. Most such devices to date have been inactive or passive; one of Lord's goals is to design and build "active" vibration-suppression devices - "smart" devices that are capable of sensing and actuating.

To this end, IAMP/Lord researchers are working to model the nonlinear dynamics of viscoelastic composite materials that are subject to large deformations. "We wanted to predict the behavior of these convoluted composites under a series of deformations," says Lord polymer scientist Lynn Yanyo, "but we didn't have the math skills." In what she describes as "absolutely a collaboration," Lord scientists have "learned a lot from the standpoint of mathematics." In the early stages, she says, it was extremely helpful to review the models in the literature - Banks and NCSU postdoc Nancy Lybeck "rederived them and pointed out the implicit assumptions that we were not previously aware of."

The students, who have been active participants in the test-design and data-gathering phases of the project, have been highly motivated to learn about what is for them a completely new subject. Yanyo views this flexibility and openness as one of the requirements for a successful collaboration: "People have to be willing to say `I don't know anything about this, but I'm willing to learn.' "

Postdoc Nancy Lybeck, the first Lord/CRSC Research Fellow, is an important participant in these efforts; with a two-year industry/university postdoctoral fellowship from the National Science Foundation, Lybeck has been spending part of her time at Lord since September 1995. The group with which she works - Yanyo, another polymer chemist, and an engineer, all from Lord, along with Banks and NCSU graduate student Yue Zhang - started modeling at the simplest level, a rod with simple extension. "We're having good success matching model results with experimental data," she reports, and the group is now beginning studies of rubber in shear.

The opportunity to apply her knowledge in a realistic situation is one of the most enjoyable aspects of her work at Lord, says Lybeck, who also likes the challenge of interacting with people in other disciplines. What the postdoc experience has taught her, she says, is that she could be happy in either an industrial or an academic setting.

Another IAMP/Lord project involves the manufacture of thin polymer coatings for use as protective layers on vinyl flooring. Seeking to incorporate recent technological advances into their design process, Lord scientists found themselves facing a substantial mathematical modeling and scientific computing effort. In the collaboration they established with NCSU, the focus has been on the development of models and numerical algorithms for the design of polymer coatings with specified macroscopic properties, such as resistance to stains, abrasion, and impact. Considered as design variables are a variety of microscopic characteristics of the materials, among them particle size, composition, molecular weight, and cohesion energies.

Last summer, the problem of the optimal design of polymer chains for use in protective coatings was posed in another setting at NCSU: the 1995 Industrial Mathematics Modeling Workshop for Graduate Students. During the ten-day workshop, 30 graduate students considered six problems, including the polymer problem, most of them presented by scientists from industry or government laboratories. The workshop, which was organized by CRSC faculty Ben Fitzpatrick and Hien Tran, was the third in a series initiated at the Claremont Colleges under the leadership of Ellis Cumberbatch and Stavros Busenberg. A highlight of the week was a visit to Lord Corp., where the students introduction to an industrial research laboratory included a demonstration of the ongoing work on the abatement of vibration-induced sound in aircraft cabins. This summer, CRSC will be conducting the fourth workshop in the series.

Other organizations with which IAMP faculty have forged partnerships include the North Carolina Department of Insurance, which is seeking to develop models of the severity and frequency of hurricanes that are more accurate than those now used in assessments of hurricane damage. In a project with IBM, two NCSU faculty, with one undergraduate and four graduate students, are carrying out a comprehensive study of forecasting problems that arise in retail inventory control. Key components of the study include the detection of major shifts in demand and the resulting changes in the forecast, methods for dealing with slow-moving items, and flexible methods for developing seasonal models with multiple scales of fluctuation.

Banks attributes the recent growth of the three-year-old IAMP (where 15 projects, involving eight faculty and about 17 graduate students, are now under way) mainly to the willingness of center faculty "to go out and do something different." Impatient with distinctions between applied and pure mathematics (he has encouraged collaborations between pure mathematicians at NCSU and the National Security Agency), he points to what may well be the most important factor in IAMP's success: "We don't send students, we take them." SIAM executive director James M. Crowley sees in the NCSU activities an extremely effective implementation of some of the recommendations of the recent SIAM Report on Mathematics in Industry. "MII recommends that we provide students with more experience in applying mathematics to real problems, especially the kinds of experience in which students have to interact with people in industry or other disciplines, formulate problems, and see them through to their solution," he says. "These workshops and collaborative research efforts are a good way of providing that experience."