Industrial applied mathematics emphasizes the importance of relevance to industry, something that must be reconsidered at the modeling, analysis, and typically, computational stages of problem-solving. Striking the right balance in this endeavor takes practice, practice that all too often comes in the form of research lines that prove too mundane or too impractical to continue. Finding the right problems to work on, and the right industrial people to work with, is critically important in forging a career that is rewarding and noteworthy.
Wouldn’t it be nice, then, if there were a forum that would introduce you to an array of industrial math problems groomed and laid out for your consideration? Problems that ranged in topic from classical fluids to stochastic dynamics, from epidemiology to fiber-optic communications? The Mathematical Problems in Industry workshop, entering its thirtieth year this June, is a week-long intensive modeling experience that brings representatives from a wide range of industries together with applied mathematicians in the academy to sharpen their industrial math skills, make real progress on the problems brought to the workshop, and forge new alliances between universities and industry.
Fig. 3. Applied mathematicians in the Worcester sun at MPI13.
MPI currently operates on a rotation among three universities: the University of Delaware, Worcester Polytechnic Institute, and New Jersey Institute of Technology, the host of MPI 2014. The academic cohort consists of university professors at various stages of their careers, postdoctoral researchers, and graduate students having just completed the Graduate Student Mathematical Modeling Camp held the week prior at Rensselaer Polytechnic Institute. MPI participants enjoy a week of relaxed but concentrated work on a single problem (or more, if they decide to “room hop”, a common practice among veteran problem-solvers), with unfettered access to the industrial researcher and colleagues with broad expertise in applied mathematics. Junior participants, including graduate students, gain valuable insight into the process of taking an industrial problem from formulation to analysis and results. MPI has recently introduced a competitive fellowship providing a stipend to one or more graduate students to follow up on the week’s work with the company that brought the problem. Senior participants form new relationships with researchers in companies rich with interesting mathematical problems. All benefit from the interaction and its products, which often include journal articles and ongoing collaboration.
Many of the same benefits are enjoyed by the industrial participants, in addition to the workshop’s “deliverables” in the form of a presentation and written report detailing the week’s results. Often the biggest benefit is the insight they gain on how to dissect the problem in a way that allows them to advance the state of the art. They also have the opportunity to assess the talents of gifted young mathematicians who will be recruited on graduation. Companies large and small from a variety of industries have participated in MPI, including Alcatel-Lucent, Corning, W.L. Gore & Associates, Hitachi, Novartis, Pall, and Standard & Poor’s. The companies show their appreciation for the value provided by the workshop by helping to fund it, with additional funding coming from the National Science Foundation, from the local host of each meeting, and from partner institutions such as the Institute for Mathematics and its Applications.
Fig. 1. Water jet cutter (Wikipedia) using a directed jet of slurry to machine heat-sensitive materials.
Examples abound of interesting problems that have emerged from the MPI workshop and others like it. Lists of past MPI problems here
, and here
outline some of them. Similar workshops based on the Oxford tradition of week-long study groups have proliferated throughout the English-speaking world and beyond; look here
for a list of recently held workshops.
To conclude I’ll briefly mention two typical problems from recent MPI workshops, the first involving modeling of an abrasive waterjet and the second involving the capture efficiency of folded filters. The OMAX® Abrasive Waterjet (Fig. 1) is an industrial cutting tool used largely for fabrication of heat-sensitive machine parts. At MPI 2013, held at Worcester Polytechnic Institute, OMAX challenged participants to model the abrasive waterjet in order to explain and mitigate factors limiting the efficiency and quality of the waterjet’s machining, including a nonuniform exit velocity distribution of the slurry particles and a wear pattern inside the waterjet’s collimator that reduced its operational lifespan. What followed was a very engaging week of analyzing free-boundary problems (air-water interface), multiphase flow models (water-particle mixture), and collision dynamics (wall deformation and erosion). Click here for the full report.
Pall makes very fine porous filter membranes, for a wide range of filtration applications. In order to achieve high membrane filtration area at small occupied volume, filters in many applications are pleated (Fig. 2) and packed into cartridges through which filtrate is passed. However, such pleated filter cartridges underperform significantly when compared to results for the equivalent area flat membrane filter. Pall hypothesized that this underperformance could be due to the actual pleating process, which could compromise the membrane integrity. The Workshop investigated this hypothesis and rejected it as unlikely; it also began an in-depth study of the fluid dynamics of filtration through a pleated membrane to see whether the underlying cause of the difference in performance was purely fluid-dynamical (preliminary results suggest it may be). Click here for the full report.
Fig. 2. A pleated filter by Pall.
My colleagues and I (Fig. 3) have found participating in past MPI workshops to be a fun, rejuvenating, and highly rewarding way to spend a week each summer. We feel it has honed our skills as applied mathematicians, has opened doors for collaboration that would not otherwise have existed, and has reminded us of the tremendous value in SIAM’s mission of bringing mathematicians and industry together. There is still time to join us at NJIT for MPI 2014. We hope to see you there!