The MEC Lab at the University of Delaware

By John A. Pelesko, University of Delaware
Print

Handling editor: Chad Topaz

The MEC Lab at the University of Delaware

John A. Pelesko, University of Delaware

Wave motion outreach activity
Graduate student Regan Beckham and Charter School of Wilmington mathematics faculty Charles Biehl ponder wave motion during an outreach activity in the University of Delaware's MEC LAB.

Introduction

The Department of Mathematical Sciences at the University of Delaware houses a unique hands-on laboratory known simply as "The MEC LAB." The MEC LAB, founded in 2002, derives its name from three key facets of applied mathematics - Modeling, Experiment, and Computation. Partially inspired by similar labs at the Courant Institute, the University of North Carolina, the University of Arizona, Georgia Tech, and the New Jersey Institute of Technology, the MEC LAB seeks to provide mathematics students at all levels with a unique educational experience as well as serve as a home for faculty and graduate student research. We accomplish this through a variety of outreach activities, an active undergraduate research program, and an innovative capstone course. In addition, we provide resources and a home for experimentally based faculty research projects.

Research Activities

The laboratory is open for use by all faculty, postdocs, and graduate students in the Department of Mathematical Sciences. Rather than serving as the home to a classic focused research "group," the lab combines the activities of many loosely connected faculty led "mini-groups." These mini-groups typically consist of one or more faculty members, postdoctoral associates, graduate students, and undergraduate researchers. The common thread linking these groups to each other and to the MEC LAB is a desire or a need to add an experimental component to their traditional applied mathematical research. Some recent research activities are described below.

Soap films. Professor John A. Pelesko leads a group consisting of two graduate students and several undergraduate researchers that focuses on the study of the statics and dynamics of soap films subjected to electric fields. In the MEC LAB, the group has built several apparatuses for creating highly symmetric soap film surfaces. They subject these films to high voltage electrostatic fields and film the resulting motion using the lab's high speed camera. The mathematical models of these systems typically consist of coupled non-linear partial differential equations. Pelesko and his group use asymptotic, numerical, and analytical methods to study these systems and compare the theory with the experiment.

The collapse of a catenoid
The collapse of a catenoid. Catenoids are a class of minimal surfaces, as proved by Euler in 1744. Filmed in the MEC LAB by graduate student Derek Moulton as part of his doctoral research on electrified soap films

Tear films. Professor Richard Braun leads a group of several faculty members, two graduate students, and two undergraduate researchers that studies tear films during human blink cycles. Part of this work requires that the team quantify the motion of an eyelid during the blink cycle. With the help of a computer science graduate student, Professor Braun and several undergraduate students used the MEC LAB's high speed camera to capture lid motion during blinking. The group developed an automated system for extracting the motion of the edge of the eyelid from this video. Finally, they then incorporated this motion into their models of tear film evolution during the blink cycle.

Tear films
An image from the Braun group's study of tear films. The red lines indicate a polynomial fit to the edges of the eyelids. Using video, a spatial polynomial is generated for each frame and so the fit evolves in time. In turn, this boundary motion is incorporated into the team's blink cycle models.

Ant foraging. Professor Louis Rossi leads a team of several undergraduate researchers that studies ant foraging trail dynamics. This team collaborates closely with faculty from the University of Delaware's Computer Science Department. In the lab, Professor Rossi and his team built a self-contained ant habitat equipped with a video camera and frame grabbing software. By placing a food source far from the ant's home and by otherwise modifying the ant's environment, they were able to obtain data on foraging dynamics that could be directly compared with their partial differential equation based mathematical model.

Foraging ants
Close up view of a foraging ant from Professor Lou Rossi's ant table in the MEC LAB.

A Focus on Undergraduate Research

The lab's most active months are the summer months. Typically there are six to twelve undergraduate students conducting research full time for ten weeks. These students are drawn largely from the pool of undergraduate mathematics majors, but occasionally come from other departments, and even other universities. In the summer of 2005, the MEC Lab had two students visit for the summer from INSA Toulouse in France. Each student conducting summer research is supervised directly by a faculty member, but they often work in conjunction with graduate students and with each other. All of the undergraduate researchers meet weekly for an informal lunch and research update session. At the end of the summer, the Department of Mathematical Sciences hosts an undergraduate research symposium at which the summer students speak. A best paper award is sponsored by the Sigma Xi Honor Society and the winning student receives a $100 prize.

The range of summer projects is immense. However, each project typically contains an experimental, a mathematical, and a computational component. The basic idea is that students perform their own experiments, gather real data, construct a mathematical model of their system, and then analyze the model using analytical and numerical techniques. In the past, students have electrified soap films, studied falling chains, created chemical oscillators, self assembled cubes, monitored phase transformations in freezing water, and analyzed the random packing of chains of spheres. A typical project is the one carried out by Professor Russell Luke and several undergraduates over the summer of 2006 and the summer of 2007. For this project the team built a diffraction optical bench and fabricated simple diffraction gratings using a laser printer and transparency film. Then, using software written by Professor Luke, students explored the physical nature of the Fourier transform and the mathematical nature of diffraction.

Diffraction grating Image obtained
Image of the diffraction grating fabricated by Professor Luke and his students (left). On the right is the diffraction image obtained when a point source is viewed through the grating on the left.

Capstone Course

During the academic year, the MEC Lab is used by many instructors for various math courses. Some instructors use pre-made demonstrations that they can carry into the classroom, some have students engage in honors or extra credit projects that involve the lab, and others integrate lab experiences more fully into their classes. Math 512: Contemporary Applications of Mathematics is the main course that makes use of the lab during the semester. This course is a capstone course and is required for all undergraduate B.S. mathematics majors. The course typically attracts students from engineering and the sciences as well. Students in Math 512 are assigned to project teams at the start of the semester. Each team is given an open-ended project that they will work on throughout the semester. In the past, student teams have studied air bearings, domino toppling, and thermal MEMS devices. As with the summer research projects, each of these projects has an experimental, computational, and modeling component. Students carry out experiments in the lab, collect data, and compare their experimental results to the models they develop. By the end of the semester, each team has written, revised, and completed a journal style report on their project.

Capstone course
Students testing the load bearing capacity of a shaped air bearing in their capstone course. This project led to a connection with a local company, New Way Air Bearings, that manufactures air bearings. They brought a new air bearing problem to the Mathematical Problems in Industry workshop held at the University of Delaware in the summer of 2004.

Outreach

The MEC LAB provides a unique opportunity to engage local high school teachers and students through various outreach activities. Most prominent among these activities are the professional development days for the mathematics faculty of local high schools. Several such workshops have been run for the faculty of the Charter School of Wilmington (CSW), a nationally recognized, Delaware-based math and science charter school. During a typical workshop, high school teachers will spend the day working in the MEC LAB on projects that use inexpensive materials to illustrate high school level mathematical concepts. The success of these workshops has led the Charter School of Wilmington to begin development of their own "CSW MEC LAB." Faculty from the Department of Mathematical Sciences at the University of Delaware continue to work with CSW faculty in developing projects and activities that can be carried out in the CSW lab. Most recently, the MEC lab has extended its outreach activities to other local high schools, last fall organizing a workshop for the mathematics faculty of McKean High School located in Hockessin, Delaware. Plans are in place to extend this activity to other local Delaware high schools.

Acknowledgements

The activities of the MEC LAB are made possible through the generous support of numerous funding agencies and organizations. Initial funding for the lab was provided by the Unidel Foundation. The Department of Mathematical Sciences at the University of Delaware provides continuing financial support. The Center for Teaching Effectiveness at the University of Delaware has sponsored several MEC LAB based projects. Various faculty have been supported by the National Science Foundation and used such funding to defray equipment costs and support graduate and undergraduate students. Many undergraduate researchers have been funded by the Science and Engineering Scholars Program at the University of Delaware as well as by the Howard Hughes Medical Institute.

References

[1] D. Moulton and J.A. Pelesko, "Theory and Experiment for Soap-film Bridge in an Electric Field," Journal of Colloid and Interface Science, in press.
[2] A. Heryudono, R.J. Braun, T.A. Driscoll, L.P. Cook, K. Maki and P.E. King-Smith, "Single-Equation Models for the Tear Film in a Blink Cycle: Realistic Lid Motion," Math. Med. Biol. 24 (2007) pp. 347-377.
[3] R.J. Braun and P.E. King-Smith, "Model Problems for the Tear Film in a Blink Cycle: Single Equation Models," J. Fluid Mech. 586 (2007) pp. 465-490.
[4] K. Johnson and L.F. Rossi, "A mathematical and experimental study of ant foraging trail dynamics," Journal of Theoretical Biology, 241 (2), pp. 360-399. 2006.

MEC Lab Logo

Please login or register to post comments.

Name:
Email:
Subject:
Message:
x