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Discovering Mathematics In Nature

posted Jul 8, 2010, 8:14 PM by Glenna Buford   [ updated Jul 8, 2010, 8:15 PM by AWM Editor ]

2005 AWM Essay Contest: 
Grand Prize Winner

By Arica Fong

Dr. Linda Smolka uses a variety of techniques to approach her work in fluid mechanics. In her lab, she captures the motion of fluids with photography. She then describes the motion she observes using differential equations derived from physical laws.

When I met with Dr. Smolka, she showed me a series of photos that captured a falling drop of oil. The droplet elongated to form a cylinder before the tear-shaped end separated from the cylinder. In another series of photos, the cylinder itself broke into several droplets as it fell. These photos have stimulated Dr. Smolka's curiousity about nature and its relationship to physical processes.

Although Dr. Smolka is now a professor of mathematics at Bucknell University in Lewisburg, Pennsylvania, she was aware of neither her interest in teaching, nor her passion for research in fluid dynamics as an undergrad. After earning her bachelors in civil engineering from Princeton, she worked for about a year in computer consulting, and then for another year as a structural engineer. However, these jobs were not challenging for her, and she missed the academic environment she had experienced at Princeton. Subsequently, she shifted her focus towards academic life when she became a mathematics teacher at The Lawrenceville School, an independent high school in New Jersey. She discovered she enjoyed teaching and continued to teach for four years. Since the school encouraged teachers to get higher degrees in the fields they taught, Dr. Smolka entered graduate school for a Masters degree, intending to return to Lawrenceville.

When Dr. Smolka was applying for graduate school, Dr. Diane Henderson was a faculty member in the mathematics department at Penn State. Dr Henderson had a background in engineering and physical oceanography. Dr. Henderson was in search of a student to work with her on droplet formulation in her experimental fluids lab. Dr. Henderson's research caught Dr. Smolka's interest because they had similar backgrounds and similar interests in applied mathematics. Dr. Smolka became fascinated by the research she started during her first years at Penn State. After completing her masters in mathematics, she decided to work on a doctorate. Of her advisors Dr. Henderson and Dr. Andrew Belmonte, Dr. Smolka says, "They were very dedicated scientists who saw the beauty in nature and instilled that in me as well."

For her dissertation, Dr. Smolka's studied the motion and stability of free surfaces, specifically the surface of a droplet. She captured wonderful images of these droplets and the cylinders they formed with high-speed photography. Depending on the density, viscosity, and surface tension of the fluid, she found that the surface of the droplet may be perturbed, and the cylinder may break up into several separate droplets. Based on physical principles, she applied mathematics to describe the motion and stability of these droplet-forming cylinders. Dr. Smolka used partial differential equations and ordinary differential equations to describe and model different free surfaces. Dr. Smolka's research can be applied ink jet printing, where printed letters are formed by ink droplets.

Since she had invested a lot in her education but still enjoyed teaching, Dr. Smolka decided she wanted to work towards a tenure track position at a university. She did her postdoc at Duke University for two and a half years through the NSF's VIGRE program. Then she came to Bucknell University. In her past two years at Bucknell, she has been teaching classes in applied mathematics and continuing her research in fluid mechanics. She has also established an experimental fluids lab. One of her goals at Bucknell is to integrate undergraduates further in her research by getting them involved in her lab, and an REU student in physics worked with her in the lab during the summer of 2005. Her lab enables her to continue her research on free surfaces in different geometries, such as the surfaces of falling liquid sheets.

Outside of her work, she likes to spend as much of her free time as possible in the outdoors, hiking, mountain biking, and gardening. She is also involved with folk music.

About the student: 
My name is Arica Fong. I am from Los Altos, California. I transferred from UC Davis to Bucknell University in 2004, and I am currently a senior mathematics major. This spring, I will travel abroad to Hungary to study in the Budapest Semesters in Mathematics program. After graduating, I plan to spend a few years working before applying to graduate school in mathematics. I am currently interested in the fields of algebra and graph theory. In my free time I enjoy participating in the Putnam Club and practicing Tae Kwon Do.