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Math Lectures Look at Raindrops and Liquid Layers Apr. 13-14

Story posted April 09, 2009

Raindrops tend to be nearly spherical.

Andrew Bernoff, professor of mathematics at Harvey Mudd College, will give a pair of lectures at Bowdoin that will look at the shape of raindrops and the layers on liquids. Both lectures are open to the public and admission is free.

The Cecil T. and Marion C. Holmes Mathematics Lecture, titled "An Introduction to Surface Tension (Or Why Raindrops are Spherical)," will be given on Monday, April 13, 2009, at 7:30 p.m. in Searles Science Building, Room 315.

A common misconception is that raindrops take the form of teardrops. In fact, they tend to be nearly spherical due to surface tension forces. This is an example of how at small scales fluid molecules' tendency to adhere to each other is the dominant effect driving a fluid's motion.

In his talk Bernoff will explain how surface tension arises from intermolecular forces, and examine examples of the behavior that can occur at small scales due to the balance between fluid-fluid and fluid-solid forces, with applications as varied as understanding how detergents help clean clothes and the design of fuel tanks in zero gravity environments.

Starbird will also present at the Department of Mathematics seminar at 4:30 p.m. Tuesday, April 14, in Searles Science Building, Room 217. The seminar, titled "Langmuir Layers: Exploring a (Nearly) Two-dimensional Fluid Experiment," is geared toward an audience with a math background.

A Langmuir Layer is a molecularly thin layer of a polymer, lipid or liquid crystal on the surface of another fluid. In this (nearly) two-dimensional layer, we can observe bubbles of a fluid phase that, even when stretched or highly contorted, always appear to return to a circular shape. The force driving these evolutions is line tension, a two-dimensional analog of surface tension. Bernoff's combined experimental, theoretical, and numerical study of Langmuir layers shows how we can deduce the strength of the line tension in the system by comparing theory and experiment. This work is the result of a collaboration with Elizabeth Mann, an experimental physicist at Kent State University, J. Adin Mann Jr., a chemical engineer at Case Western Reserve University, and James Alexander, a mathematician also at Case Western Reserve University.

A reception with Bernoff will precede this presentation, beginning at 4 p.m. in Searles Science Building, Room 214.

Andrew Bernoff's research specializes in bridging the gaps between mathematics, physics, biology and engineering with a particular emphasis on using dynamical systems methods to understanding experiments and natural phenomena.

Bernoff was an undergraduate at MIT where he earned B.S. degrees in mathematics and physics. His Ph.D. studies were on the application of dynamical systems methods in fluid mechanics in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge in England.

Bernoff has spent time on the faculty at Northwestern, Duke and the University of California at Berkeley before settling in at Harvey Mudd College, where he will chair the department commencing this fall. He is passionate about mentoring undergraduate research, coaching the Harvey Mudd College Putnam Team, and supporting Harvey Mudd College's Clinic Program, a year-long practicum in which teams of undergraduates work for industrial sponsor on real-world problems and applications.

His NSF-supported research program centers on understanding the behavior of fluids at small scales. He has spent this academic year on sabbatical at the Courant Institute of Mathematical Sciences at New York University pondering the dissipation of energy in fluids at small scales, the diversity of Manhattan's restaurant scene, and the differences between east coast and west coast culture and philosophy.

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