Speaker:  Prof. Andrew Bernoff, Department of Mathematics, Harvey Mudd College, Claremont, California

URL for Speaker:  http://www.math.hmc.edu/~ajb/

Location:  LSK 301

Intended Audience:  Public

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. We report on a combined experimental, theoretical, and numerical study of Langmuir layers and show how we can deduce the strength of the line tension in the system by comparing theory and experiment. As time permits we will also describe other phenomena observed in Langmuir systems, including collapse of gas phase bubbles, co-existence of three or more fluid phases, and formation of dogbone and labyrinth patterns due to dipolar repulsion in the layer. This work is the result of collaboration with Prof. Elizabeth Mann, an experimental physicist at Kent State University, Prof. J. Adin Mann, Jr., a chemical engineer at Case Western Reserve University, and Prof. James Alexander, a mathematician also at Case Western Reserve University and is supported by the National Science Foundation.

Andrew Bernoff is a Professor of Mathematics at Harvey Mudd College. His research specializes in bridging the gaps between mathematics, physics, biology and engineering with a particular emphasis on using dynamical systems methods to understand experiments and natural phenomena. Prof. Bernoff was an undergraduate at MIT where he received BS degrees in mathematics and physics. While an undergraduate, he founded the MIT Integration Bee. In 1978 he was awarded a Marshall Scholarship to pursue a PhD at the University of Cambridge in England. His PhD studies were on the application of dynamical systems methods in fluid mechanics in the Department of Applied Mathematics and Theoretical Physics (DAMTP). Prof. 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 is the Diana and Kenneth Jonsson Professor of Mathematics and Chair of the Mathematics Department. 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 sponsors on real-world problems and applications. His NSF-supported research program centers on understanding the behavior of fluids at small scales and modeling the swarming of organisms, in particular locusts, and is built on collaborations at multiple colleges and universities.