Applied Math Seminar: Energy driven pattern formation in thin fluid layers: The good, the bad and the beautiful
Seminar | January 26 | 4-5 p.m. | 748 Evans Hall
Andrew Bernoff, Harvey Mudd College
(Note special date and location) A wide variety of physical and biological systems can be described as continuum limits of interacting particles. Many of these problems are gradient flows and their dynamics are governed by a monotonically decreasing interaction energy that is often non-local in nature. We show how to exploit these energies numerically, analytically, and asymptotically to characterize the observed behavior. We describe three such systems. In the first, a Langmuir layer, line tension (the two-dimensional analog of surface tension) drives the fluid domains to become circular and the rate of relaxation to these circular domains can be used to deduce the magnitude of the line tension forces. In the second, a Hele-Shaw problem, vexing changes in topology are observed. The third system models the formation of the convoluted fingered domains observed experimentally in ferrofluids for which pattern formation is driven by line tension and dipole-dipole repulsion. We show that noise in this system plays an unexpected but essential role and deduce an algorithm for extracting the dipole strength using only a shape's perimeter and morphology.
Biosketch: Andrew Bernoff is the Kenneth & Diana Jonsson 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. 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 spent time on the faculty at Northwestern before settling in at Harvey Mudd College. 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 research program centers on understanding the behavior of fluids at small scales and modeling the swarming of organisms, in particular locusts.