Mathematical Sciences Department Joint Colloquium & Applied Math Seminar: Dan Anderson, George Mason University

Title: Floating objects at one- and two-fluid interfaces

Abstract: We investigate with mathematical and computational techniques, along with simple table-top experiments, the stability of floating objects.  Our focus is on long objects with uniform cross section.  We explore both simple cross sectional shapes as well has highly complex shapes.   We are motivated to explore this problem by observations of patterns on icebergs.  While the iceberg problem involves complex shape evolution associated with processes such as melting and/or calving, we focus on the simpler case of static floating objects.  We apply Archimedes' Principle along with a potential energy formulation that nonetheless offers excellent insight into some of these observations.  We compare our mathematical model predictions to measurements from simple table-top experiments.  We also demonstrate an extension of our theory to objects that float at a two-fluid interface (e.g. oil--water).  We have developed publicly-available code that, along with 3D printing technology, can be used to explore stability of floating shapes of the users own design.

Bio: Dan Anderson is a professor in the Department of Mathematical Sciences at George Mason University.  He earned degrees in Mathematics and Physics as an undergraduate at St. Olaf College in 1989 and a Ph.D. in the Department of Engineering Science and Applied Mathematics at Northwestern University in 1993.  He held postdoctoral positions at the University of Cambridge, the National Institute of Standards and Technology, and the University of North Carolina at Chapel Hill.  Dan's research interests include mathematical modeling and computation in applied problems arising in fluid mechanics, materials and environmental science, as well as in biomedical and physical sciences.