Professor Andrea Bertozzi
Departments of Mathematics and Mechanical and Aerospace Engineering
Betsy Wood Knapp Chair for Innovation and Creativity
University of California, Los Angeles
Wednesday, February 26, 2020, 4-5 p.m.
A Theory for Undercompressive Shocks in Tears of Wine
ABSTRACT: We revisit the tears of wine problem for thin films in water-ethanol mixtures and present a new model for the climbing dynamics. The new formulation includes a Marangoni stress balanced by both the normal and tangential components of gravity as well as surface tension which lead to distinctly different behavior. The combined physics can be modeled mathematically by a scalar conservation law with a nonconvex flux and a fourth order regularization due to the bulk surface tension. Without the fourth order term, shock solutions must sastify an entropy condition - in which characteristics impinge on the shock from both sides. However, in the case of a nonconvex flux, the fourth order term is a singular perturbation that allows for the possibility of undercompressive shocks in which characteristics travel through the shock. We present computational and experimental evidence that such shocks can happen in the tears of wine problem, with a protocol for how to observe this in a real life setting.
Professor Bonnie Berger
Simons Professor of Mathematics, MIT
Departments of Electrical Engineering and Computer Science, MIT
Head of Computation and Biology group at CSAIL MIT
Wednesday, February 26, 2020: 5-6 p.m.
Compressive Genomics: Leveraging the Geometry of Biological Data
ABSTRACT: Researchers around the globe are gathering biomedical information at a massive scale. We develop algorithms to compress this data that enable computation on the reduced representation. In this talk, I will discuss how we can leverage the low-dimensional true structure of biological data manifolds in order to build useable compact geometric summaries of this data. I will highlight our latest work on single-cell transcriptomic datasets, that enables an unprecedented scale of data to be effectively pooled from individuals and institutions across nations to enable novel life-saving discoveries.
Refreshments will be served following the talks.