CAREER: Combining research on dynamic metastability and hydrodynamic limits with a multifaceted outreach plan

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

Westdickenberg DMS-0955051 The investigator takes up problems in the areas of (i) slow coarsening or dynamic metastability of gradient flows, and (ii) logarithmic Sobolev inequalities (LSI) and the hydrodynamic limit. In the first part, the investigator and collaborators apply the abstract sufficient condition for dynamic metastability developed by Felix Otto and the PI to the Cahn-Hilliard Equation and then develop new but related methods to tackle the more applied problem of coarsening rates in two-dimensional epitaxial growth models. In the second part, the investigator and collaborators push forward their two-scale method for LSI and the hydrodynamic limit to prove convergence of the microscopic entropy to macroscopic entropy under general sufficient conditions. The educational and outreach component of the proposal encourages and supports women in mathematics and disseminates knowledge on multiple levels both in coordination with the research plans detailed above and through four explicit initiatives headed by the PI. The work of this project focuses on understanding the way that energy (or entropy) and energy dissipation (or entropy dissipation) affect the nonlinear dynamics of a physical system. In general, science has a good understanding of global minimizers but a very weak understanding of local minimizers and pathways between them -- where many physical systems spend all of their time. A broader understanding of multiscale energy landscapes is of both scientific and practical importance; for instance, epitaxial growth models have implications for nanotechnology and semiconductor development, technology with impact in medicine, communications technology, and other fields. The education and outreach component of the proposal addresses a critical need to recruit and keep more women in mathematics, increase diversity in the sciences, and build international ties between the scientific communities.