A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In the case where the scale of the small heterogeneities is of the same order of the scale governing the phase transition, the interaction between homogenization and the phase transitions process leads to an anisotropic interfacial energy. Bounds on the homogenized surface tension are established. In addition, a characterization of the large-scale limiting behavior of viscosity solutions to non-degenerate and periodic Eikonal equations in half-spaces is given. This is joint work with Riccardo Cristoferi (Radboud University, The Netherlands), Adrian Hagerty (USA), Cristina Popovici (USA), Rustum Choksi (McGill, Canada), Jessica Lin (McGill, Canada), and Raghavendra Venkatraman (NYU, USA).
An internationally respected educator and researcher in applied mathematics; Irene Fonseca is the director of Carnegie Mellon's Center for Nonlinear Analysis (CNA). In recognition for her contributions to the advancement of research in her area of expertise, Irene Fonseca was bestowed a knighthood in the Military Order of St. James (Grande Oficial da Ordem Militar de Santiago da Espada) by the then-President of Portugal, Jorge Sampaio, in 1997. For her teaching and research contributions to Carnegie Mellon University, Irene Fonseca was honored with the Mellon College of Science endowed chair in 2003 and named a University Professor in 2014. In 2012 she was elected President of the Society for Industrial and Applied Mathematics (SIAM), one of the largest organizations dedicated to mathematics and computational science in the world. In 2018 Irene Fonseca was installed as the first Kavčić-Moura University Professor of Mathematics. Irene Fonseca's research program sits at the interface between pure and applied analysis, and is motivated by applications in the physical sciences and engineering. Her recent work is focused on variational techniques as they apply to contemporary problems in materials sciences and computer vision, including the mathematical study of shape memory alloys, ferroelectric and magnetic materials, composites, thin structures, phase transitions, epitaxy, image segmentation, staircasing and recolorization in computer vision.