This talk overviews certain asymptotic techniques for models that describe heterogeneous or composite materials. In particular, we focus on high contrast two-phase dispersed composites that are modeled by PDEs with rough coefficients, e.g. the case of highly conducting particles that are distributed in the matrix of finite conductivity. Furthermore, we focus on densely packed composites where particles are almost touching one another. Both scalar and vectorial cases are discussed. The presented asymptotic procedures, which are also rigorously justified, yield discrete models used for capturing and characterizing various blow-up phenomena that occur in dense high contrast materials.
BIO: Yuliya Gorb received her PhD from Pennsylvania State University in 2006 followed by the postdoctoral studies in Texas A&M University in 2006-2009. In 2009, she joined faculty of the Department of Mathematics in the University of Houston (UH). Her research interests include but are not limited to asymptotic analysis and simulation of partial differential equations describing applications that arise in materials science. In 2014 she received NSF CAREER Award for her work on "Multiscale Modeling, Analysis and Simulation for High-Contrast Media''. Dr. Gorb was a faculty sponsor of the UH Association for Women in Math Student Chapter. Until January 2021, Dr. Gorb served as an Associate Editor for SIAM Journal on Applied Mathematics. In Fall 2018 Yuliya joined the Division of Mathematical Sciences in NSF as a rotating program director in Computational Mathematics program, and since Fall 2020 she is a permanent DMS staff member. At the NSF, in addition to the standard Computational Mathematics program’s duties, Yuliya has been a member of the management teams on DMREF, Mathematical Sciences Research Institutes, Quantum Algorithms Challenge, Focused Research Groups in the Mathematical Sciences (FRGMS), and AI/ML/DL venture team.