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K-State Today

April 21, 2021

Irene Fonseca to present 59th William J. Spencer Lecture

Submitted by Reta McDermott

Irene Fonseca, Kavčić-Moura university professor of mathematics at Carnegie Mellon University, will present the 59th William J. Spencer Lecture titled "Phase Transitions in Heterogeneous Media: Equilibria and Geometric Flows" as part of the Mathematics Department Women Lecture Series in celebration of the 50th anniversary of the Association for Women in Mathematics. The lecture will take place from 2:30-3:20 p.m. Thursday, April 22, via YouTube Live.  

The abstract for the lecture is: 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 homogeneities 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.

The underlying gradient flow provides unconditional convergence results for an Allen-Cahn type bi-stable reaction diffusion equation in a periodic medium. The limiting dynamics are given by an analog for anisotropic mean curvature flow, of the formulation due to Ken Brakke. As an essential ingredient in the analysis, an explicit expression for the effective surface tension, which dictates the limiting anisotropic mean curvature, is obtained.

This work is in collaboration with Riccardo Cristoferi, Radboud University, The Netherlands; Adrian Hagerty; Cristina Popovici; Rustum Choksi, McGill University; Jessica Lin, McGill University; and Raghavendra Venkatraman, Carnegie Mellon University.

The math department is a part of K-State's College of Arts and Sciences. To learn more about opportunities in math at K-State, visit the math department website.

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