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K-State Today

January 24, 2017

Mathematics Colloquium Lecture Jan. 24

Submitted by Reta McDermott

Shibin Dai, New Mexico State University, will present "Degenerate Diffusion in Phase Separations" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Tuesday, Jan. 24, in 122 Cardwell Hall.

The abstract for the lecture is: The Cahn-Hilliard equation is a widely used phenomenological diffuse-interface model for the simulations of phase separation and microstructure evolution in binary systems. We consider a popular form of the equation with a smooth double-well potential, and with phase-dependent diffusion mobilities. The latter is a feature of many materials systems and makes both theoretical analysis and accurate numerical simulations challenging. In this talk, we discuss three aspects of the equation:

1. Theoretical predictions on the coarsening dynamics based on asymptotic analysis.
2. Numerical simulations that confirm the theoretical predictions.
3. The existence of weak solutions that potentially accommodate the features predicted by asymptotic analysis and exhibited in numerical simulations.