Mathematics Seminar - 04/17/26

Abstract:

The Cahn-Hilliard (CH) equation is a classical model for phase separation, with many variations to account for different physical properties and mechanisms. In this talk we will discuss properties of the minimizers for Cahn-Hilliard type energies under strong anchoring conditions (i.e., the Dirichlet condition) on the boundary of an underlying bounded domain. We concentrate on three cases: (1) the classical CH energy with a symmetric quartic double well potential, which is convenient for analysis and numerical simulation; (2) the de Gennes-Cahn-Hilliard energy, which includes additional singularity that produces gradient flow models that  may more closely approximate surface diffusion than others in the limit when the thickness of the transition layer approaches zero; (3) the CH energy with the Flory-Huggins potential that is physically more realistic. In all three cases we reveal bifurcation phenomena mediated by the boundary condition, the thickness of the transition layer, and other factors such as the temperature of the system. 

Note:

Contact Prof. Shantia Yarahmadian at syarahmadian@math.msstate.edu or (662) 325-7143 for additional information.