Event № 300
Advisor: Nir Gavish
Abstract: The non-local Cahn-Hilliard (Ohta-Kawasaki) equation manifests spatio-temporal behaviors driven by competing short-range forces and long-range Coulombic interactions. These models
are often being employed to study di-block copolymers, and for renewable energy applications that are based on complex nano-materials, such as ionic liquids and polyelectrolyte membranes. Asymmetric properties between different materials, e.g, phase-dependent permittivity and tilted free energy potential, are included in extended Ohta-Kawasaki model.
Using perturbation methods and numerical continuation methods, we study the distinct solution families of Ohta-Kawasaki equations. Specifically, we focus on spatially localized states in 1-space dimensions, and show that in gradient coupled parabolic and elliptic PDEs (phase separation coupled to electrostatics), 1D homoclinic snaking appears as not-slanted and describe the dependence of localized stripes vs. hexagons, on the domain size.