Graduate Student Seminar- A two-species interacting system

Date and Time: Tuesday, February 22, 1-2pm

Place: Zoom
Zoom link:https://gwu-edu.zoom.us/j/92957649236?pwd=YmZIYytSUVVwcU1RdjZHYkNFak10U…

Speaker:  Guanning Zhang, GWU

Title: A two-species interacting system

Abstract: A two-species interacting system, motivated by the triblock copolymers theory, is studied on a flat torus, the quotient space of the complex plane by a lattice. The free energy of the system, which contains both short-range and long-range interactions, admits disc-disc-like stationary points. The relative displacement of the disc centers in a stationary point is related to Green’s function of the Laplace operator on the flat torus. When restricted to disc-disc configurations with relative displacements equal to half periods, the free energy is minimized with respect to the lattice and its half periods. The resulting optimal lattice depends on a single parameter. As this parameter varies, the optimal lattice may be rectangular, square, rhombic, or hexagonal. This is in sharp contrast to single-species systems where optimal lattices are always hexagonal.