Tailored nematic and magnetization profiles on two-dimensional polygons

We study dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional polygons. These systems are described by order parameter and spontaneous magnetization, the absence any external fields. stable states terms critical points an appropriately defined free energy, with nemato-magnetic coupling energy. numerically interplay between shape regular polygon, size strength for multistability this prototype system. Our notable results include (1) coexistence domain walls interior boundary defects, (2) suppression positive coupling, (3) enhancement negative coupling.