Consider sphere-valued maps which minimize the Dirichlet energy outside a finite number of 3D particles, with appropriate conditions at the particle boundaries. I will present an asymptotic expansion of their energy, as the size of the particles tends to zero. That expansion demonstrates Coulomb-like interactions between the particles. This agrees with a linearized description of liquid crystal suspensions established in the physics literature: our contribution is to precisely estimate the error introduced by that formal linearization argument. This is joint work with L.Bronsard, D.Stantejsky and R.Venkatraman.
Jérémy Heleine, David Lafontaine
