| We study the problem of minimizing the total energy of materials occupying very thin domains or films, in the presence of electromagnetic fields. We consider two types of models: micromagnetic materials and liquid crystals. They are both characterized by a (unit) vector field that describes the internal structure, magnetization in the case of a micromagnetic material, and molecular alignment, in the case of the liquid crystal. The problem consists in minimizing an energy functional with fields subject to the constraint of solving Maxwell's equations in the static case. Goals of the analysis include finding the effective energy functional and the limiting material configurations, as the thickness of the domain approaches zero. We will discuss works by R.D.James G.G.Goia, for micromagnetic materials, and works by Jinhae Park and M.C.Calderer for liquid crystals. This seminar is part of the semester concentration on studies of thin films of materials used in the design of sensor and actuator devices. |