Energies of -valued harmonic maps on polyhedra with tangent boundary conditions
Equilibrium confocal textures in a smetic-A cell
We study the textures of smectic-A liquid crystals consisting in curved, but stricdy equidistant lamellae. Assuming translational symmetry, we can generate them from a single curve. The free energy is a non-trivial functional of it. We learn how to derive the equilibrium equation for this curve, when the texture is confined between two parallel plates, which exert a weak anchoring on the orientation of the lamellae, but do not interfere direcdy with their position. Finally, we describe an instability...
Examples of condition for diffusions in a random environment.
Expansion for the Lyapunov exponent of the one-dimensional Anderson model at low disorder.