Ginzburg–Landau model of a liquid crystal with random inclusions
Leonid V. Berlyand, E. Ya. Khruslov · Journal of Mathematical Physics · 2005
We consider a Ginzburg–Landau three-dimensional functional with a surface energy term to model a nematic liquid crystal with inclusions. The locations and radii of the inclusions are randomly distributed and described by a set of finite dimensional distribution functions. We show that the presence of inclusions can be accounted for by an effective potential. Our main objectives are (a) to derive the sufficient conditions on the distribution functions such that the solutions converge in probability to a solution of a homogenized deterministic problem and (b) to compute the effective potential.