A statistical study for evolving arrays of nematic point defects

We study the dynamics of nematic point defects within a capillary tube enforcing homeotropic anchoring on the lateral boundary. At the initial time a great many of them, with topological charges alternating in sign, may be created at random along the axis of the cylinder; they then evolve, subject to their mutual interactions, and eventually reach an equilibrium configuration, possibly after having suffered many annihilations. Here we see how the arrays of surviving defects depend on both the length of the tube and the number of initial defects. We arrive at the equilibrium distribution of the distance between defects by solving the appropriate evolution equations over many simulations. The information we thus obtain on the average spacing could be tested experimentally.