SOME NOTES ON THE DYNAMICS OF NEMATIC LIQUID-CRYSTALS

The hydrodynamic equations for a nematic liquid crystal involve not on ly the densities of the conserved variables but also director fluctuat ions. Mori's generalized Langevin equation is used to obtain expressio ns for the correlation functions of the hydrodynamic variables and we give the Green-Kubo relations for the transport coefficients. The appr oach is very similar to that used previously by Forster, but there are some differences and these are discussed. Careful consideration is gi ven to what the correct microscopic expression for director fluctuatio ns might be, and to a potential plateau problem that might arise when attempting to calculate transport coefficients associated with directo r fluctuations from computer simulation. Both these topics may be of i nterest to computer simulators. Finally, a brief account is given of m ode-coupling effects in the nematic phase and the possible effects of these on the long time behaviour of several time correlation functions .