  Properties of disordered nematic elastomers and gels are theoretically
investigated with emphasis on the roles of non-local elastic interactions and
crosslinking conditions. Networks originally crosslinked in the isotropic phase
lose their long-range orientational order by the action of quenched random
stresses, which we incorporate into the affine-deformation model of nematic
rubber elasticity. We present a detailed picture of mechanical quasi-Goldstone
modes, which accounts for an almost completely soft polydomain-monodomain (P-M)
transition under strain as well as a ``four-leaf clover'' pattern in
depolarized light scattering intensity. Dynamical relaxation of the domain
structure is studied using a simple model. The peak wavenumber of the structure
factor obeys a power-law-type slow kinetics and goes to zero in true mechanical
equilibrium. The effect of quenched disorder on director fluctuation in the
monodomain state is analyzed. The random frozen contribution to the fluctuation
amplitude dominates the thermal one, at long wavelengths and near the P-M
transition threshold. We also study networks obtained by crosslinking
polydomain nematic polymer melts. The memory of initial director configuration
acts as correlated and strong quenched disorder, which renders the P-M
transition non-soft. The spatial distribution of the elastic free energy is
strongly dehomogenized by external strain, in contrast to the case of
isotropically crosslinked networks.
