Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local C �v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals �D �h � in that it contains terms violating the n → −n symmetry. First we show that these Z 2 -odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.

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We study the equilibrium thermodynamics between two ternary ionic systems in immiscible solvents characterized by different dielectric constants. We consider system geometries wherein the two phases of immiscible solvents occupy, respectively, semi-infinite regions of space separated by neutral and charged planar interfaces. Specifically we analyze the case where the ternary system is composed of a pair of symmetric ions plus a minority charged component of high valence. We describe the system by means of a nonlinear mean-field theory. We first obtain exact analytical solutions for the electrostatic potentials, as well as density profiles for a symmetric binary system, and then extend these results to the ternary case using the perturbation theory. We show that the corresponding adsorption and depletion of multivalent macroions at the interface are highly enhanced when compared with the monovalent case.

In our paper, the elastic constants K 11 and K 12 were calculated using an inconsistent expression for the bulk modulus. The expression for K below Eq. ͑4͒ should read Kϭ 1 3 (K 11 ϩK 12 ) ͓not Kϭ(K 11 ϩ2K 12 )/3]. For a 12% volume-fraction (n ϭ0.23) bcc sample, the correct values of the two elastic constants are K 11 Ϸ16.7 N/m 2 , K 12 ϷϪ2 N/m 2 , while the value of K 44 and the shear modulus range remain unchanged.A new table ͑Table I͒ with correct values of K 11 and K 12 follows.Since the directly measurable shear moduli and bulk moduli are unchanged, the errors in K 11 and K 12 do not affect our conclusions or comparison with experiment.

By mapping the interactions of colloidal particles onto the problem of minimizing areas, the physics of foams can be used to understand the phase diagrams of both charged and fuzzy colloids. We extend this analogy to study the elastic properties of such colloidal crystals and consider the face-centered cubic, body-centered cubic and A15 lattices. We discuss two types of soft interparticle potentials corresponding to charged and fuzzy colloids, respectively, and we analyze the dependence of the elastic constants on density as well as on the parameters of the potential. We show that the bulk moduli of the three lattices are generally quite similar, and that the shear moduli of the two non-close-packed lattices are considerably smaller than in the face-centered cubic lattice. We find that in charged colloids, the elastic constants are the largest at a finite screening length, and we discuss a shear instability of the A15 lattice.