Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects.

We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter.

Liquid relaxation: A new Parodi-like relation for nematic liquid crystals.

We put forward a hydrodynamic theory of nematic liquid crystals that includes both anisotropic elasticity and dynamic relaxation. Liquid remodeling is encompassed through a continuous update of the shear-stress free configuration. The low-frequency limit of the dynamical theory reproduces the classical Ericksen-Leslie theory, but it predicts two independent identities between the six Leslie viscosity coefficients.

Anisotropic wave propagation in nematic liquid crystals.

Despite the fact that quantitative experimental data have been available for more than forty years now, nematoacoustics still poses intriguing theoretical and experimental problems. In this paper, we prove that the main observed features of acoustic wave propagation through a nematic liquid crystal cell - namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation - can be explained by properly accounting for two fundamental features of the nematic response: anisotropy and relaxation. The latter concept - new in liquid crystal modelling - provides the first theoretical explanation of the structural relaxation process hypothesised long ago by Mullen and co-workers [Mullen et al.

Axial-symmetry breaking in constrained membranes.

We study the equilibrium shapes of a lipid membrane, attached to a fixed circular substrate. We show how the weakening of the boundary conditions is able to break the axial symmetry of the optimal equilibrium configuration. We derive the critical threshold of the symmetry-breaking transition, and obtain the analytical expression of the free-energy minimizers in the quasi-planar approximation.

Landau-de Gennes theory of isotropic-nematic-smectic liquid crystal transitions.

We propose a Landau-de Gennes variational theory fit to simultaneously describe isotropic, nematic, smectic- A , and smectic- C phases of a liquid crystal. The unified description allows us to deal with systems in which one, or all, of the order parameters develop because of the influence of defects, external fields and/or boundary conditions. We derive the complete phase diagram of the system, that is, we characterize how the homogeneous minimizers depend on the value of the constitutive parameters.

Inclusion-induced boundary layers in lipid vesicles.

The equilibrium shapes of lipid vesicles are perturbed by rigid inclusions. In a two-dimensional vesicle, that may also model a cylindrically elongated tubule, the shape modifications can be determined analytically, and turn out to be significant even far from the inclusion. On the contrary, previous numerical work has given evidence that in the three-dimensional case the shape perturbations decay quite rapidly and are negligible a few inclusion radii away.

Bulk and surface biaxiality in nematic liquid crystals.

Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces.

Nematic membranes: shape instabilities of closed achiral vesicles.

We consider the coupling between the local curvature tensor of a membrane and the local two-dimensional nematic order parameter, deriving it from a quasi-microscopic argument. This coupling makes the nematic director aligned along the lowest curvature eigenvector in a local metric. Local bending of a membrane may then generate nematic ordering.

Telephone-cord instabilities in thin smectic capillaries.

Telephone-cord patterns have been recently observed in smectic liquid-crystal capillaries. We analyze the effects that may induce them. As long as the capillary keeps its linear shape, we show that a nonzero chiral cholesteric pitch favors the Sm-A*-Sm-C* transition.

Curvature effects on membrane-mediated interactions of inclusions.

We study the static, long-range interactions of inclusions embedded in lipid membranes. By using a two-dimensional model, we are able to determine explicitly the closed equilibrium shape of the membrane for any value of the distance between the inclusions; our results show that these shapes cannot be obtained by linearizing the equilibrium equations near a referential shape. Moreover, by computing the membrane-mediated force between the inclusions in given static conditions, we also detect the effects on the interactions due to the curvature and the closed geometry of the membrane.