Type-I and type-II smectic-C^{*} systems: A twist on the electroclinic critical point.

We conduct an in-depth analysis of the electroclinic effect in chiral, ferroelectric liquid crystal systems that have a first-order smectic-A^{*}-smectic-C^{*} (Sm-A^{*}-Sm-C^{*}) transition, and show that such systems can be either type I or type II. In temperature-field parameter space type-I systems exhibit a macroscopically achiral (in which the Sm-C_{M}^{*} helical superstructure is expelled) low-tilt (LT) Sm-C_{U}^{*}-high-tilt (HT) Sm-C_{U}^{*} critical point, which terminates a LT Sm-C_{U}^{*}-HT Sm-^{*}C_{U} first-order boundary. Notationally, Sm-C_{M}^{*} or Sm-C_{U}^{*} denotes the Sm-C^{*} phase with or without a modulated superstructure.

Modeling the field control of the surface electroclinic effect near continuous and first-order smectic-A* to smectic-C* transitions.

We present and analyze a model for the combination of bulk and surface electroclinic effects in the smectic-A* (Sm-A*) phase near a Sm-A*-Sm-C* transition. As part of our analysis we calculate the dependence of the surface tilt on external electric field and show that it can be eliminated, or even reversed from its zero-field value, as demonstrated in previous experimental work on a system (W415) with a continuous Sm-A*-Sm-C* transition. We also analyze, for the first time, the combination of bulk and surface electroclinic effects in systems with a first-order Sm-A*-Sm-C* transition.

Critical behavior of a noncritical field: destruction of smectic order at the smectic A-C tricritical point and implications for de Vries behavior.

Critical behavior near the smectic A-C tricritical point is studied using renormalization group techniques. Critical fluctuations induce a singular softening of the smectic bulk modulus in the A phase. At the tricritical point, the quasi-long-range positional order of the smectic layers is destroyed.

Biaxial smectic-A* phase and its possible misidentification as a smectic-Cα* phase.

The biaxial smectic-A* (Sm-A(B)*) phase, appearing in the phase sequence Sm-A*-Sm-A(B)*-Sm-C*, is analyzed using Landau theory. It is found to possess a helical superstructure with a pitch that is significantly shorter than the pitch of the Sm-C* helical superstructure. The Sm-A(B)*-Sm-C* transition can be either first or second order, and correspondingly there will be either a jump or continuous variation in the pitch.

Surface electroclinic effect near the first-order smectic-A*-smectic-C* transition.

We analyze the surface electroclinic effect (SECE) in a material that exhibits a first-order bulk smectic-A* (Sm-A*)-smectic-C* (Sm-C*) transition. The effect of a continuously varying degree of enantiomeric excess on the SECE is also investigated. We show that due to the first-order nature of the bulk Sm-A*-Sm-C* transition, the SECE can be unusually strong and that as enantiomeric excess is varied, a jump in surface induced tilt is expected.

de Vries behavior of the electroclinic effect in the smectic-A* phase near a biaxiality-induced smectic-A*-smectic-C* tricritical point.

Using a generalized Landau theory involving orientational, layering, tilt, and biaxial order parameters we analyze the smectic-A* and smectic-C* (Sm-A*-Sm-C*) transitions, showing that a combination of small orientational order and large layering order leads to Sm-A*-Sm-C* transitions that are either continuous and close to tricriticality or first order. The model predicts that in such systems the increase in birefringence upon entry to the Sm-C* phase will be especially rapid. It also predicts that the change in layer spacing at the Sm-A*-Sm-C* transition will be proportional to the orientational order.

de Vries behavior in smectic liquid crystals near a biaxiality-induced smectic- A-smectic-C tricritical point.

We show that a generalized Landau theory for the smectic-A-smectic-C (Sm- A -Sm- C ) phases exhibits a biaxiality induced Sm- A -Sm- C tricritical point. Proximity to this tricritical point depends on the degree of orientational order in the system; for sufficiently large orientational order the Sm-A-Sm-C transition is three-dimensional XY -like, while for sufficiently small orientational order, it is either tricritical or first order. We investigate each of the three types of Sm-A-Sm-C transitions near tricriticality and show that for each type of transition, small orientational order implies de Vries behavior in the layer spacing, an unusually small layer contraction.

Disordering to order: de Vries behavior from a Landau theory for smectic phases.

We show that Landau theory for the isotropic (I), nematic (N), smectic-A, and smectic-C phases generically, but not ubiquitously, implies "de Vries" behavior: i.e., a continuous A-C transition can occur with little layer contraction while the birefringence increases significantly once the system moves into the C phase.

Pattern stabilization through parameter alternation in a nonlinear optical system.

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment.

Hydrodynamics of polar liquid crystals.

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local C infinity v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D infinity h) in that it contains terms violating the n --> -n symmetry. First we show that these Z2-odd terms induce a general splay instability of a uniform polarized state in a range of parameters.

Driven depinning of strongly disordered media and anisotropic mean-field limits.

Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the drive and slip along at least one of the directions transverse to the motion. In the limit of infinite-range elastic and viscous coupling this model has a tricritical point separating a region where the depinning is continuous, in the universality class of elastic depinning, from a region where depinning is hysteretic. Many of the collective transport models discussed in the literature are special cases of the generic model.