Dynamics of fluctuations below a stationary bifurcation to electroconvection in the planar nematic liquid crystal N4

Control of Coherent Light through Microperiodic Director Modulation in Nematic Films under Low-Voltage DC Electric Field

This work addresses the achievement of efficient control of laser light transmission through stationary microperiodic parallel stripe textures formed in films of nematic liquid crystals (NLCs) in planar-oriented cells upon a direct-current (DC) electric field. By varying the field intensity and, thereby, the field-induced periodic modulation of the nematic director and hence the complex transmittance function corresponding to the longitudinal domain texture induced in NLC films with initial planar alignment, the intensity of a linearly polarized laser beam passed through the films can be well controlled. In 25 µm-thick films of room-temperature NLCs pentylcyanobiphenyl (5CB), this results in a low-voltage (~4 V) sharp and deep V-shaped behavior of their electro-optically controlled transmittance. Such a reversible electro-optical effect is interesting for active control of laser beam intensity and other applications. The relevant physical mechanism is analyzed and explained.

Spatiotemporal chaos in electroconvection of a homeotropically aligned nematic liquid crystal

We present patterns of electroconvection (EC) for the homeotropically aligned nematic liquid crystal MBBA. A voltage V = square root of 2V0 sin(2pift) was applied. With increasing V0, the bend Freedericksz transition at VF was followed by the onset of EC at Vc > VF. We found four distinct pattern types. First, a primary supercritical Hopf bifurcation to traveling waves (TW's) of convection rolls occurred. The structure factor S(k) of this state reflected the azimuthal anisotropy of the underlying Freedericksz state. For f < fL approximately 75 Hz there was a superposition of two oblique-roll modes (pattern I). These patterns were chaotic in space and time. For larger f the patterns consisted of chaotic TW normal rolls (pattern II). Here the chaos was attributable to the motion of dislocations and domain walls between left- and right-traveling waves. A secondary bifurcation yielded pattern III; it had no dominant TW frequency but had broadband chaotic dynamics dominated by the motion of dislocations. This pattern type had been referred to by others as a "chevron pattern;" its structure factor still revealed azimuthal anisotropy. Finally, at somewhat larger identical with epsilon = V2/Vc2 -1 a highly disordered pattern IV with defect dynamics was found. This state had been studied before by Kai and co-workers and was referred to by them as "phase turbulence." It had a structure factor that was (within our resolution) invariant under rotation. For patterns I, II, and III, S(k) contained crescent-shaped peaks. The peak shape was qualitatively different from the case of planar EC where the structure factor has an elliptical cross section. We present measurements of the widths 1/xik and 1/xitheta in the radial (k) and the azimuthal (theta) directions. For small epsilon (patterns I and II) we found that xik was consistent with the usual Ginzburg-Landau scaling xik approximately epsilon(-nuk) with nuk approximately 1/2. However, for xitheta we found xitheta approximately epsilon(-nutheta) with nutheta approximately 3/4. Presumably this anomalous scaling of xitheta is associated with the Goldstone mode of homeotropic EC. We also show data for the height S0 of the structure factor that are consistent with S0 approximately epsilonbeta with beta approximately -0.5, implying that S0 diverges at onset. This differs from the case of domain chaos in rotating Rayleigh-Bénard convection where experiment is consistent with beta = 1/2 and thus with a vanishing S0. The difference between the shape of the structure-factor cross section and between the exponents, for the present case, for planar EC, and for domain chaos suggests that there are different universality classes for spatiotemporal chaos.

Amplitude modulation and relaxation-oscillation of counterpropagating rolls within a broken-symmetry laser-induced electroconvection strip

We report a liquid-crystal pattern-formation experiment in which we break the lateral (translational) symmetry of a nematic medium with a laser-induced thermal gradient. The work is motivated by an improved measurement (reported here) of the temperature dependence of the electroconvection threshold voltage in planar-nematic 4-methoxybenzylidene-4-butylaniline. In contrast with other broken-symmetry-pattern studies that report a uniform drift, we observe a strip of counterpropagating rolls that collide at a sink point, and a strong temporally periodic amplitude modulation within a width of 3-4 rolls about the sink point. The time dependence of the amplitude at a fixed position is periodic but displays a nonsinusoidal relaxation-oscillation profile. After reporting experimental results based on spacetime contours and wave number profiles, along with a measurement of the change in the drift frequency with applied voltage at a fixed control parameter, we propose some potential guidelines for a theoretical model based on saddle-point solutions for Eckhaus-unstable states and coupled complex Ginzburg-Landau equations.

Small-number statistics near the clustering transition in a compartmentalized granular gas

Statistical fluctuations are observed to profoundly influence the clustering behavior of granular material in a vibrated system consisting of two connected compartments. When the number of particles N is sufficiently large ( N approximately 300 is sufficient), the clustering follows the lines of a standard second-order phase transition and a mean-field description works. For smaller N , however, the enhanced influence of statistical fluctuations breaks the mean-field behavior. We quantitatively describe the competition between fluctuations and mean-field behavior (as a function of N ) using a dynamical flux model and molecular dynamics simulations.