Active turbulence in active nematics

Dense, active systems show active turbulence, a state characterised by flow fields that are chaotic, with continually changing velocity jets and swirls. Here we review our current understanding of active turbulence. The development is primarily based on the theory and simulations of active liquid crystals, but with accompanying summaries of related literature.     

Isotropic phase of nematics in porous media

We study the effect of random porous matrices on the isotropic-nematic phase transition. Sufficiently close to the cleaning temperature, both random field and thermal fluctuations are important as disordering agents. A novel random field fixed point of the renormalization group equation was found that controls the transition from isotropic to the replica symmetric phase. Explicit evaluation of the exponents in d = 6 ? ε dimensions yields to a dimensional reduction and three-exponent scaling.     

Light transmission at the uniaxial-biaxial lyotropic nematics phase transitions

Results are reported on light transmission versus the temperature near the phase transitions between lyotropic nematics. Strong pretransitional effects are observed when the phase transitions occur between biaxial nematic and uniaxial phases. The light is strongly depolarized both at the calamitic-biaxial and at biaxial-discotic phase transitions. The results are qualitatively explained.     

Interface in nematics

Summary The structures of the interface between an isotropic liquid and a nematic liquid crystal and also between different uniaxial nematic phases are studied. It is shown that, at a planar orientation in the case of the nematic-isotropic liquid interface and also at a mutually orthogonal orientation of the director in the case of two nematic phases, the interface has the structure of a biaxial nematic liquid crystal. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Optical interferometry in phase separated He---He mixture films

We report on interferometric studies of ³He---⁴He liquid mixtures. Anomalous wetting phenomena were observed in phase separated mixture films: the upper ³He-rich phase did not wet the lower ⁴He-rich phase under a small continuous feed of ⁴He atoms to the vapor phase. Instead, under this dynamic situation, floating pools of the ³He-rich phase were stabilized with a contact angle on the order of 10 mrad. In equilibrium, the concentrated ³He-rich phase was found to nucleate uniformly on the free surface, consistent with Antonow's rule.     

Shear-flow-induced transition in nematics

The distortion, induced by a shear flow in a nematic (MBBA) layer having its director initially normal to the velocity and to the velocity gradient, has been observed by a conoscopic technique. At low velocity, the sample retains an ideal planar texture. Above a certain velocity threshold v_c, a distortion is observed. The threshold is inversely proportional to the sample thickness, and can also be modified by a magnetic field. These results are in agreement with a simple calculation based on the Leslie equations.     

Mecanochromatic effect in nematics

We consider a nematic slab, with homeotropic boundary orientations (easy axis z) subjected to two simultaneous perturbations = a uniform shear flow along x and a magnetic field H oriented at 45° in the xz-plane. We find that, in a certain range of H-values, the orientation of the molecules in the mid plane of a thick slab does not correspond to a fixed angle = in this region the director rotates by many turns between the walls and the mid plane. In suitable cases, the periodicity may became comparable to an optical wavelength and the sample may become colored.     

Theory of quantum Hall nematics

Transport measurements on two-dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally ordered, compressible liquid state. We develop and analyze a microscopic theory of such a "quantum Hall nematic" (QHN) phase, predict the existence of a novel, highly anisotropic q(3) density-director mode, find that the T = 0 long-range orientational order is unstable to weak disorder, and compute the tunneling into such a strongly correlated state. This microscopic approach is supported and complemented by a hydrodynamic model of the QHN, which, in the dissipationless limit, reproduces the modes of the microscopic model.     

Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nematic is investigated i) analytically using the tensor order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular. Received 1 October 2002 and Received in final form 12 November 2002 RID="a" ID="a"e-mail: miko@cii.fc.ul.pt     

Novel dynamical effects and persistent memory in phase separated manganites

The time dependent response of the magnetic and transport properties of Fe-doped phase separated (PS) manganite La(0.5)Ca(0.5)MnO3 is reported. The nontrivial coexistence of ferromagnetic (FM) and non-FM regions induces a slow dynamics which leads to time relaxation and cooling rate dependence within the PS regime. This dynamics influences physical properties drastically. On one hand, metalliclike behavior, assumed to be a fingerprint of percolation, can be also observed before the FM phase percolates as a result of dynamical contributions. On the other hand, two novel effects for the manganites are reported, namely, the rejuvenation of the resistivity after aging and a persistent memory of low magnetic fields (<1 T), imprinted in the amount of the FM phase.     

Intergranular giant magnetoresistance in a spontaneously phase separated perovskite oxide

We present small-angle neutron scattering data proving that, on the insulating side of the metal-insulator transition, the doped perovskite cobaltite La(1-x)Sr(x)CoO(3) phase separates into ferromagnetic metallic clusters embedded in a nonferromagnetic matrix. This induces a hysteretic magnetoresistance, with temperature and field dependence characteristic of intergranular giant magnetoresistance (GMR). We argue that this system is a natural analog to the artificial structures fabricated by depositing nanoscale ferromagnetic particles in a metallic or insulating matrix; i.e., this material displays a GMR effect without the deliberate introduction of chemical interfaces.     

Topological defects in spherical nematics

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle. This arises from the high elastic anisotropy of the system in which splay (K1) is far softer than bending (K3). We also introduce and study a lattice nematic model on S2 with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We find a one-parameter family of degenerate ground states in the extreme splay-dominated limit K_{3}/K_{1}-->infinity. Thus the global defect geometry is controllable by tuning the relative splay to bend modulus.     

Excitable patterns in active nematics

We analyze a model of mutually propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations, and the nematic order parameter is allowed to vary in space and time. We show that the interplay between nonuniform nematic order, activity, and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by "bursts" of activity in which the system is elastically distorted and solvent is pumped throughout. At even higher activity, the dynamics becomes chaotic.     

Polarization-universal bandgap in periodically twisted nematics

Cholesteric liquid crystals are known to possess bandgap and exhibit strong reflection for one of two circular polarizations of light. We suggest a periodically twisted nematic liquid crystal as a medium, which possesses bandgap and exhibits strong reflection for any polarization of normally incident light. Two possible structures are considered: a sinusoidal modulation profile and a rectangular modulation profile. In both cases, the maximum bandgap of a periodically twisted structure is approximately twice as narrow as that of cholesterics. However, the polarization properties of these structures may make them more advantageous than cholesterics in a variety of applications.     

Texture rules for concentrated filled nematics

Defect textures in concentrated fiber-filled polygonal networks in nematic liquid crystals are analyzed using differential geometry and computational modeling based on Landau--de Gennes theory. Micron fibers exhibit singular cores of strength -1/2 for odd polygons and escaped cores of strength -(N-2)/2 for even polygons (N: number of sides), in agreement with experiments while simulations predict singular cores of strength -1/2 in submicron fibers. The computed textures satisfy physical and topological stability rules, and the total charge inside each polygon obeys the Poincaré-Brouwer theorem.     

Magnetization and resistivity steps in the phase separated PrCaMn NiO manganites

The low temperature magnetic and transport properties of the Pr_0.5Ca_0.5Mn_1-xNi_xO₃ manganites ( 0≤ x ≤0.1) have been investigated. The presence of Ni hinders the charge and orbital ordering observed in Pr_0.5Ca_0.5MnO₃ and favors the creation of ferromagnetic regions, leading to phase separation. The ferromagnetic fractions induced by the Ni substitution have been estimated from magnetization measurements, they are large and reach 40% for 4% of Ni. Steps are observed in the M ( H ) and ρ( H ) curves of all the samples at T < 5 K. They are similar to the steps observed in Pr_0.5Ca_0.5Mn_1-xM_xO₃, where M is a non magnetic cation (Mg²⁺, Ga³⁺,...), and for which the ferromagnetic fractions are very small (less than 2%), however, their appearance is restricted to lower temperatures (T < 5 K) with Ni dopant than with non magnetic cations. This study shows that steps can be observed in a wide range of phase-separated systems, even when the ferromagnetic fraction is very large. Received 5 April 2002 / Received in final form 8 July 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: antoine.maignan@ismra.fr     

Magnetocaloric effect in phase separated manganite probed by differential thermal analysis

Differential thermal analysis is used to measure the temperature change (ΔT) due to the application of an external magnetic field in a manganite with phase separation. The temperature dependence of ΔT is compared with the expected from magnetization measurements. A phenomenological model for the enthalpy change is used to obtain ΔT during the metamagnetic transition.