Combined Defects in Ferroelectric Nematics

Journal of Experimental and Theoretical Physics - A very important and influential idea of the so-called combined topological defects was proposed for the first time in cosmology (see, for example,...     

Steady States of Sheared Active Nematics

A continuum hydrodynamic model has been used to characterize flowing active nematics. The behavior of such a system subjected to a weak steady shear is analyzed. We explore the director structures and flow behaviors of the system in flow-aligning and flow tumbling regimes. Combining asymptotic analysis and numerical simulations, we extend previous studies to give a complete characterization of the steady states for both contractile and extensile particles in flow-aligning and flow-tumbling regimes. Another key prediction of this work is the role of the system size on the steady states of an active nematic system: if the system size is small, the velocity and the director angle files for both flow-tumbling contractile and extensile systems are similar to those of passive nematics; if the system is big, the velocity and the director angle files for flow-aligning contractile systems and tumbling extensile systems are akin to sheared passive cholesterics while they are oscillatory for flow-aligning extensile and tumbling contractile systems.     

Dynamic Charged Structures in Nematics with Negative Anisotropy of Electroconductivity

Journal of Experimental and Theoretical Physics - I would like to express my respect to Dzyaloshinski—co-author Method of Quantum Field Theory in Statistical Physics (Englewood Cliffs:...     

Nematics with quenched disorder: violation of self-averaging

We consider the isotropic-to-nematic transition in liquid crystals confined to aerogel hosts, and assume that the aerogel acts as a random field. We generally find that self-averaging is violated. For a bulk transition that is weakly first order, the violation of self-averaging is so severe that even the correlation length becomes non-self-averaging: no phase transition remains in this case. For a bulk transition that is more strongly first order, the violation of self-averaging is milder, and a phase transition is observed.     

Biaxial liquid-crystal elastomers: A lattice model

We present a simple coarse-grained lattice model for monodomain biaxial liquid-crystal elastomers and perform large-scale Monte Carlo simulations in the proposed model system. Orientational ordering --uniaxial or biaxial-- reflects in sample deformations on cooling the system. The simulation output is used to predict calorimetry data and deuterium magnetic resonance spectra.     

A Super Extension of Heisenberg Hierarchy

A super Heisenberg equation associated with a 3 × 3 matrix spectral problem is proposed take advantage of the zero-curvature equation. Its super bi-Hamiltonian structures are obtained through super trace identity and infinitely many conserved quantities of the super Heisenberg equation are constructed by means of spectral parameter expansions.     

A Super Extension of Kaup-Newell Hierarchy

With the help of the zero-curvature equation and the super trace identity, we derive a super extension of the Kaup-Newell hierarchy associated with a 3 × 3 matrix spectral problem and establish its super bi-Hamiltonian structures. Furthermore, infinite conservation laws of the super Kaup Newell equation are obtained by using spectral parameter expansions.     

A Super Extension of Kaup-Newell Hierarchy

With the help of the zero-curvature equation and the super trace identity, we derive a super extension of the Kaup--Newell hierarchy associated with a 3×3 matrix spectral problem and establish its super bi-Hamiltonian structures. Furthermore, infinite conservation laws of the super Kaup-Newell equation are obtained by using spectral parameter expansions.     

双轴晶体锥形折射扫描研究

对双轴晶体锥形折射效应进行了深入研究 ,选用 KNb O3晶体 ,获得 0～ 2 5°任意锥角的动态锥形折射。研制出一种新型的激光锥形折射扫描器 ,实现全光束大角度锥形折射扫描     

Nematics with quenched disorder: pinning out the origin of memory

Memory effects and glassy behavior have been repeatedly observed in disordered nematic liquid crystals but the connection between these effects and the system topology remained unrevealed. We present an analysis of the local and global topology of the nematic ordering in the presence of quenched disorder and we show that nematics with quenched disorder can be mapped into a system of pinned defect lines and that the memory of the system stems from the pinning of these strings.     

Biaxial Orientation Mechanism of Drawn Natural Rubber. I. Appearance of the Biaxial Orientation

Triple centrifuged natural rubber (NR) film was crystallized at room temperature by uniaxial drawing at draw ratio (λ) 6.0. Morphologies of the induced crystals were studied by wide angle X‐ray diffraction (WAXD). Using a special drawing apparatus for shifting the X‐ray beam positions, crystalline orientation was surveyed all over the drawn sample. WAXD results show the biaxial orientation (BO) with the c‐axis being parallel to the draw direction and the a‐axis parallel to the film surface. By means of the WAXD pattern with the incident beam perpendicular to the film, the drawn NR film was separated into three regions: (200+120) region indicating a low degree of BO, (200) region having a high degree of BO, and the intermediate region in between the above two regions. The degree of BO is enhanced from center to the clamping end depending on the increment of the sample width. At lower draw ratios (4.0<λ<6.0), BO was developed with increasing draw ratio. In the intermediate region, BO increases sharply with a small increment of the width. The degree of BO is lowered at the periphery of the film.     

Biaxial nematic phase in model bent-core systems

We determine the bifurcation phase diagrams with isotropic (I), uniaxial (N(U)) and biaxial (N(B)) nematic phases for model bent-core mesogens using Onsager-type theory. The molecules comprise two or three Gay-Berne interacting ellipsoids of uniaxial and biaxial shape and a transverse central dipole. The Landau point is found to turn into an I-N(B) line for the three-center model with a large dipole moment. For the biaxial ellipsoids, a line of Landau points is observed even in the absence of the dipoles.     

Biaxial surface order dynamics in calamitic nematics

Thermotropic nematic materials relax strong distortions by lowering the nematic order: the uniaxial symmetry is broken and is locally replaced by biaxial domains. We investigated the dynamics of the nematic order near a boundary surface of an asymmetric π-cell submitted to an external electric field, close to the electric order reconstruction threshold. An unexpected phenomenon is observed close, but below the threshold: the biaxial order spreads on the surface inducing a consequent bulk topological behaviour equivalent to the splay-bend fast transition allowed by order reconstruction at higher voltage.     

Biaxial Orientation Mechanism of Drawn Natural Rubber. II. Quantitative Analysis of the Biaxial Orientation

Natural rubber film was prepared from triple centrifuged latex. The film was uniaxially drawn at room temperature and the induced crystalline orientation was quantitatively studied by wide angle X‐ray diffraction. The intensity distribution of 200 and 120 reflections confirmed that the induced crystals have a biaxial orientation with the c‐axis parallel to the draw direction. The orientation of the a‐axis was evaluated by using an orientation function of the (200) plane. The function (F ₂₀₀) indicated that the crystalline a‐axis is parallel to the film surface depending on the draw ratio and on positions in the film. The experimental results are possible to explain by shish‐kebab‐like crystallization developed from a highly oriented fibril. The secondary crystallization grows perpendicularly to the draw direction along the a‐axis. The population of the secondary crystals is controlled by an ellipsoidal free space. The shape of the ellipsoid is changed by the fibril distribution depending on width and thickness of the sample film. In this study, the quantitative biaxial orientation is consistently explained by the shish‐kebab‐like crystallization and the ellipsoidal free space.     

Optical Anisotropy of Biaxial Magnetic Crystals

The two–dimensional orthogonal representation of electromagnetic waves in crystals is developed. Simple expressions determining the directions of optical axes and dependence of group and phase velocities and polarization vectors on the direction, in the general case, of triclinic crystals of magnetic dielectrics are obtained. A solution of the Maxwell equations in the form of two isonormal harmonic waves is found to be directly related to the exponential, two–dimensional spinor, and three–dimensional tensor representations.     

Biaxial nematic phase in bent-core thermotropic mesogens

A biaxial nematic phase had been predicted with D(2h) symmetry, wherein the mesogen's long and short transverse axes are simultaneously aligned along the two orthogonal, primary and secondary directors, n and m, respectively. The unique low-angle x-ray diffraction patterns in the nematic phases exhibited by three rigid bent-core mesogens clearly reveal their biaxiality. The results of x-ray diffraction can be readily reproduced by ab initio calculations that explicitly include the bent-core shape in the form factor and assume short-range positional correlations.     

Biaxial bulge testing of polymeric sheets

The through thickness total strains of hydrostatically bulged domes of materials are usually determined indirectly. The in-plane circumferential strains are readily measured, and then constancy of volume is invoked to determine the “missing” or unknown strain. Some of our recent work with polymers has shown that volume constancy in large-scale deformation does not hold so that the usual computations of stress and strain during bulging of sheet may be in error. We describe an electrical device that reduces such errors by directly measuring the through thickness (and, thus, the thickness “strain”) for nonmetallic materials.     

A Hierarchy of Heuristic-Based Models of Crowd Dynamics

We derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral Individual-Based Model of Ngai et al. (Disaster Med. Public Health Prep. 3:191–195, 2009) where pedestrians are supposed to have constant speeds. This IBM supposes that pedestrians seek the best compromise between navigation towards their target and collisions avoidance. We first propose a kinetic model for the probability distribution function of pedestrians. Then, we derive fluid models and propose three different closure relations. The first two closures assume that the velocity distribution function is either a Dirac delta or a von Mises-Fisher distribution respectively. The third closure results from a hydrodynamic limit associated to a Local Thermodynamical Equilibrium. We develop an analogy between this equilibrium and Nash equilibria in a game theoretic framework. In each case, we discuss the features of the models and their suitability for practical use.     

A Note on the Dispersionless Dym Hierarchy

We discuss the Miura map as well as the Poisson algebras associated with the dispersionless Dym hierarchy. Particularly, we study explicitly the bi-Hamiltonian structure of a truncated Dym system with two variables, in which a new hierarchy flow generated by logarithmic Hamiltonians appears. We then show that this new hierarchy emerges naturally from the topological recursion relation in the Landau–Ginzburg formulation.