Asymmetry of the time dynamics of breathers in the electroconvection twist structure of a nematic

Dynamics of breather defects in the periodic structures of rolls arising at electroconvection in nematic liquid crystals twisted by π/2 has been studied experimentally and theoretically. The axial components of the velocity of a hydrodynamic flow in the twist structures of nematics are opposite in the neighboring rolls. Dynamics of the breather defect is the periodic creation and annihilation of a pair of classical dislocations with the topological indices “+1” and “-1.” The annihilation occurs faster than the creation. It has been shown that the asymmetric time dynamics of the breather defect is described well by the solution of the perturbed sine-Gordon equation in the form of an interacting soliton and antisoliton.     

Breathers in the one-dimensional roll structure of twisted nematics

The dynamics of nonsingular defects has been studied experimentally and theoretically in the periodic roll structures arising at electroconvection in nematic liquid crystals twisted by π/2. The presence of an axial component of the velocity of the hydrodynamic flow with the opposite direction in the neighboring rolls is characteristic of roll structures in twisted nematics. The quantitative estimates of the critical frequency of the oscillations of structural defects have been obtained on the basis of the nonlinear equation of motion for the roll displacement. It has been found that the periodic creation and annihilation of a pair of edge dislocations with the topological indices +1 and −1 occur in the process of oscillations of a defect with a nonsingular nucleus. It has been demonstrated that oscillating defects with zero topological indices correspond to the solution of the sine-Gordon equation in the form of standing breathers.     

Anisotropy of the oscillation dynamics of a breather on a trap in the electroconvective twist structure of a nematic

The oscillation dynamics of dislocations with a dissociated nucleus in the electroconvective twist structure of a nematic liquid crystal has been studied. The initial state of the roll twist structure is unstable. One of the origins of this is the helical flows of the nematic in the neighboring rolls with the antiparallel axial velocity components. As a result, oscillating or “breathing” defects are formed, which have the properties of breathers and are described by the sine-Gordon equation. It has been demonstrated that the space-time anisotropy of the character of motion of the dislocations in opposite directions orthogonal to the roll structure takes place in such a nonstationary system.     

Structure and dynamics of the Frenkel-Kontorova dislocations in electroconvection in liquid crystals

The Frenkel-Kontorova instability is studied in a 1D lattice of domains formed during electroconvection in nematic liquid crystals twisted by π/2. It is found that generation of defects by such instability can be observed in this model medium. Among other things, it is shown that several types of defects with singular and nonsingular cores, as well as with a extended core, are formed in the 1D domain structure above the electroconvective instability threshold. The extended cores of dislocations are dissociated into a line, and the entire structure is isomorphic to two partial dislocations spaced by a certain distance, which are not observed in free form. Defects with a nonsingular core (zero topological index) exist owing to spiral hydrodynamic flows in convective rolls and are not observed in layers with a homogeneous orientation of molecules. It is shown that the formation of both types of defects follows the scenario of decay of dislocations with extended cores via detachment of nonsingular defects (i.e., discretely); as a result, a dislocation with a singular core is left. “Breather” defects, which are the result of periodic creation and annihilation of dislocations with a topological index of ±1, are also observed. The effect of defects on the transition from the 1D to 2D structures is considered.     

Diffusive fluxes associated with interfacial defeet motion and interaction

The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless.Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.     

Equilibrium configurations and energetics of point defects in two-dimensional colloidal crystals

We demonstrate a novel method of introducing point defects (mono- and divacancies) in a confined monolayer colloidal crystal by manipulating individual particles with optical tweezers. Digital video microscopy is used to study defect dynamics in real space and time. We verify the numerical predictions that the stable configurations of the defects have reduced symmetry compared to the triangular lattice and discover that in addition they are characterized by distinct topological arrangements of the particles in the defect core. Surprisingly, point defects are thermally excited into separated dislocations, from which we extract the dislocation pair potential.     

Tunable optical vortex arrays from a single nematic topological defect

We report on the generation of tunable structured light fields endowed with various sets of phase singularities from a single topological defect in a nematic liquid crystal mesophase. The experimental demonstration relies on the use of electric field-induced nonsingular topological defects called "umbilics."     

Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers

We use Langmuir-Blodgett molecular monolayers and nematic liquid crystals as model two- and three-dimensional orientationally ordered systems to study the stability and healing of topological defects at their contact interfaces. Integer-strength defects at the monolayer induce disclinations of similar strength in the nematic that, however, do not propagate deep into the bulk, but rather form single- or double-split arch-shaped loops pinned to the interface. This behavior is qualitatively independent of the far-field director orientation and involves either half-integer singular or twist-escaped unity-strength nonsingular nematic disclinations. These two defect configurations can be selected by varying sample preparation given their comparable free energy, consistently with direct probing by use of laser tweezers.     

Influence of the phonon viscosity and dislocation interaction on the glide of a pair of edge dislocations in a crystal with point defects

The motion of a pair of edge dislocations in an elastic field of point defects is investigated taking into account the interaction of dislocations both with each other and with the phonon subsystem of the crystal. It is demonstrated that the retarding force is a nonmonotonic function of the velocity of dislocation glide with two extrema displayed under certain conditions.     

Disclinations in the nematic phase of a magnet with spin 1

Two-dimensional topological defects, spin disclinations, exist for a magnet with spin 1 and strong biquadratic interaction, in which the spin nematic state is realized. The spin disclinations have a nonsingular macroscopic core with a saturated magnetic moment and destroyed nematic order. These singular lines have common features with disclinations in nematic liquid crystals, singular disclinations in antiferromagnets, and magnetic vortices. However, significant differences of their properties from the above-mentioned topological defects also exist. The dynamic properties of a disclination in the spin nematic are characterized by the “freezing in the condensate” and by the gyroscopic force.     

Influence of collective effects on the dynamic behavior of a single edge dislocation in a crystal with point defects

The glide of a single edge dislocation in an elastic field of point defects randomly distributed over a crystal is investigated taking into account the influence of the phonon subsystem of the crystal. The force of retardation of the dislocation motion is calculated, and the velocities at which this force has a local maximum and a local minimum are determined. A comparative analysis of the glide of a single dislocation and the glide of a pair of edge dislocations is performed.     

The interaction of a screw dislocation with point defects in bcc iron

In this study, we calculate the interaction energy of intrinsic point defects vacancies and interstitials) with screw dislocations in body-centered cubic iron. First (we calculate the dipole tensor of a defect in the bulk crystal using molecular statics. Using a formulation based on linear elasticity theory, we calculate the interaction energy of the defect and the dislocation using both isotropic and anisotropic strain fields. Second, we perform atomistic calculations using molecular statics methods to directly calculate the interaction energy. Results from these two methods are compared. We verify that continuum methods alone are unable to correctly predict the interactions of defects and dislocations near the core. Although anisotropic theory agrees qualitatively with atomistics far from the core, it cannot predict which dumbbell orientations are stable and any continuum calculations must be used with caution. Spontaneous absorption by the core of both vacancies and dumbbells is seen. This paper demonstrates and discusses the differences between continuum and atomistic calculations of interaction energy between a dislocation core and a point defect.     

Nucleation of Topological Dipoles¶in Nematic Liquid Crystals

A topological dipole is a pair of point defects with opposite topological charges. In this paper we show by example how the nucleation of such a dipole within a smooth field can drive a metastable state into a stable one. Building on our previous work, we construct a mathematical model for the dynamics of both monopoles and dipoles in a capillary filled with a nematic liquid crystal. Though our analysis is fit for liquid crystals, a similar mechanism is also likely to apply to the field theory for other ordered media. Received: 10 July 1997 / Accepted: 25 June 1998     

相反拓扑指数的Laguerre-Gaussian模的产生和模间相互作用的实验研究

实验研究了带有相反拓扑指数的Laguerre-Gaussian(LG)模间的相互作用，发现含有相反拓扑指数的两个LG模在传播过程中其光场发生变化，观察到随着传播距离的增加，两个LG模的中心位相奇点会逐渐连成为一个弧形暗线形状.实验上验证了带有相反拓扑指数的光学涡流中的螺旋位错在传播过程中会演变为边位错这一理论结果.     

Brownian motion in crystals with topological defects

The diffusion behaviour of a Brownian particle in a crystal with randomly distributed topological defects is analyzed by means of the continuum theory of defects combined with the theory of diffusion on manifolds. A path-integral representation of the diffusion process is used for the calculation of cumulants of the particle position averaged over a defect ensemble. For a random distribution of disclinations the problem of Brownian motion reduces to a known random-drift problem. Depending on the properties of the disclination ensemble, this yields various types of subdiffusional behaviour. In a random array of parallel screw dislocations one finds a normal, but anisotropic, diffusion behaviour of the mean-square displacement. Moreover, the process turns out to be non-Gaussian, and reveals long-time tails in the higher-order cumulants.Dedicated to Professor Herbert Wagner on the occasion of his 60th birthday     

带有相反拓扑指数的光学涡流间相互作用研究

对线性介质中光学涡流间相互作用做了数值分析，发现当拓扑指数相反时，含有涡流对的光场产生了类似于对称破缺的不稳定性，螺旋位错在传播过程中演变为一种新的位错——边位错，作用过程中拓扑指数守恒. 关键词： 光学涡流 拓扑指数 位错     

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     

Chevron patterns and defect lattices in an anisotropic model for electroconvection

Chevron patterns and defect lattices are unique patterns found in the electrohydrodynamic convection of nematic liquid crystals. We study numerically the stability and bifurcations of the chevron patterns and the limit-cycle oscillation of defect lattices using a two-dimensional anisotropic model equation. Simplified one dimensional models are derived by truncating Fourier modes from the two-dimensional model to qualitatively understand the chevron patterns and the defect lattices. The pattern formation and the dynamical behaviors in the one-dimensional models are compared with the numerical simulations of the two-dimensional model.     

Soliton-like molecular deformations in a nematic liquid crystal film

We study the nature of molecular deformations in a nematic liquid crystal film with elastic energy under homeotropic boundary conditions. The deformation in terms of splay, twist and bend fields of the director axis is found to be governed by the completely integrable Davey-Stewartson-I (DS-I) equation in (2+1) dimensions. Using the line soliton and breather solutions of the DS-I equation, the director axis is constructed, the components of which exhibit damped spatial oscillations. However, the splay and bend fields of the director axis exhibit localized structures of deformation.