Breatherlike defects and their dynamics in the one-dimensional roll structure of twisted nematics

The dynamics of the nonsingular defects in the periodic structures of the rolls that appear in π/2-twisted nematic liquid crystals during electroconvection is studied experimentally and theoretically. The roll structures in twisted nematics are characterized by the presence of an axial component of the hydrodynamic flow velocity with opposite directions in neighboring rolls. The critical oscillation frequency of structural defects is quantitatively estimated using a nonlinear equation of motion for roll displacements. It is found that a pair of edge dislocations with topological charges of +1 and–1 nucleates and annihilates periodically during the oscillations of a defect with a nonsingular core. Oscillating defects with a zero topological charge is shown to correspond to the solution of the sine-Gordon equation in the form of standing breathers. Asymmetry is detected in the full oscillation cycle of a breather defect, and it is related to the twist symmetry of a twist nematic. This asymmetry is taken into account as effective anisotropic friction. The behavior of a breather on a trap, namely, a classical defect (dislocation), is investigated. Dislocation motion is shown to be anisotropic in the oscillation cycle: in one direction, a dislocation moves regularly; in the second phase, the transition into the initial state proceeds via the decay of the breather into a dipole pair of dislocations of opposite signs followed by their annihilation.     

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.     

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.     

Specific features of structural defects in twisted nematic liquid crystals under conditions of electrohydrodynamic instability

The influence of inhomogeneous boundary conditions (director orientation) on the specific features of the formation and evolution of structural defects in 90·-twisted nematic liquid crystals (twisted structures) is investigated in the regime of electrohydrodynamic instability. It is found that, unlike the domain structure of nematic liquid crystals with a planar orientation, in which defects with topological indices of ±1 are formed under conditions of electrohydrodynamic instability, the domain structure of twisted nematic liquid crystals contains both the above defects and defects with a topological index of 0. It is shown that structural defects with a topological index of 0 are stable and that the existence of these defects is associated with the axial velocity u_a of nematic liquid-crystal flow in the domains.     

Structure of connections of single-walled carbon nanotubes with the use of the combined 5–7 and 4–8 topological defects

The structures of zigzag-zigzag, armchair-zigzag, zigzag-chiral, armchair-armchair, armchair-chiral, and chiral-chiral pair connections produced by single-walled carbon nanotubes 1.5–5.0 diameter with the use of the combined 5–7 and 4–8 topological defects have been calculated by molecular mechanics methods. It has been established that the use of the combined 5–7 topological defect makes it possible to produce connections between pairs of single-walled carbon nanotubes with any conductivities, chiralities, and diameters, whereas the use of the combined 4–8 topological defect provides a means for forming connections between nanotubes only with the same type of conductivity. The angles between the axes of nanotubes connected by the combined 5–7 and 4–8 topological defects lie in the ranges 145°–180° and 112°–178°, respectively. It has been revealed that there are correlations between structural parameters of the connections and the relative arrangement of the simple topological defects in the combined topological defects.     

Topological defects in incommensurate magnetic and crystal structures and quasi-periodic solutions of the elliptic sine-Gordon equation

Vortex-type singular solutions with a topological charge of the elliptic sine-Gordon equation have been studied. One- and two-dimensional vortex lattices on a homogeneous and periodic background are constructed in the explicit form using the Bäcklund transformation. The interaction of vortices is investigated and finite energy configurations are found. On the basis of the obtained results new topological defects in incommensurate magnetic and crystal structures are predicted and described. The interaction of vortex magnetic structures with nonlinear spin waves is considered.     

Aharonov-Bohm effect for plasmons in a finite-width quantum ring

The magnetoplasma oscillation frequencies of the 2D electrons in a quantum ring have been found taking into account the finite width of the ring in the model allowing for an exact solution for the single-particle spectrum. It is shown that instead of the periodic oscillations of the plasmon frequency ω typical of the 1D ring, ω in the case under consideration depends on the magnetic flux with the frequency and amplitude modulations: the period of oscillations as a function of the magnetic flux and their amplitude depend on the magnetic field strength.     

Behavior of inclusions with different value and orientation of topological dipoles in ferroelectric smectic films

Cholesteric droplets in ferroelectric free-standing films with tunable anchoring on the droplet boundary are investigated. A droplet and satellite topological defect(s) form a topological dipole. We obtained droplets with different angles α between two radial lines from the droplet center to −1/2 topological defects. Droplets with parallel dipoles form linear chains in which the interparticle distances decrease with increasing the defect angle α. For the first time, the dependence of the interparticle distance on the angle between topological defects was measured. We can adjust the magnitude and orientation of topological dipoles formed by the droplets. For the first time, the droplets with antiparallel topological dipoles were prepared in a smectic film. Interaction of the droplets with parallel and antiparallel dipoles differs drastically. Formation of antiparallel dipoles leads to a decomposition of the droplet pairs and chains of droplets. Our observations may be used to change the magnitude, anisotropy of the interparticle interaction, and structures of inclusions in liquid crystal media. The article is published in the original.     

Möbius strips and twisted ribbons in intersecting Gauss-Laguerre beams

Circularly polarized, intersecting Gauss-Laguerre beams are shown to give rise to a rich array of unusual polarization structures whose properties can be tuned by varying the angle between the beams. These structures include Möbius strips with arbitrarily large, odd numbers of half twists, twisted ribbons with arbitrarily large, even numbers of half twists, and coronets (crowns). Six topological/geometrical indices are used to characterize these structures. Analytical expressions are given for some indices; others, which still present a considerable theoretical challenge, are treated numerically and illustrated graphically. It is argued that the polarization structures described here are, or soon will be, amenable to experiment.     

Topological optical Bloch oscillations in a deformed slab waveguide

Spatial Bloch oscillations of light waves of purely topological origin are theoretically shown to exist in weakly deformed slab waveguides. As the optical rays trapped in the deformed waveguide can roll freely, wave diffraction is strongly affected by the topology of the deformed surface, which can be tailored to simulate the effect of a tilted periodic refractive index.     

Routes to chaos and mode-locking in interferometers with nematic film inserts

The influence of time-dependent periodic optical drive in the Fabry-Perot interferometer system has been investigated using a theoretical model equation. A variety of features such as different routes to chaos, multiperiodic oscillations, coexistence of multiple attractors and mode-locking with devil’s staircase are found to occur for a certain range of parametric values.     

Magnetoresistance oscillations due to Zener tunneling and microwave radiation in a 2D electron gas in GaAs quantum well with AlAs/GaAs superlattices barriers

The effect of microwave radiation in the frequency range from 1.2 to 10 GHz on the magnetoresistance of a high-mobility two-dimensional electron gas has been studied in a GaAs quantum well with AlAs/GaAs superlattice barriers. It has been found that the microwave field induces magnetoresistance oscillations periodic in the reciprocal magnetic field (1/B). It has been shown that the period of these oscillations in the covered frequency range depends on the microwave radiation power.     

Diffusion and relaxation of the fractional order in fractal media in the classical and quantum cases

Two model examples of the application of fractional calculus are considered. The Riemann–Liouville fractional derivative with 0 < α ≤ 1 was used. The solution of a fractional equation, which describes anomalous relaxation and diffusion in an isotropic fractal space, has been obtained in the form of the product of a Fox function by a Mittag-Leffler function. The solution is simpler than that given in Ref. 6 and it generalizes the result reported in Ref. 7. For the quantum case, a solution of the generalized Neumann–Kolmogorov fractional quantum-statistical equation has been obtained for an incomplete statistical operator which describes the random walk of a quantum spin particle, retarded in traps over a fractal space. The solution contains contributions from quantum Mittag-Leffler (nonharmonic) fractional oscillations, anomalous relaxation, noise fractional oscillations, and exponential fractional diffusion oscillation damping.     

Development of stochastic oscillations in a one-dimensional dynamical system described by the Korteweg-de Vries equation

The behavior of the solution of the Korteweg-de Vries equation for large-scale oscillating periodic initial conditions prescribed on the entire x axis is considered. It is shown that the structure of small-scale oscillations arising in a Korteweg-de Vries system as t→∞ loses its dynamical properties as a consequence of phase mixing. This process can be called the generation of soliton turbulence. The infinite system of interacting solitons with random phases developing under these conditions leads to oscillations having a stochastic character. Such a system can be described using the terms applied to a continuous random process, the probability density and correlation function. It is shown that for this it suffices to determine from the prescribed initial conditions amplitude distribution function of the solitons and their mean spatial density. The limiting stochastic characteristics of the mixed state for problems with initial data in the form of an infinite sequence of isolated small-scale pulses are found. Also, the problem of stochastic mixing under arbitrary initial conditions in the dispersionless limit (the Hopf equation) is completely solved. Zh. éksp. Teor. Fiz. 115, 333–360 (January 1999)     

Development of the method of electron-optical in situ monitoring for periodic structures

A series of the basic problems for the development of the method of electron-optical in situ monitoring for periodic structures are considered in this work. In particular, the problem of submicron- and nanosized inhomogeneity online monitoring in large areas of tested microelectronic structures with a typical size of the order of 100 μm is discussed to give individual inhomogeneities in detail. The Riccati equation method has been proposed to solve the problem.     

Breather states and compound solitons in a ferromagnet-insulator-metal structure

Nonlinear dynamic states with a fine internal structure, such as breathers, “breather lattices,” kinks, kink-antikink bound states, and their spatially periodic generalizations have been constructed in terms of a modified Korteweg-de Vries equation for a system of magnetostatic waves in a ferromagnet-insulator-metal structure. Specific features of the nucleation, interaction, and transformation of these states have been studied in layered magnetic structures.     

Stochastic resonance in a nonequilibrium electron-hole plasma

A photogenerated electron-hole plasma, heated in the process of Auger recombination, is studied. It is shown that in the plasma near the threshold for the appearance of uniform relaxational self-excited oscillations, weak noise transforms into a stochastic sequence of large-amplitude spikes. An additional optical periodic signal with amplitude approximately five times smaller than the noise variance, depending on the form of this signal, transforms these stochastic oscillations into low-amplitude quasiharmonic oscillations or into periodic spike self-excited oscillations of enormous amplitude. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 7, 422–427 (10 October 1999)     

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."