Drastic facilitation of the onset of global chaos in a periodically driven Hamiltonian system due to an extremum in the dependence of eigenfrequency on energy

The Chirikov resonance-overlap criterion predicts the onset of global chaos if nonlinear resonances overlap in energy, which is conventionally assumed to require a non-small magnitude of perturbation. We show that, for a time-periodic perturbation, the onset of global chaos may occur at unusually {\it small} magnitudes of perturbation if the unperturbed system possesses more than one separatrix. The relevant scenario is the combination of the overlap in the phase space between resonances of the same order and their overlap in energy with chaotic layers associated with separatrices of the unperturbed system. One of the most important manifestations of this effect is a drastic increase of the energy range involved into the unbounded chaotic transport in spatially periodic system driven by a rather {\it weak} time-periodic force, provided the driving frequency approaches the extremal eigenfrequency or its harmonics. We develop the asymptotic theory and verify it in simulations.Comment: 5 pages, 4 figures, LaTeX, to appear PR

Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media

We demonstrate that two-dimensional two-component bright solitons of an annular shape, carrying vorticities $(m,\pm m)$ in the components, may be stable in media with the cubic-quintic nonlinearity, including the \textit{hidden-vorticity} (HV) solitons of the type $(m,-m)$, whose net vorticity is zero. Stability regions for the vortices of both $(m,\pm m)$ types are identified for $m=1$, 2, and 3, by dint of the calculation of stability eigenvalues, and in direct simulations. A novel feature found in the study of the HV solitons is that their stability intervals never reach the (cutoff) point at which the bright vortex carries over into a dark one, hence dark HV solitons can never be stable, contrarily to the bright ones. In addition to the well-known symmetry-breaking (\textit{external}) instability, which splits the ring soliton into a set of fragments flying away in tangential directions, we report two new scenarios of the development of weak instabilities specific to the HV solitons. One features \textit{charge flipping}, with the two components exchanging the angular momentum and periodically reversing the sign of their spins. The composite soliton does not split in this case, therefore we identify such instability as an \textit{intrinsic} one. Eventually, the soliton splits, as weak radiation loss drives it across the border of the ordinary strong (external) instability. Another scenario proceeds through separation of the vortex cores in the two components, each individual core moving toward the outer edge of the annular soliton. After expulsion of the cores, there remains a zero-vorticity breather with persistent internal vibrations.Comment: 10 pages, 11 figure

Enhancement of Noise-induced Escape through the Existence of a Chaotic Saddle

We study the noise-induced escape process in a prototype dissipative nonequilibrium system, the Ikeda map. In the presence of a chaotic saddle embedded in the basin of attraction of the metastable state, we find the novel phenomenon of a strong enhancement of noise-induced escape. This result is established by employing the theory of quasipotentials. Our finding is of general validity and should be experimentally observable.Comment: 4 page

LC nanocomposites: induced optical singularities, managed nano/micro structure, and electrical conductivity

Microstructure, phase transitions, electrical conductivity, and optical and electrooptical properties of multiwalled carbon nanotubes (NTs), dispersed in the cholesteric liquid crystal (cholesteryl oleyl carbonate, COC), nematic 5CB and their mixtures, were studied in the temperature range between 255 K and 363 K. The relative concentration X=COC/(COC+5CB)was varied within 0.0-1.0. The concentration $C_p$ of NTs was varied within 0.01-5% wt. The value of X affected agglomeration and stability of NTs inside COC+5CB. High-quality dispersion, exfoliation, and stabilization of the NTs were observed in COC solvent ("good" solvent). From the other side, the aggregation of NTs was very pronounced in nematic 5CB solvent ("bad" solvent). The dispersing quality of solvent influenced the percolation concentration $C_p$, corresponding to transition between the low conductive and high conductive states: e.g., percolation was observed at $C_p=1$ and $C_p=0.1$ for pure COC and 5CB, respectively. The effects of thermal pre-history on the heating-cooling hysteretic behavior of electrical conductivity were studied. The mechanism of dispersion of NTs in COC+5CB mixtures is discussed. Utilization of the mixtures of "good" and "bad" solvents allowed fine regulation of the dispersion, stability and electrical conductivity of LC+NTs composites. The mixtures of COC and 5CB were found to be promising for application as functional media with controllable useful chiral and electrophysical properties.Comment: 10 pages, 9 figure

Polarization resolved angular patterns in nematic liquid crystal cells

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analyzing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the $4\times 4$ matrix formalism and the orthogonality relations are used to derive the analytical expressions for the transmission and reflection matrices. The polarization resolved angular patterns in the two-dimensional projection plane are characterized in terms of the polarization singularities: C points (points of circular polarization) and L lines (lines of linear polarization). In the case of linearly polarized plane waves incident on the homeotropically aligned cell, we present the results of detailed theoretical analysis describing the structure of the polarization singularities. We apply the theory to compute the polarization patterns for various orientational structures in the NLC cell and discuss the effects induced by the director orientation and biaxiality.Comment: pdflatex, rextex4, 22 pages, 7 figures (jpeg

A polyphonic acoustic vortex and its complementary chords

Using an annular phased array of eight loudspeakers, we generate sound beams that simultaneously contain phase singularities at a number of different frequencies. These frequencies correspond to different musical notes and the singularities can be set to overlap along the beam axis, creating a polyphonic acoustic vortex. Perturbing the drive amplitudes of the speakers means that the singularities no longer overlap, each note being nulled at a slightly different lateral position, where the volume of the other notes is now nonzero. The remaining notes form a tri-note chord. We contrast this acoustic phenomenon to the optical case where the perturbation of a white light vortex leads to a spectral spatial distribution

Observation of discrete vortex solitons in optically-induced photonic lattices

We report on the frst experimental observation of discrete vortex solitons in two-dimensional optically-induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium and study the generation of the discrete vortices from a broad class of singular beams.Comment: 4pages, 5 colour figures. to appear in PR

Supersonic optical tunnels for Bose-Einstein condensates

We propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a hollow laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilise up to 9 vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of the optical vortex can be made supersonic by inserting a laser-generated hump potential. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons. Finally, we discuss prospects of using these solitons for analogue gravity experiments.Comment: 14 pages, 3 figures, published versio

Directed transient long-range transport in a slowly driven Hamiltonian system of interacting particles

We study the Hamiltonian dynamics of a one-dimensional chain of linearly coupled particles in a spatially periodic potential which is subjected to a time-periodic mono-frequency external field. The average over time and space of the related force vanishes and hence, the system is effectively without bias which excludes any ratchet effect. We pay special attention to the escape of the entire chain when initially all of its units are distributed in a potential well. Moreover for an escaping chain we explore the possibility of the successive generation of a directed flow based on large accelerations. We find that for adiabatic slope-modulations due to the ac-field transient long-range transport dynamics arises whose direction is governed by the initial phase of the modulation. Most strikingly, that for the driven many particle Hamiltonian system directed collective motion is observed provides evidence for the existence of families of transporting invariant tori confining orbits in ballistic channels in the high dimensional phase spaces