Whispering gallery like modes along pinned vortices

We study sound propagation in stationary and locally irrotational vortex flows where the circulation is wound around a long (rotating) cylinder, using Unruh’s formalism of acoustic space-times. Apart from the usual scattering solutions, we find anomalous modes which are bound to the vicinity of the cylinder and propagate along its axis—similar to whispering gallery modes. These modes exist for subsonic and supersonic flow velocities. In the supersonic case (corresponding to an effective ergoregion in the acoustic space-time), they can even have zero frequency ω = 0 and thus the associated quasiparticles with E = ?ω = 0 are easy to excite from an energetic point of view. Hence they should be relevant for the question of stability or instability of this setup.     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

Solitons pinned to hot spots

We generalize a recently proposed model based on the cubic complex Ginzburg-Landau (CGL) equation, which gives rise to stable dissipative solitons supported by localized gain applied at a “hot spot” (HS), in the presence of the linear loss in the bulk. We introduce a model with the Kerr nonlinearity concentrated at the HS, together with the local gain and, possibly, with the local nonlinear loss. The model, which may be implemented in laser cavities based on planar waveguides, gives rise to exact solutions for pinned dissipative solitons. In the case when the HS does not include the localized nonlinear loss, numerical tests demonstrate that these solitons are stable/unstable if the localized nonlinearity is self-defocusing/focusing. Another new setting considered in this work is a pair of two symmetric HSs. We find exact asymmetric solutions for it, although they are unstable. Numerical simulations demonstrate that stable modes supported by the HS pair tend to be symmetric. An unexpected conclusion is that the interaction between breathers pinned to two broad HSs, which are the only stable modes in isolation in that case, transforms them into a static symmetric mode.     

Dissipative dynamics of superfluid vortices at nonzero temperatures

We consider the evolution and dissipation of vortex rings in a condensate at nonzero temperatures in the context of the classical field approximation, based on the defocusing nonlinear Schr?dinger equation. The temperature in such a system is fully determined by the total number density and the number density of the condensate. The collisions with noncondensed particles reduce the radius of a vortex ring until it completely disappears. We obtain a universal decay law for a vortex line length and relate it to mutual friction coefficients in the fundamental equation of vortex motion in superfluids.     

Self-focusing dynamics of polarization vortices in Kerr media

We investigate numerically and experimentally the spatial collapse dynamics and polarization stability of radially and azimuthally polarized vortex beams in pure Kerr medium. These beams are unstable to azimuthal modulation instabilities and break up into distinct collapsing filaments. The polarization of the filaments is primarily linear with weak circular components at the filaments' boundaries. This unique hybrid linear-circular polarization collapse pattern persists to advanced stages of collapse and appears to be a general feature of beams with spatially variant linear polarization.     

Lattice gas dynamics: application to driven vortices in two dimensional superconductors

A continuous time Monte Carlo lattice gas dynamics is developed to model driven steady states of vortices in two dimensional superconducting networks. Dramatic differences are found when compared to a simpler Metropolis dynamics. Subtle finite size effects are found at low temperature, with a moving smectic that becomes unstable to an anisotropic liquid on sufficiently large length scales.     

Extreme wave formation in unidirectional sea due to stochastic wave phase dynamics

The authors consider a stochastic model based on the interaction and phase coupling amongst wave components that are modified envelope soliton solutions to the nonlinear Schrödinger equation. A probabilistic study is carried out and the resulting findings are compared with ocean wave field observations and laboratory experimental results. The wave height probability distribution obtained from the model is found to match well with prior data in the large wave height region. From the eigenvalue spectrum obtained through the Inverse Scattering Transform, it is revealed that the deep-water wave groups move at a speed different from the linear group speed, which justifies the inclusion of phase correction to the envelope solitary wave components. It is determined that phase synchronization amongst elementary solitary wave components can be critical for the formation of extreme waves in unidirectional sea states.     

Semiclassical dynamics of vortices in 2D easy-plane ferromagnets

Semiclassical dynamics of magnetic vortices in 2D lattice models of easy-plane ferromagnets is investigated. It is shown that the low-energy part of the spectrum of vortices treated as quantum excitations of the system exhibits a nontrivial structure. The simplest spectrum is observed for standard magnetic vortices, in which magnetization at long distances from the center of a vortex is parallel to the basal plane. In this case, the spectrum has a band structure consisting of several nonintersecting bands, whose number is determined only by the value of atomic spin S and lattice symmetry. For purely 2D magnets with a single spin per unit cell, the number of bands is S or 2S for integral and half-integral values of spin S, respectively. For a lattice with the basis with an even number 2n of spins per unit cell, the number of bands is 2nS for any spins. The situation radically changes for vortices in the cone state as compared to standard vortices, for which the magnetization at a long distance from the center of a vortex rotates in the easy plane of the magnet. Vortices in the cone state are formed under the action of a constant external field perpendicular to the easy plane of the magnet. As a rule, the spectrum for such vortices is not a standard band spectrum and forms a set such that a forbidden energy value can be found in any small neighborhood of an allowed value, and vice versa. The possibility of an oscillatory motion of a vortex under the action of a constant external force is indicated (analog of Bloch oscillations of electrons in crystals). Possible realization of these effects in other ordered media with vortices is considered.     

Growth of taylor vortices: A molecular dynamics study

Molecular dynamics methods have been used in a quantitative study of the growth and decay of Taylor vortices in a fluid confined between concentric cylinders when the rotation of the inner cylinder is instantaneously started or stopped. Analysis of the temporal evolution of the vortex flow fields shows that the behavior of this microscopic system agrees with experiment. In order to make the analysis entirely self-contained, torque measurements have been used to determine the effective viscosity of the fluid.     

Chaotic dynamics of superconductor vortices in the plastic phase

We present numerical simulation results of driven vortex lattices in the presence of random disorder at zero temperature. We show that the plastic dynamics is readily understood in the framework of chaos theory. Intermittency "routes to chaos" have been clearly identified, and positive Lyapunov exponents and broadband noise, both characteristic of chaos, are found to coincide with the differential resistance peak. Furthermore, the fractal dimension of the strange attractor reveals that the chaotic dynamics of vortices is low dimensional.     

Nonlinear trans-resonant waves,vortices and patterns: From microresonators to the early Universe

Perturbed wave equations are considered. Approximate general solutions of these equations are constructed, which describe wave phenomena in different physical and chemical systems. Analogies between surface waves, nonlinear and atom optics, field theories and acoustics of the early Universe can be seen in the similarities between the general solutions that govern each system. With the help of the general solutions and boundary conditions and/or resonant conditions we have derived the basic highly nonlinear ordinary differential equation or the basic algebraic equation for traveling waves. Then, approximate analytic resonant solutions are constructed, which describe the trans-resonant transformation of harmonic waves into traveling shock-, jet-, or mushroom-like waves. The mushroom-like waves can evolve into cloud-like and vortex-like structures. The motion and oscillations of these waves and structures can be very complex. Under parametric excitation these waves can vary their velocity, stop, and change the direction of their motion. Different dynamic patterns are yielded by these resonant traveling waves in the x-t and x-y planes. They simulate many patterns observed in liquid layers, optical systems, superconductors, Bose-Einstein condensates, micro- and electron resonators. The harmonic excitation may be compressed and transformed inside the resonant band into traveling or standing particle-like waves. The area of application of these solutions and results may possibly vary from the generation of nuclear particles, acoustical turbulence, and catastrophic seismic waves to the formation of galaxies and the Universe. In particular, the formation of galaxies and galaxy clusters may be connected with nonlinear and resonant phenomena in the early Universe. (c) 2001 American Institute of Physics.     

Nonlinear dynamics of smectics-C

An effective action which makes it possible to take into account dynamic fluctuation effects in smectics-C is constructed. The effects associated with displacements of smectic layers are the most important. The influence of these fluctuations on the dynamics of the director is studied. The corresponding terms in the effective action are constructed and their renormalization is found. The renormalization spectrum of the director mode is obtained.     

Semiclassical dynamics of electron wave packet states with phase vortices

We consider semiclassical higher-order wave packet solutions of the Schr?dinger equation with phase vortices. The vortex line is aligned with the propagation direction, and the wave packet carries a well-defined orbital angular momentum (OAM) variant Planck's over 2pil (l is the vortex strength) along its main linear momentum. The probability current coils around the momentum in such OAM states of electrons. In an electric field, these states evolve like massless particles with spin l. The magnetic-monopole Berry curvature appears in momentum space, which results in a spin-orbit-type interaction and a Berry/Magnus transverse force acting on the wave packet. This brings about the OAM Hall effect. In a magnetic field, there is a Zeeman interaction, which, can lead to more complicated dynamics.     

Decay of MHD-scale Kelvin-Helmholtz vortices mediated by parasitic electron dynamics

We have simulated nonlinear development of MHD-scale Kelvin-Helmholtz (KH) vortices by a two-dimensional two-fluid system including finite electron inertial effects. In the presence of moderate density jump across a shear layer, in striking contrast to MHD results, MHD KH vortices are found to decay by the time one eddy turnover is completed. The decay is mediated by smaller vortices that appear within the parent vortex and stays effective even when the shear layer width is made larger. It is shown that the smaller vortices are basically of MHD nature while the seeding for these is achieved by the electron inertial effect. Application of the results to the magnetotail boundary layer is discussed.     

Gyroscopic dynamics of antiferromagnetic vortices in the orthoferrite domain wall

The method of generation of antiferromagnetic vortices on the supersound domain wall in the orthoferrites was proposed. Moving antiferromagnetic vortices were accompanied by the solitary deflection waves. These waves were used for investigation of generation and nonlinear dynamics of the antiferromagnetic vortices on a moving domain wall with the help of two- and three-fold digital high-speed photography and Faraday rotation in the orthoferrites plates cut perpendicular to the optical axis. The full velocity of antiferromagnetic vortex nonlinearly increases and saturates on the spin velocity level c. The vortices with smallest topological charges saturate earlier than with big one. The vortices velocity along the domain wall u increases up to the maximum and goes to the dependence u²+v²=c². Vortex dynamics is quasirelativistic on quasirelativistic domain wall. The theory of gyroscopic force in the domain wall of orthoferrites was elaborated by Zvezdin et al. and was confirmed our earlier experimental results.