Vortex rings and plasma toroidal vortices in homogeneous infinite media. III. Diffusion anisotropy effect in vortices

The effect of diffusion anisotropy of material particles in toroidal vortices (TVs) is experimentally studied in plasma TVs in air, in vortex rings in air and water. The essence of this effect consists in the fact that diffusion coefficients of material particles in TVs in the direction perpendicular to the rotation axis D _⊥ are much lower than in the direction parallel to this axis D _‖. The coefficient D _⊥ is determined for propane molecules in air TVs, and the dependence of the coefficient D _⊥ of ink particles in water TVs on the rotation angular velocity ω is studied. It is shown that the coefficient D _⊥ can decrease with increasing ω by a factor of 10–25 in comparison with the coefficient D _‖.     

Vortex rings and plasma toroidal vortices in homogeneous unbounded media. II. The study of vortex formation process

The conditions of the formation of toroidal vortices (TVs), i.e., the plasma TV and air vortex ring at atmospheric pressure, are experimentally determined. The TV formation process is numerically simulated. Local characteristics of the pulsed jet, induced flow of ambient medium (air), and forming TV at various time points are obtained. It is shown that the results of the preliminary numerical calculation are in agreement with experimental data.     

Vortex ring energy variation in a homogeneous medium

The equation of energy variation of vortex rings (free toroidal vortices) in a homogeneous medium (air and water at atmospheric pressure and temperature ～293 K) depending on their initial parameters and medium was derived. It was shown that the solution to this equation is in agreement with experimental data.     

Control of vortices by homogeneous fields in asymmetric ferroelectric and ferromagnetic rings

Effective Hamiltonians have been used (i) to demonstrate that the shape asymmetry of ferromagnetic rings is essential to the recently discovered switching of the chirality of their vortices by homogeneous magnetic fields, via a transition into onion states; (ii) to reveal that an electric vortex can also be controlled by a homogeneous electric field in asymmetric ferroelectric nanorings, via the formation of antiferrotoroidic pair states rather than onion states; and (iii) to provide the fundamental reason that allows such control, namely, two new interaction energies involving a vector characterizing the asymmetry, the applied field, and the toroidal moment.     

Chaotic capture of vortices by a moving body. I. The single point vortex case

The study of the dynamical properties of vortex systems is an important and topical research area, and is becoming of ever increasing usefulness to a variety of physical applications. In this paper, we present a study of a model of a rotational singularity which obeys a logarithmic potential interacting with a bluff body in a uniform inviscid laminar flow, e.g., a line vortex interacting with a cylinder in three dimensions or a point vortex with a circular boundary in two dimensions. We show that this system is Hamiltonian and simple enough to be solved analytically for the stagnation points and separatrices of the flow, and a bifurcation diagram for the relevant parameters and classification of the various types of motion is given. We also show that, by introducing a periodic perturbation to the body, chaotic motion of the vortex can be readily generated, and we present analytic criteria for the generation of chaos using the Poincare-Melnikov-Arnold method. This leads to an important dynamical effect for the model, i.e., that the possibility exists for the vortex to be chaotically captured around the body for periods of time which are extremely sensitive to initial conditions. The basic mechanism for this capture is due to the chaotic dynamics and is similar to that of other chaotic scattering phenomena. We show numerically that cases exist where the vortex can be captured around an elliptic point external to (and possibly far from) the body, and the existence of other very complicated motions are also demonstrated. Finally, generalizations of the problem of the vortex-body interaction are indicated, and some possible applications are postulated such as the interaction of line vortices with aircraft wings.     

Pulsed axisymmetric ejection of a dense plasma into a gas. 2. Conditions for the formation and stability of a plasma toroidal vortex

This work continues our previous investigations on pulsed ejection of a dense plasma into a gas. The conditions for the formation of high-temperature (plasma) and low-temperature gaseous toroidal vortices during pulsed axisymmetric ejection of a dense plasma/gas into air are investigated experimentally at different parameters of the ambient medium and jet generator. Quantitative criteria for the formation and stable propagation of such vortices are established using experimental data.     

The Neumann solution of the multiple scattering problem in a plane-parallel medium—I. The infinite medium

This paper deals with the study of the radiation field arising from a plane distribution of isotropic sources in a plane-parallel, infinite medium. The classical Neumann method is used together with the theory of singular integrals of the Cauchy type. The main advantage of this technique is that is available for a general treatment of radiative transfer problems in semi-infinite and finite spaces.     

On the evolution and gravitational collapse of a toroidal vortex

The evolution and collapse of a gaseous toroidal vortex under the action of self-gravitation are considered using the Hamiltonian mechanics approach. It is shown that evolution occurs in three main stages separated by characteristic time scales. First, a compression along the small radius to a quasi-equilibrium state takes place, followed by a slower compression along the large radius to a more stable compact vortex object. In the latter stage, the possibility of effective scattering and ejection of particles along the vortex axis (jet formation) is detected.As a result, mass, energy, and momentum losses take place, and the vortex collapses.     

Diffusion anisotropy in a toroidal (ring) vortex in water

Diffusion of paint (ink) particles in a toroidal (ring) vortex in a density-homogeneous liquid (water) was experimentally studied. Particle diffusion anisotropy in rotating water of the vortex was detected. The effect consists in the fact that the particle diffusivity in the direction perpendicular to the rotation axis of the torus core is much lower than that in the direction parallel to the rotation axis.     

On vortices and rings in extended Abelian models

A numerical search for straight superconducting vortices in a U(1) model with a Ginzburg-Landau potential containing a cubic term is presented. Such vortices exist in a small numerically determined region. The reasons of their existence in that narrow region of the parameter space, as well as of their instability in the rest of the parameter space, are explained. Then, the results of a numerical search for axially symmetric solitons in a U(1)×U(1) model with higher derivative terms, which is based on [C.G. Doudoulakis, Physica D 228 (2007) 159], are presented and discussed.     

Pinning of pancake vortices in a three-dimensional Josephson medium and structure of the vortex lattice in the “critical” state

A system of pancake vortices formed near the boundary of a sample in a monotonically increasing external magnetic field is calculated with allowance for pinning due to the cellular structure of the medium for various values of the pinning parameter I, which is proportional to the critical current of the junction and the cell diameter. The shortest distance from the outermost vortex to the nearest neighbor is proportional to I ⁻¹¹. It is shown that the pinning parameter has a critical value I _c separating two regimes with different types of critical states. For I<I _c the external magnetic field has a threshold value H _t(I), above which the field immediately penetrates the interior of the junction to an infinite distance. For I>I _c the magnetic field decays linearly from the boundary into the interior of the junction. The value obtained in the study, I _c=3.369, differs from the value of 0.9716 postulated by other authors. The dependence of the slope of the magnetic field profile near the boundary on I is determined. It is shown that the slope is independent of I in intervals 2πk<I<2πk+π. Fiz. Tverd. Tela (St. Petersburg) 39, 1958–1963 (November 1997)     

On the appearance of a convective toroidal vortex in Lake Baikal

Warm natural gas floating up from the bottom of Lake Baikal causes convection in the water column in the form of a toroidal body of revolution—toroidal vortex. The giant convection, several kilometers in size, arises once the Rayleigh number achieves a critical value (1000–2000). A linear relationship is found between the depth of a water pond and the size of the toroidal body.     

Line vortices in a three-dimensional ordered Josephson medium

Two equilibrium configurations of a line vortex in a three-dimensional ordered Josephson medium are considered: (i) the vortex core is at the center of a cell and (ii) the vortex core is on a contact. Infinite systems of equations describing these configurations are derived. In going to a finite system, the currents far away from the center are neglected. A new technique for solving the finite system of equations is suggested. It does not require smallness of phase discontinuities at all vortex cells and, therefore, can be applied for any values of pinning parameter I down to zero. The structures and energies of both equilibrium states for isolated line vortices are calculated for any I from the range considered. For I >0.3, a vortex can be thought of as fitting a square of 5×5 cells. For lower I, the vortex energy can be expressed as a sum of the energies of the small discrete core and the quasi-continuous outside. The core energy is comparable to the energy of the outside and is a major contributor to the vortex energy when I is not too small. For any I, the energy of the vortex centered on the contact is higher than the energy of the configuration centered at the center of the cell.     

Vortex rings and lieb modes in a cylindrical Bose-Einstein condensate

We present a calculation of a solitary wave propagating along a cylindrical Bose-Einstein trap. For sufficiently strong couplings of experimental interest, it is found to be a hybrid of a one-dimensional (1D) soliton and a three-dimensional vortex ring. The calculated energy-momentum dispersion exhibits characteristics similar to those of a mode proposed sometime ago by Lieb within a 1D model, as well as some rotonlike features.     

Cyclotron scattering with mode switching in plasma on degenerate stars I. Radiative relaxation in a homogeneous rarefied plasma

Population balance equations for the Landau levels in a non-relativistic rarefied plasma are written for arbitrary polarization of cyclotron modes. Self-consistent evolution of the transverse distribution of electrons interacting, by virtue of the cyclotron processes, with an isotropic radiation at frequencies near the first harmonic of the electron gyrofrequency is studied. The spectrum of the relaxation times of the system is found for a fixed radiation intensity. It is shown that the time of cyclotron relaxation under the action of the first-harmonic radiation with broad angular and frequency spectra is entirely determined by the rate of spontaneous processes and does not depend on the radiation intensity. Cyclotron radiation transfer coefficients which account for the process of mode switching at the first harmonic are obtained. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 11, pp. 1035–1053, November, 1999.     

Time evolution of an infinite number of vortices in a strip

We study the time evolution of a system of vortices in a strip in the thermodynamic limit. We prove the existence and the uniqueness of the solution of the equation of motion for a regularized version of the usual vortex dynamics. We extend this result to a system of particles interacting in one dimension via a long-range potential.Partially supported by the Italian C.N.R.