Nonsingular Vortices Research Articles

Lévy stable distributions for velocity and velocity difference in systems of vortex elements

The probability density functions (PDFs) of the velocity and the velocity difference field induced by a distribution of a large number of discrete vortex elements are investigated numerically and analytically. Tails of PDFs of the velocity and velocity difference induced by a single vortex element are found. Treating velocities induced by different vortex elements as independent random variables, PDFs of the velocity and velocity difference induced by all vortex elements are found using limit distribution theorems for stable distributions. Our results generalize and extend the analysis by Takayasu [Prog. Theor. Phys. 72, 471 (1984)]. In particular, we are able to treat general distributions of vorticity, and obtain results for velocity differences and velocity derivatives of arbitrary order. The PDF for velocity differences of a system of singular vortex elements is shown to be Cauchy in the case of small separation r, both in 2 and 3 dimensions. A similar type of analysis is also applied to non-singular vortex blobs. We perform numerical simulations of the system of vortex elements in two dimensions, and find that the results compare favorably with the theory based on the independence assumption. These results are related to the experimental and numerical measurements of velocity and velocity difference statistics in the literature. In particular, the appearance of the Cauchy distribution for the velocity difference can be used to explain the experimental observations of Tong and Goldburg [Phys. Lett. A 127, 147 (1988); Phys. Rev. A 37, 2125, (1988); Phys. Fluids 31, 2841 (1988)] for turbulent flows. In addition, for intermediate values of the separation distance, near exponential tails are found.

Topology in superfluid3He: Recent results

We discuss: the topological phase transition in nonsingular vortices in3He-A; vortices in3He-B and solitons terminating on strings; topological defects of the A-B interface: the interaction of continuous A-phase vortices with singular B-phase vortices across the interface; extended degeneracy and topology of Larmor precession; and internal topology in thin3He-A film, responsible for chiral edge states of fermions and QHE.

What happens with the doubly quantized vortex in 3He-A at the A2 → A1 phase transition

Abstract The decay of the nonsingular double quantized vortex in 3He-A into a pair of Mermin-Ho vortex textures in the immediate vicinity of the transition to the A1 phase is investigated theoretically.

Rotating superfluid 3He

The significance of the order parameter is reviewed for the familiar case of vortices in the rotating Bose superfluid 4He. The triplet p-wave Cooper pairing in the Fermi superfluid 3He introduces new and unusual possibilities. In the rotating B phase, all vortices have singular cores, and several different structures have been investigated. In the rotating A phase, an additional feature is a nonsingular vortex with two quanta of circulation.

Magnetic textural deformation in rotating3He-A

An axial magnetic field is shown to deform the type I lattice of nonsingular vortices in rotating3He-A. At a critical field of orderH D (≈30 G), this texture becomes unstable with respect to an array of doubly quantized vortices, seen in experiments at 284 G.

NMR spectroscopy of rotating superfluid3He (Soviet-Finnish Project ROTA Research)

Experimental and theoretical studies of the properties of superfluid phases of rotating liquid 3He are reviewed. The observational data on nonsingular vortex textures in the rotating A phase as well as experiments revealing a structural transition inside the cores of vortices in the A phase are discussed. The gyromagnetic effect in the rotating B phase, due to the spontaneous magnetization of the vortex cores, is described

Vortex lattice structure of superfluid3He-A in a magnetic field

A study is made of the lattice constructed from nonsingular vortices in superfluid3He-A in a strong magnetic field. In the presence of a magnetic field the vortex texture loses axial symmetry, and the ľ vector outside the vortex core is nearly uniform and is directed perpendicular to the rotation axis. It is shown that the vortex lattice is spontaneously distorted and its energy depends on the orientation of the unit cell relative to the direction of the uniform ľ vector outside the core. It is also shown that the orientation of the lattice changes when the tilting angle of the magnetic field from the rotation axis is changed. The optimum orientation angle of the distorted vortex lattice is calculated as a function of the tilting angle.

Evidence for nonsingular vorticity in the Helsinki experiments on rotating3He-A

A theory for the satellite peak in the NMR spectrum of rotating superfluid3He-A is presented. Absorption at the frequency of the satellite is produced by spin waves localized on vortex lines. The peak frequency and total intensity of the satellite are calculated for both singular and nonsingular vortices; a comparison with the Helsinki NMR data strongly suggests that nonsingular vorticity was actually observed in the experiments.

Structure and Interaction of Nonsingular Spin Vortices in Quasi Two-Dimensional Superfluid 3He-A

Because of the tensor character of the order parameter, many kinds of textures are possible to appear in superfluid 3He, and many authors have investigated them. In this paper we consider the A phase and study a two-dimensional localized structure in which only the spin space vector varies. Such a structure is very simple and is likely to be experimentally manageable as well. The order parameter is given byl),2)

Orbital motions in 3He-A

Orbital motions in /sup 3/He-A in very low magnetic field and driven by heat flow are studied using crossed detecting zero-sound fields. A precessional type of motion of the l field is frequently observed, though a rich variety of phenomena are also observed. There is no evidence for phase slip due to motion of nonsingular vortices along the surface. Motion of the l field following sudden parallel magnetic field turn-off is also observed above a threshold field change which is related to coherent dipolar energy. The time scale for these l-field changes is, however, a factor of about 10/sup 2/ larger than expected for the formation of composite solitons.