Does the Kibble Mechanism Operate in Liquid 4He?

A rapid passage of liquid ⁴He through the lambda (superfluid) transition is expected (W. H. Zurek, Nature 317, 505; 1985) to result in the production of topological defects (quantized vortices) through the Kibble mechanism, the same process that is believed to have produced cosmic strings at the GUT phase transition of the early universe. But recent experiments (Dodd et al, Phys. Rev. Lett 81, 3703; 1998)) show that the density of vortices created, if any, seems to be smaller than predicted by a factor of at least 100. Possible ways of improving the sensitivity of the experiment are discussed.     

Typical flow between enclosed corotating disks and its dependence on Reynolds number

Abstract

The flow in an enclosed co‐rotating disk pair is investigated by Laser Doppler Velocimetry (LDV) measurements and flow visualizations. First, the typical flow structure at Re = 5.25 × 10⁵ and S = 0.09 is clarified. The flow fields in the r – θ and the r – z planes are both investigated and then divided into several flow regions based on the distinct flow types observed. The flow regions found in the two different planes are also compared and integrated. Second, with S fixed, the dependence of the flow field structure upon the Reynolds number is discussed. Three regimes of the r – θ plane flow with different Reynolds numbers are identified based on the measured mean velocity and spectral intensity. When Re < 1.6 × 10⁵, no solid body region is found and the flow is in a laminar regime. In the range 1.6 × 10⁵ ≤ Re ≤ 2.0 × 10⁶, the solid body region and the outer region vortices coexist, and an empirical equation is developed to estimate the number of vortices. When Re > 2.0 × 10⁶, the flow becomes turbulent. As Re increases from 9.3 × 104 to 5.25 × 10⁵, the spectral intensity initially increases and then decreases before increasing again to an even higher level, resulting in an increasing sawtooth pattern.     

Vortices Observed and to be Observed

Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density atomic Bose-Einstein condensates as quantized vortex lines. We discuss unconventional vortices in unconventional superfluids and superconductors, which have been observed or have to be observed, such as continuous singly and doubly quantized vortices in ³ He-A and chiral Bose condensates; half-quantum vortices (Alice strings) in ³ He-A and in nonchiral Bose condensates; Abrikosov vortices with fractional magnetic flux in chiral and d-wave superconductors; vortex sheets in ³ He-A and chiral superconductors; the nexus—combined object formed by vortices and monopoles. Some properties of vortices related to the fermionic quasiparticles living in the vortex core are also discussed.     

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.     

Dynamic Remanent Vortices in Superfluid 3He-B

We investigate the decay of vortices in a rotating cylindrical sample of ³He-B, after rotation has been stopped. With decreasing temperature vortex annihilation slows down as the damping in vortex motion, the mutual friction dissipation α(T), decreases almost exponentially. Remanent vortices then survive for increasingly long periods, while they move towards annihilation in zero applied flow. After a waiting period Δt at zero flow, rotation is reapplied and the remnants evolve to rectilinear vortices. By counting these lines, we measure at temperatures above the transition to turbulence ∼0.6 T _c the number of remnants as a function of α(T) and Δt. At temperatures below the transition to turbulence T≲0.55 T _c, remnants expanding in applied flow become unstable and generate in a turbulent burst the equilibrium number of vortices. Here we measure the onset temperature T _on of turbulence as a function of Δt, applied flow velocity v=v _n−v _s, and length of sample L.     

Formation of Single Carbon Nanotube T‐Junctions

Abstract

We investigate the formation of single wall carbon nanotube T‐junctions via the fusing of two nanotubes. We propose energetically efficient pathways for formation (9, 0)–(10, 0)–(9, 0) and (5, 5)–(10, 0)–(5, 5) T‐junctions. In the proposed scheme all carbon atoms maintain their sp ² arrangements throughout and transformation is achieved through creation/annihilation of topological defects. We use tight‐binding molecular dynamics simulation to investigate energetic of proposed mechanism.     

3-mode Interactions with O(2) Symmetry and a Model for Taylor-Couette flow

We analyse the bifurcations of a general ordinary dififerential equation where is equivariant under an action of the group O(2) on. The equation represents the most general nonlinear local interaction of three O(2)-symmetric modes:a steady-state mode with mode-number k, and two periodic (Hopf) modes with mode-numbers l and m. The parameter λ is a bifurcation parameter, and α₁, α₂are unfolding parameters that split the individual modes apart. The system is assumed to be in Birkhoff normal form, so that f also commutes with an action of the 2-torus T². We discuss the existence and stability of bifurcating branches and how these break the O(2) × T² symmetry.Depending on the precise mode-numbers k l m we find up to 31 symmetry classes of possible solutions including six that combine all three modes, and thus cannot be found in any 2-mode interaction. We also discuss the possible occurrence of Sacher-Naimark torus bifurcations, providing a further 10 solution types, and 'slow drift'bifurcations.

This 10-dimensional system can occur generically in O(2)-symmetric bifurcation problems having two extra parameters, and in principle is applicable to a wide range of physical systems. The discussion here is motivated by the observed pattern formation in the Taylor–Couette system, the flow of a fluid contained between coaxial rotating cylinders. It arises by seeking a 'hidden organizing centre' that combines two previous mode-interaction models of this system: a 6-dimensional Hopf–steady-state model due to Chossat and looss (1985) and Golubitsky and Stewart (1986), and an 8-dimensional Hopf–Hopf model due to Chossat, Demay and looss (1987). We interpret the general results on the 10-dimensional system in the context of Taylor–Couette flow, giving schematic pictures of the associated flow patterns. The model incorporates almost all of the observed non-chaotic flows in the Taylor–Couette experiment into a single finite-dimensional dynamical system. It predicts the possible occur- rence of four new flow patterns (corresponding to four of the six possible solutions that combine all three modes). Theseform invariant 3-tori, and may be described as superimposed twisted vortices, superimposed wavy vortices, and two types of twisted wavy vortices. Possible torus bifurcations from states in the 10-dimensional model include various modulated spirals, three types of modulated twisted vortices, three types of modulated wavy vortices, modulated superimposed spirals, modulated interpenetrating spirals, modulated superimposed ribbons, and modulated interpenetrating ribbons. However, whether any of these new states and torus bifurcations can actually occur in Taylor–Couette flow at suitable parameter values, and if so whether they can occur stably, depend upon more detailed numerical calculations than we have performed     

Carrier transport in a diode base with locally nonuniform recombination properties

Nonuniformity of the recombination properties in the form of a layer of radiation defects is created in the base of a p ⁺−n diode. The change in the effective hole lifetime, measured by an injection-extraction method, is investigated and attributed to recombination in this layer. Pis’ma Zh. Tekh. Fiz. 23, 79–86 (May 12, 1997)     

Angular momentum of the fields of a few-mode fiber. III. Optical Magnus effect, Berry phase, and topological birefringence

It is shown that, on the one hand, the evolution of the angular rotation of the lines of nodes of the CP₁₁ mode is a manifestation of the optical Magnus effect in a few-mode fiber with a parabolic refractive index profile, and, on the other hand, the additional phase γ _b =±δβ ₂₁ z in CV and IV vortices is the Berry topological phase, which arises as a result of the cyclic change in the orientations of the orthogonal axes of dislocations. The splitting of the propagation velocities of orthogonal circularly polarized CV⁺ and IV⁻ modes in an LV vortex in a parabolic fiber is a manifestation of the phenomenon of topological birefringence of a few-mode fiber. The azimuth of the linear polarization of a vortex undergoes continuous angular rotation. In an optical fiber with a stepped index profile the CP₁₁ mode forms circularly polarized edge dislocation over lengths which are multiples of half the beat length, and over lengths which are odd multiples of the quarter beat length it forms linearly polarized fields with a purely screw dislocation. This transformation of edge and screw dislocations can be regarded formally as conversion of the polarizational angular momentum into orbital angular momentum. The conversion of angular momentum is a reflection of the dynamical unity of the optical Magnus effect and the Berry topological phase in the fields of a few-mode fiber. Pis’ma Zh. Tekh. Fiz. 23, 59–67 (December 12, 1997)     

Instability of Quantized Vortices Attached to Oscillating Boundaries in Superfluid 4He

The motion of quantized vortices is studied using a vibrating wire in superfluid ⁴He. A vortex filtering method provides a superfluid practically free of remanent vortices in which the vibration of a wire cannot generate turbulence. Vortex lines are produced by cooling through the superfluid transition and remain forming bridges between a wire and a surrounding wall. Bridged remanent vortices increase the resonance frequency of a vibrating wire: the rate of an increase due to the remanent vortices is constant in a laminar flow regime and steeply increases in a turbulent flow regime with increasing wire velocity. These results suggest that oscillation of the bridged vortices provides a linear contribution to the wire vibration in the laminar flow regime, until instability occurs in the oscillation of the vortices, causing turbulence.      

VORTEX SHEDDING FROM FIXED AND OSCILLATING RECTANGULAR PRISMS IN SHEAR FLOWS

ABSTRACT

The main focus of this paper is to study the results of experiments on six different rectangular prisms with varied side ratios, with and without forced oscillation, displaced in two shear free streams and one uniform flow. The setting of free stream shear parameters β=dU/dyxD/Uc are 0.024 and 0.032. With respect to vortex shedding phenomena, a comparison between shear flows and uniform flows is also part of the focus.

Experimental results indicate that disturbance on the two-dimensional vortex shedding of the uniform flow is caused by the longitudinal vortex of the shear flow gradient. As a result, a spanwise distribution of cells among the vortex shedding frequencies is created. Increases in the side ratios of the rectangular prisms can cause a shifting of cell boundaries toward the high-speed end. As shear parameters for the same prism increase, the cell boundaries move toward the low-speed end. During oscillation, differences arise between the vorticity structures of cells, and the vortices of each cell are more unified, with improvements in correlation.     

Effects of directional grain structure on impact properties and dislocation substructure of 6061-T6 aluminium alloy

Abstract

The effects of the grain structure direction on the impact properties and dislocation substructure of 6061-T6 aluminium alloy are investigated under room temperature conditions and strain rates of 1×10³, 3×10³ and 5×10³ s^?1 using a split-Hopkinson pressure bar system. The impact tests are performed using specimens machined from rolled 6061-T6 plates in the longitudinal, transverse and through thickness directions respectively. The results show that for all specimens, the flow stress increases with increasing strain rate. Furthermore, for all strain rates, the highest flow stress occurs in the transverse specimen. For strain rates of 1×10³ and 3×10³ s^?1, the flow stress in the through thickness specimen is greater than that in the longitudinal specimen. However, at a strain rate of 5×10³ s^?1, the flow stress in the longitudinal specimen is higher than that in the through thickness specimen due to a greater dislocation multiplication rate. For all three grain structure directions, the strain rate sensitivity increases with increasing strain rate, but decreases with increasing true strain. The highest strain rate sensitivity is observed in the longitudinal specimen at strain rates of 3×10³ to 5×10³ s^?1. The dislocation density increases markedly with increasing strain rate. Moreover, the square root of the dislocation density varies as a linear function of the flow stress in accordance with the Bailey–Hirsch relationship. The strengthening effect produced by the increased dislocation density is particularly evident in the transverse specimen, followed by the longitudinal specimen and the through thickness specimen.     

On the thermal mechanism of microwave breakdown of high-temperature superconducting films

Theoretical arguments supporting the thermal nature of the microwave breakdown of high-temperature superconducting films are compared with experimental data. A comparison of the theoretical and experimental values of the threshold field for breakdown of a uniform film, B _f, and the threshold field for breakdown at nonsuperconducting defects, B _d, confirms the dependence corresponding to a thermal mechanism: B _f, B _d∝ (T _c-T ₀)^1/2. It is shown that the space-time picture of the observed breakdown is apparently due to overheating of the film near defects with a size of 10⁻⁵–10⁻⁶ m. The amplitude of the breakdown field may ultimately be limited by the abrupt decrease in the energy of critical disturbances for the initiation of breakdown. Pis’ma Zh. Tekh. Fiz. 24, 12–17 (June 12, 1998)     

Field-ion microscopy of deformation effects near the surface in ion-implanted metals (Ir)

Field-ion microscopy is used to determine the deformation due to ion implantation (E=20 keV, D=10¹⁸ ions/cm², j=300 μA/cm²) near the surface in pure iridium. The effect is manifested as a high density of various types of defects in the near-surface volume (∼50 nm from the irradiated surface) of the material. Pis’ma Zh. Tekh. Fiz. 25, 60–64 (March 26, 1999)     

Topological birefringence and combined Rytov-Magnus effect

It is shown that the symmetry properties of the locally isotropic inhomogeneous medium of an optical fiber cause circular and linear topological birefringence. The circular birefringence δn _C in graded-index fibers is ∼(λ/ρ)² (where λ is the wavelength and ρ is the core radius), while the linear birefringence is δn _L ∼(λ/ρ)³. This topological birefringence is characterized not only by the polarization basis (as in crystals for example) but also by the magnitude and sign of the topological charge of the guided vortex. This topological birefringence forms the basis of the instability of the fiber IV vortex and is observed experimentally as the combined Rytov-Magnus effect. Pis’ma Zh. Tekh. Fiz. 25, 41–46 (March 12, 1999)     

High strain rate superplasticity of ultrafined Ti–10V–2Fe–3Al compact prepared by sintering and isothermal forging

Abstract

High strain rate superplasticity was obtained for powder Ti–10V–2Fe–3Al (Ti-1023) alloy prepared by powder sintering and isothermal forging technology. The selected powder was cold isostatic pressed, sintered and isothermal forged to prepare this powder alloy. Tensile testing was conducted at optimum superplastic temperaure of 1023 K with different initial strain rate, and the elongation to failure, the flow stress and the microstructure were analysed. The experiment results exhibited that the microstructure of this powder alloy is extraordinary uniform and fine, resulted in considerable enhancement of optimum initial strain rate increased from 3·3×10^?4 s^?1 of conventional cast and wrought Ti-1023 alloy to 3·3×10^?3 s^?1 of this powder alloy. The elongation to failure increased first and then decreased with initial strain rate from 3·3×10^?4 to 3·3×10^?2 s^?1. The strain rate sensitivity m is about 0·46 near initial strain rate of 3·3×10^?3 s^?1, larger than conventional cast and wrought Ti-1023 alloy. Microstructure observations showed that dynamic recrystallisation and grain growth were present during superplastic deforming.     

Experimental Determination of Correlations Between Spontaneously Formed Vortices in a Superconductor

We have imaged spontaneously created arrays of vortices (magnetic flux quanta), generated in a superconducting film quenched through its transition temperature at rates around 10⁹ K/s. From these images, we calculated the positional correlation functions for two vortices and for 3 vortices. We compared our results with simulations of the time dependent Ginzburg Landau equation in 2D. The results are consistent with the Kibble-Zurek scenario of spontaneous vortex creation. Effects due to fluctuations of the gauge field on the correlation functions are below our experimental resolution.     

Textures of Superfluid 3He A-like and B-like Phases in Aerogel under Rotation

Superfluid ³He A-like and B-like phases in 98% aerogel under rotation up to 2π rad/sec have been studied by cw-NMR and Homogeneous Precessing Domain (HPD) NMR at 29 mT and 3.0 MPa. In the A-like phase, a large negative frequency shift was observed in the cw-NMR spectrum and no effect of rotation on the spectrum was found. In the B-like phase, the spin wave spectrum was observed when the sample was cooled through T _c under rotation and was affected by the counter flow due to the trapped vortices. The HPD was excited in a part of the aerogel sample but introduction of vortices into the sample by rotation or trapped vortices destroyed the HPD.     

Angular momentum of the fields of a few-mode waveguide: Conversion of the angular momentum

An analysis is made of the transformation of the angular momentum density in the field of an unstable IV vortex of a few-mode optical fiber. It is shown that the effect of mode dispersion of IV vortices is observed as the conversion of the polarization and orbital components of the electrodynamic angular momentum. The angular momentum defect may be recorded experimentally as a mechanical twist of the optical few-mode fiber. Formally the dispersion process resembles the conversion of the signs of the orbital and polarization components of the angular momentum density. A complex pseudopotential, whose real and imaginary parts characterize the field lines and lines of equal pseudopotential, is introduced to describe the energy flux density of the fiber vortex. The conversion of field states with equivalent partial ê ⁺ F ₁(R)exp{−iφ} and ê2⁻ F ₁(R)exp{+iφ} vortices was investigated experimentally. Pis#x2019;ma Zh. Tekh. Fiz. 23, 58–65 (November 26, 1997)