Finite number of vortices and bending of finite vortex lines in a confined rotating Bose-Einstein condensate

The minimal energy configurations of finite N_v-body vortices in a rotating trapped Bose-Einstein condensate is studied analytically by extending the previous work [Y. Castin, R. Dum, Eur. Phys. J. D 7, 399 (1999)], and taking into account the finite size effects on z-direction and the bending of finite vortex lines. The calculation of the energy of the vortices as a function of the rotation frequency of the trap gives number, curvature, configuration of vortices and width of vortex cores self-consistently. The numerical results show that (1) the simplest regular polynomial of the several vortex configurations is energetically favored; while the hexagonal vortex lattice is more stable than square lattice; (2) bending is more stable then straight vortex line along the z-axis for λ<1; (3) the boundary effect is obvious: compared with the estimation made under infinite boundary, the finite size effect leads to a lower vortex density, while the adding vortex bending results in a less higher density because of the expansion. The results are in well agreement with the other authors' ones.     

Bose-Einstein condensates with a bent vortex in rotating traps

We consider a 3D dilute Bose-Einstein condensate at thermal equilibrium in a rotating harmonic trap. The condensate wavefunction is a local minimum of the Gross-Pitaevskii energy functional and we determine it numerically with the very efficient conjugate gradient method. For single vortex configurations in a cigar-shaped harmonic trap we find that the vortex line is bent, in agreement with the numerical prediction of Garcia-Ripoll and Perez-Garcia [Phys. Rev. A 63, 041603 (2001)]. We derive a simple energy functional for the vortex line in a cigar-shaped condensate which allows to understand physically why the vortex line bends and to predict analytically the minimal rotation frequency required to stabilize the bent vortex line. This analytical prediction is in excellent agreement with the numerical results. It also allows to find in a simple way a saddle point of the energy, where the vortex line is in a stationary configuration in the rotating frame but not a local minimum of energy. Finally we investigate numerically the effect of thermal fluctuations on the vortex line for a condensate with a straight vortex: we can predict what happens in a single realization of the experiment by a Monte Carlo sampling of an atomic field quasi-distribution function of the density operator of the gas at thermal equilibrium in the Bogoliubov approximation. Received 28 March 2002 / Received in final form 13 September 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: yvan.castin@lkb.ens.fr     

Magnetic vortex driven by non-uniform injection of spin-polarized current in nano-scale spin valves

We demonstrate that a current pulse of a non-uniform spin-polarized current density in a nanomagnet can drive, apart from magnetization reversal a static magnetic vortex. This vortex configuration can be achieved in low shape anisotropy spin valves of elliptical cross-sectional area. These non-uniform configurations exist also in presence of either ion mill damages below the nano-aperture or thermal effects at low temperature. We performed a numerical experiment of spin-torque driven ferromagnetic resonance in a magnetic vortex configuration, our results predict a frequency response with a few maxima and minima related to small oscillation of the vortex state around its equilibrium configuration.     

Bose-Einstein condensates with vortices in rotating traps

We investigate minimal energy solutions with vortices for an interacting Bose-Einstein condensate in a rotating trap. The atoms are strongly confined along the axis of rotation z, leading to an effective 2D situation in the x-y plane. We first use a simple numerical algorithm converging to local minima of energy. Inspired by the numerical results we present a variational ansatz in the regime where the interaction energy per particle is stronger than the quantum of vibration in the harmonic trap in the x-y plane, the so-called Thomas-Fermi regime. This ansatz allows an easy calculation of the energy of the vortices as function of the rotation frequency of the trap; it gives a physical understanding of the stabilisation of vortices by rotation of the trap and of the spatial arrangement of vortex cores. We also present analytical results concerning the possibility of detecting vortices by a time-of-flight measurement or by interference effects. In the final section we give numerical results for a 3D configuration. Received 16 December 1998 and Received in final form 18 March 1999     

Magnetic states of small cubic particles with uniaxial anisotropy

The lowest energy states in small cubic particles with uniaxial anisotropy are explored as a function of anisotropy strength and particle size. The investigations result in a phase diagram which contains the boundaries between the regions of one, two and three domains (flower, vortex and double vortex states). While the general features of the phase diagram are derived from energy estimates based on domain theory, the details are obtained using numerical micromagnetics. The two-domain and the three-domain phase can be subdivided into subphases. The comparison between different configurations revealed that a twisted vortex configuration with an S-shaped domain wall replaces the symmetric vortex with a straight wall at larger sizes. The three-domain phase contains two subphases which are symmetric with respect to (1 0 0) and (1 1 0) mirror planes, respectively. The transition from two to three domains occurs into the (1 1 0)-three-domain-state (diagonal state). This structure can be described as a configuration with two (quarter-) circular domain walls in two opposing corners. However, this configuration is energetically favored only in a small region within the phase diagram relative to the (1 0 0)-symmetry three-domain state with straight walls (sandwich state).     

Possibility of two-stage flux penetration in antiferromagnetic superconductors

An induced ferromagnetism in antiferromagnetic superconductors is possible, caused by a magnetic structure of vortex lines appearing in an external magnetic field strong enough to “flip over” the spins in the vortex core from their antiferromagnetic configuration. If the magnetic field is less than the “flip over” field the vortex line is entirely in the antiferromagnetic phase. Therefore the vortex interaction with the surface of a sample is altered when an applied magnetic field exceeds the “flip over” field. This mechanism makes the appearance of a new energy barrier that strongly influences the flux penetration possible. An estimation of the second critical entry field is made for DyMo₆S₈.     

Quantum turbulence in a propagating superfluid vortex front

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.     

Direct Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer at Ma = 6

Direct numerical simulation is carried out for a spatially evolving supersonic turbulent boundary layer at freestream Mach number 6. To overcome numerical instability, the seventh-order WENO scheme is used for the convection terms of Navier-Stokes equations, and fine mesh is adopted to minimize numerical dissipation. Compressibility effects on the near-wall turbulent kinetic energy budget are studied. The cross-stream extended self-similarity and scaling exponents including the near-wall region are studied. In high Mach number flows, the coherence vortex structures are arranged to be smoother and streamwised, and the hair-pin vortices are less likely tO OCCUr.     

双能隙介观超导体的涡旋结构模拟

本文运用了含时Ginzburg-Landau理论研究了双能带结构的介观超导体在外磁场作用下涡旋随时间的演化. 给出了实际温度在s波和d波的临界温度之间s波、d波以及磁场的分布, 从 理论上模拟得到涡旋进入和退出样品的磁场"过热"与"过冷"现象, 以及介观超导样品边界对涡旋结构分布的影响. 关键词： 涡旋结构 双能带 含时Ginzburg-Landau理论 超导     

Far-field detection of the dipole vortex

The energy flow lines (field lines of the Poynting vector) of electric dipole radiation exhibit a vortex structure in the near field when the dipole moment of the source is in circular rotation. The spatial extend of this vortex is smaller than a wavelength and may not be observable by a measurement in the near field. We show that the rotation of the field lines close to the source affects the image of the dipole in the far field, and this opens the possibility for observation of this vortex by a measurement in the far field.     

Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration

Relativistic formulation of Helmholtz’s vorticity transport equation is presented on the basis of Maxwell-like version of Euler’s equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg’s theory of spacelike congruence of vortex lines and \(1+1+(2)\) decomposition of the gradient of fluid’s 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid’s angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid’s angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid’s rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.     

A numerical investigation of vortex-coupled superfluidity

We have performed numerical simulations of quantized vortex lines in a model of normal fluid turbulence. The results are used to discuss the idea, put forward to explain some recent experiments, that in isothermal turbulent helium flow the high density of vortex lines locks the two fluid components together.     

收缩螺旋涡线诱导速度的快速收敛法

给出了一种计算收缩涡线(桨尖涡和内部涡线)诱导速度所有组元的快速收敛方法,该方法是由Rand和Chiu的方法(计算螺旋涡线诱导速度快速收敛法)发展而来的,它以寻求上下界截断积分解析表达式为基础。其优点是能计算尾迹中任意一点的诱导速度,并且考虑了尾迹收缩。该方法不仅避免了离散涡线引起的截断误差。而且减小了沿有限方位角所产生的误差。     

Reversal of the dipole vortex in a negative index of refraction material

When a small particle is illuminated by a circularly polarized laser beam, the induced electric dipole moment rotates in a plane. The flow lines of the emitted electromagnetic energy are the field lines of the Poynting vector. When the particle is embedded in a dielectric, these field lines have a vortex structure, and the rotation in the vortex has the same orientation as the rotation direction of the dipole. We show that when the embedding medium is a negative index of refraction material, the direction of rotation in the vortex is reversed.     

Quantum turbulence: Theoretical and numerical problems

The term “quantum turbulence” (QT) unifies the wide class of phenomena where the chaotic set of one dimensional quantized vortex filaments (vortex tangles) appear in quantum fluids and greatly influence various physical features. Quantum turbulence displays itself differently depending on the physical situation, and ranges from quasi-classical turbulence in flowing fluids to a near equilibrium set of loops in phase transition. The statistical configurations of the vortex tangles are certainly different in, say, the cases of counterflowing helium and a rotating bulk, but in all the physical situations very similar theoretical and numerical problems arise. Furthermore, quite similar situations appear in other fields of physics, where a chaotic set of one dimensional topological defects, such as cosmic strings, or linear defects in solids, or lines of darkness in nonlinear light fields, appear in the system. There is an interpenetration of ideas and methods between these scientific topics which are far apart in other respects. The main purpose of this review is to bring together some of the most commonly discussed results on quantum turbulence, focusing on analytic and numerical studies. We set out a series of results on the general theory of quantum turbulence which aim to describe the properties of the chaotic vortex configuration, starting from vortex dynamics. In addition we insert a series of particular questions which are important both for the whole theory and for the various applications. We complete the article with a discussion of the hot topic, which is undoubtedly mainstream in this field, and which deals with the quasi-classical properties of quantum turbulence. We discuss this problem from the point of view of the theoretical results stated in the previous sections. We also included section, which is devoted to the experimental and numerical suggestions based on the discussed theoretical models.     

Evolution of a single vortex in a uniform nonequilibrium medium

The problem of the evolution of a single vortex in a nonequilibrium medium with a temperature-or density-dependent energy release was solved. In a medium that is stable against small perturbations, the vortex passes to a new stationary state, and no vortex breakdown occurs. For a temperature-dependent energy release, analytical solutions that define changes in the characteristics of the vortex were obtained for high and low relaxation times. The solutions were compared with the results of numerical simulation by the Godunov method.     

Macroscopic far-field observation of the sub-wavelength near-field dipole vortex

The energy flow lines of the radiation emitted by a rotating electric dipole moment have a vortex structure near the source. The spatial extend of this vortex is well below an optical wavelength. This near-field vortex has a macroscopic effect which could be observed in the far field.     

Vortex arrays of coexisting singly and doubly quantized vortex lines in<Superscript>3</Superscript>He-A

In superfluid³He-A singly and doubly quantized vortex lines can coexist in a rotating container. We measure with NMR techniques the radial distribution of the two vortex types in an array of vortex lines. The radial composition is found to depend on the procedure by which the array has been formed. The result shows that in superfluid³He the energy barriers separating different configurations of the vortex array are inpenetrably high for a metastable state to relax.