Relative equilibria of vortex sheets

Numerical evidence is presented for the existence of relative equilibrium configurations of vortex sheets (one-dimensional singular distributions of vorticity) in a two-dimensional ideal fluid. Point vortices are used to approximate the vortex sheets.     

Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.     

Turbulent vortex rings in weakly turbulent and in turbulent ambient flow

Turbulent vortex rings were investigated in weakly turbulent flow and in three different grid generated turbulent flows to clarify the reciprocal action of the vortex ring with defined external turbulence. Assuming self-similarity and turbulent viscosity as proportional to V₀D₀ the equations for the ring diameter D(t) and the velocity of propagation V(t) were derived. The time difference Δt between the virtual origins of 1/V(t) respectively D²(t) led to an invariant term. The equation of momentum is fulfilled. – Position and diameter of the vortex rings were determined till their decay by means of an optical system, which did not disturb the vortex rings. The experimental results in weakly turbulent ambient flow obtained by the author and by others confirm the theory very well. The ambient turbulence was nearly constant in the measuring region; its effect could be described by simply adding its viscosity to the vortex ring’s internal turbulent viscosity. The results could be represented in unified non-dimensional diagrams. Moreover, an explanation was found as to why the mean internal turbulent viscosity is constant.     

KAM theory analysis of the dynamics of three coaxial vortex rings

The equations of motion of three coaxial vortex rings in Euclidean 3-space are formulated as a Hamiltonian system. It is shown that the Hamiltonian function for this system can be written as the sum of a completely integrable part H₀ (related to the motion of three point vortices in the plane) and a non-integrable perturbation H₁. Then it is proved that when the vortex strengths all have the same sign and the ratio of the mean distances among the rings is very small in comparison to the mean radius of the rings, H₁/H₀1. Moreover, it is shown that H₁/H₀ is very small for all time for certain initial positions of the rings under the same assumptions. It is proved that the decomposition of the Hamiltonian and the estimates carry over to a reduced form of the system in coordinates moving with the center of vorticity and having one less degree of freedom. Then KAM theory is applied to prove the existence of invariant two-dimensional tori containing quasiperiodic motions. The existence of periodic solutions is also demonstrated. Several examples are solved numerically to show transitions from quasiperiodic and periodic to chaotic regimes in accordance with the theoretical results.     

潜体在非均质流体中的平衡位置与平衡过程

以探空气球为例,讨论潜体在非均质流体中的平衡位置与平衡过程.     

基于双开口谐振环超表面的宽带太赫兹涡旋光束产生

提出了一种基于双开口谐振环单元结构超表面的太赫兹宽带涡旋光束产生器.该结构由金属-电介质两层构成,位于顶层的是基于双开口谐振环单元结构的超表面,底层为介质层.对单元结构阵列进行数值仿真,圆偏振的入射光可以被转换成相应的交叉偏振透射光,通过旋转表层金属谐振环,可以控制交叉偏振透射光具有相同的振幅和不同的相位.这些单元结构按照特定的规律排列,可以形成用以产生不同拓扑荷数的涡旋光束的涡旋相位板.以拓扑荷数1和2为例,设计了两种涡旋相位板,数值分析了圆偏振波垂直入射到该涡旋相位板生成交叉圆偏振涡旋光束的特性.结果表明,在1.39—1.91 THz的频率范围内产生了比较理想的不同拓扑荷数的涡旋光束,且透过率高于20%,最高可达到24%,接近单层透射式超表面的理论极限值.     

Effect of pressure evolution on the formation enhancement in dual interacting vortex rings

In the biological locomotion, the ambit pressure is of particular importance to use as a means of propulsion. The multiple vortex rings have been proved to generate additional thrust by interaction, but the mechanism of this thrust enhancement is still unknown. This study examines the effect of ambit pressure on formation enhancement in interacting dual vortex rings. The vortex rings, which have the same formation time, are successively generated in a piston-cylinder apparatus. The finite-time Lyapunov exponent (FTLE) visualizes the flow fields as an indication of Lagrangian coherent structures (LCSs), and the pressure field is calculated based on the digital particle image velocity (DPIV). We extract the back pressure of the rear vortex in dual vortices and the back pressure circulation $\varGamma_{\rm b}$, which is defined as a form of overpressure circulation $\varGamma_{\rm p}$. The $\varGamma_{\rm b}$ has a positive linear relationship with $\varGamma_{\rm p}$. A critical interval distance $d_{\rm cr}^*$ in a range of 0.32-0.42 is found where $\varGamma_{\rm b}$ and $\varGamma_{\rm p}$ reach the maximum synchronously, leading to a full-interaction mode. Moreover, an over-interaction mode and an under-interaction mode are proposed when the dimensionless interval distance $d^*$ is smaller or larger than $d_{\rm cr}^*$. To conclude, the high back pressure caused by vortex interaction can enhance the formation of vortex rings and lead to high thrust.     

部分相干涡旋光束形成的相干涡旋特性研究

推导出部分相干涡旋平顶光束的传输解析公式,并用以研究了聚焦场和自由空间中部分相干涡旋光束形成相干涡旋的特性.结果表明,相干涡旋与光束阶数N,空间相干参数α和参考点位置(x1,y1)有关.依赖于参考点的选择,光谱相干度可能存在零值点,也可能没有零值点.特别是,若选取x1=y1=0,光谱相干度零值点处的位相可以是确定的,因而不存在相干涡旋.     

Sphalerons,antisphalerons and vortex rings

We present new classical solutions of Weinberg–Salam theory in the limit of vanishing weak mixing angle. In these static axially symmetric solutions, the Higgs field vanishes either on isolated points on the symmetry axis, or on rings centered around the symmetry axis. The solutions represent systems of sphalerons, antisphalerons, and vortex rings.     

About collapse and revivals of two quantum oscillators in off-resonance interaction

The off-resonance effect and its influence on the reversibility between two quantum subsystems in interaction (single mode cavity field and a three-level atom in cascade configuration) are studied. The partial restoration condition is found at which these radiators can restore their diagonal moments, while the non-diagonal ones remain correlated after the interaction process.     

季风与极涡的异常配置下中国夏季大尺度旱涝分布

从冷暖系统配置的角度,选取东亚夏季风(EASM)和7月亚洲区极涡面积(APVA),分析了二者的气候特征与中国夏季降水分布之间的关系.在此基础上,将1951—2010年EASM和APVA的异常配置分为四种类型:A:季风强、极涡大;B:季风强、极涡小;C:季风弱、极涡大;D:季风弱、极涡小.研究发现,二者的异常配置下,中国夏季大尺度旱涝分布在季尺度上表现出多面性特征:A型年,夏季整体偏旱;B型年,夏季南涝北旱;C型年,夏季北涝南旱;D型年,夏季整体偏涝.由此可见,中国夏季旱涝总体分布除了与EASM有关外还与APVA密切相关,二者异常的不同配置下,夏季降水多寡和旱涝分布表现出了显著的差异和规律性,这对夏季降水总体趋势预测有一定的指示意义.此外,通过研究不同配置关系对应大气环流异常特征,并分析不同要素在夏季风和极涡关系变化中的作用,发现不同配置类型下夏季降水表现出的差异和规律性直接取决于环流场的整体配置,其中西太副高和中高纬阻塞形势起主导作用.     

Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution

Using the extended Huygens-Fresnel principle and the quadratic approximation of the phase structure function, and taking the Gaussian Schell-model (GSM) vortex beam as a typical example of partially coherent vortex beams, the explicit expressions for the cross-spectral density function and average intensity of GSM vortex beams with topological charge m=+1 propagating through slant atmospheric turbulence are derived, and used to study the propagation properties of GSM vortex beams in atmospheric turbulence along a slant path and evolution behavior of coherence vortices. It is shown that the spreading of GSM vortex beams along a horizontal path is larger than that along a slant path in the long atmospheric propagation. The propagation through horizontal atmospheric turbulence can be treated as a special case of the altitude-independent structure constant. The position of coherence vortices in slant atmospheric turbulence does not coincide with that in horizontal atmospheric turbulence, and the dependence of position of coherence vortices on the zenith angle, wavelength and reference point is illustrated by numerical examples. A comparison with the previous work is also made.     

Evaluation of a phase shifting method for vortex localization in optical vortex interferometry

The optical vortex interferometer uses a regular lattice of the optical vortices. In the previous papers we showed that changes in vortex lattice geometry can be related to physical quantities of the object being measured. The accuracy of such a measurement depends strongly on the precision of vortex point localization (vortex points are points where wavefront phase is undetermined). In this paper we compared the measurements of object wave tilt calculated from different localization methods applied to real interferograms and evaluate various localization methods.     

涡旋光束的产生与干涉

分别从理论上和实验上研究了涡旋光束的产生和干涉现象.理论上分析了分数阶和整数阶涡旋光束同球面波以及平面波的干涉情况,并从实验上得出了其干涉图形.实验结果和理论模拟基本上一致.研究表明,随着涡旋光束拓扑荷数的变化,干涉图形也会产生变化.这一现象可用于测定分数阶涡旋光束的拓扑荷数.     

囚禁离子在大失谐双色驻波场中的崩塌-回复特性

讨论了囚禁离子与两驻波场相互作用时的量子相干性.在大失谐的条件下,离子的振动能量呈现崩塌-回复的相干性特征,表明离子的振动态具有压缩效应.无量纲压缩参数G3愈大,囚禁离子的振动态压缩效应愈显著.进一步增大参数G3,所能得到的最大压缩反而减小.     

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.     

On collapse of wave maps

We derive the universal collapse law of degree 1 equivariant wave maps (solutions of the sigma model) from the 2+1 Minkowski space-time, to the 2-sphere. To this end, we introduce a nonlinear transformation from original variables to blowup ones. Our formal derivations are confirmed by numerical simulations.     

超声对近壁微气泡溃灭过程的影响

近壁微气泡溃灭特性的深入研究对靶向给药和基因治疗等技术具有较好的指导作用。该文基于数值模拟技术,采用有限体积法结合流体体积模型对超声作用下的近壁微气泡溃灭特性进行了研究,分析了超声对近壁微气泡溃灭动力学过程的影响。结果表明气泡溃灭最大射流速度与近壁距离无量纲参数γ在1.1～1.6范围内时成正比,与超声频率在10～60 Hz范围内时成正比,与气泡初始半径在50～100μm范围内时成反比;近壁气泡的二次溃灭最大射流速度大于一次溃灭,二次溃灭的作用更加明显。超声参数对近壁气泡溃灭过程存在较大影响,该研究为超声在医学上的应用提供了依据。     

Entanglement of a quantum optical elliptic vortex

We calculate the entanglement of a generalized elliptical vortex formed by quantized radiation field, using Wigner quasiprobability distribution function for such states. We find a critical squeezing parameter above which the entanglement is less for higher vorticity, which is counter intuitive.     

Rotation of a single vortex in dusty plasma

A single vortex is obtained in radio-frequency capacitive discharge in argon gas. The dust subsystem is confined in the horizontal plane with an asymmetrical saw structure placed on the lower electrode. The vortex rotates as a whole along the long side of the saw-teeth. Asymmetry of the saw structure plays an important role in the rotation of the vortex. Nonzero curl of the total force resulting from the local ion flow and the electric field in the plasma sheath could be attributed to the persistent rotation of vortex.