Azimuthal modulational instability of vortices in the nonlinear Schrödinger equation

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady-state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS. We briefly show how to extend the method to encompass nonlocal nonlinearities that tend to stabilize such solutions.     

Convective and absolute instabilities in the subcritical Ginzburg-Landau equation

We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity. Received 17 December 1998     

托卡马克中漂移不稳定性的回旋动理学二维本征模方程

从弗拉索夫方程出发,导出了托卡马克等离子体中漂移不稳定性的回旋动理学二维本征模积分方程组。该方程组保留了离子的动理学效应,包括沿磁场的运动、磁场梯度和曲率漂移以及有限拉莫半径效应。与传统的采用气球模表象得到的一维回旋动理学方程(其只能给出不稳定模沿磁场线的结构)不同,该方程组不仅能给出托卡马克等离子体中漂移不稳定模的径向结构,同时还考虑了由离子的环形性漂移引起的相邻极向模之间的线性耦合,进而得到模的极向结构。该结果为相应的数值模拟研究提供了理论基础。     

Azimuthal anisotropy of jet quenching at LHC

We analyze the azimuthal anisotropy of jet spectra due to energy loss of hard partons in quark-gluon plasma, created initially in nuclear overlap zone in collisions with non-zero impact parameter. The calculations are performed for semi-central Pb-Pb collisions at LHC energy.     

Gradient Driven Azimuthal Ion Acoustic Waves

An instability of a magnetized plasma column in the frequency range has been identified as an ion acoustic one. The waves are azimuthally driven by the electron diamagnetic velocity due to the radial gradient of a fast electron tail. The strongest peaks in the frequency spectrum correspond to m = 6 or 8 wave lengths on one turn. This selection can be explained as an optimum value between increasing growth rate and the resonance disturbing phase mismatch at higher mode numbers.     

Azimuthal variations in the brightness of Fabry-Perot axicon fringes

According to Fresnel relations, the transmission through an inclined dielectric plate depends on the orientation of the light vector relative to the plane of incidence. Since an axicon has a conical surface, linearly polarized incident light has different transmissivity through different portions of the axicon. It is shown that the difference in transmissivity, as a function of azimuthal angle, increases with increasing values of the vertex angle of the axicon. This effect causes inhomogeneity in the brightness of Fabry-Perot fringes, and for a slightly misaligned system can distort the shape of the scanning spectral line.     

Azimuthal correlations in high-energy multiparticle production

Some features of the two-particle correlation phenomena, studied by means of azimuthal angle variables, are discussed. Assuming Gaussian forms for the single transverse momentum distributions, it is proposed to described the two-particle correlation with only one parameter. The influence of the kinematical constraints on the proposed correlation parameter is discussed, using a limited transverse momentum phase-space model.     

Azimuthal Decomposition of the Noise of a Dual-Stream Coaxial Jet

Acoustical Physics - Azimuthal decomposition was used to study the azimuthal composition of noise of a jet issuing from a coaxial nozzle. Various combinations of the velocities of the core and...     

Azimuthal dependence of two-particle transverse momentum current correlations

The European Physical Journal C - We present a study on inclusive emissions of a double $$\Lambda _c$$ or of a $$\Lambda _c$$ plus a light-flavored jet system as probe channels in the semi-hard...     

Azimuthal and spin asymmetries in DIS

In these lectures I want to discuss how the structure functions in deep inelastic scattering relate to quark and gluon correlation functions. In particular we will consider the issue of intrinsic transverse momenta of quarks, which becomes important in processes like 1-particle inclusive leptoproduction. Some examples of cross sections and asymmetries, in particular in polarized scattering processes are discussed. We also discuss the operator structure for azimuthal asymmetries and their evolution.     

熊猫型保偏光纤定轴仿真研究

应用光波导理论分析了保偏光纤的POL定轴方法的基本原理.根据熊猫型保偏光纤的折射率分布模型,采用光束传播方法对影响熊猫型保偏光纤POL曲线分布的各种因素进行了仿真研究,包括不同观测平面、不同折射率分布(匹配型或非匹配)、是否加匹配液等因素.通过仿真结果与实验观测结果以及保偏光纤与单模光纤仿真结果比较,表明了理论分析与仿真方法的可行性.     

Bragg-grating-enhanced polarization instabilities

Experiments demonstrate a dramatic decrease in polarization-instability threshold as an optical pulse is tuned near the short-wavelength edge of the photonic bandgap formed by a fiber Bragg grating. These enhanced nonlinear interactions and birefringent effects are modeled with coupled-mode numerical simulations. Nonlinearities are shown to increase much more rapidly than the effective birefringence as the pulse wavelength approaches the bandgap edge.     

Coherent instabilities in the NICA collider

The thresholds of coherent beam instabilities in the NICA collider are analyzed in the present work. Studies were limited on the coherent oscillations in one of the rings due to the weakness of the beam-beam interaction forces when compared to the single-beam Coulomb forces. The thresholds of the single-beam and multiple-beam instabilities are estimated for the chosen collider operation scenario. Measures that have to be taken to suppress the instabilities are discussed.     

Deterministic instabilities in the magneto-optical trap

The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the experimentally observed deterministic dynamics is described extensively. Three different behaviors are distinguished. All are cyclic, but not necessarily periodic. Indeed, some instabilities exhibit a cyclic behavior with an erratic return time. A one-dimensional stochastic model taking into account the shadow effect is shown to be able to reproduce the experimental behavior, linking the instabilities to a several bifurcations. Erraticity of some of the regimes is shown to be induced by noise.Received: 27 April 2004, Published online: 23 July 2004PACS: 32.80.Pj Optical cooling of atoms; trapping - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 05.40.Ca Noise