Vortex solutions of the discrete Gross-Pitaevskii equation starting from the anti-continuum limit

In this paper, we consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schrödinger model, a model of interest both to atomic physics and to nonlinear optics. Our considerations are chiefly based on initializing such vortex configurations at the anti-continuum limit of zero coupling between adjacent sites, and continuing them to finite values of the coupling. Systematic tools are developed for such continuations based on amplitude-phase decompositions and explicit solvability conditions enforcing the vortex phase structure. Regarding the linear stability of such nonlinear waves, we find that in a way reminiscent of their 1d analogs, i.e., of discrete dark solitons, the discrete defocusing vortices become unstable past a critical coupling strength and, subsequently feature a cascade of alternating stabilization-destabilization windows for any finite lattice. Although the results are mainly geared towards the uniform case, we also consider the effect of harmonic trapping potentials often present in experimental atomic physics settings.     

On stability of spatially periodic structures of an atomic Bose-Einstein condensate

The stability of spatially periodic structures, including vortex lattices, in a dilute atomic Bose-Einstein condensate is analyzed. By using the approximate solution of the nonlocal nonlinear Schrödinger equation (the generalized Gross-Pitaevski? equation), it is shown that, in the limit of low concentrations, such structures are stable.     

Interlaced solitons and vortices in coupled DNLS lattices

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when they are exponentially or oscillatorily unstable, to structures with a smaller number of participating sites.     

Probing Yukawian gravitational potential by numerical simulations. I. Changing N-body codes

In the weak field limit general relativity reduces, as is well known, to the Newtonian gravitation. Alternative theories of gravity, however, do not necessarily reduce to Newtonian gravitation; some of them, for example, reduce to Yukawa-like potentials instead of the Newtonian potential. Since the Newtonian gravitation is largely used to model with success the structures of the universe, such as for example galaxies and clusters of galaxies, a way to probe and constrain alternative theories, in the weak field limit, is to apply them to model the structures of the universe. In the present study, we consider how to probe Yukawa-like potentials using N-body numerical simulations.     

Bifurcation analysis of steady states and limit cycles in a thermal pulse combustor model

Oscillatory behaviour of state variables is desirable in pulse combustors, as properly designed pulsations lead to improved performances, such as higher thermal efficiency and lower emissions compared to steady combustors. In the present work, we perform a systematic investigation of the stability of steady states and limit cycles of a pulse combustor model through numerical continuation. Different bifurcation parameters such as tailpipe friction factor, wall temperature, convective heat transfer coefficient, inlet temperature and inlet fuel mass fraction are varied to identify the complete ranges of those parameters at which limit cycles can be expected. This analysis identifies alternative stable periodic regimes in parameter space (e.g. friction factor). In addition, a few performance indicators such as amplitude of oscillations, cycle-averaged heat transfer and cycle-averaged specific thrust are compared between different ranges of friction factor yielding limit cycle oscillations. The comparison clearly shows that, depending upon the application, friction factor can be chosen from different regimes. The time-integration of the model is also performed to support the bifurcation results obtained from numerical continuation, wherever appropriate. The complete stability margin of limit cycle oscillations for those bifurcation parameters can be useful for improved design of the combustor and for determining the optimal operating conditions of pulse combustors.     

Synchronization in coupled nonidentical incommensurate fractional-order systems

Synchronization of fractional-order nonlinear systems has received considerable attention for many research activities in recent years. In this Letter, we consider the synchronization between two nonidentical fractional-order systems. Based on the open-plus-closed-loop control method, a general coupling applied to the response system is proposed for synchronizing two nonidentical incommensurate fractional-order systems. We also derive a local stability criterion for such synchronization behavior by utilizing the stability theory of linear incommensurate fractional-order differential equations. Feasibility of the proposed coupling scheme is illustrated through numerical simulations of a limit cycle system, a chaotic system and a hyperchaotic system.     

三维气固两相混合层湍流拟序结构的直接数值模拟

本文对三维气固两相混合层湍流拟序结构进行了直接数值模拟。气相流场应用拟谱方法对Ｎ－Ｓ方程组进行直接求解,通过模拟时间模式的混合层流动,分析流场失稳后涡的卷起、配对、合并及撕裂过程,研究三维混合层湍流拟序结构的演变特征;计算颗粒场时,采用Ｌａｇｒａｎｇｉａｎ方法,针对颗粒不同的Ｓｔｏｋｅｓ数,模拟了颗粒场的瞬态分布,并分析流场三维大涡结构对颗粒分布的影响。     

偶极玻色-爱因斯坦凝聚体在类方势阱中的Bénard-von Kármán涡街

对偶极玻色-爱因斯坦凝聚体（Bose-Einstein condensate,BEC）在类方势阱中的Bénard-von Kármán涡街现象进行了数值研究.结果表明,当障碍势在BEC中的运动速度与尺寸在适当范围内时,系统中会出现稳定的两列涡旋对阵列,即Bénard-von Kármán涡街.研究了偶极相互作用强弱、障碍势尺寸以及运动速度对尾流中产生的涡旋结构的影响,得到了相图结构.对障碍势所受拖拽力进行计算,分析了涡旋对产生的力学机理.     

Dynamics of the plane and solitary waves in a Noguchi network:Effects of the nonlinear quadratic dispersion

We consider a modified Noguchi network and study the impact of the nonlinear quadratic dispersion on the dynamics of modulated waves. In the semi-discrete limit, we show that the dynamics of these waves are governed by a nonlinear cubic Schrodinger equation. From the graphical analysis of the coefficients of this equation, it appears that the nonlinear quadratic dispersion counterbalances the effects of the linear dispersion in the frequency domain. Moreover, we establish that this nonlinear quadratic dispersion provokes the disappearance of some regions of modulational instability in the dispersion curve compared to the results earlier obtained by Pelap et al.(Phys. Rev. E 91 022925(2015)). We also find that the nonlinear quadratic dispersion limit considerably affects the nature, stability, and characteristics of the waves which propagate through the system. Furthermore, the results of the numerical simulations performed on the exact equations describing the network are found to be in good agreement with the analytical predictions.     

Periodic oscillations in transmission decay of anderson localized one-dimensional dielectric systems

It is well recognized that the transmittance of Anderson localized systems decays exponentially on average with sample size, showing large fluctuations brought up by extremely rare occurrences of necklaces of resonantly coupled states, possessing almost unity transmission. We show here that in a one-dimensional (1D) random photonic system with resonant layers these fluctuations appear to be very regular and have a period defined by the localization length xi of the system. We stress that necklace states are the origin of these well-defined oscillations. We predict that in such a random system efficient transmission channels form regularly each time the increasing sample length fits so-called optimal-order necklaces and demonstrate the phenomenon through numerical experiments. Our results provide new insight into the physics of Anderson localization in random systems with resonant units.     

Existence and stability of limit cycles in a macroscopic neuronal population model

We present rigorous results concerning the existence and stability of limit cycles in a macroscopic model of neuronal activity. The specific model we consider is developed from the Ki set methodology, popularized by Walter Freeman. In particular we focus on a specific reduction of the KII sets, denoted RKII sets. We analyse the unfolding of supercritical Hopf bifurcations via consideration of the normal forms and centre manifold reductions. Subsequently we analyse the global stability of limit cycles on a region of parameter space and this is achieved by applying a new methodology termed Global Analysis of Piecewise Linear Systems. The analysis presented may also be used to consider coupled systems of this type. A number of macroscopic mean-field approaches to modelling human EEG may be considered as coupled RKII networks. Hence developing a theoretical understanding of the onset of oscillations in models of this type has important implications in clinical neuroscience, as limit cycle oscillations have been demonstrated to be critical in the onset of certain types of epilepsy.     

Vortex emission accompanies the advection of optical localized structures

We show that the advection of optical localized structures is accompanied by the emission of vortices, with phase singularities appearing in the wake of the drifting structure. Localized structures are obtained in a light-valve experiment and made to drift by a mirror tilt in the feedback loop. Pairs of oppositely charged vortices are detected for small drifts, whereas for large drifts a vortex array develops. Observations are supported by numerical simulations and linear stability analysis of the system equations and are expected to be generic for a large class of translated optical patterns.     

高雷诺数双螺旋涡尾迹演化特性分析

螺旋状尾迹涡是直升机悬停旋翼流场的主导特征之一,其时空演化特性对旋翼气动性能具有重要影响.为了揭示悬停状态下旋翼尾迹涡的演化特征,对两桨叶刚性旋翼在高雷诺数悬停状态下的双螺旋状尾迹涡开展数值研究,采用基于流场特征的网格自适应技术,结合低耗散迎风/中心混合格式以及延迟脱体涡模拟方法对Caradonna-Tung旋翼在桨尖马赫数为0.439、桨尖雷诺数为1.92×10~6的悬停流场进行了高分辨率计算.基于欧拉和拉格朗日两种描述方法对计算结果进行了分析,揭示了双螺旋尾涡系统的演化特性:后缘尾涡面在桨尖附近的反向卷起及其与下游桨尖涡的相互作用是影响涡系稳定性以及涡-涡相互作用的重要因素;涡龄小于720°时,在固连于桨叶上的旋转坐标系中观察,涡系具有时空稳定性,涡管中心处轴向涡量随涡龄按照幂函数规律衰减.在固连于漩涡中心的局部极坐标系中,周向速度分布以及涡核半径随涡龄的变化与理论涡模型相符合,环量随涡龄的变化显示了漩涡的生长、平衡及耗散等演化阶段;模态分析结果表明,除点涡模态外,来流与点涡的复合模态在漩涡演化过程中对流动特征的转变有重要影响;涡系轴截面速度场的拉格朗日拟序结构直观地显示了漩涡场的时空演化过程,揭示了漩涡配对和共旋穿越等流动特征,同时也展示了后缘尾涡面卷起现象在漩涡演化过程中的作用.     

Electronic speckle pattern interferometry using vortex beams

We show that it is possible to perform electronic speckle pattern interferometry (ESPI) using, for the first time to our knowledge, vortex beams as the reference beam. The technique we propose is easy to implement, and the advantages obtained are, among others, environmental stability, lower processing time, and the possibility to switch between traditional ESPI and spiral ESPI. The experimental results clearly show the advantages of using the proposed technique for deformation studies of complex structures.     

转捩边界层中流向条纹的新特性

基于边界层转捩后阶段的高精度直接数值模拟结果,发现流向条纹结构的低速条纹的演化过程中存在不连续现象,以及随高速条纹的发展会出现称之为"高速斑"的新特性. 通过详细剖析边界层转捩过程中的复杂涡系结构以及上喷下扫流动现象,证实流向高低速条纹新特性与流场涡系结构的演化过程紧密相关. 关键词： 流向条纹 边界层 转捩 直接数值模拟     

Direct numerical simulation study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence

Direct numerical simulation of decaying homogeneous isotropic turbulence (DHIT) of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase "strain generation resistance" and "vorticity generation resistance", i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.     

Annihilation of quantized vortex lines in rotating<Superscript>3</Superscript>He-A

The maximum number of vortex lines at a given angular velocity Ω is obtained during deceleration when vortices annihilate at the wall of the container. The width of the vortex-free region in the decelerated state has been measured by cw NMR for vortex lines with singular and continuous core structures. It corresponds to the limit of stability of peripheral vortices for single and double quantization respectively.     

Giant vortex lattice deformations in rapidly rotating bose-einstein condensates

We have performed numerical simulations of giant vortex structures in rapidly rotating Bose-Einstein condensates within the Gross-Pitaevskii formalism. We reproduce the qualitative features, such as oscillation of the giant vortex core area, formation of toroidal density hole, and the precession of giant vortices, observed in the recent experiment [Phys. Rev. Lett., ()]]. We provide a mechanism which quantitatively explains the observed core oscillation phenomenon. We demonstrate the clear distinction between the mechanism of atom removal and a repulsive pinning potential in creating giant vortices. In addition, we have been able to simulate the transverse Tkachenko vortex lattice vibrations.     

Two-step melting of the vortex solid in layered superconductors with random columnar pins

We consider the melting of the vortex solid in highly anisotropic layered superconductors with a small concentration of random columnar pinning centers. Using large-scale numerical minimization of a free-energy functional, we find that melting of the low-temperature, nearly crystalline vortex solid (Bragg glass) into a vortex liquid occurs in two steps as the temperature increases: the Bragg glass and liquid phases are separated by an intermediate Bose glass phase. A suitably defined local melting temperature exhibits spatial variation similar to that observed in experiments.