Experimental evidence of a phase transition in a closed turbulent flow

We experimentally study the susceptibility to symmetry breaking of a closed turbulent von Kármán swirling flow from Re=150 to Re?10?. We report a divergence of this susceptibility at an intermediate Reynolds number Re=Re(χ)?90,000 which gives experimental evidence that such a highly space and time fluctuating system can undergo a "phase transition." This transition is furthermore associated with a peak in the amplitude of fluctuations of the instantaneous flow symmetry corresponding to intermittencies between spontaneously symmetry breaking metastable states.     

用连续法计算五维对流模型的定常解和周期解

利用连续算法(Continuation algorithm)对五维对流非线性动力系统的定常解和周期解进行了数值计算。在参数平面Ri-Re上计算出实分岔点曲线、极限点曲线、Hopf分岔点曲线,绘出了分岔图。在分岔图上的不同区域,存在性质不同的稳定解如定常吸引子、周期吸引子等。分析了定常解、周期解的分岔过程。计算结果很好地说明大气中由基本态到对流态再到波动态最后到湍流态的物理转换过程。 连续算法对研究非线性动力系统的分岔以及耗散结构是很有效的计算方法。     

Slow dynamics in a turbulent von Kármán swirling flow

An experimental study of a turbulent von Kármán flow in a cylinder is presented. The mean flow is stationary up to a Reynolds number Re=10(4) where a bifurcation takes place. The new regime breaks some symmetries of the problem and becomes time dependent because of equatorial vortices moving with a precession movement. In the exact counterrotating case, a bistable regime appears and spontaneous reversals of the azimuthal velocity are registered. A three-well potential model with additive noise reproduces this dynamic. A regime of periodic response is observed when a very weak forcing is applied.     

Continuation of periodic solutions in the waveguide array mode-locked laser

We apply the adjoint continuation method to construct highly accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities. The method allows for the construction of solution branches and the identification of their bifurcation structure. Supplementing the adjoint continuation method with a computation of the Floquet multipliers allows for explicit determination of the stability of each branch. This method reveals that, when gain is increased, the multi-pulsing transition starts with a Hopf bifurcation, followed by a period-doubling bifurcation, and a saddle-node bifurcation for limit cycles. Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions. Although this method is applied specifically to the waveguide array mode-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from other models.     

Bifurcation structures into chaos of delay-differential equations for a passive optical ring resonator

The delay-differential equation system describing the passive optical ring cavity is investigated. A survey of different bifurcation scenarios into chaos of the solutions on one branch and specific transitions between different branches of the multistable system are discussed. Precipitation via a heteroclinic cycle and crisis induced intermittency are found.     

Dynamics of three-tori in a periodically forced navier-stokes flow

Three-tori solutions of the Navier-Stokes equations and their dynamics are elucidated by use of a global Poincare map. The flow is contained in a finite annular gap between two concentric cylinders, driven by the steady rotation and axial harmonic oscillations of the inner cylinder. The three-tori solutions undergo global bifurcations, including a new gluing bifurcation, associated with homoclinic and heteroclinic connections to unstable solutions (two-tori). These unstable two-tori act as organizing centers for the three-tori dynamics. A discrete space-time symmetry influences the dynamics.     

Dynamics of a deformable body in a fast flowing soap film

We study the behavior of an elastic loop embedded in a flowing soap film. This deformable loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a two-dimensional flexible body interacting in a two-dimensional flow. This coupled fluid-structure system shows bistability, with both stationary and oscillatory states. In its stationary state, the loop remains essentially motionless and its wake is a von Kármán vortex street. In its oscillatory state, the loop sheds two vortex dipoles, or more complicated vortical structures, within each oscillation period. We find that the oscillation frequency of the loop is linearly proportional to the flow velocity, and that the measured Strouhal numbers can be separated based on wake structure.     

耦合振子系统的多稳态同步分析

本文讨论了一维闭合环上Kuramoto相振子在非对称耦合作用下同步区域出现的多定态现象. 研究发现在振子数N≤3情形下系统不会出现多态现象, 而N≥4多振子系统则呈现规律的多同步定态. 我们进一步对耦合振子系统中出现的多定态规律及定态稳定性进行了理论分析, 得到了定态渐近稳定解. 数值模拟多体系统发现同步区特征和理论描述相一致. 研究结果显示在绝热条件下随着耦合强度的减小, 系统从不同分支的同步态出发最终会回到同一非同步态. 这说明, 耦合振子系统在非同步区由于运动的遍历性而只具有单一的非同步态, 在发生同步时由于遍历性破缺会产生多个同步定态的共存现象.     

Bifurcations in a system of two identical diffusion-coupled relaxational brusselators

We propose a two-parameter bifurcation analysis of the dynamics of a system of two identical asymmetrically coupled Brusselators. The stability boundaries of the inhomogeneous steady states and periodic attractors are calculated as the functions of the constraint force and one of the free parameters. The coexistence of different attractors giving rise to multirhythmicity of the dynamics is studied as well as the bifurcation transitions between them. It is shown that the relaxation ability of an oscillator plays an important role in the simplification of the phase diagram, since it removes the overlapping of the existence region for different solutions. We assume that the results primarily characterize the properties of the diffusion coupling and, therefore, they can be applied in the study of other oscillator systems.P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 5, pp. 373–401, May, 1995.     

Comparison of a low- to high-confinement transition theory with experimental data from DIII-D

From our recent theory based on the generation of shear flow and field in finite beta plasmas, the criterion for bifurcation from low to high confinement mode yields a critical parameter proportional to T(e)/square root (L(n)), where T(e) is the electron temperature and L(n) is the density scale length. The predicted threshold shows very good agreement with edge measurements on discharges undergoing low-to-high transitions in DIII-D. The observed differences in the transitions with the reversal of the toroidal magnetic field are reconciled in terms of this critical parameter. The theory also provides an explanation for pellet injection H modes in DIII-D, thereby unifying unconnected methods for accomplishing the transition.     

Transport of magnetic field by a turbulent flow of liquid sodium

We study the effect of a turbulent flow of liquid sodium generated in the von Kármán geometry, on the localized field of a magnet placed close to the frontier of the flow. We observe that the field can be transported by the flow on distances larger than its integral length scale. In the most turbulent configurations, the mean value of the field advected at large distance vanishes. However, the rms value of the fluctuations increases linearly with the magnetic Reynolds number. The advected field is strongly intermittent.     

Macroscopic phase-field model of partial wetting: bubbles in a capillary tube

Drops and bubbles are nonspreading, local, compactly supported features. They are also equilibrium configurations in partial wetting phenomena. Yet, current macroscopic theories of capillary-dominated flow are unable to describe these systems. We propose a framework to model multiphase flow in porous media with nonspreading equilibrium configurations. We illustrate our approach with a one-dimensional model of two-phase flow in a capillary tube. Our model allows for the presence of compactons: nonspreading steady-state solutions in the absence of external forces. We show that local rate dependency is not needed to explain globally rate-dependent displacement patterns, and we interpret dynamic wetting transitions as the route from equilibrium, capillary-dominated configurations, towards viscous-dominated flow. Mathematically, these transitions are possible due to nonclassical shock solutions and the role of bistability and higher-order terms in our model.     

A multi-stable energy harvester: Dynamic modeling and bifurcation analysis

A theoretical investigation is conducted on the dynamic and energetic characteristics of a multi-stable bimorph cantilever energy harvester that uses magnetic attraction effect. The multi-stable energy harvester under study is composed of a bimorph cantilever beam with soft magnetic tip and two externally fixed permanent magnets that are arranged in series. With this configuration, the magnetic force and the moment that are exerted on the cantilever tip tend to be highly dependent on the magnetic field induced by the external magnets. Such an energy harvester can possess multi-stable potential functions, ranging from mono-stable to penta-stable. The mechanism that governs the formation of this multi-stability is thoroughly identified and examined thorough a bifurcation analysis performed on the system?s equilibrium solutions. From this analysis, it is found that the transitions between these multi-stable states occur through very complicated bifurcation scenarios that include degenerate pitchfork bifurcations and mergers of pitchfork bifurcations or saddle-node bifurcations. Bifurcation set diagram is obtained, which is composed of five separate parametric regions, from mono- to penta-stability. The resulting stability map satisfactorily describes the multi-stable characteristics of the present energy harvester. In addition, the dynamic and energetic characteristics of the present multi-stable energy harvester are more thoroughly examined using its potential energy diagrams and a series of numerical simulations, and the obtained results are compared with those for the equivalent bi-stable cases.     

非线性传送带系统的复杂分岔

讨论了一类单自由度非线性传送带系统. 首先通过分段光滑动力系统理论得出系统滑动区域的解析分析和平衡点存在性条件; 其次利用数值方法, 对系统几种类型的周期轨道进行单参数和双参数延拓, 得到系统的余维一滑动分岔曲线和若干余维二滑动分岔点, 以及系统在参数空间中的全局分岔图. 通过对系统分岔行为的研究, 反映出传送带速度和摩擦力振幅对系统动力学行为有较大影响, 揭示了非线性传送带系统的复杂动力学现象. 关键词： 传送带系统 滑动分岔 周期运动     

Memory effects are relevant for chaotic advection of inertial particles

A systematic investigation of the effect of the history force on particle advection is carried out in a paradigmatic model flow of chaotic advection, the von Kármán flow. All investigated properties turn out to heavily depend on the presence of memory when compared to previous studies neglecting this force. We find a weaker tendency for accumulation and for caustics formation. The Lyapunov exponent of transients becomes larger, the escape rates are strongly altered. Attractors are found to be suppressed by the history force, and periodic ones have a very slow, t(-1/2)-type convergence towards the asymptotic form.     

Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser

A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super-from the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping.     

风力发电机自循环蒸发内冷系统稳定性的研究

自循环蒸发内冷系统的冷却效率高,可以实现无泵自循环,运行安全可靠,基本免维护,因此适合在大型风力发电机中使用.蒸发内冷系统的稳定性对风力发电机的安全运行十分重要,本文基于非线性分岔理论及其数值延拓法,对自循环蒸发内冷系统应用于风力发电机的的静态稳定性进行了深入研究.获得了系统静态分岔解图,分析了系统演化特性,同时分析了系统分岔现象的参数效应.搭建了实验平台,通过实验观测到了自循环蒸发内冷系统的静态分岔现象,验证了理论计算的正确性.     

Yielding and flow in adhesive and nonadhesive concentrated emulsions

The nonlinear rheological response of soft glassy materials is addressed experimentally by focusing on concentrated emulsions where interdroplet attraction is tuned through varying the surfactant content. Velocity profiles are recorded using ultrasonic velocimetry simultaneously to global rheological data in the Couette geometry. Our data show that nonadhesive and adhesive emulsions have radically different flow behaviors in the vicinity of yielding: while the flow remains homogeneous in the nonadhesive emulsion and the Herschel-Bulkley model for a yield stress fluid describes the data very accurately, the adhesive system displays shear localization and does not follow a simple constitutive equation, suggesting that the mechanisms involved in yielding transitions are not universal.     

One to one resonant double Hopf bifurcation in aeroelastic oscillators with tuned mass dampers

The effects of a tuned added mass on the aeroelastic stability of a single degree of freedom bluff body exposed to a steady flow are investigated. The model captures the essential aspects of the behaviour of flexible structures equipped with Tuned Mass Dampers undergoing galloping oscillations. The system exhibits simple as well double Hopf bifurcations, of non-resonant and 1:1 resonant type. Postcritical behaviour of the system in the neighbourhood of the 1:1 resonant type bifurcation is investigated. Employing the Multiple Scale Method, a second order bifurcation equation in the complex amplitude of motion is obtained. Analytical solutions are used to describe the bifurcation scenario in the cases of both undercritical and supercritical aerodynamic behaviour of the bluff body. The effectiveness of the Tuned Mass Damper even in the postcritical range is proved.