磁场中旋转运动圆板的分叉与混沌研究

应用数值模拟方法研究磁场中旋转运动圆板的分叉与混沌问题。首先,基于薄板理论和麦克斯韦电磁场方程组,给出了动能、应变势能、外力虚功以及电磁力的表达式,再利用哈密顿原理,得到磁场中旋转运动圆板横向振动的非轴对称非线性磁弹性振动微分方程组。其次,采用贝塞尔函数作为圆板的振型函数进行伽辽金积分,得到了轴对称情况下横向振动的常微分方程组表达式。最后,针对主共振,取周边夹支边界条件的圆板作为算例,得到了当振型函数取一阶时,将磁感应强度、外激励振幅和激励频率作为控制参数的分叉图及庞加莱映射图等计算结果,并讨论了分叉参数对系统的分叉与混沌的影响。数值计算结果表明,这些控制参数的变化影响系统稳定性,在分叉参数逐渐变化的过程中,系统经历从混沌到多倍周期运动再到混沌的往复过程。     

Nonlinear Responses of a Magnetoelastic Beam in a Step-Pulsed Magnetic Field

A theoretical study is carried out on the dynamics of a magnetoelastic beam being in a step-pulsed magnetic field. For this aim, the magnetic potential and elastic energies are determined for the beam and partial differential equations are established according to Hamilton's principle. It is proven that the magnetoelastic beam can give a variety of complex behavior in the case of step-pulsed field excitations. An intermediate regime of two-well chaos is observed. Theoretical findings were found to be in a good agreement with the experimental results for the specific system parameters. On leave from Institute of Physics, University of Bayreuth, 65440 Bayreuth, Germany An erratum to this article is available at .     

控制一类磁性刚体航天器的混沌姿态运动

本文研究一类磁性航天器的混沌姿态运动及其控制,建立了在近地球赤道面圆轨道上运动受万有引力矩、磁力矩作用磁性刚体航天器姿态运动的动力学方程。采用时间历程、Poincare截面、Lyapunov指数和功率谱对系统的动力学行为进行数值识别,结果表明随着磁场参数的增大系统动力学行为由准周期环面破裂而出现混沌。利用输入－输出反馈精确线性化的方法将航天器的混沌姿态控制运动控制为姿态静止和按给定的周期规律运动,数值结果表明该控制方法的有效性。     

力学系统混沌的主动控制

对混沌进行控制是将非线性科学应用于工程技术的新研究领域．本文首先综述对力学系统混沌运动进行控制的各种策略，然后讨论了实现中的关键问题，介绍了成功的实验．最后，指出了该领域中值得注意的若干问题．     

Competitive modes for the Baier–Sahle hyperchaotic flow in arbitrary dimensions

In this article, the stretch-twist-fold (STF) flow is numerically studied using phase portraits, sensitive dependence on initial conditions, Lyapunov exponents, power spectrum, and the Poincaré map. The stretch-twist-fold flow is a two-parameter family of Stokes flows defined in a unit sphere that is associated with the fluid particle motion that naturally arises in the dynamo theory, which proposes a mechanism by which celestial bodies, such as earth and sun can maintain and amplify the magnetic field continuously. For this continuous growth of magnetic field, scientists are interested to invent new tools for the nonfuel consumption magnetism propulsion for the low earth orbit of spacecrafts or satellites. General properties of a chaotic dynamical system reference to the stretch-twist-fold flow model are addressed and numerical solutions are generated to explain some of these properties. Analytically, we studied the local behavior at equilibrium points. The predictability of chaos in the STF flow with the numerical calculation of Lyapunov exponents and Poincaré map is presented in this paper.     

MULTI-MODE OSCILLATIONS AND HAMILTON ENERGY FEEDBACK CONTROL OF A CLASS OF MEMRISTOR NEURON$^{\bf 1)}$

根据法拉第电磁感应定律,在离子穿越细胞膜或者在外界电磁辐射下,细胞内外的电生理环境会产生电磁感应效应,继而会影响神经元的电活动行为. 基于此,本文考虑电磁感应影响下的 Hindmarsh-Rose (HR) 神经元模型,研究了其混合模式振荡放电特征,并设计一个 Hamilton 能量反馈控制器,将其控制到不同的周期簇放电状态. 首先,通过理论分析发现磁通 HR 神经元系统的 Hopf 分岔使其平衡点的稳定性发生了改变,并产生极限环,进而研究了 Hopf 分岔点附近膜电压的放电特征. 基于双参数数值仿真发现该系统具有丰富的分岔结构,在不同的参数平面上存在倍周期分岔、伴有混沌的加周期分岔、无混沌的加周期分岔以及共存的混合模式振荡. 最后,为了有效控制膜电压的混合模式振荡,利用亥姆霍兹理论计算出磁通 HR 神经元系统的 Hamilton 能量函数并设计 Hamilton 能量反馈控制器,通过数值仿真分析了膜电压在不同反馈增益下的簇放电状态,发现该控制器能够有效地控制膜电压到不同的周期簇放电模式. 本文的研究结果为探究电磁感应下神经元的分岔结构及其能量控制领域提供了有用的理论支撑.     

一类忆阻神经元的电活动多模振荡及Hamilton 能量反馈控制

根据法拉第电磁感应定律,在离子穿越细胞膜或者在外界电磁辐射下,细胞内外的电生理环境会产生电磁感应效应,继而会影响神经元的电活动行为. 基于此,本文考虑电磁感应影响下的 Hindmarsh-Rose (HR) 神经元模型,研究了其混合模式振荡放电特征,并设计一个 Hamilton 能量反馈控制器,将其控制到不同的周期簇放电状态. 首先,通过理论分析发现磁通 HR 神经元系统的 Hopf 分岔使其平衡点的稳定性发生了改变,并产生极限环,进而研究了 Hopf 分岔点附近膜电压的放电特征. 基于双参数数值仿真发现该系统具有丰富的分岔结构,在不同的参数平面上存在倍周期分岔、伴有混沌的加周期分岔、无混沌的加周期分岔以及共存的混合模式振荡. 最后,为了有效控制膜电压的混合模式振荡,利用亥姆霍兹理论计算出磁通 HR 神经元系统的 Hamilton 能量函数并设计 Hamilton 能量反馈控制器,通过数值仿真分析了膜电压在不同反馈增益下的簇放电状态,发现该控制器能够有效地控制膜电压到不同的周期簇放电模式. 本文的研究结果为探究电磁感应下神经元的分岔结构及其能量控制领域提供了有用的理论支撑.      

单调激活函数惯性项神经耦合系统的混沌共存

混沌及其稳态共存是神经网络系统中一个重要研究热点问题．本文基于惯性项神经元模型,利用非线性单调激活函数构造了一个惯性项神经耦合系统,采用理论分析和数值模拟相结合的方法,研究了系统平衡点以及静态分岔的类型,分析了系统两种不同模式的混沌及其稳态共存．具体来说,我们通过选取不同的初始值,利用相应的相位图和时间历程图,展现了系统混沌对初值的敏感依赖性．进一步,采用耦合强度作为动力学的分岔参数,研究了混沌产生的倍周期分岔机制,得到了单调激活函数耦合下的惯性项神经元系统混沌共存现象．     

The danger of wishing for chaos

With the discovery of chaos came the hope of finding simple models that would be capable of explaining complex phenomena. Numerous papers claimed to find low-dimensional chaos in a number of areas ranging from the weather to the stock market. Years later, many of these claims have been disproved and the fantastic hopes pinned on chaos have been toned down as research with more realistic objectives follows. The difficulty in calculating reliable estimates of the correlation dimension and the maximal Lyapunov exponent, two of the hallmarks of chaos, are explored. Given that nonlinear dynamics is a relatively new and growing field of science, the need for statistical testing is greater than ever. Surrogate data provides one possible approach but great care is needed in generating relevant surrogates and in interpreting the results. Examples of misleading applications and challenges for the future of research in nonlinear dynamics are discussed.     

Numerical prediction of the influence of uncertain inflow conditions in pipes by polynomial chaos

Nearly all types of flow measurement devices installed in pipes are affected by the flow conditions at their inlet section, which can lead to measurement errors of several per cent. To evaluate the influence of uncertain inflow profiles on the flow field at different positions of the flow meter, a non-intrusive polynomial chaos approach is applied to simulations of turbulent pipe flow. This allows us to estimate the expected variations of the flow profiles as a function of the distance to the inlet of the pipe in an efficient way. The polynomial chaos approach shows reasonable convergence already for a small number of function evaluations. The results are validated by comparison with a quasi-Monte Carlo method and an exact solution, where available. The approximation error of the polynomial chaos method with 10 function evaluations is smaller than the one for the quasi-Monte Carlo method with 100 runs.     

Chaos Theory and the Problem of Change in Family Systems

In spite of the fact that nonlinear dynamical models have been used for almost half a century in the area of family process theory, an appreciation of the potential of chaos models is a relatively recent development. The present paper discusses the shift of focus in our understanding of family processes resulting from Prigogine's chaos framework, and outlines a chaos approach to family interaction. It is argued that this approach allows us to more effectively address one of the central outstanding questions in the field, namely, how self regulatory behavior can contribute to structural transformation of the family system.     

Bifurcation and chaos analysis of torsional vibration in a PMSM-based driven system considering electromechanically coupled effect

The rotor of PMSM-based electromechanically driven system is a typical electromechanically coupled system. In this paper, we analyzed the nonlinear magnetic interaction torque of permanent magnet synchronous motor (PMSM) and deduced the nonlinear electromechanically coupled equation of PMSM-based electromechanical driven system using Lagrange–Maxwell theory. We determined the equation of the movement of the dynamic system from his asymmetric double well potential. The unperturbed system was classified to several categories based on the shapes of potential functions and phase portraits. An analytical criterion for homoclinic chaos is written in terms of the system parameters by means of Melnikov’s method. Detailed numerical studies including phase portrait, Poincare map, and bifurcation diagram confirm the analytical prediction and reveal the effect of excitation amplitude and damp on the system transition to chaos. The conclusion can provide reference for deeply research the dynamic behaviors of mechanical drive system.     

Chaotic attitude motion of a magnetic rigid spacecraft

IntroductionAttitudedynamicsofspacecraftisascientificresearchsubjectwithgreatsignificance[1,2 ].Aschaosiswidelyanddeeplyinvestigated ,muchattentionhasbeenpaidonchaoticattitudemotionofspacecraft.Itnotonlyprovidesadefiniteengineeringbackgroundforexploringchaos,butalsooffersanewviewpointfordesigningspacecraft.Ithasbeenshownthatthereexistschaoticattitudemotioninsomemodelsofspacecraft,suchasspinningsatellitesinacircularorbit,gyrostatsatellitesinthegravitationalfield ,andtetheredsatellites[3 ,4].Ho…     

Experimental investigation on heat transfer characteristics of magnetic fluid flow around a fine wire under the influence of an external magnetic field

Experimental investigation is conducted to get insight into convective heat transfer features of the aqueous magnetic fluid flow over a fine wire under the influence of an external magnetic field. The convective heat transfer coefficient of the aqueous magnetic fluid flow around the heated wire is measured in both the uniform magnetic field and the magnetic field gradient. The effects of the external magnetic field strength and its orientation on the thermal behaviors of the magnetic fluids are analyzed. The experimental results show that the external magnetic field is a vital factor that affects the convective heat transfer performances of the magnetic fluids and the control of heat transfer processes of a magnetic fluid flow can be possible by applying an external magnetic field.     

Chaotic attitude motion of a magnetic rigid spacecraft and its control

This paper deals with chaotic attitude motion of a magnetic rigid spacecraft with internal damping in a circular orbit near the equatorial plane of the earth. The dynamical model of the problem is established. The Melnikov analysis is carried out to prove the existence of a complicated non-wandering Cantor set. The dynamical behaviors are numerically investigated by means of time history. Poincare map, power spectrum and Lyapunov exponents. Numerical simulations indicate that the onset of chaos is characterized by the intermittency as the increase of the torque of the magnetic forces and decrease of the damping. The input-output feedback linearization method is applied to control chaotic attitude motions to the given fixed point and periodic motion.     

Experiments and mechanism analysis of pool boiling heat transfer enhancement with water-based magnetic fluid

A pool boiling heat transfer comparison among water-based magnetic fluids in the absence and presence of a magnetic field with its carrier liquid water was made. The experimental results show that the boiling heat transfer of magnetic fluid increased much in the absence of a magnetic field, and the applied magnetic field made the boiling heat transfer of magnetic fluid enhance further. The effect of a magnetic field on bubbles was analyzed. It was clarified that the nonuniform magnetic field changed the bubble departure diameter and shape during boiling.     

Dynamical analysis of axially moving plate by finite difference method

The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion of the plate is derived by Newton’s second law. The finite difference method in spatial field is applied to the differential equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion, and then the periodic motion becomes chaotic motion by period-doubling bifurcation.     

Review of chaos in the dynamics and rheology of suspensions of orientable particles in simple shear flow subject to an external periodic force

We review results obtained over a period of about a decade on a class of technologically and fundamentally important problems in suspension rheology viz., the dynamics and rheology of dipolar suspensions of orientable particles in simple shear flow. The areas explored in this review include effects such as the fluid flow field, external forcing, Brownian diffusion, hydrodynamic interactions and their impact on the rheological properties of the suspension. The main feature of the presentation is the use of a uniform framework in which one or more of the above effects can be studied, based on Langevin type equations for particle orientations combined with a brute-force technique for computing orientational averages. These models are capable of capturing complex dynamical behaviour in the system such as the presence of subharmonics or chaos, both in the dynamics and rheology. The tools developed allow for investigating how chaos in the system is affected by Brownian diffusion and hydrodynamic interactions. The presence of chaos opens up a number of novel possibilities for dynamical and rheological behaviour of the system, which can be put to efficient use in many ways, e.g. in separating particles by aspect ratio and possibly developing computer controlled intelligent rheology. The results also have implications for certain areas of chaos theory, such as a new intermittency route to chaos and the possibility of non-trivial collective behaviour in spatially extended systems. These studies highlight certain deficiencies in current techniques in the literature for handling the rheology of dilute and semi-dilute suspensions. In the presence of Brownian motion the proposed method computes the averages by simulating a set of deterministic ordinary differential equations rather than stochastic differential equations. The systems considered may also serve as a paradigm for analysing how microscopic chaotic fluctuations in spatially extended systems affect macroscopic averages. We also attempt to put our results into context with respect to recent work on rheochaos in complex fluids such as liquid crystals and nematic polymers.     

不同初始磁场对激波冲击R22重气柱过程影响的数值模拟

基于磁流体动力(magneto-hydrodynamic,MHD)方程,采用CTU+CT方法,对在不同初始磁场作用下的平面入射激波与磁化R22重质气柱作用过程进行了数值研究。数值结果清晰地描述了不同初始磁场条件时激波诱导R22气柱界面不稳定性的过程,揭示了磁场控制界面不稳定性的机理。另外,还分析了磁感应强度对界面不稳定性的影响,发现在磁场较小时,涡层附着于界面,但随着磁感应强度的增大,平均涡量随之增大,涡层与界面逐渐分离,最终更好地抑制了界面不稳定性。同时,还发现平均涡度拟能随着磁感应强度的增大而减小,而垂直磁场比平行磁场更能降低平均涡度拟能,因而平均涡度拟能可较好地反映磁场对不稳定性的影响效果。     

Effect of the magnetic field on the pulsatile flow through a rigid tube

I.IntroductionThefunctionofanaPbliedmagneticfield\onhumanbodieshasbeenknownandservedasakindofthemedicaltreatmentforalongtime.ThemagneticstoneusedasamedicineisrdeordedinShennongMaterlbMedica,'which.isthefirstChinesemedicinebookandwaswrittenin200A.D..ItwasalsorecordedtyancientGreecethatholdingmagneticstQnesinhandsandfeetcouldrelievethepainandspasml'l.However,beinglimitedbythelevelQfproductionandmedicaltreatmentsatthattime,themagnetictreatmentwasmainlyusedforlocallydephlogisticating,relievin…