Landau damping of ion-acoustic waves with simultaneous effects of non-extensivity and non-thermality in the presence of hybrid Cairns-Tsallis distributed electrons

The dispersion properties and Landau damping rate of ion-acoustic waves (IAWs) with the hybrid Cairns-Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov-Poisson's equations. For both super-extensive (q < 1) and sub-extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θ_{i, e} (ion-to-electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super-extensive and sub-extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non-thermal parameter α and non-extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θ_{e, i} (electron-to-ion temperature ratio), on decreasing the values of the non-extensive parameter and increasing values of the non-thermal parameter, the weak damping rate is observed (vice versa) in super-extensive or super-thermal plasma, although the trend of the damping rate in sub-thermal plasma is similar (as in the case of super-thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non-thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.     

Coherence and chaos in the driven,damped sine-Gordon chain

Representative example of preliminary numerical results are presented for solutions of the deterministic sine-Gordon equation under the influence of damping and a sinusoidal uniform driving force. Depending on the choice of (inhomogeneous) initial conditions and values of the amplitude and frequency of the driving force, we find a great variety of possible responses, including: (i) permanent spatial structures riding on an overall background motion which can be temporally chaotic or not, (ii) intermittent transitions between at least two metastable spatial structures which are typically a localized breather-like structure and an extended wave train, in the presence of temporal chaos or not and with large- or small-amplitude background motion. For some parameter values, we find very similar power spectra for different initial conditions, while other cases show considerable dependence on initial conditions. Both the spatial and temporal behavior of the response can exhibit extreme sensitivity to small changes in the parameters.     

Temperature dependence of the Raman bandwidths and intensities of a lattice mode near the tricritical and second order phase transitions in NH4Cl

We calculate here the temperature dependence of the damping constant using the expressions derived from the Matsushita's theory and the temperature dependence of the order parameter from the molecular field theory for the tricritical (1.5?kbar) and second order (2.8?kbar) phase transitions in NH₄Cl. Our calculations are performed for the ν ₅ (174?cm^?1) Raman mode of NH₄Cl for the pressures studied. Predictions for the damping constant are in good agreement with our observed Raman bandwidths of this lattice mode for both pressures. The Raman intensities calculated from the molecular field theory by means of the order parameter are also in good agreement with our observed Raman intensities of the ν ₅ (174?cm^?1) mode for both tricritical (1.5?kbar) and second order (2.8?kbar) phase transitions in NH₄Cl. In this study our observed Raman intensities of this lattice mode are analysed using a power-law formula with the critical exponent β for the order parameter at those two pressures considered in NH₄Cl. From our analysis, the value of β?=?0.5 is obtained as the mean field value.     

On the notion of a rotating fluid force induced by swirling flow

The Bently/Muszynska (B/M) model shows that oil whirl and oil whip are both self-sustained vibrations associated with two unstable modes of a rotor–fluid system. The model includes a rotating fluid damping and inertia force. In certain configurations, the rotating damping force overcomes the frictional internal damping of the rotor and pushes the rotor into a stable limit cycle of circular orbiting. Such a notion of a rotating fluid force is based on bulk-flow models of fluid-filled clearances that could be approximated as narrow since the tangential velocity of the fluid then translates to one angular velocity at a certain radial distance defined by an average radius. This paper scrutinizes the assumption of a rotating fluid inertia force and pinpoints the additional inertial effects of the swirling flow as the gap width increases. These effects are clarified by deriving the equation of motion of a body with a mass subjected to motion-induced fluid forces of a confined swirling flow. We show that the inertial effects of the swirling flow counteract the destabilizing effect of the rotating damping force. However, if the body mass is larger than the displaced fluid mass, instability follows. The frequency of the unstable mode is unchanged by the additional inertial effects and is always equal to the frequency of the damping that induces the instability.     

Optimization of deconvolution in Compton profile measurements

The method of generalized least squares has been used to deconvolute the Compton profile measurements in nickel. The method depends on two arbitrary parameters namely the cut-off parameterK and the damping factor λ. This has been discussed and a method suggested to optimize the damping parameter.     

Experimental characterization and modeling of microsliding on a small cantilever quartz beam

The design of mechanical systems requires various studies in order to ensure an optimal behavior during operation. In particular, the study of its dynamic behavior makes it possible to evaluate the role of a connection in the energy dissipation mechanisms. In this context, an experimental setup dedicated to small structures has been developed to quantify damping due to microsliding at the beam–clamp interface. The mechanical characterization of the clamped connection is carried out by experimental dynamic tests on a free-clamped structure. The instantaneous frequencies and damping are identified by the wavelet transform technique of a slightly nonlinear system. In parallel, numerical prediction of the equivalent damping is achieved thanks to the implementation of the regularized Coulomb law in a finite element model. A genetic algorithm and artificial neural networks are used to update the stiffness parameter and the friction coefficient. The optimized model is in good agreement with experimental results. It allows for determining the spatial distribution of microsliding and tangential force along the contact interface. The dissipated energy and equivalent damping are finally deduced according to the dynamic deflection of the free part of the beam.     

The influence of a wieghardt type elastic foundation on the stability of some beams subjected to distributed tangential forces

In this investigation, the influence of a Wieghardt type elastic foundation on the stability of cantilever and clamped-hinged beams subjected to either a uniformly or a linearly distributed tangential force is considered. In addition to the usual transverse foundation modulus, the Wieghardt model includes the effects of inertia and shear deformation in the foundation. Approximate solutions of the Ritz type are obtained for the pertinent eigenvalue problems, and numerical calculations are reported for various combinations of the internal damping, inertia, transverse foundation modulus and shear foundation modulus parameters. The numerical results reveal that, in general, for a fixed value of the transverse foundation modulus parameter κ, an increase in the shear foundation modulus increases the critical load, whereas an increase in the foundation inertia parameter tends to decrease the critical load. The system consisting of a clamped-hinged beam subjected to a uniformly distributed tangential force loses stability through divergence, provided that the value of κ is sufficiently small. However, when κ becomes large enough, stability will be lost through flutter. In this case, the critical load considered as a function of κ possesses a discontinuity at the transition between divergence and flutter, and its value will either increase or decrease, depending upon the degree of damping in the system.     

Spring pendulum: Parametric excitation vs an external force

The method of multiple scales is applied to obtain an approximate solution to the nonlinear dynamic equations describing a spring pendulum with the vertical oscillations of the suspension point up to and including the fourth order corrections. The solutions of these equations, where an external force enters the equations multiplicatively, are compared with the solution considered earlier, for the behavior of a spring pendulum subject to an external force, which enters the appropriate equations additively. It turns out that in lower orders in small parameter, the two solutions coincide for the case where the external force and viscous damping force are equally small, but they differ when the damping is much smaller than the external force.     

有限温度下光频支声子-磁振子相互作用对磁振子寿命的影响

在二维复式正方Heisenberg铁磁系统的基础上建立了磁振子-声子相互作用模型.利用松原格林函数理论研究了系统的磁振子寿命,计算了布里渊区的主要对称点线上的磁振子衰减的变化曲线,比较了磁性离子的与非磁性离子的光频支声子对磁振子衰减的影响以及各项参数的变化和温度对磁振子衰减的影响.发现光频支声子-磁振子耦合对磁振子衰减起主要作用,尤其是纵向光频支声子对磁振子衰减起更大的作用,并且非磁性离子的光频支声子对磁振子衰减的作用比磁性离子的光频支声子对磁振子衰减的作用更显著.根据关系式-Im∑^*(1)(k)=/(2τ)可以对磁振子寿命进行判断. 关键词： 光频支声子-磁振子相互作用 磁振子衰减 磁振子寿命 绝缘复式正方铁磁体系统     

Longitudinal Dust Lattice Shock Wave in a Strongly Coupled Complex Dusty Plasma

The effect of hydrodynamical damping that arises due to the irreversible processes within the system have been studied on 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. Analytical investigation shows that the nonlinear wave is governed by Korteweg‐de Vries Burgers' equation. This hydrodynamical damping induced dissipative effect is responsible for the Burgers' term that causes the generation of shock wave in dusty plasma crystal. Numerical investigation on the basis of the glow‐discharge plasma parameters reveal that LDLW exhibits both oscillatory and monotonic shock. The shock is compressive in nature and its strength decreases (increases) with the increase of the shielding parameter κ (characteristic length L). The effects of dust‐neutral collision are also discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the destabilizing effect of damping on discrete and continuous circulatory systems

The ‘Ziegler paradox’, concerning the destabilizing effect of damping on elastic systems loaded by nonconservative positional forces, is addressed. The paper aims to look at the phenomenon in a new perspective, according to which no surprising discontinuities in the critical load exist between undamped and damped systems. To show that the actual critical load is found as an (infinitesimal) perturbation of one of the infinitely many sub-critically loaded undamped systems. A series expansion of the damped eigenvalues around the distinct purely imaginary undamped eigenvalues is performed, with the load kept as a fixed, although unknown, parameter. The first sensitivity of the eigenvalues, which is found to be real, is zeroed, so that an implicit expression for the critical load multiplier is found, which only depends on the ‘shape’ of damping, being independent of its magnitude. An interpretation is given of the destabilization paradox, by referring to the concept of ‘modal damping’, according to which the sign of the projection of the damping force on the eigenvector of the dual basis, and not on the eigenvector itself, is the true responsible for stability. The whole procedure is explained in detail for discrete systems, and successively extended to continuous systems. Two sample structures are studied for illustrative purposes: the classical reverse double-pendulum under a follower force and a linear visco-elastic beam under a follower force and a dead load.     

The behaviour of an isolated impurity near a phase transition in a spherical-like model

The behaviour of an isolated impurity in a crystal undergoing a displacive phase transition is investigated in an exactly soluble spherical-like model. We find, depending on the parameter of the impurity, either a global phase transition at the bulkT _c or a freezing-out of local order at a temperatureT _c ^loc >T _c driven by a soft local mode. We furthermore discuss the dynamic autocorrelation function of the impurity by introducing a phenomenological damping.Work Supported by The Swiss National Science Foundation     

分数阶质量涨落谐振子的共振行为

针对黏性介质引起的Brown粒子质量存在随机涨落以及阻尼力对历史速度具有记忆性等问题, 本文首次提出分数阶质量涨落谐振子模型, 以考察黏性介质中Brown粒子的动力学特性. 首先, 将Shapiro-Loginov 公式分数阶化, 使之适用于对含指数关联随机系数的分数阶随机微分方程的求解. 然后, 利用随机平均法和分数阶Shapiro-Loginov公式推导系统稳态响应振幅的解析表达式, 并据此研究系统的共振行为; 最后, 通过仿真实验验证理论结果的可靠性. 研究表明: 1)质量涨落噪声可诱导系统产生随机共振行为; 2)记忆性阻尼力可诱导系统产生参数诱导共振行为; 3)不同参数条件下, 系统表现出单峰共振、双峰共振等多样化的共振形式. 关键词： 黏性介质 质量涨落 阻尼记忆性 分数阶谐振子     

Determination of time-varying contact length,friction force,torque and forces at the bearings in a helical gear system

This paper deals with determining various time-varying parameters that are instrumental in introducing noise and vibration in a helical gear system. The most important parameter is the contact line variation, which subsequently induces friction force variation, frictional torque variation and variation in the forces at the bearings. The contact line variation will also give rise to gear mesh stiffness and damping variations. All these parameters are simulated for a defect-free and two defective cases of a helical gear system. The defective cases include one tooth missing and two teeth missing in the helical gear. The algorithm formulated in this paper is found to be simple and effective in determining the time-varying parameters.     

New approach for obtaining the time-evolution law of chaotic light field in damping—gaining process

A new approach for studying the time-evolution law of chaotic light field in damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator ρ(t) is derived and the solution of f′ for damping and gaining processes are studied separately. Our approach is direct and the result is concise since it is not necessarily for us to know the Kraus operators in advance.     

Spin density polarization effects in the presence of Coriolis force on ion acoustic waves in quantum plasma

Ion acoustic solitary waves in a quantum plasma, which is slowly rotating around an axis at an angle θ with the direction of magnetic field, are investigated. Quantum hydrodynamic model is under consideration with the effects of rotations which are included via Coriolis force. Fermions are degenerate and have different spin density states, that is, up and down characterized via parameter α. Linear analysis is performed by applying Fourier transformation to derive dispersion relation. For nonlinear analysis, we apply reductive perturbation method to derive Korteweg de Vries equation (KdV). The effects of variations of Coriolis force, spin polarization, and quantum parameter on characteristics of solitary structure are discussed. These results are applicable to astrophysical and laboratory plasmas.     

Stability of a nonlinear oscillator with random damping

A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be predicted from the analysis of the moments of the linearized equation. In the case of a white noise, an exact formula for the Lyapunov exponent of the system is derived. We then calculate the critical damping for which the nonlinear system becomes unstable. We also characterize the intermittent structure of the bifurcated state above threshold and address the effect of temporal correlations of the noise by considering an Ornstein-Uhlenbeck noise.     

Effect of baffle on gravity-gradient-excited slosh waves and spacecraft moment and angular-momentum fluctuations in microgravity

Summary The dynamical behavior of fluids affected by the asymmetric gravity gradient acceleration has been investigated. In particular, the effects of surface tension on partially filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank with and without baffles are studied. Results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient acceleration indicate that the gravity gradient acceleration is equivalent to the combined effect of a twisting force and a torsional moment acting on the spacecraft. The results are clearly seen from one-up one-down and one-down one-up oscillations in the cross-section profiles of two bubbles in the vertical (r, z)-plane of the rotating dewar, and from the eccentric contour of the bubble rotating around the axis of the dewar in a horizontal (r, θ)-plane. As the viscous force, between liquid and solid interface, greatly contributes to the damping of slosh wave excitation, a rotating dewar with baffles provides more areas of liquid-solid interface than that of a rotating dewar without baffles. Results show that the damping effect provided by the baffles reduces the amplitude of slosh wave excitation and lowers the degree of asymmetry in liquid-vapor distribution. Fluctuations of angular momentum and fluid moment caused by the slosh wave excited by gravity gradient acceleration with and without baffle boards are also investigated. It is also shown that the damping effect provided by the baffles greatly reduces the amplitudes of angular momentum and fluid moment fluctuations.     

Damped dust lattice shock wave in a strongly coupled complex (dusty) plasma

Taking into account “hydrodynamic damping” due to irreversible processes that occur within the system and the neutral drag due to the dust-neutral collision, a Burgers’ equation with a linear damping term is derived for a 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. The hydrodynamic damping generated-dissipative effect causes the generation of a shock wave in a dusty plasma crystal, whereas the neutral drag-induced dissipative effect causes the decay of the shock intensity with time. The width of the observed compressive shock increases (decreases) with an increase in shielding parameter κ (characteristic length L). Its implication in a glow-discharge plasma is briefly discussed. The text was submitted by the author in English.     

Weakly dissipative dust acoustic solitons in the presence of superthermal particles

An investigation of the linear and non‐linear properties of low‐frequency electrostatic (dust acoustic) waves in a collisional dusty plasma with negative dust grains, Maxwellian electrons, and κ ‐distributed ions is carried out. Low dust–neutral collisions accounting for dissipation (wave damping effect) is considered. The linear properties of dust acoustic excitations are discussed for varying values of relevant plasma parameters. It is shown that large wavelengths (beyond a critical value) are overdamped. In the limit of low dust–neutral collision rate, we have derived a damped Korteweg de Vries (KdV) equation by using the reductive perturbation technique. Supplemented by vanishing boundary conditions, the time‐varying solution of damped KdV equation leads to a weakly dissipative negative potential soliton. The soliton evolution with the damping parameter and other physical plasma parameters (superthermality, dust concentration, ion temperature) is delineated.