Convective Brillouin amplification in a homogeneous plasma slab

The coupled-mode Brillouin backscatter equations, describing weakly nonlinear decay of a damped pump into two damped daughter waves, are solved analytically in the convective instability regime, yielding the convective instability threshold and backward amplification of a noise source.     

QUANTUM FLUCTUATIONS IN A MESOSCOPIC DAMPED LC PARALLEL CIRCUIT IN DISPLACED SQUEEZED FOCK STATE

We study the quantum effects of a damped LC parallel circuit considering its different performance from an RLC series circuit in classical physics. The damped LC parallel circuit with a source is quantized and the quantum fluctuations of magnetic flux and electric charge in the circuit in displaced squeezed Fock state are investigated. It is shown that, as in the RLC series circuit, the fluctuations only depend on the squeezing parameter and the parameters of the circuit components in the damped LC parallel circuit, but the effects of the circuit components on the fluctuations are different in the two circuits.     

Particles on a string: Towards understanding a quantum mechanical divergence

The dynamics of two harmonically coupled solidbodies connected to a finitely extended mechanical field (string) is solved exactly and explicitly in the Lagrange formalism. For infinite length of strings the particles motion becomes damped, but not as a simple linearly damped harmonic oscillator. The model allows for a detailed discussion of its quantum mechanics, in particular of a previously recognized ultraviolet divergence.     

An analytical formulation of the forced responses of damped rings

An analysis in which an interaction formulation is used for the forced vibratory responses of a ring having a number of mass segments adhered to it by a viscoelastic material is presented. The mass segments are discretely distributed around the circumference of the ring, and the excitation is a concentrated vibratory radial force located on the surface of the ring. The mass segments may not have to be identical, nor do their distributions have to be uniform. The analysis can readily be extended to more complicated damped shell structural systems. The driving point mechanical impedances at a location midway between two mass segments for a given damped system are given as an example. These solutions compare very well with experimental data and theoretical results available. Also presented is a comparison of driving point mechanical impedances for two damped systems with different thicknesses of the viscoelastic layers.     

Rijke管热声振荡的稳定性切换行为研究

采用数值方法模拟了强弱两种阻尼条件下传热迟滞时间对一维Rijke管热声系统稳定性的影响,发现Rijke管系统存在稳定性切换现象.在推导了无量纲形式的管内声波动量方程和能量方程之后,利用Galerkin方法对控制方程进行展开并在时间域内数值求解.分析了强阻尼和弱阻尼条件下,给定热源的Rijke管热声振荡的稳定性与传热迟滞时间的关系.结果显示:在两类阻尼条件下,持续增大传热与速度的迟滞时间,系统均呈现出稳定性切换现象,即系统在稳定和不稳定两个状态间持续转变;但弱阻尼系统的不稳定区域宽于强阻尼系统的不稳定区域,系统最大振幅相对增大,且系统热声振荡的主模态在不同模态之间发生转换.最后,通过求解系统各阶模态极限环幅值随传热迟滞时间的变化,发现Rijke管热声振荡稳定性切换现象与迟滞时间存在近似周期性关系.     

The influence of Landau quantization on the propagation of solitary structures in collisional plasmas

In this work, we study damped ion acoustic solitary wave structures in magnetized dense plasmas. The collisional effects of ions with electrons and neutrals are considered. The trapping effects of electrons and Landau quantization are included in the plasma model under consideration. We assume that magnetic field is quantized such that the condition■ is satisfied. We have derived the damped Korteweg–de Vries(dKdV) equation by using small amplitude reductive perturbation technique. The time-dependent analytical and numerical solutions of the dKdV equation are presented. For numerical solutions we apply a two level finite difference scheme with the help of the Runge Kutta method. The effects of variations of different plasma parameters on the propagation characteristics of damped solitary structures in the presence of collisions are discussed.     

Observation of transition from a reactive-medium instability to an inverse Landau damping in a beam-plasma system

The wave excited by a coaxial probe in a beam-plasma system usually propagates as two waves which are independent of each other, i.e., a damped Trivelpiece mode of the plasma and a growing space charge wave of the beam (referred to a reactive-medium instability). While, when the beam velocity is equal to or slightly larger than the phase velocity of the plasma wave, the inverse Landau damping of the wave is observed, instead of the damped Trivelpiece mode.     

Crystal structure analysis in (3+d) dimensions

Inelastic neutron scattering on in situ grown bcc single crystals of the group 4 metals Ti, Zr and Hf show a band of low energy and strongly damped phonons. Geometrical considerations show how these damped lattice vibrations achieve the displacements necessary for the two martensitic phase transitions from bcc to ω (under pressure) and from bcc to hcp (upon lowering the temperature). The low energy and temperature dependent phonons are precursor fluctuations of the hcp or ω phase within the bcc phase.     

A real decoupled method and free interface component mode synthesis methods for generally damped systems

This paper reports on the development of a new transformation method. In contrast to most existing mode transformation methods in which the first-order state-space equation of the damped vibration system is transformed into a decoupled form with complex coefficient matrices, using the decoupled method presented in this paper, the equation of the damped system can be decomposed into a decoupled equation with real coefficient matrices. Two new free interface component mode synthesis methods are also presented. The equivalent full-mode matrix of the damped structure is used to capture the effects of the higher-order modes. Additionally, this work modifies the compatibility conditions at the junctions that are employed in most of the previous component mode synthesis methods for generally damped systems. The first component mode synthesis method is performed in complex space, whereas the second method can be applied in real space. Because the coefficient matrices of the coupled equation constructed by the second component mode synthesis method are all real-valued, the solution of the eigenproblem for this coupled equation can be performed in real space as well. Additionally, numerical examples demonstrate the accuracy and validity of these two component mode synthesis methods.     

Quantum Damped Oscillator in Probability Representation

The probability distribution describing quantum states of the damped oscillator in the framework of the Caldirola-Kanai model is introduced. The probability distributions for coherent states and Fock states of the damped oscillator are found explicitly. The transition probability for the damped oscillator is expressed in terms of distributions describing initial and final states.     

关于线性阻尼振子第一积分的研究

通过引入一维线性阻尼振子基本积分来构造其他第一积分, 包括不含时的积分. 将这种方法推广到多维情形, 构造二维和n维线性阻尼振子不同形式的第一积分; 证明不同类型的二维线性阻尼振子都存在三个独立的不含时的第一积分, n维线性阻尼振子存在2n-1个独立的不含时的第一积分. 利用变量变换将线性阻尼振子的第一积分变换成简谐振子形式的第一积分. 关键词： 线性阻尼振子 第一积分 基本积分 简谐振子     

Bending vibration of axially loaded Timoshenko beams with locally distributed Kelvin-Voigt damping

Utilizing the Timoshenko beam theory and applying Hamilton's principle, the bending vibration equations of an axially loaded beam with locally distributed internal damping of the Kelvin-Voigt type are established. The partial differential equations of motion are then discretized into linear second-order ordinary differential equations based on a finite element method. A quadratic eigenvalue problem of a damped system is formed to determine the eigenfrequencies of the damped beams. The effects of the internal damping, sizes and locations of damped segment, axial load and restraint types on the damping and oscillating parts of the damped natural frequency are investigated. It is believed that the present study is valuable for better understanding the influence of various parameters of the damped beam on its vibration characteristics.     

利用视频分析测量阻尼振子的阻尼系数

文中利用视频捕捉和分析软件研究空气中弹簧振子的阻尼运动,在较高时间分辨率下得到其完整的位置数据。通过使用MATLAB软件对这些数据进行分析及拟合,得到了振子振幅衰减曲线并由此测量出弹簧振子在空气中的阻尼系数。     

Substructuring and modal synthesis for damped systems

A new approach to complex mode synthesis for damped systems is presented. The technique involves using two successive transformations of the equations written in first order, state space form. The transformations are applied to each subsystem, with consecutive use being made of free interface undamped modes in the existing physical co-ordinates followed by fixed interface damped modes in the generalized co-ordinates. The system eigenvalues are obtained by the QR method in the EISPACK matrix programs. An advantage of the technique is that it can be applied to systems or subsystems possessing rigid body motion. The new method compares very well in accuracy and applicability with other existing methods.     

A fuzzy finite element procedure for the calculation of uncertain frequency-response functions of damped structures: Part 1—Procedure

This work introduces a numerical algorithm to calculate frequency-response functions (FRFs) of damped finite element (FE) models with fuzzy uncertain parameters. Part one of this paper describes the numerical algorithm for the solution of the underlying interval finite element (IFE) problem. First, the IFE procedure for the calculation of undamped envelope FRFs is discussed. Starting from the undamped procedure, a strategy is developed to analyse damped structures based on the principle of Rayleigh damping. This is achieved by analysing the effect of the proportional damping coefficients on the subsequent steps of the undamped procedure. This finally results in a procedure for the calculation of fuzzy damped FRFs based on an analytical extension of the undamped algorithm. Part one of this paper introduces the numerical procedure. Part two of this paper illustrates the application of the methodology on four numerical case studies.     

Modulational instabilities in Josephson oscillations of elongated coupled condensates

We study the Josephson oscillations of two coupled elongated condensates. Linearized calculations show that the oscillating mode uniform over the length of the condensates (uniform Josephson mode) is unstable: modes of non zero longitudinal momentum grow exponentially. In the limit of strong atom interactions, we give scaling laws for the instability time constant and unstable wave vectors. Beyond the linearized approach, numerical calculations show a damped recurrence behavior: the energy in the Josephson mode presents damped oscillations. Finally, we derive conditions on the confinement of the condensates to prevent instabilities.     

Quantum interference induced by initial system–environment correlations

We investigate the quantum interference induced by a relative phase in the correlated initial state of a system which consists in a two-level atom interacting with a damped mode of the radiation field. We show that the initial relative phase has significant effects on both the evolution of the atomic excited-state population and the information flow between the atom and the reservoir, as quantified by the trace distance. Furthermore, by considering two two-level atoms interacting with a common damped mode of the radiation field, we highlight how initial relative phases can affect the subsequent entanglement dynamics.     

Vibrations of three layered damped sandwich plate composites

Theoretical and experimental results are presented and discussed for the transverse driving point mechanical impedances, as well as for the transfer impedances, of damped composite plates made up of a thin viscoelastic layer sandwiched between two elastic layers. Analytical results are determined by finite element approximations. Due to the elements used and the system to be modeled, several fundamental assumptions or restrictions usually adopted in analytical investigations are removed. The dependence on frequency and temperature of the dynamic properties of the viscoelastic materials is taken into consideration. A companion experiment was conducted, for comparison purposes, on such damped composite plates suspended in air by lightweight elastic shock cords and driven at the center by an electromechanical vibration shaker. Good correlations between the test data and analytical solutions are obtained over a wide frequency range for two configurations.     

The Quantum Fluctuations of Mesoscopic Damped Mutual Capacitance Coupled Double Resonance RLC Circuit in Excitation State of the Squeezed Vacuum State

Mesoscopic damped double resonance mutual capacitance coupled RLC circuit is quantized by the method of damped harmonic oscillator quantization. The Hamiltonian is diagonalized by unitary transformation. The eigenenergy spectra of this circuit are given. The quantum fluctuations of the charges and current of each loop are researched in excitation state of the squeezed vacuum state, the squeezed vacuum state and in vacuum state. It is show that, the quantum fluctuations of the charges and current are related to not only circuit inherent parameter and coupled magnitude, but also quantum number of excitation, squeezed coefficients, squeezed angle and damped resistance. And, because of damped resistance, the quantum fluctuation decay along with time. PACS numbers: 03.65.-w,42.50.Lc.     

Prediction of averaged energy for moderately damped systems with strong coupling

In this paper, the prediction of averaged energy of damped structural-acoustic systems is investigated. A simplified energy finite element method, referred to as EFEM⁰, is developed based on the energy flow analysis (EFA) equations and implemented using the finite volume method. The resulting formulations can be incorporated into statistical energy analysis (SEA) software and extends SEA application to moderately damped systems with strong coupling. The formulations are verified against analytical solutions for a single beam and coupled beams with both strong and weak coupling. A hybrid technique consisting of the EFEM⁰ approximation superimposed on a direct field is used to model moderately damped plates. For lightly damped systems, both methods produce acceptable results. For moderately damped two-dimensional systems, the EFEM⁰ method augmented with the direct field component produces significantly improved results.