Plasma waves in a nonideal plasma

This paper shows how the concepts commonly used for a Debye plasma—Landau damping, collisional damping, short-range and long-range collisions, and plasma waves—must be revised to describe a nonideal electron-ion plasma. The degrees of freedom of a nonideal plasma are divided into collective and individual. The increase and saturation of the fraction of collective degrees of freedom as the coupling constant increases is discussed. The Tatarskii approach for a system of coupled oscillators makes it possible to model the collective degrees of freedom of a nonideal plasma by a set of Langevin oscillators in a thermostat. The correlation energy and the energy of the plasma waves are found. The concepts developed here made it possible to determine the dispersion of the plasma waves and their damping. The effect of damping on the discrepancy between the position of the maximum of the dynamic structure factor and the real part of the solution of the dispersion equation is considered. The effective collision frequency of the individual degrees of freedom (the electrons) is estimated, taking into account both short-range pairwise scattering and scattering at plasma waves. Zh. éksp. Teor. Fiz. 113, 880–896 (March 1998)     

Interaction of nonlinear energy sink with a two degrees of freedom linear system: Internal resonance

We investigate the dynamics of 2DOF linear subsystem with close frequencies with attached nonlinear energy sink (NES). In this system, simultaneous targeted energy transfer from both linear oscillators to the NES is possible. It was demonstrated that the process of the TET can be analytically described as transient beats of relaxation—like motion arising due to the internal resonance. Contrary to previously studied models, the approach based on Hamiltonian structure of the system (study of the periodic orbits in the absence of the damping) fails to provide insight into the TET process. The reason of that is large number of secondary resonances activated through interaction between two primary 1:1 resonances. In the damped system these resonances are eliminated and then averaging—based approach is applicable. It was shown by the Hilbert Vibration Decomposition (HVD) that in the damped case there is a single significant component of the response regarded to the 1:1:1 resonance. Analytical model was verified numerically and a fairly good correspondence was observed.     

Review of scattering and extinction cross-sections, damping factors, and resonance frequencies of a spherical gas bubble

Perhaps the most familiar concepts when discussing acoustic scattering by bubbles are the resonance frequency for bubble pulsation, the bubbles' damping, and their scattering and extinction cross-sections, all of which are used routinely in oceanography, sonochemistry, and biomedicine. The apparent simplicity of these concepts is illusory: there exist multiple, sometimes contradictory definitions for their components. This paper reviews expressions and definitions in the literature for acoustical cross-sections, resonance frequencies, and damping factors of a spherically pulsating gas bubble in an infinite liquid medium, deriving two expressions for "resonance frequency" that are compared and reconciled with two others from the reviewed literature. In order to prevent errors, care is needed by researchers when combining results from different publications that might have used internally correct but mutually inconsistent definitions. Expressions are presented for acoustical cross-sections associated with forced pulsations damped by liquid shear and (oft-neglected) bulk or dilatational viscosities, gas thermal diffusivity, and acoustic re-radiation. The concept of a dimensionless "damping coefficient" is unsuitable for radiation damping because different cross-sections would require different functional forms for this parameter. Instead, terms based on the ratio of bubble radius to acoustic wavelength are included explicitly in the cross-sections where needed.     

A real-time plane-wave decomposition algorithm for characterizing perforated liners damping at multiple mode frequencies

Perforated liners with a narrow frequency range are widely used as acoustic dampers to stabilize combustion systems. When the frequency of unstable modes present in the combustion system is within the effective frequency range, the liners can efficiently dissipate acoustic waves. The fraction of the incident waves being absorbed (known as power absorption coefficient) is generally used to characterize the liners damping. To estimate it, plane waves either side of the liners need to be decomposed and characterized. For this, a real-time algorithm is developed. Emphasis is being placed on its ability to online decompose plane waves at multiple mode frequencies. The performance of the algorithm is evaluated first in a numerical model with two unstable modes. It is then experimentally implemented in an acoustically driven pipe system with a lined section attached. The acoustic damping of perforated liners is continuously characterized in real-time. Comparison is then made between the results from the algorithm and those from the short-time fast Fourier transform (FFT)-based techniques, which are typically used in industry. It was found that the real-time algorithm allows faster tracking of the liners damping, even when the forcing frequency was suddenly changed.     

Experimental verification of synchronization in pulse-coupled oscillators with a refractory period and frequency distribution

We propose herein globally pulse-coupled electronic-circuit oscillators with a refractory period and frequency distribution. The synchronization of such oscillators, which was analyzed by Konishi and Kokame [Chaos 18, 033132 (2008)], is verified by circuit experiments. Furthermore, we investigate a cluster state in the oscillators and analytically derive a simple condition to estimate the maximum possible number of clusters, which is confirmed by the circuit experiments.     

Decay of capillary turbulence on the surface of a viscous liquid

Decay of the turbulence of capillary waves on the surface of a real liquid is studied in the presence of the viscous damping of the waves at all frequencies after stepwise removal of external pumping. The investigation is performed using two different models: the weak turbulence approximation and the local turbulence model in which the energy redistribution over frequencies is described by the polynomial expression in the wave-occupation number. It is shown that the decay of turbulence in the viscous liquid proceeds self-similarly and begins at high frequencies. In the decay process, the frequency distribution of the energy of waves is close to the stationary form E _ω ～ ω^?3/2 in a wide frequency range below the boundary frequency of the inertial range during a relatively long time after removal of the external force. The calculation results agree qualitatively with the results of the experiments on capillary turbulence on the charged surface of liquid hydrogen.     

Propagation of electrostatic energy through a quantum plasma

The theory of propagation of electrostatic energy through an infinite, homogeneous electron–ion quantum plasma is presented. Simple expressions for the energy flow, energy density, and energy velocity of longitudinal oscillation waves in the system are derived using the linearized quantum hydrodynamic theory for the electron fluid, which incorporates the important quantum statistical pressure and electron diffraction force, while the optical response of the ion particles is characterized by the classical frequency‐dependent dielectric function, ?_ion. Both cases of plasmon (high‐frequency) and quantum ion‐acoustic (low‐frequency) waves are considered.     

A feasibility study of the use of bounded beams resembling the shape of evanescent and inhomogeneous waves

Plane waves are solutions of the visco-elastic wave equation. Their wave vector can be real for homogeneous plane waves or complex for inhomogeneous and evanescent plane waves. Although interesting from a theoretical point of view, complex wave vectors normally only emerge naturally when propagation or scattering is studied of sound under the appearance of damping effects. Because of the particular behavior of inhomogeneous and evanescent waves and their estimated efficiency for surface wave generation, bounded beams, experimentally mimicking their infinite counterparts similar to (wide) Gaussian beams imitating infinite harmonic plane waves, are of special interest in this report. The study describes the behavior of bounded inhomogeneous and bounded evanescent waves in terms of amplitude and phase distribution as well as energy flow direction. The outcome is of importance to the applicability of bounded inhomogeneous ultrasonic waves for nondestructive testing.     

Scattering from a ribbed finite cylindrical shell with internal axisymmetric oscillators

A theoretical formalism is elaborated to determine the acoustic field scattered from a finite cylindrical shell reinforced by a set of ribs with internal axisymmetric oscillators, the locations and properties of which can vary arbitrarily along the cylinder axis. Analytical expressions are derived for the scattered pressure and approximate expressions are proposed to calculate the backscattered field. Some applications have been carried out to investigate the problem of backscattering from a periodically ribbed finite cylindrical shell in the presence of rib aperiodicity or axisymmetric internal oscillators. The modifications of the main features associated with scattering from helical and Bloch-Floquet waves are examined and numerical results are presented with respect to the mean rib spacing and to the total mass of the internal structures.     

Dissipative tunneling at finite temperature

A simple theory is presented for the influence of a weakly coupled interaction system on the tunneling of a particle out of a metastable well. It is based on the standard model of momentum and energy transfer to an infinite set of oscillators and is applied to the case of phase tunneling in a Josephson contact. The distribution of the energy transfer and in particular the Debye-Waller factor for elastic processes is determined by the imaginary part of the dielectric function. For small damping γ the main influence of dissipation on the total tunneling probability is contained in a factor exp —AMγ(Δq)². The numerical coefficientA and the distance Δq under the barrier depend on the considered tunneling state andA(T) vanishes at a temperatureT ^* above which classical activation prevails. The tunneling probability of any level is therefore predicted to increase with temperature. In additional general expressions are derived for the correlation functions of a damped quantum oscillator in terms of the classical response of the interaction system.     

Generating macroscopic chaos in a network of globally coupled phase oscillators

We consider an infinite network of globally coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case.     

Resonant filtering of compositional waves in multicellular networks

Theoretically predicting the stationary and traveling compositional wave patterns observed over trivial multicellular topologies is common place in biology. Systematic methods are needed to find the relationships between the forms of such waves and the underlying network topologies. Here, we introduce one such method based on the Interface Response Theory (IRT) that combines models of intracellular biochemical reactions with those of intercellular networks to analytically track time variations of concentration profiles across nontrivial cellular network topologies. Cellular chains of infinite length are shown to sustain traveling planar waves under certain conditions among the coefficients of the intracellular chemical reactions. A non-trivial cellular network composed of a finite length side chain attached to the infinite backbone leads to the formation of a standing wave pattern upstream from the site of attachment. Downstream, the wave proceeds although a limited number of frequency bands are filtered out of the original content with that number being equal to the number of cells in the side chain.     

Resonant response of a thermalized ensemble of nonlinear oscillators

The analysis is carried out of the response of the center of gravity (dipole moment) of the distribution of noninteracting thermalized nonlinear oscillators to a sinusoidal driving force. Heat bath coupling is modeled by damping and noise. The driving is weak, but the frequency is resonant, so that there is a nonlinear resonance in the phase space. The response has a linear part that can be obtained from the perturbation analysis and a small nonlinear correction that is specific for the resonant structure.     

Energy dissipation prediction in a line of colliding oscillators

In this paper the impact of a line of adjacent structures, or oscillators, is studied using an energy formulation. The energy exchange and dissipation from a collision of a pair of oscillators is studied by creating an equivalent oscillator pair, one has the energy of the in-phase motion and the other has the out-of-phase energy. It is found that the energy exchange between colliding oscillators is proportional to the initial kinetic energy difference of the oscillators and that work in the collision is proportional to the out-of-phase energy or difference energy. The kinetic energy at contact is then related to the mean oscillator energy, permitting a power balance equation to be written for each oscillator in line. The power balance equations have three independent variables for each pair of oscillators: the oscillator time averaged energies and the phase difference. This equation is run in a time-stepping procedure, with steps at the mean collision rate. The work in the collisions and internal oscillator dissipation is output as a function of time. A parameter study is conducted to see how the work changes with oscillator: separation, contact stiffness and contact damping.     

INDUCED DAMPING BY A NEARLY CONTINUOUS DISTRIBUTION OF NEARLY UNDAMPED OSCILLATORS: LINEAR ANALYSIS

The induced damping in a master oscillator contributed by a set of satellite oscillators is obtained in terms of a summation over a discrete distribution of the set. (The distribution is with respect to the resonance frequencies of the satellite oscillators in the set. The distribution is cast in an ascending order and is assumed to be centered about the resonance frequency of the master oscillator in isolation). If the modal overlap parameters are less than unity, significant undulations are present in the induced damping; the less the modal overlap parameters are compared with unity, the more prominent are the undulations. The undulations are largely suppressed when the local modal overlap parameters exceed unity. Moreover, appropriately averaging the undulations yields values for the induced damping that coincide with those obtained when the modal overlap parameters exceed unity. Further, it transpires that these common values are independent of the individual modal overlap parameters. When the summation is replaced by an integration, the first order results are undulations-free and the values, so obtained, again, coincide with those pertaining to modal overlap parameters that exceed unity. Without defining the excursions in the undulations, the transition from a discrete-to-a continuous distribution, that is implied by a summation-to-an integration, must assume that the modal overlap parameters exceed unity. In particular, without careful and meaningful qualifications, it may be misleading to assume, a priori, that the modal overlap parameters are equal to zero.     

Plasmon-polariton surface waves at the interface of a dielectric and a nanocomposite with metal inclusions

The features of the propagation of the surface waves a plasmon-polariton-type at the interface of a dielectric and a nanocomposite material with spherical metal inclusions have been considered. The analysis has been performed taking into account damping of propagating waves, which results in the complexity of dispersion relations, and taking into account the nanoparticle size. The frequency dependences of the group velocity and the depth of surface wave penetration into each medium have been constructed, and the distributions of energy fluxes in the structure have been obtained.     

Classical light dispersion theory in a regular lattice

We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by all the other particles, and to the radiation reaction expressed according to the Lorentz-Dirac equation. Exact normal mode solutions, describing the propagation of plane electromagnetic waves through the lattice, are obtained for the complete linearized system of infinitely many oscillators. At variance with all the available results, our method is valid for any values of the frequency, or of the ratio between wavelength and lattice parameter. A remarkable feature is that the proper inclusion of radiation reaction in the dynamics of the individual oscillators does not give rise to any extinction coefficient for the global normal modes of the lattice. The dispersion relations resulting from our solution are numerically studied for the case of a simple cubic lattice. New predictions are obtained in this way about the behavior of the crystal at frequencies near the proper oscillation frequency of the dipoles.     

Dynamics of linear discrete systems connected to local, essentially non-linear attachments

The dynamics of a linear periodic substructure, weakly coupled to an essentially non-linear attachment are studied. The essential (non-linearizable) non-linearity of the attachment enables it to resonate with any of the linearized modes of the subtructure leading to energy pumping phenomena, e.g., passive, one-way, irreversible transfer of energy from the substructure to the attachment. As a specific application the dynamics of a finite linear chain of coupled oscillators with a non-linear end attachment is examined. In the absence of damping, it is found that the dynamical effect of the non-linear attachment is predominant in neighborhoods of internal resonances between the attachment and the chain. When damping exists energy pumping phenomena are realized in the system. It is shown that energy pumping strongly depends on the topological structure of the non-linear normal modes (NNMs) of the underlying undamped system. This is due to the fact that energy pumping is caused by the excitation of certain damped invariant NNM manifolds that are analytic continuations for weak damping of NNMs of the underlying undamped system. The bifurcations of the NNMs of the undamped system help explain resonance capture cascades in the damped system. This is a series of energy pumping phenomena occurring at different frequencies, with sudden lower frequency transitions between sequential events. The observed multi-frequency energy pumping cascades are particularly interesting from a practical point of view, since they indicate that non-linear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure, in compatibility with the design objectives.     

Vibration control by recursive time-delayed acceleration feedback

This paper presents a theoretical basis of time-delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators. The control signal is synthesized by an infinite, weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past. The proposed method is shown to have controlled linear resonant vibrations, low-frequency non-resonant vibrations, primary and 1/3 subharmonic resonances of a forced Duffing oscillator. The concept of an equivalent damping and natural frequency of the system is also introduced. It is shown that a large amount of damping can be produced by appropriately selecting the control parameters. For some combinations of the control parameters, the effective damping factor of the system is shown to be inversely related to the time-delay in the small delay limit. Selection of the optimum control parameters for controlling the forced and free vibrations is discussed. It is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time-delay parameter. However, the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain. The delay values for the optimal forced response may be different from that required for the optimum transient response. When both are important, a suboptimal choice of the delay parameters with unity recursive gain is recommended.     

Bending wave intensity in a thick beam

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