Propagation Of Large-amplitude Waves Research Articles

Propagation of elastic solitons in chains of pre-deformed beams

We use a combination of experiments, numerical analysis and theory to investigate the nonlinear dynamic response of a chain of precompressed elastic beams. Our results show that this simple system offers a rich platform to study the propagation of large amplitude waves. Compression waves are strongly dispersive, whereas rarefaction pulses propagate in the form of solitons. Further, we find that the model describing our structure closely resembles those introduced to characterize the dynamics of several molecular chains and macromolecular crystals, suggesting that our macroscopic system can provide insights into the effect of nonlinear vibrations on molecular mechanisms.

Large-amplitude electromagnetic waves in magnetized relativistic plasmas with temperature

Abstract. Propagation of large-amplitude waves in plasmas is subject to several sources of nonlinearity due to relativistic effects, either when particle quiver velocities in the wave field are large, or when thermal velocities are large due to relativistic temperatures. Wave propagation in these conditions has been studied for decades, due to its interest in several contexts such as pulsar emission models, laser-plasma interaction, and extragalactic jets. For large-amplitude circularly polarized waves propagating along a constant magnetic field, an exact solution of the fluid equations can be found for relativistic temperatures. Relativistic thermal effects produce: (a) a decrease in the effective plasma frequency (thus, waves in the electromagnetic branch can propagate for lower frequencies than in the cold case); and (b) a decrease in the upper frequency cutoff for the Alfvén branch (thus, Alfvén waves are confined to a frequency range that is narrower than in the cold case). It is also found that the Alfvén speed decreases with temperature, being zero for infinite temperature. We have also studied the same system, but based on the relativistic Vlasov equation, to include thermal effects along the direction of propagation. It turns out that kinetic and fluid results are qualitatively consistent, with several quantitative differences. Regarding the electromagnetic branch, the effective plasma frequency is always larger in the kinetic model. Thus, kinetic effects reduce the transparency of the plasma. As to the Alfvén branch, there is a critical, nonzero value of the temperature at which the Alfvén speed is zero. For temperatures above this critical value, the Alfvén branch is suppressed; however, if the background magnetic field increases, then Alfvén waves can propagate for larger temperatures. There are at least two ways in which the above results can be improved. First, nonlinear decays of the electromagnetic wave have been neglected; second, the kinetic treatment considers thermal effects only along the direction of propagation. We have approached the first subject by studying the parametric decays of the exact wave solution found in the context of fluid theory. The dispersion relation of the decays has been solved, showing several resonant and nonresonant instabilities whose dependence on the wave amplitude and plasma temperature has been studied systematically. Regarding the second subject, we are currently performing numerical 1-D particle in cell simulations, a work that is still in progress, although preliminary results are consistent with the analytical ones.

Propagation of large-amplitude waves on dielectric liquid sheets in a tangential electric field: Exact solutions in three-dimensional geometry

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

Inflation waves in non-linear distensible tubes

A mathematical model for large amplitude wave propagation in a thin walled distensible tube is developed. The tube wall is considered as a membranic shell made of an incompressible, non-linear viscoelastic material with cylindrical orthotropy. The fluid is regarded as incompressible and inviscid and the flow is quasi-one-dimensional. The case of a pressure step applied at one end of a uniform straight tube is solved as an example. The system of partial differential equations, describing the motions of the fluid and the wall, are integrated numerically by using a two-step explicit scheme. Flow and deformation variables as well as the wave velocity are determined in time and space.

Mechanical properties of collapsible tubes and propagation of large amplitude waves

Large amplitude pressure wave propagation through collapsible tubes are phenomenon which are thougth to be relevant to the flow through airways and blood vessels.

Electromagnetic ion waves in cold relativistic plasmas

The high-energy processes which occur in many astrophysical objects have motivated recent studies (e.g., Tsintsadze and Tsikarishvili, 1976; Ferrariet al., 1978; Sweeney and Stewart, 1978) of large amplitude wave propagation in plasmas. Such investigations are also of interest for laboratory experiments where strong laser radiation interacts with a high-density target. In the present paper we shall show that even rather small amplitude waves in the presence of an external magnetic field can induce particle velocities which are comparable to the velocity of light. In this ultrarelativistic limit we shall demonstrate that two completely new types of circularly polarized waves appear and that under certain conditions, modulational instabilities occur. Finally we look at the possibility to relate the amplitudes and wavelengths of such waves to pulsar data.

Electric field measurements in the solar wind, bow shock, magnetosheath, magnetopause, and magnetosphere

Electric field measurements are reported at 11 magnetopause crossings that occurred during a single in-bound ISEE-1 satellite pass near a local time of 10:30. In combination with magnetic field data, these measurements show the existence of electric field components tangential to the actual magnetopause in the frame of rest of the magnetopause on every crossing of the current carrying layers associated with the 11 magnetopause traversals. These tangential electric field components were oriented with respect to the magnetopause sheet currents such that there was an electrical power dissipation of between 30 and 110 W km-2 on 10 of the 11 crossings. These results are in agreement with requirements of reconnection theories. Histograms of the normal electric field components and of the orientation, velocity, and thickness of the current carrying layer are presented. Suggestions of the existence of a parallel electric field in the magnetosheath near the magnetopause and of propagation of large amplitude waves along the magnetopause are also made.

Approximate theory of large-amplitude wave propagation

An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.

Computational study of nonlinear plasma waves: II. Sideband instability and satellite growth

The low-noise plasma simulation model is applied to study two phenomena associated with large amplitude wave propagation and the resulting particle trapping: sideband instability and satellite wave growth. Simulations are carried out to observe amplification of test waves and growth from noise. They are performed in parameter ranges for which detailed quantitative comparison with available theories is possible, and which are readily accessible experimentally. The study of sideband instability confirms the applicability of quasi−linear theory at short times, and parametric coupling theory in the time-asymptotic limit, and reproduces features analogous to those observed in laboratory experiments. The growth of a satellite wave in the presence of a large amplitude wave and a test wave is shown to be explicable by a simple theory involving slow modulation of the large amplitude wave.

A study of finite amplitude waves using Bell's parabolic law

It is known that the Karman-Taylor-Rakhmatulin theory of the propagation of finite amplitude waves is applicable when rods of various metals and alloys are subjected to impact loading. Using a generalized parabolic law, we have extended the theory for a three dimensional state of stress. In particular, we consider the effect of lateral inertia on the propagation of large amplitude plane waves in rods. Also the propagation of combined tension-torsion waves in thin walled tubes is discussed. On the basis of this investigation, we can explain some phenomena observed by Bell and others in their experimental studies on the propagation of large amplitude waves in annealed metals and alloys.

Propagation of large amplitude waves in annealed brass

An experimental investigation of large amplitude wave propagation in annealed α-brass polycrystals demonstrates the applicability of the generalized parabolic stress-strain relationship to a binary alloy of low stacking-fault energy. Several discrete deformation modes are found to be operative depending on the material history prior to free-flight impact of rods. The results are found to be in agreement with quasi-static deformation of brass single crystals and polycrystals. It is concluded that, in spite of the large difference in the stacking-fault energies of brass and aluminum, the deformations of each can be precisely described without explicitly including “strain rate” into the constitutive equation of either.

Propagation of a large amplitude longitudinal wave in a semi-infinite elastic rod

A general solution is given to the problem of large amplitude wave propagation in a semi-infinite elastic thin rod. The solution is obtained by the method of characteristics. An explicit form of the solution is given in the case where an end velocity, which is a step function of time, is prescribed. More general types of end velocity can be accommodated provided that the variation with time is monotonically increasing; otherwise shocks will form and the present solution is no longer valid.

Single, Temperature-Dependent Stress-Strain Law for the Dynamic Plastic Deformation of Annealed Face-Centered Cubic Metals

Large amplitude wave propagation in annealed aluminum is studied experimentally to within 70°C of the melting point of the metal. The strain-rate-independent, finite amplitude wave theory is found to apply at all temperatures. The governing stress-strain law in each instance is parabolic. The coefficient of the parabolic stress-strain law varies linearly with the absolute temperature. The annealed, face-centered cubic metals of aluminum, copper, lead, gold, and silver are all found to have the same parabolic stress-strain law at absolute zero. Thus, from experiments using the author's diffraction grating technique, a single stress-strain law is found which is applicable at any temperature to any of these annealed metals whose melting point is specified.

Propagation of Large Amplitude Waves in Annealed Aluminum

An experimental study of large amplitude compression waves in annealed aluminum for the case of constant velocity impact has given a close agreement with the strain rate independent theory of one-dimensional plastic wave propagation. Radial effects in the first diameter are observed and calculations of Poisson's ratio indicate the presence of relatively large dilatation. Propagation velocities, maximum strain, and energy considerations are in agreement with predictions from the slopes of the static stress-strain curve. These data were obtained using the author's diffraction grating technique for measuring strain and surface angle.