Study of the scattering of nonlinearly interacting plane acoustic waves by an elongated spheroid

The scattering of nonlinearly interacting plane acoustic waves on a rigid elongated spheroid is considered. The foci of the spheroid coincide with foci of the spheroidal coordinate system. The method of successive approximations is used to obtain the solutions to the inhomogeneous wave equation in the first and second approximations. Asymptotic expressions are offered for the components of the total acoustic pressure of the difference frequency wave, and the scattering diagrams for these components are presented.     

Power spectra of nonlinearly coupled waves

Swinney et al. (1977) have found that turbulence in rotational Couette flow results from a small number of instabilities. They have raised the question of whether these instabilities conform with the ideas of Ruelle and Takens (1971). We show that a simple model of the Couette flow yields power spectra similar to those seen in the experiments. The model is consistent with the Ruelle and Takens picture.     

Modulational instability of nonlinearly interacting incoherent sea states

The modulational instability of nonlinearly interacting spatially incoherent Stokes waves is analyzed. Starting from a pair of nonlinear Schrödinger equations, we derive a coupled set of wave-kinetic equations by using the Wigner transform technique. It is shown that the partial coherence of the interacting waves induces novel effects on the dynamics of crossing sea states.     

Instability of water jet: Aerodynamically induced acoustic and capillary waves

High-speed water jet cutting has important industrial applications. To further improve the cutting performance it is critical to understand the theory behind the onset of instability of the jet. In this paper, instability of a water jet flowing out from a nozzle into ambient air is studied. Capillary forces and compressibility of the liquid caused by gas bubbles are taken into account, since these factors have shown to be important in previous experimental studies. A new dispersion equation, generalizing the analogous Rayleigh equation, is derived. It is shown how instability develops because of aerodynamic forces that appear at the streamlining of an initial irregularity of the equilibrium shape of the cross-section of the jet and how instability increases with increased concentration of gas bubbles. It is also shown how resonance phenomena are responsible for strong instability. On the basis of the theoretical explanations given, conditions for stable operation are indicated.     

Diffraction of optical waves by nonlinearly induced cylinders

The diffraction of optical waves by transparent and opaque cylinders formed by laser beams in defocusing nonlinear media has been investigated for the first time. The wave flow around a single beam (cylinder) and wave signal percolation through the slits formed by closely spaced laser beams have been numerically modeled.     

Small-scale structure of nonlinearly interacting species advected by chaotic flows

We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and nonsmooth forcing sources. The small-scale structure can be obtained in terms of characteristic Lyapunov exponents of the flow and of the chemical dynamics. Different kinds of morphological transitions are identified. Numerical results from a three-component plankton dynamics model support the theory, and they serve also to illustrate the influence of asymmetric couplings. (c) 2002 American Institute of Physics.     

Influence of nonlinearly induced diffraction on spatial solitary waves

Spatial solitary waves carried by a TE mode in planar optical waveguides with Kerr-type of nonlinearity are investigated based on a modified nonlinear (1 + 1) Schrödinger equation. Looking for effects instigated by the spatial inhomogeneity of the nonlinear polarization, the nonzero divE-term is taken into account in the nonlinear guided wave equation together with the nonparaxial approach and vector model. It is shown that, at self-focusing of beams in a (1 + 1) geometry, the effect coming out from the divergence term predominates over modifications related to the nonparaxial vector model. This term is interpreted as nonlinearly induced diffraction which plays the role of an effective saturation. Analytical solutions supported by numerical results are found.     

Instability of magnetoelastic waves in ferrites

The magnetoelastic instability that arises in parallel pumping is studied by methods of quantum theory. A general expression for the instability threshold and a dispersion equation for magnetoelastic waves for any phonon polarization and any direction of magnetization in crystals with cubic symmetry'are obtained. Some special cases are examined.The author thanks A. I. Pil'shchikov for useful discussion.     

Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves

We investigate experimentally the competition between spatial and temporal breakup due to modulational instability in chi((2)) nonlinear mixing. The modulation of the wave packets caused by the energy exchange between fundamental and second-harmonic components is found to be the prevailing trigger mechanism which, according to the relative weight of diffraction and dispersion, leads to the appearance of a multisoliton pattern in the low-dimensional spatial or temporal domain.     

Instability of electromagnetic waves in bistable media

It is shown that boundary-condition peculiarities can give rise to a situation in which stable of weak and strong absorption are not realized in an optically bistable medium. Then, a wave entering the medium is in an unstable state, as a result of which the radiation is modulated.Scientific-Industrial Organization Laser Technology, Erevan University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, Nos. 3, 4, pp. 226–233, March–April, 1992.     

Collisional effect on the saturation amplitude of nonlinearly excited plasma waves

The collisional effect is found to be more important than the relativistic effect in controlling the saturation amplitude of plasma waves nonlinearly excited by two laser beams under existing experiment conditions.     

Instability of traveling waves in an optical waveguide

Instability of traveling IR waves within a waveguide structure is discussed. A practical model of a traveling wave amplifier of a solid state is proposed, utilizing an optical waveguide. The mechanism of instability is interpreted in terms of an interaction between a plasmon wave and a circuit one under a constraining boundary condition. Properties of the traveling amplification and related problems are discussed, with appropriately suggested semiconductor materials and device designs. The features of the amplifier are a simple structure, a low DC biasing power dissipation for room-temperature operation, unidirectionality, and a wide wavelength range from IR or submillimeter order, suited to various applications.     

Instability of electromagnetic waves in transversely magnetised semiconductor-plasmas

Using the hydrodynamic model of plasmas the general dispersion relation is derived in the collisiondominated regime when a d.c. magnetic field is applied (Y-axis) transversly to the propagation vector k (Z-axis), and the d.c. electric field is inclined to the Z-axis in the X-Z plane. The dispersion relation is solved for intrinsic and extrinsic semiconductors to explore the possibility of wave instability. The threshold conditions of wave oscillations are obtained. In n-InSb the frequency of the oscillation attains a maximum value when the electron cyclotron frequency is equal to the electron collision frequency. In intrinsic InSb instability is possible only in the long wavelength region for E₀ ? 10 kVm^?1 when B₀> 0.2 T, while for lower values of B₀, E₀ should be greater 20kVm^?1. The energy dependent collision frequency has a significant effect on the threshold frequency of oscillation.     

Instability of plasma waves in an electromagnetic field

Summary In the presence of a weak laser field the plasma scattering by electrons is discussed.

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Riassunto In presenza di un campo laser debole, si discute la diffusione del plasma mediante elettroni.

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Резюме В присутствии слабого лазерного поля обсуждается рассеяние плазмы на электронах.

     

Charged cosmic strings interacting with gravitational and electromagnetic waves

Under a particular choice of the Ernst potential, we solve analytically the Einstein–Maxwell equations to derive a new exact solution depending on five parameters: the mass, the angular-momentum (per unit mass), α, the electromagnetic-field strength, k, the parameter-p and the Kerr-NUT parameter, l. This (Petrov Type D) solution is cylindrically symmetric and represents the curved background around a charged, rotating cosmic string, surrounded by gravitational and electromagnetic waves, under the influence of the Kerr-NUT parameter. A C-energy study in the radiation zone suggests that both the incoming and the outgoing radiation is gravitational, strongly focused around the null direction and preserving its profile. In this case, the absence of the k-parameter from the C-energy implies that, away from the linear defect the electromagnetic field is too weak to contribute to the energy-content of the cylindrically symmetric space-time under consideration. In order to explain this result, we have evaluated the Weyl and the Maxwell scalars near the axis of the linear defect and at the spatial infinity. Accordingly, we have found that the electromagnetic field is concentrated (mainly) in the vicinity of the axis, while falling-off prominently at large radial distances. However, as long as k ≠ 1, the non-zero Kerr-NUT parameter enhances those scalars, both near the axis and at the spatial infinity, introducing some sort of gravitomagnetic contribution.     

Loss of coherence of pure and mixed states for a multimode radiation field interacting nonlinearly with a qubit

We study the loss of coherence of pure and mixed states for a nonlinear interaction between the multimode field and a qubit. We calculate analytically partial entropies of the qubit and field subsystems, which are used to measure the loss of coherence. We find that the loss of coherence loss is sensitive to the initial field states, the number of modes, and the nonlinear-interaction parameter.