Converging spherical and cylindrical shock waves

The self-similar solutions for converging spherical and cylindrical strong shock waves in a non-ideal gas satisfying the equation of state of the Mie-Gruneisen type are investigated. The equations governing the flow, which are highly non-linear hyperbolic partial differential equations, are first reduced to a Poincaré-type ordinary differential equation with suitable approximation. Such an approximation helps in obtaining the self-similar solutions and the similarity exponent numerically by phase-plane analysis.     

Propagation of spherical shock waves in water

The propagation and attenuation of spherical shock waves in water, produced by the explosion of spherical charge, is studied. Our results compare favourably with experimental data.     

Passage of spherical shock waves through thermals

A study is made of the complex flow which develops in the passage of a shock wave through a cloud of hot gas. Several new effects are discovered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 2, pp. 270–275, August, 1989.     

Vortex array generation by interference of spherical waves

Interferometric methods of vortex generation involve the interference of three or more plane waves. We show that spherical wave interference can produce vortex lattices similar to the one produced in the three-beam interference of plane waves. Three spherical waves of the same curvature are made to interfere in a shear interferometer introduced in a Mach-Zehnder configuration.     

Scintillation correlation between forward and return spherical waves

According to the point-source point-receiver (PSPR) reciprocity, the received field remains equal when the positions of a point source and point receiver are interchanged. We extend the PSPR scenario to a finite receiver that spatially averages scintillation over its aperture. By use of weak-fluctuation theory, an analytical expression for the correlation coefficient between the received powers at both link ends is provided. The effects of turbulence profile, receiver aperture size, and central obscuration on the correlation are assessed. Because correlation is obtained to the detriment of antenna gain and aperture averaging, the net benefit of the channel reciprocity is highly scenario dependent.     

Propagation of waves from a spherical cavity with and without a shell embedment

Summary A spherical cavity in an infinite, elastic medium with and without a shell embedment is subjected to axisymmetric, non-torsional surface loads in the radial and meridional directions. The so-called Residual Variable Method (RVM) is used to obtain exact, closed-form solutions of the wave propagation problems. Some representative numerical results are presented graphically for the stresses created in two realistic loading situations.     

Periodic shock waves in spherical resonators (survey)

This article surveys the literature on the problem of shock waves in spherical resonators. The published data is used to examine the feasibility of exciting shock waves in such resonators by means of a source of low-amplitude harmonic oscillations. A nonlinear wave equation is obtained to describe the propagation of unidimensional spherical waves in solids, liquids, and gases, as well as in bubbly liquids. A solution to the equation is constructed by the small-parameter method with the use of traveling-wave functions. Then, in solving boundary-value problems, linearized equations are integrated and the resonance frequencies at which the amplitudes of the oscillation increase without limit according to the linear solution are determined. Near these frequencies, the linear analysis is then refined by allowing for the nonlinear terms in the boundary-value problems. It is shown that an increase in the amplitude of the oscillations at resonance frequencies may lead to the formation of spherical periodic shock waves in the given resonators. An analogy is made between these waves and resonance shock waves excited in long unidimensional resonators.Translated from Problemy Prochnosti, No. 10, pp. 49–73, October, 1995.     

Scattering of SH waves by a spherical layer

In the frame work of the theory of classical elasticity we study the interaction of spherical elastic SH waves of harmonic type with a spherical layer when the source is placed outside the layer. The exact solution of this scattering problem is investigated in detail after a generalized Debye's expansion is established. The presence of the spherical layer is evident from the second term of this development. The interpretations obtained for a one-sphere model remain valid. However, among the differences we note that the surface waves created on the outer face of the layer rise or die out according to an angle which depends on the mechanical and geometrical features of the layer.     

Highly nonlinear solitary waves in chains of hollow spherical particles

We study the dynamic response of one- dimensional granular chains composed of uniform hollow spheres excited by an impulse, and we observe the formation and propagation of highly nonlinear solitary waves. We find that the dynamics of these solitary waves are different from the solitary waves forming in chains composed of uniform solid spheres, because of the changes in the contact interaction between particles. We study the quasi-static contact interaction between two hollows spheres using finite element (FE) simulations, and approximate their response as a power-law type function in the range of forces of interest for this work. The experimental data obtained by testing a chain of particles shows good agreement with theoretical predictions obtained using a long wavelength approximation, and with numerical simulations based on discrete particle and FE models. We also investigate the effect of hollow spheres’ wall thickness on the dynamic response of the chains.     

Generalized thermoelastic waves in spherical curved plates without energy dissipation

In this article, the propagation of thermoelastic waves in orthotropic spherical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green–Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The theoretical formulation is based on the linear GN thermoelastic theory. The coupled wave equation and heat conduction equation expressed by the displacement and temperature are obtained. By the Legendre orthogonal polynomial series expansion approach, the coupled controlling equations are solved. The convergence of the method is demonstrated through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding purely elastic spherical plate are also shown to analyze the influence of thermoelasticity on elastic modes. The displacement, temperature and stress distributions of both elastic modes and thermal modes are calculated to show their differences. A thermoelastic spherical plate with a different ratio of radius to thickness is considered to show the influence of the ratio on the characteristics of thermoelastic waves.     

Deltan/deltaT measurements performed with guided waves and their application to the temperature sensitivity of wavelength-division multiplexing filters

Measurements of partial differentialn/ partial differentialT of thin films by the m-lines technique are presented. The importance of the substrate material is shown. An example of the wavelength shift of an optical thin-film filter with temperature is studied both theoretically and experimentally. The theoretical wavelength shift of a dense wavelength-division multiplexing filter is discussed.     

Encrypted optical storage with angular multiplexing

We present the first, to our knowledge, demonstration of an encrypted optical storage based on double-random phase encoding by using angular multiplexing in a photorefractive material. Original two-dimensional data are encrypted by use of two random phase codes located in the input and the Fourier planes and are then stored holographically in a LiNbO(3):Fe crystal. The retrieval of the original data can be achieved with a phase-conjugated readout scheme. We demonstrate the encryption and the decryption of multiple frames of two-dimensional digital data by using angular multiplexing. We also evaluate numerically the influence of the bandwidth of the optical system on the decrypted digital data. The bit error rate as a function of the optical system bandwidth is presented.     

Elastic waves generated by loading applied to surface of spherical cavity

The elastodynamic problem of an unbounded body, subjected to a rotationally symmetric application of tractions at the surface of a spherical cavity, is studied. In general this problem involves three independent variables, which are the radius, colatitude and time, but it is shown how the method of characteristics for one spatial variable and time can be applied when the dependent variables are expanded as series of Legendre Polynomials. The procedure is in contrast to ones employed previously in that it does not involve integral transforms or asymptotic approximations and the field variables can be obtained for small and large times.     

Scattering of electromagnetic spherical waves by a buried spheroidal perfect conductor

We examine the electromagnetic scattering of spherical waves by a buried spheroidal perfect conductor. The proposed analysis is based on the integral equation formalism of the problem and focuses on the establishment of a multiparametric model describing analytically the scattering process under consideration. Both the theoretical and the numerical treatment are presented. The outcome of the analysis is the determination of the scattered field in the observation environment along with its multivariable on several physical and geometric parameters of the system.     

Similarity analysis of strong converging spherical shock waves in radiating gas

Summary In this paper the influence of radiation upon the classical adiabatic self-similar solution of a converging spherical shock wave is investigated. The medium is assumed to be an optically thick, inviscid and ideal gas with a constant ratio of specific heats. In front of the shock wave it is considered to be uniform and at rest, and its counter pressure is neglected. The presented paper restricts itself to presenting those similarity solutions which show the least possible deviation from the classical adiabatic solution. Their eigenvalues are determined numerically and listed. The flow profiles of nonadiabatic similarity solutions are shown and compared with the flow profiles of the adiabatic similarity solution.     

Acoustic scattering of spherical waves incident on a long fluid-saturated poroelastic cylinder

Acoustic scattering of spherical waves generated by a monopole point source in a perfect (inviscid and ideal) compressible fluid by a fluid-saturated porous cylinder of infinite length is studied theoretically in the present study. The formulation utilizes the Biot theory of dynamic poroelasticity along with the appropriate wave-field expansions, the translational addition theorem for spherical wave functions, and the pertinent boundary conditions to obtain a closed-form solution in the form of infinite series. The analytical results are illustrated with a numerical example in which a monopole point source within water is located near a porous cylinder with a water-saturated Ridgefield sandstone formation. The numerical results reveal the effects of source excitation frequency, the cylinder interface permeability condition, and the location of the point source and the field point on the backscattered pressure magnitudes. Limiting cases are considered, and the obtained numerical results are validated by already well-known solutions.     

Some elastic properties of reinforced solids,with special reference to isotropic ones containing spherical inclusions

Based on Mori and Tanaka's concept of “average stress” in the matrix and Eshelby's solutions of an ellipsoidal inclusion, an approximate theory is established to derive the stress and strain state of constituent phases, stress concentrations at the interface, and the elastic energy and overall moduli of the composite. Both “stress-free” strain (polarization strain) and “strain-free” stress (polarization stress) are employed in these derivations under the traction- and displacement-prescribed conditions. The theory was developed first for a general multiphase, anisotropic composite with arbitrarily oriented anisotropic inclusions; explicit results are then given for a suspension of uniformly distributed, multiphase isotropic spheres in an isotropic matrix. Numerical results for stress concentrations in the spherical inclusions and at the interface are given for a 2-phase composite. Further, it is shown that the derived moduli are related to the Hashin-Shtrikman bounds and that, when the shear moduli are equal, the overall bulk modulus of a 2-phase composite reduces to Hill's exact solution. As compared with experimental data, the theory also provides reasonably accurate estimates for the Young's modulus of some 2- and 3-phase composites.     

Multichannel wavelength division multiplexing with photonic crystals

A multichannel wavelength-division-multiplexing system consisting of a two-dimensional photonic crystal is proposed. The system consists of two parts, a waveguiding element, realized by defects in a photonic crystal, and frequency-selective elements, realized by photonic crystal microcavities. Simulations, performed with a two-dimensional finite-difference time-domain technique with a perfectly matched layer absorbing boundary condition, showed the ability to filter an incident pulse into six spectral channels with a FWHM of 2 nm.     

On the propagation of waves from spherical and cylindrical cavities in anisotropic materials

The propagation of waves from a spherical or cylindrical cavity in an inhomogeneous anisotropic elastic solid is considered. In the first instance, integral transforms are used to provide solutions to specific boundary value problems involving elastic media exhibiting certain inhomogeneities. It is then noted that the Bergman integral operator method provides a more general analysis. Finally, an asymptotic approach having a wide range of application is discussed and employed to construct wavefront and high-frequency expansions for the solution field in general media.