The total acoustic impedance of a prolate spheroid performing transverse oscillatory movements

Using the theory of spheroidal wave functions, the total acoustic impedance is determined for a prolate spheroid performing transverse translational and rotational oscillatory movements. Expressions for the radiation resistance, the added mass, and the added moment of inertia are derived. It is shown that, in the lowfrequency approximation, this mass and moment of inertia reach limiting values identical to hydrodynamic ones. The components of the total acoustic impedance are calculated for spheroids of different relative thicknesses at an arbitrary frequency.     

Theory of Cosmical Coherent Avalanche Catastrophes

Abstract

Recently pulses of the electromagnetic cosmic radiation of varies frequency ranges were detected by means of space flight equipment [1]. But so far the physical nature of the sources of these pulses are not well known. Since the generators of these pulses are at far distances obviously, the latters should have considerable power. But in this case we are forced to accepte that that the radiation is generated not only by the surface but also by the bulk mass of the distant object. It is also reasonable to propose that the objects are superdense ones [2]. In the Latter case the electromagnetic radiation cann't difused up to the surface of a superdense object from the centre and so no electromagnetic and acoustic processes can give radiation from the bulk mass of an object. On the contrary gravitational and neutrino radiation may be generated by the bulk mass of a massive object and at the surface of these objects these radiations tightly bounded to matter may be partly transformed into electromagnetic radiation [3]. And we can suppose that namely this very small part of the whole radiational energy is at time registrated at the earth and space laboratories. The mauy ask why all of the remaining purt of teh rediated energy has not been detected yet? There where made some attempts to performe neutrino astronony equipment out no solar neuttinos have been detected yet. As to the camical gravitational radiation it is pregently inveutigated only at low frequencles and no distinet conclucion about its occurence in been reached in the lilorature.     

Excitation of a tube wave in a borehole by an external isotropic point source

The excitation of a tube wave in an infinite fluid-filled borehole by an external isotropic point source is considered. The solution to the problem is obtained in the form of a double integral with respect to the ray parameter (slowness) and frequency. The integral with respect to the slowness is transformed to a contour integral in the complex slowness plane and then reduced to the integral over the edges of the cut of the vertical slowness function and the semiresidues at the poles. An asymptotic expression for the wave field in the borehole is obtained with allowance for the radiation condition at infinity. It is shown that, when a longitudinal spherical wave is incident on the borehole, only one low-frequency Stoneley wave is excited and not two, as was assumed earlier [1].     

Response of infinite length rods and beams with periodically varying area

This paper develops a solution method for the longitudinal motion of a rod or the flexural motion of a beam of infinite length whose area varies periodically. The conventional rod or beam equation of motion is used with the area and moment of inertia expressed using analytical functions of the longitudinal (horizontal) spatial variable. The displacement field is written as a series expansion using a periodic form for the horizontal wavenumber. The area and moment of inertia expressions are each expanded into a Fourier series. These are inserted into the differential equations of motion and the resulting algebraic equations are orthogonalized to produce a matrix equation whose solution provides the unknown wave propagation coefficients, thus yielding the displacement of the system. An example problem of both a rod and beam are analyzed for three different geometrical shapes. The solutions to both problems are compared to results from finite element analysis for validation. Dispersion curves of the systems are shown graphically. Convergence of the series solutions is illustrated and discussed.     

Solitary wave dynamics in shallow water over periodic topography

The problem of long-wave scattering by piecewise-constant periodic topography is studied both for a linear solitary-like wave pulse, and for a weakly nonlinear solitary wave [Korteweg-de Vries (KdV) soliton]. If the characteristic length of the topographic irregularities is larger than the pulse length, the solution of the scattering problem is obtained analytically for a leading wave in the framework of linear shallow-water theory. The wave decrement in the case of the small height of the topographic irregularities is proportional to delta2, where delta is the relative height of the topographic obstacles. An analytical approximate solution is also obtained for the weakly nonlinear problem when the length of the irregularities is larger than the characteristic nonlinear length scale. In this case, the Korteweg-de Vries equation is solved for each piece of constant depth by using the inverse scattering technique; the solutions are matched at each step by using linear shallow-water theory. The weakly nonlinear solitary wave decays more significantly than the linear solitary pulse. Solitary wave dynamics above a random seabed is also discussed, and the results obtained for random topography (including experimental data) are in reasonable agreement with the calculations for piecewise topography.     

Analytic solution of the wave equation for an electron in the field of a molecule with an electric dipole moment

We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger representation space that incorporates an analytic solution for the non-central electric dipole potential cosθ/r², which was believed not to belong to the class of exactly solvable potentials. Therefore, we were able to obtain a closed form solution of the three-dimensional time-independent Schrödinger equation for a charged particle in the field of a point electric dipole that could carry a nonzero net charge. This problem models the interaction of an electron with a molecule (neutral or ionized) that has a permanent electric dipole moment. The solution is written as a series in a basis composed of special functions that support a tridiagonal matrix representation for the angular and radial components of the wave operator. Moreover, this solution is for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The expansion coefficients of the radial and angular components of the wavefunction are written in terms of orthogonal polynomials satisfying three-term recursion relations. For the Coulomb-free case, where the molecule is neutral, we calculate critical values for its dipole moment below which no electron capture is allowed. These critical values are obtained not only for the ground state, where it agrees with already known results, but also for excited states as well.     

Two-dimensional coupled mode equation for grating waveguide excitation by a focused beam

The problem of grating coupling of a focused incident beam under non-normal incidence into a slab waveguide is given a complete three-dimensional (3D) solution. The diffracted field is expressed as the Fourier integral of a regular part and of a singular part resulting from the existence of the coupled guided mode. A suitable expression of the field in the neighborhood of the pole and a rigorous definition of the modal field lead to a generalized coupled mode equation relating the incident field and the two-dimensional (2D) modal field propagating in the plane of the slab waveguide. The phenomenological parameters involved in the coupled wave equation: the propagation constant, the radiation coefficient as well as the modal field shape are derived from the exact treatment of plane wave diffraction in the same structure. The solution of the complete coupling problem is given in the particular case of a Gaussian incident beam, and of a high index step-index waveguide.     

On the theory of polarization radiation in media with sharp boundaries

Polarization radiation generated when a point charge moves uniformly along a straight line in vacuum in the vicinity of media with a finite permittivity ɛ(ω) = ɛ′ + iɛ″ and sharp boundaries is considered. A method is developed in which polarization radiation is represented as the field of the current induced in the substance by the field of the moving charge. The solution to the problem of radiation induced when a charge moves along the axis of a cylindrical vacuum channel in a thin screen with a finite radius and a finite permittivity is obtained. Depending on the parameters of the problem, this solution describes various types of radiation (Cherenkov, transition, and diffraction radiation). In particular, when the channel radius tends to zero and the outer radius of the screen tends to infinity, the expression derived for the emitted energy coincides with the known solution for transition radiation in a plate. In another particular case of ideal conductivity (ɛ″ → ∞), the relevant formula coincides with the known results for diffraction radiation from a circular aperture in an infinitely thin screen. The solution is obtained to the problem of radiation generated when the charge flies near a thin rectangular screen with a finite permittivity. This solution describes the diffraction and Cherenkov mechanisms of radiation and takes into account possible multiple re-reflections of radiation in the screen. The solution to the problem of radiation generated when a particles flies near a thin grating consisting of a finite number of strips having a rectangular cross section and a finite permittivity and separated by vacuum gaps (Smith-Purcell radiation) is also obtained. In the special case of ideal conductivity, the expression derived for the emitted energy coincides with the known result in the model of surface currents.     

A diffraction method for measuring the diameter of ultrathin metal fibers

The problem of diffraction of a plane electromagnetic wave by a metal fiber with a circular cross section is considered for the case in which the diameter of the fiber differs only slightly from the radiation wavelength. Relations between the positions of the first diffraction minima and the fiber diameter are derived. The formulas obtained are used to determine the diameter of an ultrathin fiber.     

Efficient evaluation of edge diffraction integrals using the numerical method of steepest descent

For the problem of edge diffraction from an edge of finite length a frequency-domain solution, obtained from an analytical time-domain solution, has been presented by Svensson et al. [Acta. Acust. Acust. 95, 568-572]. This formulation takes the form of a Fourier-type integral whose evaluation is expensive in the high frequency range. This paper demonstrates that by using tailored highly oscillatory quadrature methods based on asymptotic properties of the integral, accurate approximations in the high frequency case can be obtained with little computational effort.     

辐射超声速扩散传输产生条件的研究

 利用1维辐射扩散方程的解析理论，在外加辐射源为恒温源的条件下，对能够产生辐射超声速扩散传输的条件进行了研究，可以解析地得出在固定物质密度下能够产生超声速扩散流的参数区域。分析得出：对于一个固定的恒温外源，随着时间的增加，热波波头位置是随时间的平方根增长的，光学厚度正比于波头位置，也是随时间而逐渐增加的；而马赫数是按时间平方根倒数减少的。并推导出在不同密度下恰好产生超声速扩散时，辐射源温度和辐射热波波头位置满足的临界值条件，它们是关于介质密度的函数关系式。最后以SiO₂泡沫为算例，对这些结果的物理图像做了简要的阐述，对它们的应用进行了具体的说明和分析。     

Influence of circumferential partial coating on the acoustic radiation from a fluid-loaded shell

Acoustic compliant coatings are a common approach to mitigate the radiation and scattering of sound from fluid-loaded submerged structures. An acoustic compliant coating is a coating that decouples an acoustic source from the surrounding acoustic medium; that is, it provides an acoustic impedance mismatch (different density and speed of sound product). Such a coating is distinct from an ordinary compliant coating in that it may not be resilient in the sense of low stiffness, but still provides an acoustic impedance mismatch. Ideally, the acoustic coating is applied uniformly over the entire surface of the fluid-loaded structure to minimize the acoustic radiation and scattering. However, in certain instances, because of appendages, it may not be practically possible to completely cover the surface of a fluid-loaded structure to decouple it from the adjacent acoustic medium. Furthermore, there may be some inherent advantages to optimizing the distribution of the coating around areas from which the acoustic radiation appears to be dominant. This would be analogous to the application of damping treatment to a vibrating structure in areas where the vibration levels are highest. In the case of the acoustic radiation the problem is more complex because of the coupling between the acoustic fluid and the structure. In this paper, the influence of a partial coating on the acoustic radiation from a fluid-loaded, cylindrical shell of infinite extent and excited by either a line force or an incident plane acoustic wave is examined. The solution to the response and scattered pressure is developed following the procedure used by the authors in previous work on the scattering from fluid-loaded plates and shells. The coating is assumed to be normally reacting providing a decoupling layer between the acoustic medium and the structure; that is, it does not add mass or stiffness to the base structure. The influence of added mass or stiffness of the coating can be included as an added inhomogeneity and treated separately in the solution.     

Magnetic structure of Ce<Subscript>2</Subscript>Fe<Subscript>17 − <Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> intermetallic compounds

The magnetic structure of intermetallic compounds Ce₂Fe_{17 − x} Mn _x (0 ≤ x ≤ 3) was studied using neutron diffraction. The neutron diffraction patterns measured at 4.2 K contain satellites indicating a modulated structure with the wave vector k = [0, 0, τ]. As the concentration x increases, the value of τ increases, while the average magnetic moment of Fe/Mn atoms decreases. A change in the magnitudes of the average magnetic moment and wave vector k is explained by competition between exchange interactions at distances of nearest neighbor transition element atoms.     

The analysis of the impact response of a thin plate via fractional derivative standard linear solid model

The impact of a rigid body upon an infinite isotropic plate is investigated for the case when the viscoelastic features of the plate represent themselves only in the place of contact and are governed by the standard linear solid model with fractional derivatives. Thus, the problem concerns the shock interaction of the dropping mass and the target, wherein instead of the Hertz contact law the generalized fractional derivative standard linear solid law is employed as a law of interaction. The part of the plate beyond the contact domain is assumed to be elastic, and its behaviour is described by the equations of motion which take rotary inertia and shear deformations into account. It is assumed that transient waves generate in the plate at the moment of impact, the influence of which on the contact domain is considered using the theory of discontinuities. To determine the desired values behind the transverse shear wave front, one-term ray expansions are used, as well as the equations of motion of the falling mass and the contact region. As a result, we are led to a set of two linear differential equations, the solution of which is found analytically by the Laplace transform and by the Euler substitution method. This allows the contact force to be determined as a function of time.     

An extension of implicit Monte Carlo diffusion: Multigroup and the difference formulation

Implicit Monte Carlo (IMC) and Implicit Monte Carlo Diffusion (IMD) are approaches to the numerical solution of the equations of radiative transfer. IMD was previously derived and numerically tested on grey, or frequency-integrated problems [1]. In this research, we extend Implicit Monte Carlo Diffusion (IMD) to account for frequency dependence, and we implement the difference formulation [2] as a source manipulation variance reduction technique. We derive the relevant probability distributions and present the frequency dependent IMD algorithm, with and without the difference formulation. The IMD code with and without the difference formulation was tested using both grey and frequency dependent benchmark problems. The Su and Olson semi-analytic Marshak wave benchmark was used to demonstrate the validity of the code for grey problems [3]. The Su and Olson semi-analytic picket fence benchmark was used for the frequency dependent problems [4]. The frequency dependent IMD algorithm reproduces the results of both Su and Olson benchmark problems. Frequency group refinement studies indicate that the computational cost of refining the group structure is likely less than that of group refinement in deterministic solutions of the radiation diffusion methods. Our results show that applying the difference formulation to the IMD algorithm can result in an overall increase in the figure of merit for frequency dependent problems. However, the creation of negatively weighted particles from the difference formulation can cause significant numerical instabilities in regions of the problem with sharp spatial gradients in the solution. An adaptive implementation of the difference formulation may be necessary to focus its use in regions that are at or near thermal equilibrium.     

Wave radiation in lattice fracture

The square and triangular lattices are considered, where the uniform crack growth is accompanied by the wave radiation. The radiation energy and structure are studied. The energy radiated to the bulk of the lattice is found in a direct way. The radiation structure is described based on the crack problem solution and by means of the analysis of two-dimensional dispersion relations for the intact lattice. The mode III problem for square lattice is discussed in detail, whereas, in the case of the plane problem for the triangular lattice, the only those results are derived which follow from the two-dimensional dispersion relations. It is shown that there exists a finite crack-speed-dependent region of wavenumbers corresponding to the waves radiated to the bulk of the lattice. In the case of the triangular-cell lattice, in addition, one or several lattice Rayleigh waves are radiated. For the square lattice a complete solution for the wave field is presented with the crack-speed-dependent far-field asymptote. The latter is characterized by the wave amplitude asymptotically decreasing as the distance from the crack front in power −1/3. The asymptotically significant crack-speed-dependent direction of the radiation is determined. Such asymptotic results are also valid for the triangular lattice.     

Multilayer Anisotropic Bi-periodic Diffraction Gratings

The formalism of Rokushima and Yamakita [J. Opt. Soc. Am. 73 (1983) 901] treating the diffraction on planar multilayered 1D anisotropic gratings is extended to the diffraction on anisotropic 2D multilayer grating structures bi-periodic in the plane parallel to the interfaces. In addition to the oblique incidence of plane waves, the case of normal incidence is also treated. The goal of the paper is to provide a basis for the formal analysis of 2D patterned multilayers with natural or induced anisotropies. For example, such structures are of interest in the design of new magnetic and magneto-optic devices. In view of the fact that the anisotropies have often a negligible effect on the energy distribution among diffracted modes with respect to the isotropic case the optical response is alternatively expressed in terms of the ellipsometric parameters of diffracted waves. The present analysis represents generalization of the problem of electromagnetic wave interactions in planar multilayers consisting of layers characterized by a general permittivity tensor treated by Yeh [J. Opt. Soc. Am. 69 (1979) 742].     

Scattering of a plane inhomogeneous electromagnetic wave by a spherical particle

We extend an analytical solution for the problem of diffraction of a plane wave by a spherical particle to the case of an inhomogeneous wave. Numerical examples showing a significant change in the scattered-wave structure compared with the case of diffraction of a homogeneous wave are presented. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 72–81, January 2006.     

Diffractive Multifocal Focusing of Gaussian Beams

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the quasi-optical approximation. It is shown that when a Gaussian beam illuminates a bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The proposed diffractive method allows the focusing of the wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensive and high-power radiation.     

中子星的转动惯量与表面红移的研究

在温度、密度及同位旋相关的核物质状态方程的基础上,通过求解Tolman–Oppenheimer–Volkoff方程,得到了中子星的转动惯量与表面红移.计算结果表明,中子星的转动惯量较强地依赖于核物质的不可压缩系数与对称能强度系数,而对核子有效质量不太敏感;中子星的表面红移却对对称能强度系数不太敏感,而较强地依赖于不可压缩系数与核子有效质量.