Elastic interaction between a dislocation and a near-by inclusion

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.     

The reciprocal theorem and rigid spherical inclusion vis-à-vis certain point singularities

The elastic interaction of certain point singularities with a rigid spherical inclusion embedded into an otherwise infinite elastic medium is investigated. The particular singularities considered are point force, force-dipole (with and without moment), centre of dilatation and concentrated moment. In each case, simple, closed form expressions are deduced by application of Betti's reciprocal theorem for the net force and net torque acting on the inclusion.     

Interfacial evolution of a spherical particle in a uniaximal straining flow

The growth behavior of a spherical particle in undercooled melt,affected by uniaxial straining flows,is studied.The analytical solution obtained by the matched asymptotic expansion method shows that the uniaxial straining flow effect results in higher local growth rate near the surface where the flow comes in and lower local growth rate near the surface where the flow goes out,and that the uniaxial straining flow causes an initially spherical particle to evolve into an oblate spheroid.     

Scattering of on-axis polarized Gaussian light beam by spheroidal water coating aerosol particle

Small particle light scattering can produce light with polarization characteristics different from those of the incident beam. An analytical solution to the scattering by a spheroid with inclusion for an on-axis polarized Gaussian beam incidence is provided within the generalized Lorenz-Mie theory framework. The shapes of the inclusion can be spherical, confocal spheroid, or non-confocal spheroid. The Muller scattering matrix elements are computed for plane wave incidence or Gaussian light beam incidence. The effect of the size and shape of the inclusion or the coating on the polarized Oaussian light scattering characteristics by a spheroidal water coating aerosol Darticle are commlted and a,nalvzed.     

Elastic dipole interaction of point defects in a sphere of elastically anisotropic cubic material

The elastic field of centres of dilatation at arbitrary positions in a spherical specimen with cubic elastic constants is studied. The influence of the (free) boundary, which is of central importance due to the long-range nature of the elastic interaction, is included. For materials with small elastic anisotropy expansions in terms of vector spherical harmonics are obtained for the displacements due to one defect, as well as for the interaction energy of two defects. Infinite material expressions and surface contributions are given separately. The general treatment is exemplified by presenting explicit results for the case of hydrogen atoms dissolved in vanadium.     

Two-dimensional shear waves scattering by a large rigidity strip with interface crack

A two-dimensional problem of shear horizontal (SH) waves scattering by a finite width planar elastic (piezoelectric) inclusion partially debonded from its surrounding elastic matrix is investigated using the effective boundary conditions and singular integral equations technique. The case of large rigidity inclusions with blunted tips is considered, in which the upper face of the inclusion is perfectly bonded to the matrix. The debonding region is modeled as interface crack with non-contacting faces. Using the Green theorem the mixed boundary value problem is reduced to a system of the hypersingular integral equations. Numerical results of the scattering fields characteristics are presented. The effects of incidence direction, various material parameters of the strip on the scattering field are discussed and phenomenon of the non-specular reflection of SH waves is considered. The accuracy of the numerical results is confirmed by the use of analytical approximate problem solution of high-frequency SH waves scattering on a finite hard/soft inclusion.     

Eshelby's tensor fields and effective conductivity of composites made of anisotropic phases with Kapitza's interface thermal resistance

Eshelby's results and formalism for an elastic circular or spherical inhomogeneity embedded in an elastic infinite matrix are extended to the thermal conduction phenomenon with a Kapitza interface thermal resistance between matrix and inclusions. Closed-form expressions are derived for the generalized Eshelby interior and exterior conduction tensor fields and localization tensor fields in the case where the matrix and inclusion phases have the most general anisotropy. Unlike the relevant results in elasticity, the generalized Eshelby conduction tensor fields and localization tensor fields inside circular and spherical inhomogeneities are shown to remain uniform even in the presence of Kapitza's interface thermal resistance. With the help of these results, the size-dependent overall thermal conduction properties of composites are estimated by using the dilute, Mori–Tanaka, self-consistent and generalized self-consistent models. The analytical estimates are finally compared with numerical results delivered by the finite element method. The approach elaborated and results provided by the present work are directly applicable to other physically analogous transport phenomena, such as electric conduction, dielectrics, magnetism, diffusion and flow in porous media, and to the mathematically identical phenomenon of anti-plane elasticity.     

Time-Domain Mapping of Electromagnetic Ray Movement Inside Anisotropic Spherical Resonator

This paper presents the analytical proof of Time-Domain Mapping Method for the spherical resonator made up of uniaxial crystal. In this way, the main types of caustics inside the spherical resonator made up of uniaxial crystal, which were investigated numerically before, are confirmed analytically. It is engraved that the problem of the ray flow inside the spherical resonator can be reduced to the problem of the ray flow inside metal cavity shaped as spheroid.     

Scattering of spatially inhomogeneous sound waves by a spherical particle

The problem of monopole, dipole, and rotational scattering of a spatially inhomogeneous time-harmonic sound field by an arbitrary spherical particle is solved for the cases of the medium being a viscous compressible liquid or an isotropic elastic medium. Equations for the spherical mean fields at the particle are obtained. These equations are used to derive the formulas for the scattered fields. Different limiting cases of particle behavior are considered. In particular, it is shown that the dipole scattering is determined by two components of particle oscillations, one of which corresponds to translational oscillatory motion and the other to oscillations of two antiphase monopoles. For these types of particle oscillations, a scattering matrix, which determines the scattering of an arbitrary field by a particle, is constructed. The matrix allows the formalization of the processes of multiple sound scattering by particles and is valid for any distances between the particles down to their contact.     

Spontaneous emission of an atom placed near a prolate nanospheroid

The frequency shift and linewidth variation of an atomic oscillator placed next to a prolate dielectric or metal spheroid are found within the framework of the classical approach. Both the frequency shift and linewidth are shown to be substantially dependent on the location of the atom and the form of the nanospheroid and capable of reaching very high values near the surface of the nanospheroid under plasmon (polariton) resonance conditions. The predictions are compared with those found for spherical and cylindrical geometries. The prolate spheroid is treated as a model of a needle tip in apertureless optical scanning microscopy. Effects of sharpness of interaction between the nanospheroid tip and atoms are considered. Received 2 January 2002 and Received in final form 3 April 2002 Published online 28 June 2002     

Radiation of an Electric Dipole from a Small Plasma Spheroid

We obtain and analyze an analytical solution of the boundary-value problem of the field of an electric dipole located in a small spheroid filled with a cold isotropic plasma. The conditions of resonant amplification of the field in vacuum are studied for various shapes and curvatures of the plasma spheroid. It is shown that for a certain spheroid shape, the resonant amplification increases several times compared with the case of spherical plasma environment. The obtained results are compared with the resonant radiation of a dipole from a narrow elliptical plasma cylinder.     

Monoenergetic electron parameters in a spheroid bubble model

A reliable analytical expression for the potential of plasma waves with phase velocities near the speed of light is derived.The presented spheroid cavity model is more consistent than the previous spherical and ellipsoidal models and it explains the mono-energetic electron trajectory more accurately,especially at the relativistic region.The maximum energy of electrons is calculated and it is shown that the maximum energy of the spheroid model is less than that of the spherical model.The electron energy spectrum is also calculated and it is found that the energy distribution ratio of electrons △E/E for the spheroid model under the conditions reported here is half that of the spherical model and it is in good agreement with the experimental value in the same conditions.As a result,the quasi-mono-energetic electron output beam interacting with the laser plasma can be more appropriately described with this model.     

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.     

Scattering of electromagnetic radiation by a two-layer nonconfocal spheroid that is small compared to the wavelength

We have considered the electrostatic problem for a two-layer nonconfocal spheroid. The approach is based on surface integral equations that are similar to equations in terms of the extended boundary condition method for wave problems. Electrostatic fields are related to scalar potentials, which are represented as expansions in terms of eigenfunctions of the Laplace equation in two spheroidal coordinate systems, while unknown expansion coefficients are determined from infinite systems of linear algebraic equations. The constructed rigorous solution to the problem coincides with the known solution in a particular case of a confocal two-layer spheroid. In addition, for the nonconfocal two-layer spheroid, we have constructed an explicit approximated solution assuming that the field in the particle core is constant. This solution coincides with the rigorous solution if the scatterer shells are confocal. The formula found for the polarizability of the two-layer nonconfocal spheroid has a very simple form compared to the previously proposed cumbersome algorithm (B. Posselt et al., Measur. Sci. Technol. 13, 256 (2002)) and is more efficient numerically.     

Effect of inclusions on heterogeneous crack nucleation in nanocomposites

A two-dimensional theoretical model is proposed for the heterogeneous nucleation of a grain-boundary nanocrack in a nanocomposite consisting of a nanocrystalline matrix and nanoinclusions whose elastic moduli are identical to those of the matrix. The inclusions have the form of rods with a rectangular cross section and undergo dilatation eigenstrain induced by the differences in the lattice parameters and thermal expansion coefficients of the matrix and inclusions. In terms of the model, a mode-I–II nanocrack nucleates at the negative disclination of a biaxial dipole consisting of wedge grain-boundary (or junction) disclinations; then, the nanocrack opens along a grain boundary and reaches an inclusion boundary. Depending on the relative positions and orientations of the initial segment of the nanocrack and the inclusion, the nanocrack can either penetrate into the inclusion or bypass it along the matrix-inclusion interface. The nanocrack nucleation probability increases near an inclusion with negative (compressive) dilatation eigenstrain. A decrease in the inclusion size decreases (increases) the probability of a crack opening along the interface if the dilatation eigenstrain is negative (positive).     

基片及其上方回转椭球粒子极化光散射

基于BV理论建立基片及其上方回转椭球粒子的复合散射模型,通过矢量球谐函数展开,对散射过程进行了分析,对散射场及微分散射截面详细求解,并给出了数值计算结果,与离散源方法做了比较,同时退化为球粒子与扩展Mie理论做了比较,说明了此方法的有效性。并详细讨论分析了微分散射截面随不同入射角,散射角,回转椭球粒子的尺寸、长短轴比例,距基片的距离,介电常数,粒子取向角的变化关系。结果表明:同一散射角下入射角越大,其微分散射截面越大;粒子尺寸越大,相互作用越大,其微分散射截面越大;长短轴比例越大,其微分散射截面越小;距离基片的距离越大,微分散射截面越大;微分散射截面的变化主要依赖于相对介电常数实部、虚部数值较大的一方,并且随粒子取向角的增大而增大。     

Non-spherical quasi-black holes

Quasi-black holes are objects having some of the properties of black holes but which have no horizon and are non-singular. Up till now those found have been spherical. I give solutions of the Einstein–Maxwell equations representing spheroidal quasi-black holes, made of electrically counterpoised dust. They contain a parameter a which governs the external gravitational and electrical fields of the spheroid: as a tends to zero those fields become spherical in spite of the spheroidal character of the source.     

Theoretical investigation of resonance frequencies in long wavelength electromagnetic wave scattering process from plasma prolate and oblate spheroids placed in a dielectric layer

Response of a prolate spheroid plasma and/or an oblate spheroid plasma in presence of long wavelength electromagnetic wave has been studied. The resonance frequencies of these objects are obtained and it is found that they reduce to the resonance frequency of spherical cold plasma. Moreover, the resonant frequencies of prolate spheroid plasma and oblate spheroid plasma covered by a dielectric are investigated as well. Furthermore, their dependency on dielectric permittivity and geometry dimensions is simulated.     

Electroelastic field of a sphere located in the vicinity of a plane piezoelectric surface

The electric field generated by a scanning probe microscope is determined. Analytical expressions for the electroelastic field in a piezoelectric sample and the external electric field are derived for a spherical probe. It is demonstrated that the coupling of elastic and electrostatic fields in the piezoelectric material leads to energy redistribution between such fields. This circumstance causes variations in the normal component of the electric field strength at the interface and the capacitance of a probe.     

Scattering of Millimeter Waves from Acid Rain

A theoretical investigation of scattering characteristics of millimeter waves from acid rain is conducted using the method of vector spherical function expansion. The particles of acid rain are considered as the double-layered spheroid. The method is used to derive an analytical solution to the problem of scattering of millimeter waves by a coated dielectric spheroid. The normalized bistatic cross section versus scattering angle for the acid raindrop is calculated at frequencies of 35 GHz and 94 GHz. This is the first part of our study scattering characteristics of millimeter waves from acid rain.