Electrostatic potential of point charges inside dielectric oblate spheroids

As a sequel to a previous paper on electrostatic potential of point charges inside dielectric prolate spheroids [1], this note further presents the exact solution to the electrostatic problem of finding the electric potential of point charges inside a dielectric oblate spheroid that is embedded in a dissimilar dielectric medium. Numerical experiments have demonstrated the convergence of the proposed series solutions.     

Stability of charged drops of spheroidal shapes with respect to axisymmetric deformation

The stability of a strongly charged spherical drop with respect to deformations of its shape to prolate and oblate spheroids has been studied. It is shown that drops can become unstable and can break apart provided that the virtual shape is a prolate spheroid. Deforming a drop to an oblate spheroid does not cause it to break apart. Zh. Tekh. Fiz. 68, 33–36 (July 1998)     

Proof of expansion of the reciprocal distance in spheroidal coordinates

A concise proof is given for the expansion of the reciprocal distance between two points in spheroidal harmonics. The proof is given for an oblate and a prolate spheroid.     

Electrostatic potential of point charges inside dielectric prolate spheroids

The exact solution to an electrostatic problem of finding the electric potential of point charges inside a dielectric prolate spheroid is discussed in this note by using the classical electrostatic theory, where the prolate spheroid is embedded in a dissimilar dielectric medium. Such a problem may find its application in hybrid solvent biomolecular simulations, in which biomolecules and a part of solvent molecules within a dielectric cavity are explicitly modeled while a surrounding dielectric continuum is used to model bulk effects of the solvent beyond the cavity. Numerical experiments have demonstrated the convergence of the proposed series solutions.     

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     

The symmetry of the relative motion of excitons in semiconductor heterostructures

A theoretical model of excitonic states in semiconductor heterostructures is presented. The approach employs the envelope function approximation, and involves a two parameter variational calculation in which the symmetry of the component of the wave function representing the relative motion is allowed to vary between the two- and three-dimensional limits. Detailed calculations are described for a variety of single quantum wells and superlattices. The results show that the excitons are neither 2D nor 3D like, but are intermediate in character. Furthermore, in the main, they assume the symmetry of a prolate spheroid. An exception to this occurs in the special case of an asymmetric double quantum well close to resonance, where two stable exciton states are found for the same one-particle states. One of these ‘twin’ exciton states is an oblate spheroid. The results illustrate the need for accurate determination of excitonic properties if the dynamical evaluation of exciton states, in for example, quantum well lasers, is to be readily determined.     

长椭圆旋转介质球中的半波振子天线

本文从麦克斯韦方程出发,求出有损耗的长椭圆旋转介质球中一个同焦点的小的长椭圆旋转形半波振子发射天线上的电流分布和其输入阻抗,以及它在有损耗的介质球中和外部自由空间中所产生的场。     

Near-field calculations for a rigid spheroid with an arbitrary incident acoustic field

A general spheroidal coordinate separation-of-variables solution is developed for the determination of the acoustic pressure distribution near the surface of a rigid spheroid for a monofrequency incident acoustic field of arbitrary character. Calculations are presented, for both the prolate and oblate geometries, demonstrating the effects of incident field orientation and character (plane-wave, spherical wave, cylindrical wave, and focused beam) on the resultant acoustic pressure distribution.     

The shape of a drop in a constant electric field

The variation of the shape of a drop immersed in an immiscible liquid under the action of an electric field is calculated. The charge is transferred both by ohmic current through the interface and by the convective component over the interface. A solution quadratic in the parameter that is the ratio of the electric pressure to the capillary pressure is analyzed. Conditions where the drop transforms into a spheroid that is prolate or oblate along the electric field vector are found. An experimental study of the drop deformation by electric forces is carried out.     

Image systems for the reaction field inside spheroidal dielectric objects and applications

Charges inside a dielectric object embedded in a dissimilar dielectric medium polarize the surrounding medium, which in turn makes a contribution, called the reaction field, to the electric field inside the object. In this work, we develop complete image systems for the reaction field inside a prolate or oblate spheroidal dielectric object embedded in an infinite dissimilar dielectric medium. In either case, an image system consists of a point image and a symmetric surface image over an exterior confocal spheroid that passes through the point image. As an application, the point image is applied into the generalized image charge solvation model (GICSM) and is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM simulation as references. The results indicate that, for both the prolate and oblate cases, the single point image charge approximation for the reaction field inside the dielectric cavity of the model is good enough for the GICSM to faithfully reproduce typical static and dynamic properties of the liquid water at least when the spheroidal cavity has relatively small eccentricity.     

Application of the electrostatic mean value theorem to electrostatic sensor electrodes

We present a method for approximating the potential of conducting objects due to a known electrostatic source. The method involves averaging the incident potential over the conductor surface or volume region, which is known to give the exact value for a perfectly conducting sphere. The method is extended to spheroidal geometries, both prolate and oblate, to study the error incurred for deviations from the spherical case. Exact values for the spheroid potentials are derived and compared with those obtained by the mean value approximations. The result for the oblate spheroid is extended to the case of a two-dimensional electrostatic disk. The approximations are proposed as a method for predicting the potential of conducting electrodes used with electrostatic sensors for the measurement of electrostatic field disturbances. In this regard, the mean value approximation is applied to determine the source to electrode mutual capacitance, which is implemented in the model for the sensor system. Electrostatic disk electrodes are used with an electrostatic disturbance sensor to experimentally validate the application of the mean value approximation.     

Stability of a charged drop having the form of a triaxial ellipsoid

The stability of a highly charged, isolated conductive drop is analyzed within the principle of minimum potential energy of a closed system. A treatment of the stability of drops of ellipsoidal shape shows that both spherical drops and drops having an oblate spheroidal shape experience instability at sufficiently large charges according to a single scheme, i.e., they deform to a prolate spheroid. Zh. Tekh. Fiz. 68, 48–51 (November 1998)     

Two-dimensional particle-in-cell plasma source ion implantation of a prolate spheroid target

A two-dimensional particle-in-cell simulation is used to study the time-dependent evolution of the sheath surrounding a prolate spheroid target during a high voltage pulse in plasma source ion implantation. Our study shows that the potential contour lines pack more closely in the plasma sheath near the vertex of the major axis, i.e. where a thinner sheath is formed, and a non-uniform total ion dose distribution is incident along the surface of the prolate spheroid target due to the focusing of ions by the potential structure. Ion focusing takes place not only at the vertex of the major axis, where dense potential contour lines exist, but also at the vertex of the minor axis, where sparse contour lines exist. This results in two peaks of the received ion dose, locating at the vertices of the major and minor axes of the prolate spheroid target, and an ion dose valley, staying always between the vertices, rather than at the vertex of the minor axis.     

Sensitivity of surface plasmon resonances in spheroidal metal nanoparticles

The sensitivity of the surface plasmon resonance wavelength position in prolate and oblate metal nanoparticles to the refractive index of an embedding solution, nanoparticle shape, and temperature is studied theoretically. The influence of dissipation factor on plasmon resonance is discussed as well. The new approach specifying the optimal nanoparticle shape to reach the maximal sensitivity is proposed. The calculations are illustrated on the example of Na nanoparticle.     

Optical phonons in semiconductor quantum rods

Surface polar-optical phonons are analyzed for semiconductor quantum rods (QR). The cylindrical symmetry is modelled in the form of a prolate spheroid where the aspect-ratio is identified with the corresponding ratio of the ellipsoid semiaxes. Using a theory based on the dielectric continuum approach, we consider a single CdSe QR inserted in a host material, assumed as an infinite dielectric, and viewed as an inactive rigid medium to the oscillations. Our results for CdSe are discussed, together with the differences from spherical and quasi-spherical quantum dots. We believe these are important steps to help the understanding of future experiments in this new class of materials.     

Critical equilibrium spheroidal deformation of a drop of dielectric liquid in a uniform electrostatic field

The stability of a dielectric drop, which in an external electrostatic field takes on the equilibrium shape of a prolate spheroid, is analyzed using the principle of minimum total potential energy of an isolated system. The values of the Taylor parameter and degree of spheroidal deformation at which the drop loses stability are determined for a wide range of dielectric constants of the substance of the drop. Zh. Tekh. Fiz. 69, 23–28 (July 1999)     

Analysis of long wavelength electromagnetic scattering by a magnetized cold plasma prolate spheroid

Abstract

Using dielectric permittivity tensor of the magnetized prolate plasma, the scattering of long wavelength electromagnetic waves from the mentioned object is studied. The resonance frequency and differential scattering cross section for the backward scattered waves are presented. Consistency between the resonance frequency in this configuration and results obtained for spherical plasma are investigated. Finally, the effective factors on obtained results such as incident wave polarization, the frequency of the incident wave, the plasma frequency and the cyclotron frequency are analyzed.     

Investigation on dynamics of double emulsion droplet in a uniform electric field

Phase field method based on Cahn–Hilliard free energy formulation is adopted for predicting the behavior of double emulsion droplet suspended in a continuous phase under the influence of a uniform electric field. The role played by the inner droplet on the electric-field-driven fluid flow, and also on deformation of the outer droplet is predicted by present numerical simulation. Three different kind of deformation type of outer and inner droplet (prolate–oblate, prolate–prolate and oblate–prolate) has been observed. With increase in the volume fraction of inner drop, transition in the deformation of outer drop from prolate to oblate occurs at lower value of fluid permittivity ratio.     

Acoustic radiation impedance of rectangular pistons on prolate spheroids

The self and mutual radiation impedances for rectangular piston(s) arbitrarily located on a rigid prolate spheroidal baffle are formulated. The pistons are assumed to vibrate with uniform normal velocity and the solution is expressed in terms of a modal series representation in spheroidal eigenfunctions. The prolate spheroidal wave functions are obtained using computer programs that have been recently developed to provide accurate values of the wave functions at high frequencies. Results for the normalized self and mutual radiation resistance and reactance are presented over a wide frequency range for different piston sizes and spheroid shapes.     

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.