Spheroidal Cavity Research Articles

Semiclassical theory to optical resonant modes of a transparent dielectric spheroidal cavity.

We study the resonant scattering of light by a transparent dielectric spheroid. We try to understand the features of the resonant modes of a spheroidal optical cavity. In this way, we use an analogy between optics and quantum mechanics. Through this analogy it is possible to interpret resonances as quasibound states of light. Using semiclassical methods such as the WKB method and a uniform asymptotic expansion for spheroidal radial functions, we developed algorithms that permit us to calculate the resonance position as well as the resonance width.

Fluid instabilities in precessing spheroidal cavities

We study by direct numerical simulation the motion of incompressible fluid contained in an ellipsoid of revolution with ellipticity 0.1 or less which rotates about its axis of symmetry and whose rotation axis is executing precessional motion. A solution to this problem for an inviscid fluid given by Poincaré (1910) predicts motion of uniform vorticity. The simulations show how the orientation of the average vorticity of a real fluid is influenced by both pressure and viscous torques exerted by the boundaries. Axisymmetric shear layers appear which agree well with those observed experimentally by Malkus (1968). Shear caused by deviations from a velocity field with uniform vorticity triggers an instability consisting of waves propagating around the average rotation axis of the fluid. The Ekman layers at the boundaries may also become unstable.

Experimental evidence of inertial waves in a precessing spheroidal cavity

We have demonstrated experimentally the existence of inertial waves in a slowly precessing spheroid of fluid. Although such oscillatory internal shear layers have been predicted theoretically and numerically, previous precession experiments had shown no evidence of their presence. Using an ultrasonic Doppler velocimetry technique, profiles of radial velocity have been measured in our precession experiment. Comparison of these profiles with their synthetic counterparts obtained numerically, proves the presence of the predicted internal shear layers. They are emitted from the breakdown of the Ekman layer at the two critical latitudes of the fluid (around 30° and −30°) and propagate through the entire volume on conical surfaces. The asymptotic laws for these oscillatory layers, confirmed experimentally and numerically, lead us to predict an oscillatory flow of 10−6 m/s along such characteristic cones in the Earth's fluid outer core.

Periodic-orbit bifurcations and superdeformed shell structure.

We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle variables were performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell-correction energies are in good agreement with quantum-mechanical results. We find that the bifurcations of some dominant short periodic orbits lead to an enhancement of the shell structure for "superdeformed" shapes related to those known from atomic nuclei.

Bifurcation of periodic orbit as semiclassical origin of superdeformed shell structure

Classical periodic orbits responsible for emergence of the superdeformed shell structure of single-particle motion in spheroidal cavities are identified and their relative contributions to the shell structure are evaluated. Fourier transforms of quantum spectra clearly show that three-dimensional periodic orbits born out of bifurcations of planar orbits in the equatorial plane become predominant at large prolate deformations. A new semiclassical method capable of describing the shell structure formation associated with these bifurcations is briefly discussed.

4-Vinylpyridine-Modified Nickel and Cobalt Dibenzoylmethanates as New Hosts: Inclusions with Carbon Tetrachloride and Chlorobenzene

Bis(4-vinylpyridine)bis(dibenzoylmethanato)metal(II), [M(ViPy)2(DBM)2] (M = Ni(II), Co(II); ViPy = 4-Vinylpyridine; DBM = C6H5COCHCOC6H5 −, dibenzoylmethanate) is a new metal-complex host. Its inclusions with carbon tetrachloride (host:guest = 1:2; triclinic, P 1, Z = 1) and chlorobenzene (host:guest = 1:1; monoclinic, P2 1 /c, Z = 4) are consistent with the van der Waals packing of neutral complex (host) and solvent (guest) molecules. In the host unit, four oxygens from two chelate DBM-units provide a square-planar environment around the metal center that is extended to octahedral coordination by two apical nitrogens from two vinylpyridine moieties in the trans-position. In the carbon tetrachloride inclusions, the host traps two guest molecules in large prolate spheroidal cavities. In the chlorobenzene inclusions, guest species are located inside 8-shaped serpentine channels along the y-axis. The nickel and cobalt versions of the inclusion compounds were found to be very similar.

Deformation and seismicity in the Coso geothermal area, Inyo County, California: Observations and modeling using satellite radar interferometry

Interferometric synthetic aperture radar (InSAR) data collected in the Coso geothermal area, eastern California, during 1993–1999 indicate ground subsidence over a ∼50 km2 region that approximately coincides with the production area of the Coso geothermal plant. The maximum subsidence rate in the peak of the anomaly is ∼3.5 cm yr−1, and the average volumetric rate of subsidence is of the order of 106 m3 yr−1. The radar interferograms reveal a complex deformation pattern, with at least two irregular subsidence peaks in the northern part of the anomaly and a region of relative uplift on the south. We invert the InSAR displacement data for the positions, geometry, and relative strengths of the deformation sources at depth using a nonlinear least squares minimization algorithm. We use elastic solutions for a prolate uniformly pressurized spheroidal cavity in a semi‐infinite body as basis functions for our inversions. Source depths inferred from our simulations range from 1 to 3 km, which corresponds to the production depths of the Coso geothermal plant. Underpressures in the geothermal reservoir inferred from the inversion are of the order of 0.1–1 MPa (except a few abnormally high underpressures that are apparently biased toward the small source dimensions). Analysis of the InSAR data covering consecutive time intervals indicates that the depths and/or horizontal extent of the deformation sources may increase with time. This increase presumably reflects increasing volumes of the subsurface reservoir affected by the geothermal exploitation. We show that clusters of microearthquakes associated with the geothermal power operation may result from perturbations in the pore fluid pressure, as well as normal and shear stresses caused by the deflation of the geothermal reservoir.

Subsurface tension permeametry

A new method for determining subsurface unsaturated hydraulic conductivity in situ was developed. Steady state flow conditions were established from spheroidal cavities under subatmospheric pressure. Several borehole tension permeameter devices were constructed and field tested in four different soils. While the capillary length parameter (α) values were generally consistent with previously reported values, the estimates for saturated hydraulic conductivity (Ks) were, in some cases, 1 order of magnitude lower than reported values for the test soils. In part, this can be traced to the rigid log linear shape of conductivity to pressure head used by the Gardner [1958] model, which produces overly small intercept values (K(0) = Ks) when measured for drier conditions. Transformation of the estimated parameters to the Brooks and Corey [1964] model seems to extend the useful range of the parameters. A potential combination of near‐saturation measurements [Shani and Or, 1995] with the proposed method could lead to improved characterization of subsurface K(h).

Use of Polypropyleneimine Tetrahexacontaamine (DAB-Am-64) Dendrimer as a Single-Molecule Template To Produce Mesoporous Silicas

The use of DAB-Am-64 amine dendrimer as a single-molecule template to produce mesoporous cavities in silica sol−gels is reported. The method is meant to afford the synthesis of spheroidal cavities and is likely to enjoy generality, since there are a number of dendritic molecules commercially available today. X-ray diffraction confirms that a coherent distance of ∼25 A is obtained upon calcination, and the modeling of nitrogen adsorption data by a modified Horvath-Kawazoe formalism for spherical cavities reveals that voids of ∼23 A in diameter had been formed.

The thermoelectroelastic state of a transversally isotropic piezoceramic body with a spheroidal cavity in a uniform heat flow

A static thermoelectroelastic problem for an infinite transversally isotropic body containing a spheroidal cavity is explicitly solved. The symmetry axis of the spheroid coincides with the anisotropy axis of the body. It is assumed that at a rather large distance from the cavity the body is in a uniform heat flow directed along the anisotropy axis. Formulas are derived for the stress components and the projections of the electric displacement vector near the cavity, which depend on the heat-flow value, cavity geometry, and the thermoelectroelastic properties of the material. The solution of the problem for a body with a disk-like crack is obtained as a partial case from the solution of the problem for a piezoceramic body with a spheroidal cavity. The stress intensity factors for the force and electric fields are determined near the crack

Expérimentation microonde sur la diffraction par des biréseaux métalliques de cavités hémisphéroïdales

The general theory of the diffraction of an electromagnetic plane wave from a bigrating of prolate spheroidal cavities hollowed in a perfectly conducting metallic plate has been carried out and numerical results were recently published. To valide these numerical results, an experimentation in microwave range with two deep bigratings has been realized. Numerical and experimental results, which concern the efficiency in the (0,0)-order versus the wavelength and for quasi-normal incidence are in a good agreement and allow us to extend the possibilities of our codes.

Equilibrium of piezoceramic cylinder with spheroidal cavity

A conjugated electrostatic field surrounded by a spheroidal cavity in a piezoceramic cylinder is studied for a particular case of static loading. The uniformly extending stresses were preset at the cylinder ends, with an electric potential being applied to them. Graphs of the stress components and induction-vector projection in the spheroid body and apexes as functions of the external load and the ratio of the spheroid axes are provided.

Spectroscopic Studies of Hexadecylquinolinium Tricyanoquinodimethanide

Hexadecylquinolinium tricyanoquinodimethanide (1), a unimolecular rectifier of electrical current with a large ground-state dipole moment (43 ± 8 D), reveals large hypsochromic shifts of the absorption spectrum. Two fluorescent emissions were observed: one in the visible region (quantum yield φ ≈ 0.01, not solvatochromic) and one in the near-infrared spectrum (weakly solvatochromic). Using a prolate spheroidal cavity model and the absorption maxima measured in eight solvents, the excited-state dipole moment of 1 is estimated as 8.7 D. The NMR spectral lines broaden above 330 K and lose the multiplet structure. The core-level N 1s XPS spectrum reveals the three expected N valence states. The valence-level XPS spectrum can be correlated with theory. Simultaneous cyclic voltammetry and electron spin resonance of the radical anion of 1 shows that the spin density in the LUMO of 1 is concentrated on the tricyanoquinodimethanide portion of the anion. The molecule is clearly zwitterionic in the ground state, bo...

Acoustic eigenfrequencies in a spheroidal cavity with a concentric penetrable sphere

The acoustic eigenfrequencies fnsm in a spheroidal cavity containing a concentric penetrable sphere are determined analytically, for both Dirichlet and Neumann conditions in the spheroidal boundary. Two different methods are used for the evaluation. In the first, the pressure field is expressed in terms of both spherical and spheroidal wave functions, connected with one another by well-known expansion formulas. In the second, a shape perturbation method, this field is expressed in terms of spherical wave functions only, while the equation of the spheroidal boundary is given in spherical coordinates. The analytical determination of the eigenfrequencies is possible when the solution is specialized to small values of h=d/(2R2), (h≪1), with d the interfocal distance of the spheroidal boundary and 2R2 the length of its rotation axis. In this case exact, closed-form expressions are obtained for the expansion coefficients gnsm(2) and gnsm(4) in the resulting relation fnsm(h)=fns(0)[1+h2gnsm(2)+h4gnsm(4)+O(h6)]. Analogous expressions are obtained with the use of the parameter v=1−(R2/R2′)2, (|v|≪1), with 2R2′ the length of the other axis of the spheroidal boundary. Numerical results are given for various values of the parameters.

Semiclassical Origin of Superdeformed Shell Structure in the Spheroidal Cavity Model

Classical periodic orbits responsible for emergence of the superdeformed shell structures for single-particle motions in spheroidal cavities are identified and their relative contributions to the shell structures are evaluated. Both prolate and oblate superdeformations (axis ratio about 2:1) as well as prolate hyperdeformation (axis ratio about 3:1) are investigated. Fourier transforms of quantum spectra clearly show that three-dimensional periodic orbits born out of bifurcations of planar orbits in the equatorial plane become predominant at large prolate deformations, while butterfly-shaped planar orbits bifurcated from linear orbits along the minor axis are important at large oblate deformations.

Damage in a viscoplastic material—Part II. Overall behaviour

The overall behaviour of a damaged viscoplastic material under axisymmetric loading is addressed in this paper. A linear viscous matrix containing aligned spheroidal cavities is first considered. Its overall behaviour is estimated by means of a differential scheme. The damage-induced morphological anisotropy, due to the shape of the voids, is then analyzed. It is shown to be significant even at low volume fractions of cavities ( ƒ < 0.05 ), when the latter are prolate or oblate. These results are then used to predict the behaviour of a nonlinear viscous matrix containing aligned spheroidal cavities, by means of a variational principle proposed by Ponte Castañeda (1991). Two types of nonlinear matrix behaviour are considered: a power law corresponding to metal forming at moderate strain rates and a linear law with nonzero intercept suited to high strain rates.The constitutive equations of such nonlinear damaged materials have been used in a companion paper in order to study the influence of matrix compressibility on the growth of a spheroidal cavity during straining.

Electromagnetic Eigenfrequencies in a Spheroidal Cavity (Calculation By Spheroidal Eigenvectors)

The electromagnetic eigenfrequencies fnsm in a perfectly conducting spheroidal cavity are determined analytically. The analytical determination is possible in the case of small values of h = d/(2a), (h « 1), where d is the interfocal distance of the spheroidal cavity and 2a the length of its rotation axis. In this case exact, closed-form expressions are obtained for the expansion coefficients g(2) nsm and g(4) nsm in the resulting relation fnsm(h) = fns (0) [1 + h2g(2) nsm + h4g(4) nsm + O(h6)]. Analogous expressions are obtained with the use of the parameter v = 1- a2/b2 (for |v| << 1) , where 2b is the length of the other axis of the spheroidal cavity. The electromagnetic field is expressed in terms of spheroidal eigenvectors. Numerical results are given for the lower-order modes.

Radiation heat transfer across a compressed spheroidal cavity

AIChE JournalVolume 43, Issue 9 p. 2368-2372 R&D Note Radiation heat transfer across a compressed spheroidal cavity Sean P. Fitzgerald, Sean P. Fitzgerald Dept. of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556Search for more papers by this authorWilliam Strieder, Corresponding Author William Strieder Dept. of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556Dept. of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556Search for more papers by this author Sean P. Fitzgerald, Sean P. Fitzgerald Dept. of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556Search for more papers by this authorWilliam Strieder, Corresponding Author William Strieder Dept. of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556Dept. of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556Search for more papers by this author First published: 17 June 2004 https://doi.org/10.1002/aic.690430922Citations: 3AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume43, Issue9September 1997Pages 2368-2372 RelatedInformation

Electromagnetic Eigenfrequencies in a Spheroidal Cavity

The electromagnetic eigenfrequencies fnsm in a perfectly conducting spheroidal cavity are determined analytically, by a shape perturbation method. The analytical determination is possible in the case of small values of the quantity = 1- a2/b2, (|1), where 2a and 2b are the lengths of the rotation axis and the other axis of the spheroidal cavity, respectively. In this case, exact, closed-form expressions are obtained for the expansion coefficients and in the resulting relation fns (0) [1 + + There is no need for using any spheroidal eigenvectors in our solution. The electromagnetic field is expressed in a series of spherical eigenvectors, while the equation of the spheroidal boundary is given in terms of the spherical coordinates. Numerical results are given for the eigenfrequencies of the lower-order magnetic and electric modes.

Radiation heat transfer down an elongated spheroidal cavity

AbstractEffects of elongation on the radiation heat transport down a spheroidal cavity, located in a conducting solid with a diffusely reflecting cavity–solid interface, are examined. An effective conductivity λe and a void radiation conductivity λr are obtained as a function of cavity eccentricity α; and surface emissivity ε. To facilitate the calculations and produce readily applicable equations, a rigorous variational principle is used. Exact solutions are generated in the neighborhood of the spherical cavity (α2 → 0) for any ε &gt; 0, a long needle‐shaped void (α2 → 1) for any ε &gt; 0, and a perfect reflector (ε → 0) for arbitrary elongation (0 ≤α2 ≤ 1). Significant differences arising from the shape change are observed. The α2 → 0 edge demonstrates a linear increase in λr with ε. At the opposite edge α2 → 1 and positive ε, λr is a horizontal line independent of ε, much like the long cylinder, whose conductivity is a factor of 32/(9π) (= 1.13) larger. In the neighborhood of ε 0, λr is always zero for any 0 ≤ α2 ≤ 1. The emissivity slope for ε → 0 starts from unity at α2 = 0 and increases monotonically with elongation to a singularity 3π[16(1 – α2)]‐1 as α2 → 1 for the long needle.