Showing papers on "Spherical shell published in 2003"

The buckling of thin cylindrical shells under axial compression

Abstract: In two previous papers [1,2] the authors have discussed in detail the inadequacy of the classical theory of thin shells in explaining the buckling phenomenon of cylindrical and spherical shells. It was shown that not only the calculated buckling load is 3 to 5 times higher than that found by experiments, but the observed wave pattern of the buckled shell is also different from that predicted. Furthermore, it was pointed out that the different explanations for this discrepancy advanced by L. H. Donnell [3] and W. Flugge [4] are untenable when certain conclusions drawn from these explanations are compared with the experimental facts. By a theoretical investigation on spherical shells [1] the authors were led to the belief that in general the buckling phenomenon of curved shells can only be explained by means of a non-linear large deflection theory. This point of view was substantiated by model experiments on slender columns with non-linear elastic support [2] . The non-linear characteristics of such structures cause the load necessary to keep the shell in equilibrium to drop very rapidly with increase in wave amplitude once the structure started to buckle. Thus, first of all, a part of the elastic energy stored in the shell is released once the buckling has started; this explains the observed rapidity of the buckling process. Furthermore, as it was shown in one of the previous papers [2] the buckling load itself can be materially reduced by slight imperfections in the test specimen and vibrations during the testing process.

Analysis of the Flux and Polarization Spectra of the Type Ia Supernova SN 2001el: Exploring the Geometry of the High-Velocity Ejecta

Abstract: SN 2001el is the first normal Type Ia supernova to show a strong, intrinsic polarization signal. In addition, during the epochs prior to maximum light, the Ca II IR triplet absorption is seen distinctly and separately at both normal photospheric velocities and at very high velocities. The high-velocity triplet absorption is highly polarized, with a different polarization angle than the rest of the spectrum. The unique observation allows us to construct a relatively detailed picture of the layered geometrical structure of the supernova ejecta: in our interpretation, the ejecta layers near the photosphere (v ? 10,000 km s-1) obey a nearly axial symmetry, while a detached, high-velocity structure (v ? 18,000-25,000 km s-1) with high Ca II line opacity deviates from the photospheric axisymmetry. By partially obscuring the underlying photosphere, the high-velocity structure causes a more incomplete cancellation of the polarization of the photospheric light and so gives rise to the polarization peak and rotated polarization angle of the high-velocity IR triplet feature. In an effort to constrain the ejecta geometry, we develop a technique for calculating three-dimensional synthetic polarization spectra and use it to generate polarization profiles for several parameterized configurations. In particular, we examine the case in which the inner ejecta layers are ellipsoidal and the outer, high-velocity structure is one of four possibilities: a spherical shell, an ellipsoidal shell, a clumped shell, or a toroid. The synthetic spectra rule out the spherical shell model, disfavor a toroid, and find a best fit with the clumped shell. We show further that different geometries can be more clearly discriminated if observations are obtained from several different lines of sight. Thus, assuming that the high-velocity structure observed for SN 2001el is a consistent feature of at least a known subset of Type Ia supernovae, future observations and analyses such as these may allow one to put strong constraints on the ejecta geometry and hence on supernova progenitors and explosion mechanisms.

Analysis of the Flux and Polarization Spectra of the Type Ia Supernova SN 2001el: Exploring the Geometry of the High-velocity Ejecta

Abstract: SN 2001el is the first normal Type Ia supernova to show a strong, intrinsic polarization signal. In addition, during the epochs prior to maximum light, the CaII IR triplet absorption is seen distinctly and separately at both normal photospheric velocities and at very high velocities. The high-velocity triplet absorption is highly polarized, with a different polarization angle than the rest of the spectrum. The unique observation allows us to construct a relatively detailed picture of the layered geometrical structure of the supernova ejecta: in our interpretation, the ejecta layers near the photosphere (v \approx 10,000 km/s) obey a near axial symmetry, while a detached, high-velocity structure (v \approx 18,000-25,000 km/s) with high CaII line opacity deviates from the photospheric axisymmetry. By partially obscuring the underlying photosphere, the high-velocity structure causes a more incomplete cancellation of the polarization of the photospheric light, and so gives rise to the polarization peak and rotated polarization angle of the high-velocity IR triplet feature. In an effort to constrain the ejecta geometry, we develop a technique for calculating 3-D synthetic polarization spectra and use it to generate polarization profiles for several parameterized configurations. In particular, we examine the case where the inner ejecta layers are ellipsoidal and the outer, high-velocity structure is one of four possibilities: a spherical shell, an ellipsoidal shell, a clumped shell, or a toroid. The synthetic spectra rule out the spherical shell model, disfavor a toroid, and find a best fit with the clumped shell. We show further that different geometries can be more clearly discriminated if observations are obtained from several different lines of sight.

SN 1993J VLBI. III. The Evolution of the Radio Shell

Abstract: A sequence of images of supernova 1993J at 31 epochs, from 50 days to ~9 yr after shock breakout, shows the evolution of the expanding radio shell of an exploded star in detail. The images were obtained from 24 observing sessions at 8.4 GHz and 19 at 5.0 GHz and from our last session at 1.7 GHz. The images are all phase-referenced to the stable reference point of the core of the host galaxy M81. This allows us to display them relative to the supernova explosion center. The earliest image shows an almost unresolved source with a radius of 520 AU. The shell structure becomes discernible 175 days after shock breakout. The brightness of the ridge of the projected shell is not uniform, but rather varies by a factor of 2, having a distinct peak or maximum to the southeast and a gap or minimum to the west. Over the next ~350 days, this pattern rotates counterclockwise, with the gap rotating from west to north-northeast. After 2 years, the structure becomes more complex with hot spots developing in the east, south, and west. The pattern of modulation continues to change, and after 5 years the hot spots are located to the north-northwest, south, and south-southeast. After 9 years, the radio shell has expanded to a radius of 19,000 AU. The brightness in the center of the images is lower than expected for an optically thin, spherical shell. Absorption in the center is favored over a thinner shell in the back and/or front. Allowing for absorption, we find that the thickness of the shell is 25% ? 3% of its outer radius. We place a 3 ? upper limit of 4.4% on the mean polarization of the bright part of the shell, consistent with internal Faraday depolarization. We find no compact source in the central region above a brightness limit of 0.05 mJy beam-1 at 8.4 GHz, corresponding to 30% of the current spectral luminosity of the Crab Nebula. We conclude either that any pulsar nebula in the center of SN 1993J is much fainter than the Crab or that there is still significant internal radio absorption.

Collapse of charged scalar fields

Abstract: We explore numerically the evolution of a collapsing spherical shell of charged, massless scalar field. We obtain an external \RN space-time, and an inner space-time that is bounded by a singularity on the Cauchy Horizon. We compare these results with previous analysis and discuss some of the numerical problems encountered.

Quasigeostrophic models of convection in rotating spherical shells

Abstract: [1] The use of a quasigeostrophic, two-dimensional approximation in the problem of convection in a rapidly rotating spherical shell has been limited so far to investigations of the qualitative behavior of the solution. In this study, we build a quasigeostrophic model that agrees quantitatively with full three-dimensional solutions of the onset of convection in the case of differential heating. Reducing the dimensionality of the problem also permits the simulation of finite amplitude regimes of convection, up to quasigeostrophic turbulence. The nonlinear behavior of the system is studied in detail and compared to ultrasonic Doppler velocimetry measurements performed in a convecting, rapidly rotating spherical shell filled with water and liquid gallium. The results are quantitatively satisfactory and open the way to less computer-demanding, and still accurate, simulations of the geodynamo.

Some Recent Advances in the Investigation of Shell Buckling

Abstract: A survey is presented which includes the buckling of shells under loads for which the shell is sensitive to initial imperfections. Results for such cases show that improvements in experiment and theory have produced previously unobtainable agreement. The necessity of the correct (and consistent) theoretical specification of boundary conditions is then demonstrated. Recent stiffened cylinder results are surveyed to expose the large effects on the buckling strength of internal or external stiffening, axial load applied eccentric to the wall neutral surface, and the addition of small meridional curvature.

SN 1993J VLBI (III): The Evolution of the Radio Shell

Abstract: We present two sequences of VLBI images of SN1993J in M81, with 24 images at 8.4 GHz and 19 images at 5.0 GHz, These sequences, from 50 d to ~9 yr after shock breakout, show the evolution of the expanding radio shell of an exploded star in detail. The images are all phase-referenced to the stable reference point of the core of M81, allowing us to display them relative to the supernova explosion center. At 50 d, SN1993J is almost unresolved with a radius of 520 AU. The shell structure becomes discernible at 175 d. The brightness of the ridge of the projected shell is not uniform, but rather varies by a factor of two, having a distinct maximum to the south-east and a minimum to the west. Over the next ~350 d, this pattern appears to rotate counter-clockwise. After two years, the structure becomes more complex with hot spots developing in the east, south, and west. The pattern of modulation continues to change, and after five years the three hot spots have shifted somewhat. After nine years, the radio shell has expanded to a radius of 19,000 AU. The brightness in the center of the images is lower than expected for an optically thin, spherical shell. Absorption in the center is favored over a thinner shell in the back and/or front. Allowing for absorption, we find that the thickness of the shell is (25+/-3)% of its outer radius. We find no compact source in the central region and conclude that any pulsar nebula in the center of SN 1993J is either much fainter than the Crab or affected by remaining significant internal radio absorption.

A Three-dimensional Spherical Nonlinear Interface Dynamo

Abstract: A fully three-dimensional, nonlinear, time-dependent spherical interface dynamo is investigated using a finite-element method based on the three-dimensional tetrahedralization of the spherical system. The spherical interface dynamo model consists of four zones: an electrically conducting and uniformly rotating core, a thin differentially rotating tachocline, a uniformly rotating turbulent convection envelope, and a nearly insulating exterior. The four regions are coupled magnetically through matching conditions at the interfaces. Without the effect of a tachocline, the conventional nonlinear α2 dynamo is always stationary, axisymmetric, and equatorially antisymmetric even though numerical simulations are always fully three-dimensional and time dependent. When there is no tachocline, the azimuthal field is confined to the convection zone while the poloidal magnetic field penetrates into the radiative core. The effects of an interface dynamo with a tachocline having a purely axisymmetric toroidal velocity field are as follows: (1) the action of the steady tachocline always gives rise to an oscillatory dynamo with a period of about 2 magnetic diffusion units, or about 20 yr if the magnetic diffusivity in the convection zone is 108 m2 s-1; (2) the interface dynamo solution is always axisymmetric, selects dipolar symmetry, and propagates equatorward (for the assumed form of α) although the simulation is fully three-dimensional; (3) the generated magnetic field mainly concentrates in the vicinity of the interface between the tachocline and the convection zone; and (4) the strength of the toroidal magnetic field is dramatically amplified by the effect of the tachocline. Extensions of Cowling's theorem and the toroidal flow theorem to multilayer spherical shell regions with radially discontinuous magnetic diffusivities are presented.

Influence of shell strength on shape transformation of micron-sized, monodisperse, hollow polymer particles

Abstract: Micron-sized, monodisperse, non-spherical polymer particles with "rugby ball" and "red blood corpuscle"-like shapes were produced by seeded polymerization of the dispersion of (divinylbenzene/vinylbiphenyl/xylene)-swollen polystyrene particles prepared by utilizing the dynamic swelling method which the authors proposed in 1991. Their non-spherical shapes were based on buckling of the shell of the resultant hollow particles. In this article, the reversible shape transformation of the hollow composite polymer particle between spherical and such non-spherical shapes was studied in detail by controlling the shell strength. A part of the shell was buckled by external pressure which was caused by evaporation of xylene from the hollow when the shell had the tensile modulus below the critical value calculated from the pressure-buckling relationship of a spherical shell proposed by Uemura. The plasticization of the shell by a good solvent was one of key factors for the shape transformation.

CLASS $\\textrm{VII}_0$ SURFACES WITH $b_2$ CURVES

Abstract: We give an affirmative answer to the following conjecture of Ma, Kato: Let $S$ be a compact complex surface in Kodaira's class $\rm {VII_{0}}$ which contains a strictly positive number of rational curves being exactly equal to the second Betti number of $S$. Then $S$ admits a global spherical shell.

Coupling spectral elements and modes in a spherical Earth: an extension to the ‘sandwich’ case

Abstract: SUMMARY We present an extension to the coupling scheme of the spectral element method (SEM) with a normal-mode solution in spherical geometry. This extension allows us to consider a thin spherical shell of spectral elements between two modal solutions above and below. The SEM is based on a high-order variational formulation in space and a second-order explicit scheme in time. It combines the geometrical flexibility of the classical finite-element method with the exponential convergence rate associated with spectral techniques. In the inner sphere and outer shell, the solution is sought in terms of a modal solution in the frequency domain after expansion on the spherical harmonics basis. The SEM has been shown to obtain excellent accuracy in solving the wave equation in complex media but is still numerically expensive for the whole Earth for high-frequency simulations. On the other hand, modal solutions are well known and numerically cheap in spherically symmetric models. By combining these two methods we take advantage of both, allowing high-frequency simulations in global Earth models with 3-D structure in a limited depth range. Within the spectral element method, the coupling is introduced via a dynamic interface operator, a Dirichlet-to-Neumann operator which can be explicitly constructed in the frequency and generalized spherical harmonics domain using modal solutions in the inner sphere and outer shell. The presence of the source and receivers in the top modal solution shell requires some special treatment. The accuracy of the method is checked against the mode summation method in simple spherically symmetric models and shows very good agreement for all type of waves, including diffracted waves travelling on the coupling boundary. A first simulation in a 3-D D �� -layer model based on the tomographic model SAW24b16 is presented up to a corner frequency of 1/12 s. The comparison with data shows surprisingly good results for the 3-D model even when the observed waveform amplitudes differ significantly from those predicted in the spherically symmetric reference model (PREM).

Interface optical phonons in spherical quantum-dot/quantum-well heterostructures

Abstract: Interface optical phonons are studied in the case of a spherical quantum-dot/quantum-well (QD/QW) heterostructure by applying a dielectric continuum approach. The prototypical case is a QD/QW of CdS/HgS in the form of spherical shell of HgS embedded on a spherical CdS QD, a kind of structure intensively investigated in the latter times. We also assume the QD/QW hetrerostructure surrounded by a host material which is modeled in the form of an infinite dielectric medium which does not participate of the polar optical vibrations. The possible interface phonon modes (CdS-and HgS-SO phonons), the corresponding frequencies and the electron-phonon interaction Hamiltonian are reported. A detailed discussion is made of the SO phonons fundamental characteristics and of the strength of the electron-phonon interaction.

Control volume method for the dynamo problem in the sphere with the free rotating inner core

Abstract: A model of thermally driven dynamo in the Boussinesq approximation in the spherical shell with the free rotating inner core is considered. To solve equations we use a new in dynamo modeling control volume technique (for details of this method for hydrodynamics see Patankar, 1980). The main advantage of this method over previous attempts to solve magnetohydrodynamics equations in the spherical grids is that no filtering of high harmonics in the pole regions is needed. We present the results of simulations for the self-consistent dynamo system evolution over the diffusion time and longer periods. Different ways of stabilizations of magnetohydrodynamics equations, when convective terms are of the same order (or larger) as conductive ones, are considered.

Oscillations of magnetic stars: I. Axisymmetric shear Alfvén modes of a spherical shell in a dipolar magnetic field

Abstract: We carry out an investigation of axisymmetric shear Alfven waves in a spherical layer of an incompressible resistive fluid when a strong dipolar magnetic field is applied. A decomposition on the spherical harmonics base is used to compute the eigenmodes of the system. Numerical results show that the least-damped Alfvenic modes naturally concentrate near the magnetic polar axis. These modes also show internal shear/magnetic layers associated with resonant field lines. This model is useful when modelling planetary cores sustaining a dynamo, magnetic neutron stars or to the magnetic layer of roAp stars. In this latter case, it shows that shear Alfven waves provide a good instance of non-perturbative effects due to the strong magnetic field of such stars.

Casimir densities for a spherical shell in the global monopole background

Abstract: We investigate the vacuum expectation values for the energy–momentum tensor of a massive scalar field with general curvature coupling and obeying the Robin boundary condition on a spherical shell in the (D + 1)-dimensional global monopole background. The expressions are derived for the Wightman function, the vacuum expectation values of the field square, the vacuum energy density, radial and azimuthal stress components in both regions inside and outside the shell. A regularization procedure is carried out by making use of the generalized Abel–Plana formula for the series over zeros of cylinder functions. This formula allows us to extract from the vacuum expectation values the parts due to the global monopole gravitational field in the situation without a boundary, and to present the boundary-induced parts in terms of exponentially convergent integrals, useful, in particular, for numerical calculations. The asymptotic behaviour of the vacuum densities is investigated near the sphere surface and at large distances. We show that for small values of the parameter describing the solid angle deficit in global monopole geometry the boundary-induced vacuum stresses are strongly anisotropic.

Thermal and mechanical instability of an imperfect shallow spherical cap

Abstract: In this article, the thermal and mechanical buckling loads of a cap of a shallow spherical shell of isotropic material and geometrically imperfect shell are considered The equilibrium and stability equations are based on Donnell-Mushtari-Velasov (DMV) theory and are derived using the variational method The Sander's nonlinear strain-displacement relations are used The shell is under external pressure for mechanical loading and uniform temperature rise and radial temperature difference for thermal loadings A simply supported boundary condition is assumed The solutions for thermal and mechanical buckling loads are obtained using the stability equations and the Galerkin method One-term approximation for the middle-plane shell displacement is considered The expressions for the thermal and mechanical buckling loads are obtained analytically and are given by closed-form solutions

On the buckling of imperfect squarely-reticulated shallow spherical shells supported by elastic media

Abstract: Non-linear buckling behaviors of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections and continuously supported on springs have been studied in this paper. The shell structure is subjected to uniform vertical load and the imperfection has been assumed to have the same mode as that of transverse displacement of the shell, but the specific form of mode has not been presumed. Using the asymptotic iteration method, an analytical solution is obtained on the basis of a theoretical model proposed by the author. The resulting nondimensional expression between the external load and central transverse displacement (deflection) can be conveniently adopted to analyze non-linear behaviors of the structures and evaluate the effects of various parameters (e.g., stiffness of spring, imperfect factor and boundary conditions, etc.) on buckling behaviors. Numerical examples are given and compared with available results. Effects of several factors are also demonstrated.

Radial vibrations of orthotropic laminated hollow spheres.

Abstract: The three-dimensional elasticity problem of the radial vibrations of a composite hollow spherical shell laminated of spherically orthotropic layers is considered. After formulating the equations, the exact determinantal equation from which the frequencies of vibration can be extracted is developed. Some calculated results for combinations of isotropic and orthotropic materials indicate the sensitivity of the frequencies to the geometry and material make up of the shells.

Temperature-induced pair correlations in clusters and nuclei

Abstract: The pair correlations in mesoscopic systems such as nanometer-size superconducting clusters and nuclei are studied at a finite temperature for the canonical ensemble of fermions in model spaces with a fixed particle number: (i) a degenerate spherical shell (strong-coupling limit), (ii) an equidistantly spaced deformed shell (weak-coupling limit). It is shown that after the destruction of the pair correlations at T=0 by a strong magnetic field or rapid rotation, heating can bring them back. This phenomenon is a consequence of the fixed number of fermions in the canonical ensemble.

Non-linear static and dynamic instability of complete spherical shells using mixed finite element formulation

Abstract: The finite element method based on the total Lagrangian description of the motion and the Hellinger–Reissner principle with independent strain is applied to investigate the non-linear static and dynamic responses of spherical laminated shells under external pressure. The non-linear dynamic problem is solved by employing the implicit time integration method. The critical load of thin spherical laminated panels is investigated by examining the static and dynamic responses. The critical dynamic load is determined by the phase-plane and the Budiansky–Roth criteria. The effect of the artificial coefficient of Rayleigh damping on the dynamic response is considered. The dynamic response with damping included converges to the static response. The damping coefficient greatly affects a highly non-linear dynamic response. For a thin spherical panel with the snapping phenomena, the critical dynamic load is lower than the static one.

The general solution of spherically isotropic magnetoelectroelastic media and its applications

Abstract: A general solution of the three-dimensional equilibrium problem of spherically isotropic magnetoelectroelastic media is presented. Base on the obtained general solution, exact and compact form solutions are obtained for (1) a spherically isotropic magnetoelectroelastic cone subjected to concentrated force, concentrated couple, a point charge and a point electric current at its apex; (2) a spherically isotropic magnetoelectroelastic space with a concentrated force at the origin; (3) a spherical shell under spherically symmetric deformation; and (4) stress concentration around a spherical cavity subjected to remote uniform tensile force, electric charge and electric current.

Gravitational hedgehog, stringy hedgehog and stringy sphere

Abstract: We investigate the solutions of Einstein equations such that a hedgehog solution is matched to different exterior or interior solutions via a spherical shell. In the case where both the exterior and the interior regions are hedgehog solutions or one of them is flat, the resulting spherical shell becomes a stringy shell. We also consider more general matchings and see that in this case the shell deviates from its stringy character.