Showing papers on "Spherical shell published in 2004"

Elliptical instability in a rotating spheroid

Abstract: Summary This study concerns the elliptical instability of a flow in a rotating deformed sphere. The aim of our work is to observe and measure the characterics of this instability in experiments and to compare them with theorical predictions. For this purpose, an elastic and transparent hollow sphere has been moulded. The flow is visualised using Kalliroscope flakes as the sphere is set into rotation and compressed by two rollers. The elliptical instability occurs by the appearance of the so-called ’spin-over’ mode whose growth rates and saturations are measured for different Eckman numbers by video image analysis. These growth rates compare avantageously to theorical calculations which are performed using classical asymptotic expansions. The linear analysis is then completed by a non linear model which predicts correctly the asymptotic regimes for high Eckman numbers. Some results that concern the elliptic instability in a rotating deformed spherical shell or the triangular instability will also be presented.

Casimir Energies and Pressures for $\delta$-function Potentials

Abstract: The Casimir energies and pressures for a massless scalar field associated with $\delta$-function potentials in 1+1 and 3+1 dimensions are calculated. For parallel plane surfaces, the results are finite, coincide with the pressures associated with Dirichlet planes in the limit of strong coupling, and for weak coupling do not possess a power-series expansion in 1+1 dimension. The relation between Casimir energies and Casimir pressures is clarified,and the former are shown to involve surface terms. The Casimir energy for a $\delta$-function spherical shell in 3+1 dimensions has an expression that reduces to the familiar result for a Dirichlet shell in the strong-coupling limit. However, the Casimir energy for finite coupling possesses a logarithmic divergence first appearing in third order in the weak-coupling expansion, which seems unremovable. The corresponding energies and pressures for a derivative of a $\delta$-function potential for the same spherical geometry generalizes the TM contributions of electrodynamics. Cancellation of divergences can occur between the TE ($\delta$-function) and TM (derivative of $\delta$-function) Casimir energies. These results clarify recent discussions in the literature.

Casimir energies and pressures for δ-function potentials

Abstract: The Casimir energies and pressures for a massless scalar field associated with δ-function potentials in 1 + 1 and 3 + 1 dimensions are calculated. For parallel plane surfaces, the results are finite, coincide with the pressures associated with Dirichlet planes in the limit of strong coupling, and for weak coupling do not possess a power-series expansion in 1 + 1 dimension. The relation between Casimir energies and Casimir pressures is clarified, and the former are shown to involve surface terms, interpreted as the quantum vacuum energies of the surfaces. The Casimir energy for a δ-function spherical shell in 3 + 1 dimensions has an expression that reduces to the familiar result for a Dirichlet shell in the strong-coupling limit. However, the Casimir energy for finite coupling possesses a logarithmic divergence first appearing in third order in the weak-coupling expansion, which seems unremovable. The corresponding energies and pressures for a derivative of a δ-function potential for the same spherical geometry generalizes the TM contributions of electrodynamics. Cancellation of divergences can occur between the TE (δ-function) and TM (derivative of δ-function) Casimir energies. These results clarify recent discussions in the literature.

Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell

Abstract: [1] A new numerical finite difference code has been developed to solve a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell. A kind of the overset (Chimera) grid named “Yin-Yang grid” is used for the spatial discretization. The grid naturally avoids the pole problems which are inevitable in the latitude-longitude grids. The code is applied to numerical simulations of mantle convection with uniform and variable viscosity. The validity of the Yin-Yang grid for the mantle convection simulation is confirmed.

Varying the spherical shell geometry in rotating thermal convection

Abstract: The effect of spherical shell geometry on rapidly-rotating thermal convection is studied in a suite of high resolution three-dimensional numerical simulations. The geometry is characterized by the radius ratio, χ = ri/ro , where ri is the inner shell radius, and ro is the outer shell radius. In this study, χ is varied over the broad range 0.10 to 0.92 in calculations of Boussinesq rotating convection subject to isothermal, rigid boundary conditions. Simulations are performed at Prandtl number Pr = 1 and for Ekman numbers E = 10−3, 3 × 10−4 and 10−4. Near the onset of convection, the flow takes the form of rolls aligned parallel to the rotation axis and situated adjacent to the inner shell equator. The dimensionless azimuthal wavelength, λ c , of the rolls is found to be independent of the shell geometry, only varying with the Ekman number. The critical wave number, mc , of the columnar rolls increases in direct proportion to the inner boundary circumference. For our simulations the critical Rayleigh numbe...

Vibration suppression of laminated shell structures investigated using higher order shear deformation theory

Abstract: Third-order shear deformation theories of laminated composite shells are developed using the strain–displacement relations of Donnell and Sanders theories. These theories also account for geometric nonlinearity in the von Karman sense. Analytical (Navier) solutions for vibration suppression in cross-ply laminated composite shells with surface mounted smart material layers are developed using the linear versions of the two shell theories and for simply supported boundary conditions. Numerical results are presented to bring out the parametric effects of shell types (cylindrical, spherical, and doubly curved shells) and material properties on vibration suppression. A simple negative velocity feedback control in a closed loop is used.

Instabilities of the Stewartson layer Part 2. Supercritical mode transitions

Abstract: We investigate, both experimentally and numerically, the fluid flow in a spherical shell with radius ratio ri/ro=2/3. Both spheres rotate about a common axis, with Ωi>Ωo. The basic state consists of a Stewartson layer situated on the tangent cylinder, the cylinder parallel to the axis of rotation and touching the inner sphere. If the differential rotation is sufficiently large, non-axisymmetric instabilities arise, with the wavenumber of the most unstable mode increasing with increasing overall rotation. In the increasingly supercritical regime, a series of mode transitions occurs in which the wavenumber decreases again. The experimental and numerical results are in good agreement regarding this basic sequence of mode transitions, and the numerics are then used to study some of the finer details of the solutions that could not be observed in the experiment.

First polarimetric images of NML Cyg at 1612 and 1665 MHz

Abstract: We present the first view of the magnetic field structure in the OH shell of the supergiant NML Cygni (NML Cyg). MERLIN interferometric observations of this object were obtained in 1993 October in full polarization, at 1612 and 1665 MHz. They reveal a complex structure in both total intensity and polarization. At 1612 MHz, the majority of the components lie along a north-west-south-east (NW-SE) geometrical axis along which a velocity gradient is clearly evident. The polarization vectors associated with these maser spots are roughly aligned on that same NW-SE axis. The distribution of the external and fainter components is spherical and the associated polarization vectors have a tangential distribution. The total extent of the maser emission at 1612 MHz is about 5.3 arcsec. At 1665 MHz, the maser spot distribution reveals an incomplete spherical shell of total extent about 2.5 arcsec. As observed for the 1612-MHz spherical emission, the polarization vectors associated with the 1665-MHz spherically distributed maser spots show a tangential distribution. This dichotomy strongly suggests the existence of two distinct OH shells; an older shell, exhibiting the spherical maser spot distribution and a tangential distribution of the polarization vectors, and a more recent shell showing a NW-SE maser spot distribution with associated polarization vectors along that same axis.

Application of the spectral‐element method to the axisymmetric Navier–Stokes equation

Abstract: SUMMARY We present an application of the spectral-element method to model axisymmetric flows in rapidly rotating domains. The primitive equations are discretized in space with local tensorized bases of high-order polynomials and in time with a second-order accurate scheme that treats viscous and rotational effects implicitly. We handle the pole problem using a weighted quadrature in elements adjacent to the axis of rotation. The resulting algebraic systems are solved efficiently using preconditioned iterative procedures. We validate our implementation through comparisons with analytic and purely spectral solutions to laminar flows in a spherical shell. This axisymmetric tool is the kernel on which complexity will be added subsequently in the long-term prospect of building a parallel spectral-element based geodynamo model.

Finite Element and Experimental Investigation of Piezoelectric Actuated Smart Shells

Abstract: In the recent years, research on the use of piezoelectric actuators for shape and vibration control of structures has been gaining prominence. Analytical and finite element models have been developed to analyze structures under piezoelectric actuation, but experimental studies, particularly on curved structures, are limited. In the current study, a finite element model is developed for piezoelectric actuated shell structures, based on Ahmad’s reduced shell element. Experiments have been conducted on a number of structures like straight beams, curved beams, and shells. Finite element and experimental results have been shown to match well. Nonlinear behavior has been observed in the experiments, particularly at higher fields, and complete hysteresis loops have been presented. The finite element is then applied to the study of deformation of a typical paraboloid shell (representative antenna shell) under piezoelectric actuation. It has been shown that piezoelectric actuation can be used to induce desired deformation shapes in the antenna shell, which result in beam steering and shaping.

Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations

Abstract: In this paper the numerical approximations of the Ginzburg-Landau model for a superconducting hollow spheres are constructed using a gauge invariant discretization on spherical centroidal Voronoi tessellations. A reduced model equation is used on the surface of the sphere which is valid in the thin spherical shell limit. We present the numerical algorithms and their theoretical convergence as well as interesting numerical results on the vortex configurations. Properties of the spherical centroidal Voronoi tessellations are also utilized to provide a high resolution scheme for computing the supercurrent and the induced magnetic field.

Thin-shell magnetohydrodynamic equations for the solar tachocline

Abstract: We present a new system of equations designed to study global-scale dynamics in the stably-stratified portion of the solar tachocline. This system is derived from the 3D equations of magnetohydrodynamics in a rotating spherical shell under the assumption that the shell is thin and stably-stratified (subadiabatic). The resulting thin-shell model can be regarded as a magnetic generalization of the hydrostatic primitive equations often used in meteorology. It is simpler in form than the more general anelastic or Boussinesq equations, making it more amenable to analysis and interpretation and more computationally efficient. However, the thin-shell system is still three-dimensional and as such represents an important extension to previous 2D and shallow-water approaches. In this paper we derive the governing equations for our thin-shell model and discuss its underlying assumptions, its context relative to other models, and its application to the solar tachocline. We also demonstrate that the dissipationless thin-shell system conserves energy, angular momentum and magnetic helicity.

Development of a Simulation Code for MHD Dynamo Processes Using the GeoFEM Platform

Abstract: We have developed a magnetohydrodynamic (MHD) simulation code for a fluid in a rotating spherical shell, modeled on the earth's outer core, using the parallel finite-element method (FEM). This simulation code is designed to elucidate the geodynamo processes and the dynamics of a conductive fluid in the earth's outer core. To connect the magnetic field in the fluid shell and the potential magnetic field in an insulator, a finite element mesh is constructed for the inner core and the mantle as well as for the outer core, and the vector potential of the magnetic field is used to solve for the magnetic field. In the present study, a total of 7.8 × 104 elements are used in the simulation domain. The simulation is performed in 105 time steps spanning 2.5 times the magnetic diffusion time. To reduce the computational time, symmetry with respect to the equatorial plane is assumed. The results show that the magnetic energy generated is approximately four times the kinetic energy. Comparing our results with a spher...

Characterization of electromagnetic scattering by a plasma anisotropic spherical shell

Abstract: Scattering of a plane wave by a plasma anisotropic spherical shell is considered in this paper and scattered fields are obtained in spherical coordinates. The electromagnetic fields in a plasma medium and in a free space are expanded in terms of the spherical vector wave functions (SVWFs) for a plasma anisotropic medium and the SVWFs in an isotropic medium. Numerical results for very general properties of the plasma dielectric material spherical shells are given. And those results obtained in a special case using the present method and the method integrating the method of moments (MoM) and the conjugate-gradient fast-Fourier-transform (CG-FFT) approach are compared, and a very good agreement is found. The results presented here can be used in antenna design, satellite communications channel design and characterization, and target shielding studies.

Shell Model from a Practitioner's Point of View

Abstract: The lecture presents an introduction to shell model applications in nu- clear spectroscopy. The evaluation of single particle energies, two-body interactions and effective operators and their correlation with the choice of model space is de- scribed. The results of the empirical shell model approach in a minimum valence space and of large-scale shell model calculations are summarised for various re- gions in the nuclidic chart. The mapping of the deformed and the spherical shell model is demonstrated, and the evolution of shell structure towards exotic nuclei is discussed.

Casimir densities for two concentric spherical shells in the global monopole space–time

Abstract: The quantum vacuum effects are investigated for a massive scalar field with general curvature coupling and obeying the Robin boundary conditions given on two concentric spherical shells with radii a and b 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 the region between the shells. A regularization procedure is carried out by making use of the generalized Abel–Plana formula for the series over zeros of combinations of the cylinder functions. This formula allows us to extract from the vacuum expectation values the parts due to a single sphere on background of the global monopole gravitational field, and to present the "interference" parts in terms of exponentially convergent integrals, useful, in particular, for numerical evaluations. The vacuum forces acting on the boundaries are presented as a sum of the self-action and interaction terms. The first one contains well-known surface divergences and needs a further regularization. The interaction forces between the spheres are finite for all values a

Spinor Casimir densities for a spherical shell in the global monopole spacetime

Abstract: We investigate the vacuum expectation values of the energy–momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In order to do that, we use the generalized Abel–Plana summation formula. As we shall see, this procedure allows us to extract from the vacuum expectation values the contribution coming from the unbounded spacetime and to explicitly present the boundary induced parts. As regards the boundary induced contribution, two distinct situations are examined: the vacuum average effects inside and outside the spherical shell. The asymptotic behaviour of the vacuum densities is investigated near the sphere centre and near the surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in the global monopole geometry, the sphere induced expectation values are exponentially suppressed. We discuss, as a special case, the fermionic vacuum densities for the spherical shell on the background of the Minkowski spacetime. Previous approaches to this problem within the framework of the QCD bag models have been global and our calculation is a local extension of these contributions.

Diffusion MRI using spherical shell sampling

Abstract: A diffusion MRI technique that employs a sampling/reconstruction scheme that samples the diffusion signal directly on the sphere and reconstructs the diffusion function directly on the sphere is presented.

Spherical Radiative Transfer Model with Computation of Layer Air Mass Factors and Some of Its Applications

Abstract: A radiative transfer model was designed for use in inverse problems of atmospheric optics. The model calculates intensities and their derivatives with respect to absorption. In other notations, these derivatives are known as weighting functions or layer air mass factors. Multiple scattering radiation in the model is evalu- ated by the Monte Carlo method. Radiative transfer is simulated for a spherical shell atmosphere taking into account polarization, Rayleigh and aerosol scattering, gas and aerosol absorption, and Lambert surface albedo. The speed of intensity computations accurate to 1% is approximately the same as in other authors' pseudospher- ical models used for comparison. The time required for simultaneous computation of intensities and their deriv- atives is only 1.2-1.8 times as much as the time required for the computation of intensities alone. The model was compared with other spherical and pseudospherical models for geometries in which the sphericity of the atmosphere is important: twilight observations from the ground and limb scatter observations from space. The layer air mass factors calculated by different models were also compared. The influence of approximate (single scattering) computation of weighting functions on the accuracy of ozone profile retrievals was investigated for the Umkehr method used as an example. It was shown that the single scattering approximation gives additional large retrieval errors.

Dynamics of a Hyperelastic Gas-Filled Spherical Shell in a Viscous Fluid

Abstract: The dynamical response of a gas-filled, spherical elastic shell immersed in a viscous fluid is of interest in a number of different scientific and technological contexts. In this article, this problem is formulated and studied numerically, within a purely mechanical setting. For spherically symmetric motions, a neo-Hookean shell material, and an incompressible surrounding fluid, the equation of motion can be obtained through an integration in the radial coordinate. The rerouting nonlinear initial-value problem must be integrated numerically. An interesting feature of the system response is the possibility of a departure from bounded oscillation for large-amplitude far-field forcing. The amplitude at which this departure occurs is found to be highly dependent on the forcing frequency. A stability map in the forcing frequency/amplitude plane is an important result of this study.

Control volume method for the thermal convection problem in a rotating spherical shell: test on the benchmark solution

Abstract: The development of the control volume method for the thermal convection problem in a rotating spherical shell is presented. In contrast to the spectral methods, commonly used in geodynamo simulations, the control volume method belongs to the class of grid methods (the solution is approximated by a set of discrete values in physical space). In the present paper we concentrate on some problems of convergence and stability of the method. Case 0 of the numerical dynamo benchmark (Christensen et al., 2001, Phys. Earth Planet. Inter., 128, 25-34) was used to check the correctness of our computer code. The results demonstrate good convergence to the suggested standard solution.

Adhesion induced buckling of spherical shells

Abstract: Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters Cs/ and Cb/, where Cs and Cb are respectively the stretching and the bending constants, and is the depth of the van der Waals potential. As a function of Cb/, we find both continuous and discontinuous buckling transitions for small and large Cs/, respectively, which is analogous to van der Waals fluids or gels. Some scaling arguments are employed to explain the adhesion induced buckling transition.

Effect of Core Materials on the Formation of Hollow Alumina Microspheres by Mechanofusion Process

Abstract: Core/shell structures have been prepared via a mechanofusion system by employing several kinds of spherical polymers as a core material and Al2O3 powder or a mixture of Al2O3 and SiO2 powders as a shell material. The effect of the kind of core polymers on the quality of the resulting hollow alumina microspheres has been discussed on the basis of the thermal decomposition behavior of spherical polymers used as a core material. A large fraction of hollow alumina microspheres reflecting the shape and the particle size distribution of the core polymer could be fabricated after sintering at 1600°3C for 3 h, when highly cross-linked poly(methyl methacrylate) (PMMA) microspheres with a gel fraction of 99.03% were used as a core polymer, and abrupt firing at temperatures higher than 500°3C was adopted to remove the PMMA microspheres. The addition of 5 mass% SiO2 to the Al2O3 shell layer was found to be useful for maintaining the spherical shell structure during the firing process and for fabricating a large fraction of hollow alumina microspheres after the sintering.

Some Properties of the Boundary Value Problem of Linear Elasticity in Terms of Stresses

Abstract: The relation between the classical formulation of linear elastic problems in displacements and the stress formulation proposed by Pobedria is studied. It is shown that if the Navier and Pobedria differential operators are elliptic then corresponding boundary value problems are equivalent. The values of parameters for which Pobedria's boundary value problem has the Fredholm property are found. The homogeneous Pobedria's system is considered as a spectral problem with Poisson's ratio as a spectral parameter. The points of the essential spectrum are found and classified. The example of solving Pobedria's system for the Lame problem for a spherical shell is presented.

Field Inside a Random Distribution of Parallel Dipoles

Abstract: We determine the probability distribution for the field inside a random distribution of electric or magnetic dipoles. Although the average contribution from any spherical shell around the probe position vanishes, at the center of a spherical distribution of parallel dipoles, the Levy stable distribution of the field is symmetric around a nonvanishing field amplitude. Omission of contributions from a small volume around the probe leads to a field distribution with a vanishing mean, which, in the limit of vanishing excluded volume, converges to the shifted distribution.

Optically retro-reflecting sphere

Abstract: An optically retro-reflecting sphere includes an inner sphere and an outer concentric spherical shell, and can be coupled to a reflective surface. Light entering the optically retro-reflecting sphere from an incident direction is reflected by the sphere generally towards an exit direction, where the exit direction is parallel and opposite to the incident direction. The inner sphere and outer shell have different refractive indices, selected so that the reflected light is reflected with a non-uniform angular distribution about the exit direction.

Inelastic Deformation of Flexible Spherical Shells with Two Circular Openings

Abstract: Elastoplastic analysis of thin-walled spherical shells with two identical circular openings is carried out with allowance for finite deflections. The shells are made of an isotropic homogeneous material and subjected to internal pressure of known intensity. The distributions of stresses (strains or displacements) along the contours of the openings and in the zone of their concentration are studied by solving doubly nonlinear boundary-value problems. The solution obtained is compared with the solutions that account for only physical nonlinearity (plastic deformations) and only geometrical nonlinearity (finite deflections) and with a numerical solution of the linearly elastic problem. The stress–strain state near the two openings is analyzed depending on the distance between the openings and the nonlinear factors accounted for

Oscillations of magnetic stars II. Axisymmetric toroidal and non-axisymmetric shear Alfvén modes in a spherical shell

Abstract: We carry out numerical and mathematical investigations of shear Alfven waves inside of a spherical shell filled with an incompressible conducting fluid, and bathed in a strong dipolar magnetic field. We focus on axisymmetric toroidal and non- axisymmetric modes, in continuation of a previous work by Rincon & Rieutord (2003, A&A, 398, 663). Analytical expressions are obtained for toroidal eigenmodes and their corresponding frequencies at low diffusivities. These oscillations behave like magnetic shear layers, in which the magnetic poles play a key role, and hence become singular when diffusivities vanish. It is also demonstrated that non-axisymmetric modes are split into two categories, namely poloidal or toroidal types, following similar asymptotic behaviours as their axisymmetric counterparts when the diffusivities become arbitrarily small.

Stresses induced in continental lithospheres by axisymmetric spherical convection

Abstract: SUMMARY We employ an axisymmetric spherical shell model of mantle convection to examine the magnitude of deviatoric tensile stresses generated in a stationary continental plate resulting from the subduction of oceanic plate material below an active continental margin. The model includes depth-dependent physical properties, uniform internal heating, compressibility and mineral phase-change boundaries at depths of 400 and 660 km. Below 100 km, mantle viscosity is assumed constant. Above 100 km, plate-like behavior may be approximated in axisymmetric spherical geometry by imposing (i) a factor of 10 viscosity contrast between the upper 100 km and the underlying mantle and (ii) a small variation of surface velocity within each plate such that plate mass is conserved and significant vertical mass flux at the base of the plates is therefore confined to the near vicinity of the plate boundaries. We find surface stresses generated by counterflow under our model continental margins is insufficient to actively rift a supercontinent in all but one case. Earth-like curvature appears to be a major factor in reducing surface stresses relative to those found previously in constant viscosity models in plane layer geometry. A simple internal loading model allows us to estimate this effect as a 20 per cent average reduction in stress generation. This suggests that continental rifting requires the pre-existence of localized zones of weakness.