Showing papers on "Spherical shell published in 1988"

Numerical simulations of mantle convection: time-dependent, three-dimensional, compressible, spherical shell

Abstract: We describe nonlinear time-dependent numerical simulations of whole mantle convection for a Newtonian, infinite Prandtl number, anelastic fluid in a three-dimensional spherical shell for conditions that approximate the Earth's mantle. Each dependent variable is expanded in a series of 4,096 spherical harmonics to resolve its horizontal structure and in 61 Chebyshev polynomials to resolve its radial structure. A semiimplicit time-integration scheme is used with a spectral transform method. In grid space there are 61 unequally-spaced Chebyshev radial levels, 96 Legendre colatitudinal levels, and 192 Fourier longitudinal levels. For this preliminary study we consider four scenarios, all having the same radially-dependent reference state and no internal heating. They differ by their radially-dependent linear viscous and thermal diffusivities and by the specified temperatures on their isothermal, impermeable, stress-free boundaries. We have found that the structure of convection changes dramatically a...

Finite amplitude convection and magnetic field generation in a rotating spherical shell

Abstract: Finite amplitude solutions for convection in a rotating spherical fluid shell with a radius ratio of η=0.4 are obtained numerically by the Galerkin method. The case of the azimuthal wavenumber m=2 is emphasized, but solutions with m=4 are also considered. The pronounced distinction between different modes at low Prandtl numbers found in a preceding linear analysis (Zhang and Busse, 1987) is also found with respect to nonlinear properties. Only the positive-ω-mode exhibits subcritical finite amplitude convection. The stability of the stationary drifting solutions with respect to hydrodynamic disturbances is analyzed and regions of stability are presented. A major part of the paper is concerned with the growth of magnetic disturbances. The critical magnetic Prandtl number for the onset of dynamo action has been determined as function of the Rayleigh and Taylor numbers for the Prandtl numbers P=0.1 and P=1.0. Stationary and oscillatory dynamos with both, dipolar and quadrupolar, symmetries are close...

Heavy ion beam interaction with spherical shell and super-range planar targets

Abstract: A simple model for the heavy ion beam driven implosion of uniform spherical shell targets is constructed. The model equation is obtained by averaging the fluid equation of conservation of energy over the thickness of the shell. The energy balance contains the thermal and kinetic energies of the region absorbing the beam energy. The driving power is considered as a constant. The model gives the dependence of the implosion properties on the ion energy and the results are in agreement with published simulation data. The dynamics of a plane slab heated by an intense ion beam with range smaller than the slab thickness is described by a modified version of the model. It yields the temporal behavior of the hydrodynamics efficiency and its dependence on the ratio between the payload and the absorber masses such as is observed in simulation results.

Magnetically insulated and inertially confined fusion — MICF

Abstract: By combining the benefits of magnetic and inertial fusion, a new fusion scheme is proposed. A plasma with a density of ?1021 cm?3 is confined by the inertia of a heavy, cannonball-type metallic shell; its heat is insulated by a self-generated magnetic field of ?100 T. The plasma and the magnetic field are produced by ablation due to direct impact of a laser (or particle) beam on solid fuel which constitutes the coating of the inner surface of the spherical metallic shell. Preliminary experimental and simulation results, using a 100 J CO2 laser on a target of a few millimetre parylene shell, gave n? ? 5 ? 1012 cm?3?S, with T ? 500 eV. A 1-D spherical hydrodynamic code, HISHO, with the radial heat conductivity reduced by an assumed magnetic field of 103 T, leads to ignition at an absorbed energy of the order of 20 MJ deposited during a confinement time of approximately 100 ns. These results provide supporting evidence for the feasibility of the scheme as a realistic reactor.

Stability of a spherical shell distribution of pickup ions

Abstract: The stability of a spherical shell (complete or incomplete) is investigated. The study is motivated by the research of cometary pickup ions. The present discussion is restricted to low-frequency electromagnetic waves propagating along the ambient magnetic field. It is found that a complete shell is stable, whereas an incomplete shell can be unstable. The numerical results are reported and discussed.

Geoid and topography for infinite Prandtl number convection in a spherical shell

Abstract: Geoid anomalies and surface and lower-boundary topographies are calculated for numerically generated thermal convection for an infinite Prandtl number, Boussinesq, axisymmetric spherical fluid shell with constant gravity and viscosity, for heating both entirely from below and entirely from within. Convection solutions are obtained for Rayleigh numbers Ra up to 20 times the critical Ra in heating from below and 27 times critical for heating from within. Geoid parallels surface undulations, and boundary deformation generally increases with increasing cell wavelength. Dimensionless geoid and topography in heating from below are about 5 times greater than in heating from within. Values for heating from within correlate more closely with geophysical data than values from heating from below, suggesting a predominance of internal heating in the mantle. The study emphasizes that dynamically induced topography and geoid are sensitive to the mode of heating in the earth's mantle.

Scattering from an open spherical shell having a circular aperture and enclosing a concentric dielectric sphere

Abstract: The generalized dual series solution is presented for the scattering of an arbitrary plane wave from an open spherical shell having a circular aperture and enclosing a concentric homogeneous dielectric sphere. This solution explicitly exhibits the correct edge behavior, and it can handle spheres that are electrically small or large without special considerations. A variety of cross-section results is presented for the normally incident case. It is shown that effects corresponding to the presence of the interior cavity dominate all of the scattering data. In particular, the cross sections exhibit new resonance features that are due to the cavity-backed nature of the aperture and depend on the characteristics of the interior sphere. The results demonstrate that interior information is contained in the exterior scattering data. >

Elastic-plastic dynamic buckling of thin-shell finite elements with asymmetric imperfections

Abstract: In an earlier study of the phenomena of dynamic buckling of shells in the elastic range using a 48 degree-offreedom doubly curved quadrilateral imperfect thin-shell finite element, the interesting destabilizing effects of initial imperfections on a spherical shell, a spherical cap, and a hemispherical shell were found. The formulation was based on the Kirchhoff-Love shell theory with geometric imperfections. In this study, the earlier formulation is extended to include the effect of plasticity in tensor form so that a wide range of practical problems can be considered in order to study more completely the effects of dynamics, amplitude of imperfection, and plasticity. The effect of viscous damping is also considered by using the Rayleigh damping concept. Examples include static and dynamic buckling analyses of 1) axisymmetrically imperfect spherical shells, 2) axisymmetrically imperfect spherical caps, and 3) asymmetrically imperfect spherical caps, all in both elastic and elastic-plastic ranges. For case 3, there seems to be no previous results available for comparison. From the wide variety of examples studied, the previous conclusions for shells with axisymmetric imperfections were reconfirmed for shells with asymmetric imperfections, i.e., dynamic effect, imperfection, and plastic deformation, which all have the effect of reducing the buckling load to various degrees. On the contrary, the viscous damping has the effect of increasing the dynamic buckling load. Such an effect is quantified in two examples.

Multi-element spherical shell generation

Abstract: A nozzle assembly in a multi-element spherical shell generation system includes first and second side-by-side spaced apart nozzles and a web portion extending between and connecting the nozzles. The first nozzle has an inner orifice adapted to discharge a first filler material and an outer annular orifice separated from and defined in concentric relation about the inner orifice and adapted to discharge a first shell material. The second nozzle has an inner orifice adapted to discharge a second filler material and an outer annular orifice separated from and defined in concentric relation about the inner orifice and adapted to discharge a second shell material. A multi-element spherical shell can be formed through employment of the nozzle assembly by merger with one another after discharge from the outer orifices of the nozzles of a pair of adjacent annular streams of liquid or molten shell wall material of different compositions and encapsulation by the mixed shell wall materials of a common encapsulated core fluids also simultaneously discharged by the inner orifices nozzles. On the other hand, the pair of encapsulating streams of shell wall material can be of the same material which merge together and encapsulate core fluids of different compositions which will merge together after discharge from the nozzles.

Stability of a water tower

Abstract: The stability of a water tower, consisting of a spherical shell rigidly attached to the top of a vertical column, is analyzed. At first, it is shown on a simple conceptual model that problems of this type are imperfection insensitive; thus, the first bifurcation load from the straight state of equilibrium could be considered the buckling load. This is followed by the analysis of the water tower problem taking into consideration the flexibility of the column, the own weight of the structure, the weight of the liquid, and the rotational stiffness of the soil base. Although the differential equation of the resulting eigenvalue problem has a variable coefficient, the problem is solved exactly in closed form. To simplify the utilization of the obtained results, they are presented graphically for a range of water tower and soil stiffness parameters. Model tests were conducted that confirmed the analytical findings. However, nearP cr , at the smallest disturbance the model underwent large oscillatory motions. This finding suggests that, for water tower design, only a fraction ofP cr should be used.

Long‐range scattering in a deep oceanic waveguide

Abstract: A general formalism is developed for the scattering from an arbitrarily shaped elastic shell in a range‐independent, inhomogeneous‐layered waveguide with an arbitrary sound‐speed profile. This formalism is exact and valid through all orders of multiple scattering between the scatterer and the waveguide. The waveguide is terminated with a rigid bottom to avoid the branch cut associated with an infinite half‐space, however there is sufficient flexibility to include multilayered, bottom sediment structure. This formalism is applied to the long‐range, low‐frequency acoustic scattering of a broadband acoustic pulse by an elastic spherical shell in a range‐independent, deep ocean waveguide.

Measurement of the directional electron contributions to dose in a phantom irradiated by 8 MV x-rays

Abstract: A method of measuring the directional components of electron dose in a material exposed to 8 MV X-rays is described. A hollow wooden spherical shell which is divisible into ten sectors is used. The detector is a conventional thin-walled ionisation chamber. The internal diameter of the shell is large compared with the dimensions of the ionisation chamber. The dose contribution from each sector is separately measured and expressed as a fraction of the full equilibrium dose. The principles of the method are discussed and some correction factors are described. The build-up of dose with thickness of material in each sector is measured and tabulated. The measured data are used to calculate the loss of electron equilibrium at a point in an air channel in an otherwise uniform body.

Korn’s constant for a spherical shell

Abstract: Upon invoking the variational characterization of Korn's constant and Dafermos' technique to reduce it to a boundary value problem, the Korn constant of a spherical shell of arbitrary thickness has been evaluated. The classical result of Payne and Weinberger for the sphere is recovered as the special case of vanishing interior radius, while as the thickness of the shell tends to zero, Korn's constant tends to infinity in a nonuniform sense.

Production of uniform electrostatic fields by a slotted conducting spherical shell

Abstract: A spherical structure that specifies electric potential on a spherical surface to produce a uniform electric field near the center of the sphere is considered. The surface is divided on lines of constant latitude (polar angle), and the resulting bands are constrained to have particular voltages. The particular case of three conducting surfaces with voltages V/sub 1/, 0, and -V/sub 1/ is considered in detail. Polar angles are determined that give the required uniformity of the field. >

Finite particle number effects and the relationship of the fermion dynamical symmetry model with the Nilsson model

Abstract: The fermion dynamical symmetry model is applied to an odd mass system via a strong coupling scheme and a direct comparison with the Nilsson model is made. Consequently, the deformed shell model Fermi-surface effect can be calculated from the fermion dynamical symmetry model as an approximate solution to the spherical shell model. Also, the finite particle number effect is studied with the fermion dynamical symmetry model; its effect is to renormalize the moment of inertia and deformation as well as to cause an attenuation of the Coriolis interaction.

On the nonlinear stability of a truncated shallow spherical shell under A uniformly distributed load

Abstract: A problem of practical interest for nonlinear axisymmetrical stability of a clamped truncated shallow spherical shell with a nondeformable rigid body under a uniformly distributed load is studied in this paper. By using modified iteration method, some important analytic results are obtained and the corresponding numerical results are given in figures.

An analysis of the thermally induced formation of a uniform liquid layer of ternary deuterium–tritium mixture inside a cryogenic spherical shell inertial confinement fusion target

Abstract: The values of the externally applied thermal gradients that give rise to uniform liquid layers of a ternary deuterium–tritium mixture inside a cryogenic spherical shell inertial confinement fusion target are calculated using a model recently developed by the authors. It is shown that the surface tension gradients induced by the component separation at the liquid–vapor interface pull the liquid upward, thus counteracting the gravity‐induced fuel sagging and forming dynamically stable uniform liquid layers. The governing equations are the equations of continuity, momentum, energy, and mass diffusion–convection, which are solved using finite‐difference methods. The solutions indicate that one needs fairly large positive thermal gradients, obtained by keeping the top of the target warmer than the bottom, in order to create uniform liquid layers on the inner surface of the target.

Externally-Pressurised Torispheres - Plastic Buckling and Collapse

Abstract: SUMMARY Buckling/collapse pressures for perfect clamped steel torispherical shells subjected to external pressure are given in the paper. The BOSOR 5 shell buckling program was used in the computations and the geometric parameters investigated were the spherical radius-to-thickness ratio (R S /t), the toroidal radius-to-cylinder diameter ratio ( r /D) and the spherical radius-to-cylinder diameter ratio (R S /D); the yield point of the steel, σ yp , was also varied. For r /D r /D S /t and r /D seemed to have most influence on the mode of failure. The post-collapse response of the shells was also strongly influenced by the r /D-ratio. The collapse pressures were also plotted against the parameter for a spherical shell. However, unlike the results for hemispheres, a curve independent of σ yp was not obtained. As might be expected, the curves obtained for torispheres depended on r /D and R S /D as well. If the -parameter is going to be useful in the design of general torispheres, then p yp and p cr should involve the two principal radii of curvature (i.e. r and R S ).

Free vibration of a spinning spherical shell.

Abstract: An analysis is presented for the free vibration of a spinning spherical shell. For this purpose, the governing equations and the boundary conditions of the shell are derived by applying Hamilton's principle to the strain and kinetic energies of the shell. The variables in the equations can be written as summation of the quasi-static components which are independent of time and the dynamic ones. The linear equations on the vibration about the deformed state are solved by using the transfer matrix method. The method is applied to a spinning clamped-free spherical shell. The quasi-static and dynamic displacements and the frequency parameters are calculated numerically, and the effects of the spinning of the shell on the free vibration are studied.

Distorted flux lines behavior in type II superconducting spherical shell:. Application to high temperature superconductor

Abstract: A model of a type II superconducting grains (of a spherical shell shape) is suggested to verify the properties of distorted flux lines (FLs) in high temperature superconductors (HTS). The magnetic fields distributions and current density are formulated. It will be shown that the magnetic field inside a superconducting region is composed of the penetrating applied field, FLs fields, and a stray field. Outside the superconductor, there is only the applied field and the stray field . However, in the normal interior region (r < a), there is only the stray field. Moreover, the forces on the flux line (FL) segments are completely determined.

On the nonlinear stability of a truncated shallow spherical shell under a concentrated load

Abstract: In this paper, the axisymmetric nonlinear stability of a clamped truncated shallow spherical shell with a nondeformable rigid body at the center under a concentrated load is investigated by use of the modified iteration method. The analytic formulas of second approximation for determining the upper and lower critical buckling loads are obtained.

Effects of compressibility on the temperature jump at the interface of layered, spherical‐shell convection

Abstract: Large temperature jumps at the interface of layered convection are important to the argument used against the likelihood of separate circulations in the upper and lower mantles. This problem was studied within the framework of a compressible, constant viscosity spherical-shell model. Both mechanical and thermal coupling configurations are considered. Although the temperature jumps are reduced by compressibility, their magnitudes remain quite large, in the case of mechanical coupling. For thermal coupling, the temperature jumps become smaller but still are substantial, between 500 to 1000 C. In layered spherical-shell convection, flows in the lower mantle are several times greater than the surface velocities.

Application of the Finite Element Method to Elastic-Plastic Creep Buckling Analysis of Partial Spherical Shell

Abstract: In the present paper, the finite element method is applied to the creep buckling of a partial spherical shell subject to a uniform external pressure. In the analysis, plastic strain is included in addition to elastic and creep strains. Not only the axisymmetric mode but also the bifurcation mode are considered in the creep buckling analysis. Three types of plastic constitutive equation that is, the flow theory the modified flow theory, and the deformation theory are used to predict the critical time of creep buckling. It is found from the analysis that the critical times of the modified flow theory and the deformation theory are smaller than that of the flow theory.

The equations of motion for a general orbiting large space flexible system

Abstract: General motion equations in compact form using dyadic notation are developed for an orbiting flexible body of arbitrary shape. The equations are applied to three typical flexible space systems: a flexible beam, a flexible plate, and a flexible shallow spherical shell in orbit. The inertia dyadic of these flexible bodies may be calculated using the equations which have been obtained.