Showing papers on "Spherical shell published in 1999"

Some uses of microencapsulation for electric paper

Abstract: Bichromal balls have two hemispheres, typically one black and one white, each having different electrical properties. Each ball is enclosed within a spherical shell and then a space between the ball and shell is filled with a liquid to form a microsphere so that the ball is free to rotate in response to an electrical field. The microspheres can then be mixed into a substrate which can be formed into sheets or can be applied to any kind of surface. The result is a film which can form an image from an applied electrical field.

Computational aspects of a code to study rotating turbulent convection in spherical shells

Abstract: The coupling of highly turbulent convection with rotation within a full spherical shell geometry, such as in the solar convection zone, can be studied with the new anelastic spherical harmonic (ASH) code developed to exploit massively parallel architectures. Inter-processor transposes are used to ensure data locality in spectral transforms, a sophisticated load balancing algorithm is implemented and the Legendre transforms, which dominate the workload for large problems, are highly optimized by exploiting the features of cache memory and instruction pipelines. As a result, the ASH code achieves around 120 Mflop/s per node on the Cray T3E and scales nearly linearly for adequately large problem sizes.

Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 2: Numerical Evaluations

Abstract: The mixed layerwise shell theories that are presented in the companion article (E. Carrera, Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 1: Governing Equations' AIAA Journal, Vol. 37, No. 9, 1999, pp. 1107-1116) are evaluated here by solving several problems related to orthotropic cross-ply laminated, circular, cylindrical, and spherical shells subjected to static loadings for which closed-form solutions are given. Particular cases related to layerwise and equivalent single-layer models, based on classical displacement formulations, are evaluated for comparison purpose. A further comparison with three-dimensional elasticity exact solutions and to other higher-order shear deformations studies have been made. Results are given in the form of tables and diagrams. Approximations introduced by Donnell's shallow shell theories are evaluated for most of the problems. It has been concluded that the proposed mixed layerwise theories leads to a better description than the related analyses, which are based on displacement formulations. An excellent agreement, with respect to the exact solution, has been found for displacement and transverse stress components. These stresses have been herein calculated a priori. The importance of an adequate description of curvature terms related to the shell thickness to radii ratio h/R is also underlined. These effects have been contrasted by extensive use of fictitious interfaces in the conduced layerwise investigations.

Gravito-inertial waves in a rotating stratified sphere or spherical shell

Abstract: The properties of gravito-inertial waves propagating in a stably stratified rotating spherical shell or sphere are investigated using the Boussinesq approximation. In the perfect fluid limit, these modes obey a second-order partial differential equation of mixed type. Characteristics propagating in the hyperbolic domain are shown to follow three kinds of orbits: quasi-periodic orbits which cover the whole hyperbolic domain; periodic orbits which are strongly attractive; and finally, orbits ending in a wedge formed by one of the boundaries and a turning surface. To these three types of orbits, our calculations show that there correspond three kinds of modes and give support to the following conclusions. First, with quasi-periodic orbits are associated regular modes which exist at the zero-diffusion limit as smooth square-integrable velocity fields associated with a discrete set of eigenvalues, probably dense in some subintervals of [0, N], N being the Brunt–Vaisala frequency. Second, with periodic orbits are associated singular modes which feature a shear layer following the periodic orbit; as the zero-diffusion limit is taken, the eigenfunction becomes singular on a line tracing the periodic orbit and is no longer square-integrable; as a consequence the point spectrum is empty in some subintervals of [0, N]. It is also shown that these internal shear layers contain the two scales E1/3 and E1/4 as pure inertial modes (E is the Ekman number). Finally, modes associated with characteristics trapped by a wedge also disappear at the zero-diffusion limit; eigenfunctions are not square-integrable and the corresponding point spectrum is also empty.

Driven inertial oscillations in spherical shells

Abstract: The flow of a fluid in a rapidly rotating spherical shell whose rotation rate is modulated sinusoidally in time is simulated numerically. Different inertial modes are excited as the modulation frequency is varied. The inertial modes are structured by internal layers. Internal layers are reflected at the boundaries such that at certain modulation frequencies, the layers are focused onto ``attractors'' after multiple reflections. The geometric properties of these attractors and their relevance for the response of the fluid is investigated.

Spectral methods for the simulation of incompressible flows in spherical shells

Abstract: SUMMARY A spatial discretization of the incompressible Navier‐Stokes equation is presented in which the velocity is decomposed using poloidal and toroidal scalars whose spatial dependence is given in terms of spherical harmonics and Chebychev polynomials. The radial resolution needs to be large enough at any given angular resolution in order to avoid instability in the simulation of rotating flows. Several semi-implicit time steps are discussed. The most accurate scheme is an integrating factor technique. Copyright © 1999 John Wiley & Sons, Ltd.

Elastic instabilities of inflated rubber shells.

Abstract: Using a simple constitutive law for elastic behavior that includes the feature of a maximum allowable strain, equations are derived for inflation pressure as a function of the amount of inflation for three rubber shells: a thin-walled spherical balloon, a small spherical cavity in a large rubber block, and a thin-walled cylindrical tube. The results are compared with those obtained using the neo-Hookean constitutive law. Uniform expansion is generally predicted to become unstable at a modest degree of inflation but the new relations give a second stable inflation state, in accord with experience.

Dog toy for dispensing dog food

Abstract: A ball-like dog toy includes a spherical shell and a cylindrical valve, the spherical shell being formed of two symmetrical half shells, the half shells having ribs and partition boards, the cylindrical valve being mounted in a hole on the spherical shell and retained between the ribs and partition boards of the half shells and rotated within a limited angle, wherein dog food is discharged out of the spherical shell through the cylindrical valve when the spherical shell is rolled on the ground; discharging of dog food is stopped when the dog stops from playing with the dog toy.

Axial compression of metallic spherical shells between rigid plates

Abstract: Aluminium spherical shells of R/t values between 15 and 240, were axially compressed in an INSTRON machine between flat plates. The modes of their collapse, load-compression and energy-compression curves, and mean collapse loads are presented. A simple analytical model has been developed for the prediction of load-compression and energy-compression curves for the metallic spherical shells, by using the concepts of stationary and rolling plastic hinges. The results thus obtained match well with the experimental results. These results have also been compared with the solutions proposed in earlier studies. Behaviour of these shells is compared with the response of spherical shells (aluminium, mild steel and galvanised steel) of shallow depth, which were also subjected to axial compression between rigid plates. Their load-deformation curves are presented, and their energy-compression behaviour and mean collapse loads are discussed.

Generation of plumes under a localized high viscosity lid in 3‐D spherical shell convection

Abstract: We conduct numerical simulations of incompressible infinite Prandtl number convection in a spherical shell with a single localized high viscosity lid (HVL) on the top surface to understand the possible effects of the continental lithosphere on plume generation. The temperature under the HVL increases rapidly after the emplacement of the HVL on constant viscosity convection with internal and bottom heatings. Later. upwellings at the bottom merge into a large scale flow and a large plume emerges under the HVL. This time-scale depends on the existence of phase changes. In our model, whose Rayleigh number is 10 6 , the large plume is formed on a time-scale of 1 Gyr. A simple scaling suggests that this time-scale may be reduced by a several times, if the Rayleigh number is around 10. Despite the complicated 3-D thermal structure, it is dominated by an I = 1 pattern controlled by the position of the HVL.

Magnetohydrodynamic flow in precessing spherical shells

Abstract: Flow in a rapidly rotating, precessing spherical shell is studied with and without an applied magnetic dipole field in order to model the Earth's core. The primary response of the fluid to precessional forcing is a solid body rotation about an axis other than the rotation axis of the shell. The orientation and energy of that flow is predicted well by an asymptotic theory. Ekman layers at the boundaries of the shell break down at critical latitudes and spawn internal shear layers. The limit of small precession rate is investigated in particular: at zero magnetic field, the strongest shear layers are inclined at 30° with respect to the rotation axis of the shell and erupt at 30° latitude from the inner core. When a magnetic dipole field with its dipole oriented along the rotation axis of the shell is applied, shear zones develop additional structure and change position and orientation. At an Elsasser number of 10, most flow structures tend to align with the rotation axis of the shell.

Perturbative check on the Casimir energies of nondispersive dielectric spheres

Abstract: For an optically dilute solid sphere of radius a and dielectric constant independent of frequency, the Casimir energy is evaluated to second order in , subject to an exponential cut-off on wavenumbers, using only standard perturbation theory and elementary mathematics. It is hoped that this can serve to elucidate other far more elaborate methods that aim to determine exactly by summing zero-point energies. For the electromagnetic field, the perturbative result reads http://ej.iop.org/images/0305-4470/32/3/008/img6.gif with V the volume and S the surface area. The term of order is related in a simple way to the Casimir-Polder (retarded) potential between polarizable bodies. This relation also yields some insight into the net pressure on a thin spherical shell.

Three-Dimensional Vibration Analysis of Thick Shells of Revolution

Abstract: A 3D method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight-line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components \iu\dφ, \iu\i\dz, and \iu\dθ in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the φ and \iz directions. Potential (strain) and kinetic energies of the entire body are formulated, and upper-bound values of the frequencies are obtained by minimizing the frequencies. As the degree of polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations and completely free boundaries. Convergence to four-digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.

Nonlinear r-modes in a spherical shell: issues of principle

Abstract: We use a simple physical model to study the nonlinear behaviour of the r-mode instability. We assume that r-modes (Rossby waves) are excited in a thin spherical shell of rotating incompressible fluid. For this case, exact Rossby wave solutions of arbitrary amplitude are known. We find that: (a) These nonlinear Rossby waves carry ZERO physical angular momentum and positive physical energy, which is contrary to the folklore belief that the r-mode angular momentum and energy are negative. (b) Within our model, we confirm the differential drift reported by Rezzolla, Lamb and Shapiro (1999). Radiation reaction is introduced into the model by assuming that the fluid is electrically charged; r-modes are coupled to electromagnetic radiation through current (magnetic) multipole moments. We find that: (c) To linear order in the mode amplitude, r-modes are subject to the CFS instability, as expected. (d) Radiation reaction decreases the angular velocity of the shell and causes differential rotation (which is distinct from but similar in magnitude to the differential drift reported by Rezzolla et al.) prior to saturation of the r-mode growth. This is contrary to the phenomenological treatments to date, which assume that the loss of stellar angular momentum is accounted for by the r-mode growth. We demonstrate, for the first time, that r-mode radiation reaction leads to differential rotation. (e) We show that for l=2 r-mode electromagnetic radiation reaction is equivalent to gravitational radiation reaction in the lowest post-Newtonian order.

The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell

Abstract: We calculate the zero-point energy of a massive scalar field in the background of an infinitely thin spherical shell given by a potential of the delta-function type. We use zeta-functional regularization and express the regularized ground state energy (GSE) in terms of the Jost function of the related scattering problem. We then find the corresponding heat-kernel coefficients and perform the renormalization, imposing the normalization condition that the GSE vanishes when the mass of the quantum field becomes large. Finally, the GSE is calculated numerically. Corresponding plots are given for different values of the strength of the background potential, for both attractive and repulsive potentials. The formal transition from a delta-function potential to Dirichlet boundary conditions is not found to take place in the renormalized GSE.

Forming Uniform HD Layers in Shells Using Infrared Radiation

Abstract: Generating a volumetric heat source in solid deuterium hydride, HD, allows the formation of a spherical crystalline shell of HD inside a transparent plastic shell. Pumping the infra-red (IR) collis...

Natural frequencies of a fluid-filled anisotropic spherical shell

Abstract: In this paper, the general nonaxisymmetric free vibration of a spherically isotropic elastic spherical shell filled with a compressible fluid medium is investigated. To this end, the three-dimensional elasticity solution method recently developed by the authors [H. J. Ding and W. Q. Chen, Int. J. Solids Struct. 33, 2575–2590 (1996)] is employed. The effect of fluid is considered by introducing a relation between the normal displacement and the normal stress of the shell at the inner spherical surface. It is shown that the coupled vibration can be divided into two independent classes as in the case of empty spherical shell. The exact three-dimensional frequency equations are then derived. As the exact elasticity solution can serve as a benchmark to check various approximate theories, frequency equations of three typical shell theories are also presented. Numerical examples are given and comparisons between four theories are made.

Laboratory Study of Spherical Convection in Simulated Central Gravity

Abstract: This work reports the first terrestrial laboratory study of thermal convection in a central body-force field. The force field is produced by gradients of magnetic field magnitude imposed on a spherical shell of heated, magnetizable fluid. Cells of thermal convection consistent with the notion of continental drift are detected using infrared imaging. Transitions of symmetry for the patterns of convection are observed in the range of Earth's Rayleigh number.

On the analogy between gravity modes and inertial modes in spherical geometry

Abstract: Analysing similarities and differences between gravity modes and inertial modes, we derive the analytic expression of gravity modes in an axisymmetric ellipsoid for a diffusionless fluid. We also give the expression of the dispersion relation for these modes in such a geometry. The case of a spherical shell is then considered. After deriving a class of analytical solutions, we exhibit the analogous structure of singular gravity modes and singular inertial modes. Finally, we show why singular modes should play an important part in the transport properties of a stratified or rotating fluid.

Estimates on diagnostic methods for investigations of thermal convection between spherical shells in space

Abstract: Thermal convection in a spherical shell represents an important model in fluid dynamics and geophysics. Investigations on thermal convective instabilities occurring in the spherical gap flow under terrestrial conditions are of basic importance, especially for the understanding of symmetry-breaking bifurcations during the transition to chaos. Microgravity experiments on thermal convection with a simulated central force field are important for the understanding of large-scale geophysical motions such as the convective transport phenomena in the Earth's liquid outer core. More than one diagnostic tool is needed to examine and characterize the different flow types. Flow visualization, Wollaston shearing interferometry and laser Doppler velocimetry should be available for space experiments. This report summarizes concurrent theoretical, numerical and experimental studies for the preparation of a Get Away Special (Shuttle) experiment as well as a Space Station experiment inside the Fluid Science Laboratory. The special experimental device for investigations of supercritical and turbulent thermal convection in spherical shells under a central force field with respect to geophysical simulations is called an electrohydrodynamic container. A central symmetric force field similar to the gravity field acting on planets can be produced using the effect of the dielectrophoretic force field by applying a high-voltage potential difference to the inner and outer sphere.

The action of an electrostatic potential on the electron mass

Abstract: An experiment herewith described proves that the electron '5 mass is changed when it is placed anywhere inside a charged spherical shell at Coulomb potential U.

Applications of Iterative Elastic Techniques for Elastic-Plastic Analysis of Pressure Vessels

Abstract: The paper presents an application of iterative elastic techniques for the determination of elasto-plastic stress-strain fields, limit and shakedown loads The iterative elastic method relies on iterative modification of elastic modulus in regions at which elastically calculated effective stress exceeds material yield strength The technique is applied first to thick spherical and cylindrical shells under combined pressure and thermal gradient Results showed good correlation with analytical elasto-plastic solutions The elastic compensation technique is then applied to predict elasto-plastic stresses and shakedown loads of thin spherical shell with cylindrical nozzle subjected to internal pressure or end-thrust loading Predicted shakedown loads were found to be in good agreement with the well-known Leckie and Penny results adopted in pressure vessel codes