Showing papers on "Spherical shell published in 1995"
406 citations
17 Sep 1995
TL;DR: It is shown that lattice codes can achieve capacity on the additive white Gaussian noise channel and there exists a lattice code with rate no less than R and average error probability upper-bounded by e.
Abstract: It is shown that lattice codes can achieve capacity on the additive white Gaussian noise channel. More precisely, for any rate R less than capacity and e>0, there exists a lattice code with rate no less than R and average error probability upper-bounded by e. These lattice codes include all points of the (translated) lattice within the spherical bounding region (not just the ones inside a thin spherical shell).
164 citations
TL;DR: In this paper, the authors present a direct numerical solution of a particular inertial oscillation, the so-called spin-over mode, in spherical geometry and demonstrate that the oscillatory Ekman layer breaks down at k30" latitude, and that this breakdown spawns internal shear layers.
Abstract: We present a direct numerical solution of a particular inertial oscillation, the so-called ' spin-over' mode, in spherical geometry. This mode is particularly relevant to the fluid flow within a precessing oblate spheroid. We demonstrate that the oscillatory Ekman layer breaks down at k30" latitude, and that this breakdown spawns internal shear layers. We show that the structure of these shear layers is different for a full sphere and a spherical shell, as noted in the preceding paper (Kerswell 1995). Despite the existence of these shear layers, however, the numerical decay rates agree to within 1 % with the asymptotic decay rates, which neglect any possible shear layers. Finally, we consider the nonlinear mean flow profiles driven by this mode, and demonstrate that our numerical results agree reasonably well with experimental results.
146 citations
Patent•
25 May 1995
TL;DR: In this paper, an irradiation attachment for an optical fiber which provides an output of light that has a highly uniform intensity is described. But the device is not suitable for photodynamic therapy.
Abstract: An irradiation attachment for an optical fiber (4) which provides an output of light that has a highly uniform intensity. The device includes a hollow spherical shell (1) having a diffusive reflective surface or target (11) supported (12) therein. Light is directed into the hollow spherical shell (1) so that it reflects off the diffusive reflective surface or target (11). The reflected light is internally reflected off the inner surface of the hollow spherical shell (1) several times before passing through an output aperture (8). As a result of the internal reflection within the hollow spherical shell (1), the light leaving the device has a highly uniform intensity. The device is particularly useful for photodynamic therapy.
101 citations
TL;DR: It is suggested that the onset of rotational motion in the rare earth nuclei is due to the promotion of the eight particle blocks to the major shells above the ones currently filling.
Abstract: Exact diagonalizations with a realistic interaction show that configurations with four neutrons in a major shell and four protons in another---or the same---major shell, behave systematically as backbending rotors. The dominance of the {ital q}{center_dot}{ital q} component of the interaction is related to an approximate ``quasi-SU3`` symmetry. It is suggested that the onset of rotational motion in the rare earth nuclei is due to the promotion of the eight particle blocks to the major shells above the ones currently filling. Assuming a ``pseudo-SU3`` coupling for the particles in the lower orbits, it is possible to account remarkably well for the observed {ital B}({ital E}2) rates at the beginning of the region.
99 citations
TL;DR: In this paper, high angular resolution and high sensitivity maps of IRC+10216 were obtained, showing that the molecules SiS and CS are mostly found in the inner parts of the envelope, but are still detectable in the outer region (r ~ 15”) where the products of photochemistry are found.
Abstract: We have obtained high angular resolution ~ 3”), and high sensitivity maps of IRC+10216. SiC2 is found both in a spherical shell and in the very central region, indicating it is formed both in the inner envelope close to the star, and in the outer shell. The molecules SiS and CS are mostly found in the inner parts of the envelope, but are still detectable in the outer region (r ~ 15”) where the products of photochemistry are found. The maps show that IRC+10216 has a very clumpy envelope, with strong departures from spherical symmetry; an axis oriented NS-SW (P.A. 20°) can be seen in all maps. The radial brightness distribution of CS has secondary maxima, at the radius where the SiC2 shell has its peak emission. A preliminary map shows CN in the same shell, but also in a still larger outer shell. Time variations in the mass loss rate, could be invoked to explain the multiple shell structure of this envelope.
77 citations
TL;DR: The structure of thermal convection in a three-dimensional rotating spherical shell of electrically conducting fluid with an imposed toroidal magnetic field depends on the Elsasser number, the ratio of Lorentz to Coriolis forces, and the geometry of the shell as discussed by the authors.
55 citations
TL;DR: In this article, a theoretical and numerical study of the stress distribution in nutshells being compressed between two rigid plates is presented, and an analytical solution for the contact between a spherical shell and rigid plates has been obtained based on conventional shell theories and Hertz' contact hypothesis, and the results correlate very well with finite element analysis.
Abstract: A theoretical and numerical study of the stress distribution in nutshells being compressed between two rigid plates is presented in Part 1 of this two-part paper. An analytical solution for the contact between a spherical shell and rigid plates has been obtained based on conventional shell theories and Hertz' contact hypothesis, and the results are found to correlate very well with finite element analysis. The effect of the kernel on the deformation and fracture of complete nut-in-shells is also studied using finite element analysis, which shows that the effect of the kernel can be generally ignored as long as the shear modulus of the kernel is lower than that of the shell by two orders of magnitude. A series of tests have been conducted on Macadamia nuts, and the experimental data are discussed in terms of the stress analysis results.
45 citations
TL;DR: In this article, the eigenfrequencies of the lowest-order inertial modes (azimuthal wavenumber m = 0,1,2) in a spherical shell with the same aspect ratio as the liquid core of the Earth were computed.
42 citations
TL;DR: In this article, a three-dimensional, spherical-shell model of mantle convection with strongly temperature-dependent viscosity is investigated. But the model is not suitable for the analysis of the Earth's geoid and seismic tomography.
Abstract: We investigate a three-dimensional, spherical-shell model of mantle convection with strongly temperature-dependent viscosity. Numerical calculations of convection in an infinite Prandtl number, Boussinesq fluid heated from below at a Rayleigh number of Ra = 10 5 are carried out for the isoviscous case and for a viscosity contrast across the shell of 1,000. In the isoviscous case, convection is time dependent with quasi-cylindrical upflow plumes and sheet-like downflows. When viscosity varies strongly across the shell, convection is also time dependent, but major quasi-cylindrical downflows with spider-like extensions occur at both poles and interconnected upflow plumes occur all around the equator. The surface expression of mantle convection in the Earth (downwelling sheets at trenches, upwelling plumes at hot spots, and upwelling sheets at midocean ridges) resembles structures seen in both the isoviscous and variable viscosity models. The dominance of spherical harmonic degree l = 2 in the variable viscosity model agrees with the l = 2 dominance in the Earth's geoid, topography, and seismic tomography. The overall pattern of convection in the variable viscosity case is similar to the distribution of major highlands and volcanic rises on Venus.
38 citations
TL;DR: It is demonstrated that the field adjusts to the Bondi-Gold theorem, according to which the field in the insulators inside and outside the shell cannot grow on the fast time scale, by becoming increasingly self-contained within the shell.
Abstract: We consider the evolution of a magnetic field in a spherical shell of highly conducting fluid surrounded by an insulator. We impose an axisymmetric, time-dependent flow, having large regions of chaotic particle paths. This flow appears to yield fast dynamo action, in which the field grows on the fast advective, rather than on the slow diffusive time scale. We demonstrate that the field adjusts to the Bondi-Gold theorem, according to which the field in the insulators inside and outside the shell cannot grow on the fast time scale, by becoming increasingly self-contained within the shell.
TL;DR: In this article, a solution for stresses and displacements in a thick spherical shell subjected to internal and external pressure loads is presented for pressure vessel modeling of fuel and target particles of the New Production Modular High Temperature Gas-Cooled Reactor (NP-MHTGR).
TL;DR: In this article, three-dimensional models of thermal convection in a spherical shell are presented for five different cases, each characterized by a unique ratio, f, of the radii of the inner and outer bounding surfaces.
Abstract: Three-dimensional models of thermal convection in a spherical shell are presented for five different cases, each characterized by a unique ratio, f, of the radii of the inner and outer bounding surfaces. These solutions are compared to comparable two-dimensional solutions in axisymmetric spherical, cylindrical and Cartesian coordinates. All solutions were obtained with a Rayleigh number of 105, stress free, isothermal boundaries and no internal heating in a constant property Boussinesq fluid of infinite Prandtl number. Similarities and differences between three-dimensional and two-dimensional curvilinear models are discussed in terms of scales and stability of the flow patterns, mean radial temperature profiles and heat transport. It is shown that diagnostic statistics such as mean temperature and Nusselt number may be scaled from one degree of curvature to another for both three- and two-dimensional curvilinear models, provided the aspect ratio and plan form of the flow solutions are comparable....
TL;DR: Sun et al. as mentioned in this paper demonstrated a simple ray approximation for the backscattering of sound by a thin empty cylindrical shell in water at normal incidence, applied to the region near the coincidence frequency and is used to interpret prominent features in that region associated with a subsonic guided wave.
Abstract: A simple ray approximation is demonstrated for the backscattering of sound by a thin empty cylindrical shell in water at normal incidence. The approximation is applied to the region near the coincidence frequency and is used to interpret prominent features in that region associated with a subsonic guided wave. With increasing ka, the features exhibit a transition from resonance behavior dominated by interference with the specular reflection. Another feature is the interference of resonance contributions of the leaky s0 Lamb wave which may produce maxima or minima in the amplitude depending on the ka region. The cylinder studied is 2.5% thick stainless steel for ease of comparison with a similar spherical shell [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 92, 3315–3319 (1992)] and the guided wave properties were computed from elasticity theory rather than shell approximations. A novel geometric derivation is given for the relative phases of the coupling coefficients of subsonic waves on cylinders and ...
TL;DR: In this article, the authors derived equations for thermal convection in a rotating spherical shell in the presence of a uniform azimuthal magnetic field, assuming the convection is organized along columns parallel to the rotation axis.
TL;DR: In this article, the governing equations of the free vibrations of spherical and cylindrical shells with a regular singularity, are solved by Frobenius Series Method in the form of matrix.
Abstract: The governing equations of the free vibrations of spherical and cylindrical shells with a regular singularity, are solved by Frobenius Series Method in the form of matrix. Considering the relationship of the roots of the indicial equation, we get some various expressions of solutions according to different cases. This work lays a foundation of solving certain elastic problems by analytical method.
TL;DR: In this article, the acoustic scattering by two spherical elastic shells in close proximity insonified by plane waves at arbitrary angles of incidence is analyzed exactly in the low and intermediate frequency ranges.
Abstract: The acoustic scattering by two spherical elastic shells in close proximity insonified by plane waves at arbitrary angles of incidence is analyzed exactly in the low‐ and intermediate‐frequency ranges. The incident and scattering wave fields are expanded in terms of the classical modal series and the addition theorem for the spherical wave functions facilitates the exact expression of the sound fields scattered by each spherical elastic shell in the presence of the other, referred to coordinate systems at the centers of either spherical shell. The solution to the scattering problem is obtained by simultaneously solving the Helmholtz equation governing the wave motion in the fluid medium in which the two shells are submerged and the two sets of equations of motion of the two elastic shells satisfying the boundary conditions at all fluid–shell interfaces and the far‐field radiation condition. Numerical computation of the scattered wave pressure involves the solution of the truncation of an ill‐conditioned complex matrix system the size of which depends on how many terms of the modal series are required for convergence. This in turn depends on the value of the frequency, and on the proximity of the two spherical elastic shells. The ill‐conditioned matrix equation is solved using the Gauss–Seidel iteration method and Twersky’s method of successive iteration double checking each other. Backscattered echoes from two identical spherical elastic shells are extensively calculated. The result also demonstrates that the large amplitude low‐frequency resonances of the echoes of the neighboring elastic shells shift downward with proximity to each other. This can be attributed to the increase of added mass for the vibration of the shells.
TL;DR: In this paper, a vibro-acoustic model of a finite cylindrical shell partially covered with a compliant material layer is presented, where the shell is terminated by a rigid baffle and is covered by strips of compliant material lying parallel to the shell axis.
TL;DR: In this paper, an empty stainless-steel spherical shell was used for backscattering from a PVDF sheet with water in contact with both sides, and the shell's calculated impulse response was observed over a wide frequency interval.
Abstract: A novel source was developed to produce a plane‐wave unipolar pressure impulse with a wide range of frequency components. The source consisted of a PVDF sheet with water in contact with both sides. The PVDF was driven by a step voltage. This source is nearly acoustically transparent and was used for backscattering from an empty stainless‐steel spherical shell. The shell was placed in the near field of the source where it experienced a plane‐wave pressure impulse followed much later by edge contributions resulting from the finite source size. A hydrophone was placed in the far field of the scatterer on the opposite side of the source. Prominent features in the shell’s calculated impulse response are observed over a wide frequency interval. Time records reveal an approximately Gaussian wave packet from the excitation of the subsonic a0− wave associated with the backscattering enhancement near the coincidence frequency (≊309 kHz). Superposed on the same records are large contributions from the low‐frequency excitation of the a0− wave and from the s0 wave. A bipolar feature of the initial response was found to be associated with the finite inertia of the shell and the null frequency. An approximate theory predicts that the associated relaxation time depends on the mass per area of the shell and the density and sound speed of the surrounding water. The shell used in the experiment has a thickness to radius ratio of 2.3% and the scattering phenomena of interest occur between 8 and 450 kHz corresponding to ka from approximately 1 to 70. The 10‐kHz ringing of the target associated with the a0− wave is quite pronounced.
TL;DR: In this paper, a rapidly rotating compressible fluid spherical shell is considered and the effect of introducing compressibility for different choices of the Prandtl number, Pr, comparing their results with those for a similar model of Glatzmaier and Gilman.
Abstract: We consider a rapidly rotating compressible fluid spherical shell, and study linear perturbations of a polytropic equilibrium state. Instead of considering the fully compressible problem, we make the anelastic approximation. We start from Boussinesq solutions and study the effect of introducing compressibility for different choices of the Prandtl number, Pr, comparing our results with those for a similar model of Glatzmaier and Gilman (1981). For Pr = 1 and 10, the results are similar. As compressibility is increased, convection becomes localised near to the inner boundary, an effect which is magnified by increasing the rotation rate. When we consider Pr = 0.1 we find different results. As compressibility is introduced, the critical Rayleigh number, R c decreases sharply and becomes negative. This behaviour was not found by Glatzmaier and Gilman.
TL;DR: In this article, the onset of convection in a rotating spherical shell with an imposed magnetic field was studied, which is relevant to understanding the dynamics of the Earth's outer core.
Abstract: The problem of the onset of convection in a rotating spherical shell with an imposed magnetic field is studied. This problem is relevant to understanding the dynamics of the Earth's outer core. The...
TL;DR: In this article, a series of NVT Monte Carol simulations on systems of molecules interacting via a Gay-Berne (GB) potential within a spherical cavity modelling a polymer-dispersed liquid-crystal (PDLC) droplet is presented.
Abstract: We report results of a series of NVT Monte Carol simulations on systems of molecules interacting via a Gay–Berne (GB) potential within a spherical cavity modelling a polymer-dispersed liquid-crystal (PDLC) droplet. The cavity walls have been simulated by constructing a spherical shell of GB particles, each oriented towards the centre of the drop in an attempt to promote radial boundary conditions. The wall–fluid interactions have been modelled with a modified 1–3 GB potential (with energy exponents µ-1 and ν= 3, respectively) to favour radial alignment. We show results for the molecular organization in the droplet for a 2–1 and 1–3 fluid–fluid potential. We also show the radial order parameter as a function of temperature and droplet size. It is found that at low scaled temperatures a layer of radially aligned particles is formed, but this ordering does not propagate towards the centre of the drop unless the drop is relatively large or all the fluid–fluid interactions are modelled with the 1–3 potential. In this situation, concentric shells of aligned particles are formed, with a small smectic-like domain in the centre.
TL;DR: In this article, a numerical method for the solution of equilibrium problems of elastic solids with bounded tensile strength is proposed, where boundary value problems are solved numerically and the solution obtained is compared to the exact one.
TL;DR: The first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid was made in this paper, where it was shown that a steady axisymmetric magnetic field loses its stability to a non-axisymetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20.
Abstract: This paper presents the first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid. We find that a steady axisymmetric poloidal magnetic field loses its stability to a non-axisymmetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20. Comparing this with observed fields, we find that, for any reasonable estimates of the appropriate parameters in planetary interiors, our theory predicts that all planetary poloidal fields are stable, with the possible exception of Jupiter. The present study therefore provides strong support for the physical relevance of magnetic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman-Taylor theorm. This suggests that the most rapidly growing perturbation arranges itself in such a wa...
TL;DR: In this paper, the authors derived closed-form expressions for membrane stress resultants in a liquid-filled triaxial ellipsoidal storage vessel and applied them to the design of storage vessels and water tanks.
TL;DR: In this article, the authors derived a solution by embedding a composite sphere, consisting of an inclusion particle surrounded by a spherical shell of matrix material, within an effective medium, for the Al/TiC MMC that illustrate the development during cooling of these residual fields and their dependence on the concentration of the TiC particles.
Abstract: When the fabrication of a metal-matrix composite (MMC) involves its cooling from a high temperature stress-free state, plastic-elastic residual deformation fields can be generated within and around the particles due to the differential thermal expansion between the particle and matrix material. These residual fields are obtained for the situation where the particles are spherical, of equal radius and randomly distributed in the matrix. The solution is derived by embedding a composite sphere, consisting of an inclusion particle surrounded by a spherical shell of matrix material, within an effective medium. Specific results are presented for the Al/TiC MMC that illustrate the development during cooling of these residual fields and their dependence on the concentration of the TiC particles.
TL;DR: In this article, the authors obtain analytic solutions for the surface universality class of extraordinary transitions for a spherical shell, which may serve as a starting point for a pertubative calculation.
Abstract: In the framework of mean-field theory the equation for the order-parameter profile in a spherically-symmetric geometry at the bulk critical point reduces to an Emden-Fowler problem. We obtain analytic solutions for the surface universality class of extraordinary transitions ind=4 for a spherical shell, which may serve as a starting point for a pertubative calculation. It is demonstrated that the solution correctly reproduces the Fisherde Gennes effect in the limit of the parallel-plate geometry.
TL;DR: The main effort of the ICF target fabrication group is support of the experiments performed on the ISKRA-4 and Iskra-5 laser systems The main types of targets used in these experiments are direct drive, inverted corona, and indirect drive targets as discussed by the authors.
Abstract: The main effort of the ICF target fabrication group is support of the experiments performed on the ISKRA-4 and ISKRA-5 laser systems The main types of targets used in these experiments are direct drive, inverted corona, and indirect drive A direct drive target is a glass spherical container coated with a metal or polymeric film and filled with a D-T mixture and some diagnostic gas 1,2 The inverted corona target is a spherical shell with holes for introducing laser radiation The inside surface of the shell is coated with a compound containing heavy hydrogen isotopes 3,4 The indirect drive target is assembled from a spherical shell with holes for introducing laser radiation and a direct drive target placed in the shell center The inside surface of the shell is coated with high-Z material 5 (Fig1) For production of direct drive targets, manufacturing techniques have been developed for both hollow glass and polystyrene microspheres Hollow glass microspheres are fabricated by free-fall of liquid glass drops or dry gel in a 4 meter vertical kiln 6 These methods allow us to manufacture glass microspheres with diameters from 50 μm to 1 mm, wall thicknesses from 05 to 10μm, and aspect ratios (radius/wall) from 20 to 500 The microspheres have a thickness inhomogeneity less than 5% and non-sphericity less than 1% Polystyrene microspheres are fabricated from polystyrene particles with a blowing agent in a similar vertical kiln Polystyrene microspheres are fabricated with diameter up to 800 μm and wall thicknesses from 1 to 10 μm
TL;DR: In this paper, a geometrically non-linear quasi-conforming nine-node quadrilateral degenerated solid shell element has been constructed from generalization of a linear quasilinear finite element method.
Abstract: In this paper, a geometrically non-linear quasi-conforming nine-node quadrilateral degenerated solid shell element has been constructed from generalization of a linear quasi-conforming nine-node quadrilateral degenerated solid shell element, 10 based upon the non-linear quasi-conforming finite element method. First, the geometrical description and displacement model of the nine-node quadrilateral degenerated solid shell element is given. Then, the non-linear quasi-conforming finite element method is discussed and assumed strains and weighed functions are given. Last, analysis of numerical examples for a clamped square plate, a circular arch, a spherical shell, two cylindrical shells, the patch test and a simply supported square plate is carried out. The results are compared with exact and other finite element solutions. The results indicate that the shell element in the paper is accurate and efficient