Showing papers on "Spherical shell published in 1997"
TL;DR: In this paper, the structure and spectrum of inertial waves of an incompressible viscous fluid inside a spherical shell are investigated numerically, and it is shown that these modes appear to be strongly featured by a web of rays which reflect on the boundaries.
Abstract: The structure and spectrum of inertial waves of an incompressible viscous fluid inside a spherical shell are investigated numerically. These modes appear to be strongly featured by a web of rays which reflect on the boundaries. Kinetic energy and dissipation are indeed concentrated on thin conical sheets, the meridional cross-section of which forms the web of rays. The thickness of the rays is in general independent of the Ekman number E but a few cases show a scaling with E1/4 and statistical properties of eigenvalues indicate that high-wavenumber modes have rays of width O(E1/3). Such scalings are typical of Stewartson shear layers. It is also shown that the web of rays depends on the Ekman number and shows bifurcations as this number is decreased.This behaviour also implies that eigenvalues do not evolve smoothly with viscosity. We infer that only the statistical distribution of eigenvalues may follow some simple rules in the asymptotic limit of zero viscosity.
222 citations
TL;DR: In this paper, the authors derived the acoustic radiation force on a spherical particle assuming that the surrounding fluid is viscous and heat conducting and that the incident sound field pressure amplitude is small enough such that nonlinear effects like generation of subharmonics do not occur.
Abstract: The acoustic radiation force exerted by an axisymmetric sound field on a spherical particle is calculated assuming that the surrounding fluid is viscous and heat conducting. The incident sound field pressure amplitude is supposed to be small enough such that nonlinear effects like generation of subharmonics do not occur. No restrictions are imposed on the particle size, which means that the particle can be of an arbitrary radius with respect to the sound, viscous, and thermal wavelengths in the surrounding fluid. The obtained formula for the radiation force is general in that it is applicable to first, any axisymmetric sound field, such as a plane, traveling or standing wave and a spherical wave, and, second, any of the following types of dispersed particles: a gas bubble, a liquid drop, a rigid or elastic sphere, a spherical shell, etc. The force is expressed in terms of the linear scattering coefficients to be determined by the particle type. Thus, to obtain the force on a specific particle the problem of linear scattering for that particle must be solved. Problems of this sort are known not to be mathematically difficult, but can be laborious enough if a particle at issue has a complicated internal structure. The radiation forces on particles of most interest are examined in papers that follow [J. Acoust. Soc. Am. 101, 722–740 (1997)].
127 citations
TL;DR: In this article, the authors compared four types of axially symmetric radiative transfer models with the data, including spherical shells with an ellipsoidal inner cavity, a disk, a spherical shell with one or two inhomogeneities or clumps, and a set of thin partial shells with a -xed distance between them.
Abstract: Visibility observations at 11 km of o Ceti have been made with the University of California (Berkeley) Infrared Spatial Interferometer during the time period 1988E1995. The observed visibilities change dra- matically from one epoch to another and are not consistent with simple heating or cooling of the dust with change in luminosity as a function of stellar phase. Instead, large temporal variations in the density of dust within a few stellar radii of the photosphere of o Ceti have occurred. Spherically symmetric models of the dust distribution with two dust shells, one within three stellar radii of the photosphere of the star, the other approximately 10 stellar radii from the star, can account reasonably well for the observed changes. Four types of axially symmetric radiative transfer models were also compared with the dataEa spherical shell with an ellipsoidal inner cavity, a disk, a spherical shell with one or two inhomogeneities or clumps, and a set of thin partial shells with a -xed distance between them. Of the four models, only the one with the ellipsoidal inner cavity is excluded. The data were best--tted with the last two models, which emphasize inhomogeneities or clumps. To -t the observed temporal changes in the visibility data, all models must include a change in the densityEincreasing and decreasingEof dust close to the photosphere of the star. The axially symmetric models had clumps placed at distances from the star in agreement with distances of the spherical models. Good -ts to the observed broadband spec- trum of the star were also obtained with these models. Subject headings: circumstellar matter E infrared: stars E stars: individual (o Ceti) E stars: mass loss E stars: variables: long-period variables E techniques: interferometric
90 citations
TL;DR: In this paper, a finite element model of convection in a spherical, axisymmetric shell is used to simulate upwelling thermal plumes in the mantle, and the effect of temperature-dependent viscosity on the structure of new plumes originating at the core-mantle boundary is investigated.
58 citations
Patent•
[...]
08 Jul 1997
TL;DR: A spherical puzzle toy as mentioned in this paper consists of two semi-spherical shells turned on an axis relative to each other, a plurality of partition panels mounted around the spherical shell and defining three intersected tracks along the spherical base along the X,Y and Z axes, where the intersections of the tracks are switched to one another to change the combination of the slides.
Abstract: A spherical puzzle toy includes a spherical shell, which consists of two semi-spherical shells turned on an axis relative to each other, a plurality of partition panels mounted around the spherical shell and defining three intersected tracks around the spherical base along the X,Y and Z axes, and a plurality of slides marked with different marks and moved in the intersected tracks, and wherein the intersected tracks are switched to one another to change the combination of the slides by turning the semi-spherical shells relative to each other.
53 citations
TL;DR: In this paper, the application of coupled Lagrangian-Eulerian analysis to various types of underwater shock problems was investigated, with the verification and validation of this analysis approach in mind.
Abstract: The application of coupled Lagrangian—Eulerian analysis to various types of underwater shock problems was investigated, with the verification and validation of this analysis approach in mind. Analyses were conducted for a simple TNT detonation problem and for the classical problems of an infinite cylindrical shell and a spherical shell loaded by a plane acoustic step wave. The advantages, disadvantages, and limitations of this approach are identified and discussed.
52 citations
TL;DR: In this paper, it was shown that the growth rate of the instability is approximately proportional to the perturbation amplitude and the rotation rate of a rotating fluid contained in a thick spherical shell, and that in the absence of dissipation the e-folding time for growth would be on the order of several thousand years.
44 citations
TL;DR: In this paper, a constant-density electrically conducting fluid is confined to a rapidly rotating spherical shell and is permeated by an axisymmetric potential magnetic field with dipole parity; the regions outside the shell are rigid insulators.
Abstract: Constant-density electrically conducting fluid is confined to a rapidly rotating spherical shell and is permeated by an axisymmetric potential magnetic field with dipole parity; the regions outside the shell are rigid insulators. Slow steady
axisymmetric motion is driven by rotating the inner sphere at a slightly slower rate. Linear solutions of the governing magnetohydrodynamic equations are derived in the small
Ekman number E -limit for values of the Elsasser number Λ less than order unity. Attention is restricted to the mainstream outside the Ekman–Hartmann layers adjacent to the inner and outer boundaries.
44 citations
TL;DR: In this article, the Casimir energy or stress due to modes in a $D$-dimensional volume subject to TM (mixed) boundary conditions on a bounding spherical surface is calculated.
Abstract: The Casimir energy or stress due to modes in a $D$-dimensional volume subject to TM (mixed) boundary conditions on a bounding spherical surface is calculated. Both interior and exterior modes are included. Together with earlier results found for scalar modes (TE modes), this gives the Casimir effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a spherical shell. Known results for three dimensions, first found by Boyer, are reproduced. Qualitatively, the results for TM modes are similar to those for scalar modes: Poles occur in the stress at positive even dimensions, and cusps (logarithmic singularities) occur for integer dimensions $Dl~1$. Particular attention is given the interesting case of $D=2$.
43 citations
TL;DR: In this paper, the authors compare a Fourier-based pseudospectral (Fourier-PS) implementation with one using spherical harmonics for convective flows over a sphere or within a spherical shell.
Abstract: For modeling convective flows over a sphere or within a spherical shell, pseudospectral (PS) methods are in general far more cost-effective than finite difference- (or finite element) methods. This study confirms this, and proceeds by comparing a Fourier-PS implementation (based on a longitude-latitude grid) with one using spherical harmonics. For similar resolutions, these are found to be of similar accuracy. However, the former is computationally about ten times faster.
37 citations
TL;DR: In this article, the authors used direct numerical simulation of a thermally driven MHD Boussinesq flow in a rotating spherical shell to investigate the generation and reversals of the magnetic field.
Abstract: The generation and reversals of the magnetic field are investigated by the use of direct numerical simulation of a thermally driven MHD Boussinesq flow in a rotating spherical shell. Moderately strong magnetic field, the energy of which is 30% of the kinetic, is generated in a thermal convection field composed of five pairs of cyclonic and anti-cyclonic vortex columns. The dipole moment of the magnetic field aligns with the rotation axis of the shell most of the time, and changes the direction almost periodically. The magnetic field itself is also reversed simultaneously. The intensity of the dipole moment becomes weak at the transition times.
01 Jan 1997
TL;DR: In this article, the authors proposed a quasi-static approach to estimate the in-plane and interlaminar normal and shear stresses in composite plate cylindrical/spherical shell panels subjected to low velocity impact.
TL;DR: In this article, the problem of magnetic field generation by fluid motions driven by thermal buoyancy in a rotating spherical shell is considered, and particular attention is devoted to questions of numerical convergence and of sequences of bifurcations.
Abstract: The problem of magnetic field generation by fluid motions driven by thermal buoyancy in a rotating spherical shell is considered. In extension of earlier work on this problem particular attention is devoted to questions of numerical convergence and of sequences of bifurcations. Finite amplitude convection and nonlinear dynamo solutions are found at Rayleigh numbers below the critical value for the onset of convection. Chaotic solutions appear to be preferred in large regions of the parameter space of the problem.
TL;DR: In this paper, a spherical shell model is invoked to treat the nuclear potential, where the nuclear and core charges are smeared out into a shell of constant surface charge density and the valence electron distribution and the electrostatic potential are efficiently computed by integration of the Thomas-Fermi equation, subject to the shell boundary conditions.
Abstract: We study C${}_{60}$ with the use of the March model [N. H. March, Proc. Camb. Philos. Soc. 48, 665 (1952)]. A spherical shell model is invoked to treat the nuclear potential, where the nuclear and core charges are smeared out into a shell of constant surface charge density. The valence electron distribution and the electrostatic potential are efficiently computed by integration of the Thomas-Fermi equation, subject to the shell boundary conditions. Total energy is numerically calculated over a range of shell radii, and the mechanical stability of the model is explored with attention to the constraints of Teller's theorem [E. Teller, Rev. Mod. Phys. 34, 627 (1962)]. The calculated equilibrium radius of the shell is in fair agreement with experiment.
TL;DR: In this paper, a convoluted pattern of streamlines in a steady state of thermal convection of a Boussinesq fluid between two concentric spheres rotating with a common angular velocity is investigated numerically at Rayleigh number 3200, Taylor number 8000, Prandtl number 1, and the radius ratio 0.5 of the two spheres.
Abstract: A convoluted pattern of streamlines in a steady state of thermal convection of a Boussinesq fluid between two concentric spheres rotating with a common angular velocity is investigated numerically at Rayleigh number 3200, Taylor number 8000, Prandtl number 1, and the radius ratio 0.5 of the two spheres. Five pairs of Taylor - Proudman vortex columns with opposite rotation are generated alternately arranged parallel to the axis of rotation across the middle of the equatorial plane of the spherical shell. These vortex columns retrograde at a constant angular velocity. The flow field is steady in a frame rotating with this angular velocity. The velocity field is symmetric with respect to the equatorial plane. Three kinds of non-trivial closed streamlines which turn once around the rotating axis of the spheres and seven different kinds of non-trivial stagnation points of velocity are found in the steady-flow frame. The entangled topological structure of the velocity field is resolved by observation of closed streamlines and streamlines emanating from stagnation points.
TL;DR: In this paper, the authors investigated the gross structural properties of Ne, Mg, Si, S, Ar and Ca nuclei, starting from the proton-drip line till the neutron drip-line.
Abstract: We have investigated the gross structural properties of Ne, Mg, Si, S, Ar and Ca nuclei, starting from the proton-drip line till the neutron drip-line. An axially deformed self-consistent relativistic mean-field approach is used. All possible shapes (prolate, oblate or spherical) are searched, using three sets of force parameter, the NL2, NL-SH and TM2. Agreement between the calculation and experiment is found to be good, particularly for the TM2 force parameters. We find a sizeable deformation of the neutron/proton-rich Ne and Mg isotopes near the drip lines. Also, deformations of nuclei at and near the spherical magic shell N=28 are found to be large, in agreement with experiments. The breaking/non-breaking of the spherical shell gap at N=28 is also observed, dependent on the choice of force parameters and pairing strength. A large number of cases of shape coexistence are identified. The effects of pairing strength on the calculated properties are also discussed.
TL;DR: In this paper, the authors show that the flow pattern of the convection in a spherical shell at relatively low Ra, at least, less than lo6, is characterized by narrow upwelling and broad downwelling, which is similar to the opposite flow patterns of internally heated convection.
Abstract: SUMMARY Recent studies on the relationship between the Nusselt (Nu) and Rayleigh (Ra) numbers for base-heated convection in a spherical shell with a constant viscosity show that the power-law index is around 114, which is different from the value of 1 I3 predicted by a simple boundary layer theory. We show that such a difference may be caused by the flow pattern due to the geometry. The flow pattern of the convection in a spherical shell at relatively low Ra, at least, less than lo6, is characterized by narrow upwelling and broad downwelling, which is similar to the opposite flow pattern of internally heated convection. Convection in the internally heated case predicts the power-law index of 114. We demonstrate this relationship based on the concept of ‘local’ Rayleigh (Ral) and Nusselt (Nul) numbers
TL;DR: Thin shallow spherical shell theory is used to derive the general influence function, owing to uniform and/or discrete (actuators) loads, for a thin shallow meniscus-shaped mirror of uniform thickness with a central hole and supported at discrete points.
Abstract: Thin shallow spherical shell theory is used to derive the general influence function, owing to uniform and/or discrete (actuators) loads, for a thin shallow meniscus-shaped mirror of uniform thickness with a central hole and supported at discrete points. Small elastic deformations are considered. No symmetry on the load distribution constrains the model. Explicit analytical expressions of the set of equations are given for calculating the influence functions. Results agree with the finite element analysis (FEA) to within 1%. When the FEA requires megabytes of RAM memory, the analytical method needs only kilobytes and typically runs 30 times faster. This is a crucial advantage for the iterative optimization of mirror supports such as large passive or active meniscus-shaped primary mirror supports or Cassegrain/Gregorian adaptive secondary actuator configurations. References are given on estimating the shear effects (thick mirror), the thickness variation effect, and the influence of the size of the support pads.
Patent•
15 Oct 1997
TL;DR: In this paper, a spherical shell body moving apparatus is provided with an inversion preventing means mounted on the traveling body while being positioned in proximity to or in contact with the internal of the spherical body.
Abstract: PROBLEM TO BE SOLVED: To eliminate the unmovable state of a spherical shell body which enables returning of a traveling body to the normal attitude even when the attitude of the traveling body is worsened with respect to the spherical shell body to turn itself top side down. SOLUTION: This spherical shell body moving apparatus 8 is provided with a spherical shell body 9 freely rotatable with respect to the ground plane and a traveling body 10 which is arranged in the spherical shell body 9 to have a drive wheel 14 being in contact with the internal surface of the spherical shell body 9 and makes it run relatively with respect to the spherical shell body 9 to roll the spherical shell body. An inversion preventing means 11 is mounted on the traveling body 10 while being positioned in proximity to or in contact with the internal of the spherical shell body 9 opposite to the center of gravity of the traveling body sandwiching the center of the spherical shell body 9 to prevent the inversion of the traveling body 10 within the spherical shell body. COPYRIGHT: (C)1999,JPO
TL;DR: In this article, the authors analyzed the acoustic scattering by two fluid-filled spherical elastic shells in close proximity to each other and insonified by plane waves at arbitrary angles of incidence.
Abstract: The acoustic scattering by two fluid-filled spherical elastic shells in close proximity to each other and insonified by plane waves at arbitrary angles of incidence is analyzed exactly in the frequency range that includes the midfrequency or coincidence enhancement region of the backscattered echoes. The incident and scattered wave fields are expanded in terms of the classical modal series and the addition theorem for the spherical wave functions is used to determine the exact expression for 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 found by simultaneously solving the Helmholtz equations governing the wave motion in the fluid medium in which the two shells are submerged as well as in the fluid media contained in the shells, together with the two sets of equations of motion of the two elastic shells obtained from the complete three-dimensional elasticity theory after satisfying the boundary conditions at all fluid-shell interfaces as well as the far-field radiation condition. Again, the numerical computation of the scattered pressure wave involves the solution of a truncated 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. Backscattered and bistatic echoes from two identical spherical elastic shells are extensively calculated. The result also exhibits the large enhancement present in the backscattered echoes for the endfire situation after the midfrequency or coincidence enhancement has taken place. This can be attributed to the effects of focusing by the front elastic shell and to the reflection and refocusing by the back elastic shell of the a0 Lamb wave reradiation in the observer’s direction.
TL;DR: In this article, the onset of convection in a rotating, gravitationally unstable spherical fluid layer bounded above or below by a stable spherical corotating layer is investigated, showing that convective motions penetrate from the unstable layer all the way through the outermost stable layer with nearly the same amplitude as in the underlying unstable layer.
Abstract: The onset of penetrative convection in a rotating, gravitationally unstable spherical fluid layer bounded above or below by a stable spherical corotating layer is investigated. Rapid rotation and spherical geometry produce new phenomena in the context of penetrative convection that are fundamentally different from what has been observed in the well-studied plane-layer model. In a slowly rotating or nonrotating spherical system, the character of penetration is qualitatively similar to that in plane fluid layers. In a rapidly rotating spherical system with a spherical layer of stable fluid bounded above by an unstable spherical layer, the stable fluid prevents penetration of convection across the interface between the stable and unstable spherical layers. In the reciprocal situation, however, when a spherical layer of stable fluid is bounded below by an unstable spherical layer, convective motions penetrate from the unstable layer all the way through the outermost stable layer with nearly the same amplitude as in the underlying unstable layer. The phenomena can be explained as a direct consequence of the combined effects of rapid rotation and spherical layer geometry.
TL;DR: In this paper, an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D was shown to lower the effective bending elasticity of the walls and induce spontaneous symmetry breaking, i.e. bending.
Abstract: We apply results derived in other contexts for the spectrum of the Laplace operator in curved geometries to the study of an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D and conclude that the free energy compared to its value for an uncurved box of the same thickness and volume is lower when D 3. Thus, confining an ideal polymer chain to a cylindrical shell lowers the effective bending elasticity of the walls and might induce spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned results show that any shell in D = 3 induces this effect, except for a spherical shell.) We compute the contribution of this effect to the bending rigidities in the Helfrich free energy expression.
TL;DR: The method proposed here offers several advantages over 3-D Delaunay algorithms for finite-element mesh generation, and is the method of choice for the related problem of trivariate scattered data interpolation.
Abstract: SUMMARY A new spherical mesh generator is described. It represents an efficient, deterministic packing of tetrahedra into a solid sphere, a spherical shell, or both. The mesh can be used for finite-element solutions to a wide variety of global numerical modelling problems in the geosciences. The nodes within the mesh are distributed uniformly, and long, thin tetrahedra are avoided. The method proposed here offers several advantages over 3-D Delaunay algorithms for finite-element mesh generation. For the related problem of trivariate scattered data interpolation, which is not considered here, the 3-D Delaunay algorithms are the method of choice.
TL;DR: In this article, the axi-symmetric free vibrations of an isotropic thin oblate spheroidal shell were investigated using a continuous function analytical formation, where the radii and opening angles of the spherical elements were chosen according to the eccentricity of the spheroid.
Patent•
21 Oct 1997
TL;DR: A rear view mirror coupling assembly as mentioned in this paper includes a glass carrier for supporting a mirror and including a spherical projection having a first spherical surface and a second spherical surface, a mirror drive housing, and a spherical shell disposed between and in contact with the spherical projection and the spherical recess, each of the contacting spherical surfaces being movable along at least one axis relative to the respective contacting spherical surface.
Abstract: A rear view mirror coupling assembly includes a glass carrier for supporting a mirror and including a spherical projection having a first spherical surface and a second spherical surface, a mirror drive housing including a mirror drive mechanism and including a spherical recess having a first surface, a spherical shell disposed between and in contact with the spherical projection and the spherical recess, the spherical shell having a first spherical surface contacting the second spherical surface of the spherical projection and a second spherical surface contacting the first surface of the spherical recess, a threaded bolt having a distal end and a head including a spherical underside surface in contact with the first spherical surface of the glass carrier, a threaded nut threaded onto the distal end of the threaded bolt to secure the glass carrier, the spherical shell, and the mirror drive housing together, and a spring element tensioned by the nut for urging the glass carrier, the spherical shell, and the mirror drive housing together, each of the contacting spherical surfaces being movable along at least one axis relative to the respective contacting spherical surface to provide adjustment of the glass carrier relative to the mirror drive housing.
TL;DR: In this paper, a spherical shell model for turbulence, obtained by coupling N replicas of the Gledzer, Okhitani and Yamada shell model, is considered, and the rate of convergence to the K41 solution is linear in 1/N.
Abstract: A spherical shell model for turbulence, obtained by coupling N replicas of the Gledzer, Okhitani and Yamada shell model, is considered. Conservation of energy and of a helicity-like invariant is imposed in the inviscid limit. In the N → ∞ limit this model is analytically soluble and is remarkably similar to the random coupling model version of shell dynamics. We have studied numerically the convergence of the scaling exponents toward the value predicted by Kolmogorov theory (K41). We have found that the rate of convergence to the K41 solution is linear in 1/N. The restoring of Kolmogorov law has been related to the behaviour of the probability distribution functions of the instantaneous scaling exponent.
TL;DR: In this article, the static and dynamic buckling of polar orthotropic antisymmetrically laminated, moderately thick shallow spherical shells under uniformly distributed loading was studied and the governing equations of motion for shells undergoing large deformations were derived and expressed in terms of normal deflection W, slope ϑ and stress function Ψ.
TL;DR: In this article, free vibrations of a spherically isotropic spherical shell embedded in an elastic medium of Pasternak type are studied by using a sixmode shell theory that includes effects of shear deformation, rotary inertia, and transverse normal strain.
Abstract: In this paper, free vibrations of a spherically isotropic spherical shell embedded in an elastic medium of Pasternak type are studied by using a six-mode shell theory that includes effects of shear deformation, rotary inertia, and transverse normal strain. The separable homogeneous solution for displacements and stresses in a deep spherical shell is derived and two classes of vibrations are obtained by the introduction of five auxiliary variables. Numerical results are compared with those predicted by two simpler shell theories mentioned in the paper and those by three-dimensional elastic theory. Spherical and cylindrical shells are commonly used in practical engineering such as underground mining.
TL;DR: In this article, the boundary conditions of the Casimir energy of a conducting spherical shell were evaluated by imposing boundary conditions on the potential, and on the ghost fields, and the results showed that the ghost modes cancel exactly the contribution of transverse and temporal modes of the potential.
Abstract: The zero-point energy of a conducting spherical shell is evaluated by imposing boundary conditions on the potential, and on the ghost fields. The scheme requires that temporal and tangential components of perturbations of the potential should vanish at the boundary, jointly with the gauge-averaging functional, first chosen of the Lorenz type. Gauge invariance of such boundary conditions is then obtained provided that the ghost fields vanish at the boundary. Normal and longitudinal modes of the potential obey an entangled system of eigenvalue equations, whose solution is a linear combination of Bessel functions under the above assumptions, and with the help of the Feynman choice for a dimensionless gauge parameter. Interestingly, ghost modes cancel exactly the contribution to the Casimir energy resulting from transverse and temporal modes of the potential, jointly with the decoupled normal mode of the potential. Moreover, normal and longitudinal components of the potential for the interior and the exterior problem give a result in complete agreement with the one first found by Boyer, who studied instead boundary conditions involving TE and TM modes of the electromagnetic field. The coupled eigenvalue equations for perturbative modes of the potential are also analyzed in the axial gauge, and for arbitrary values of the gauge parameter. The set of modes which contribute to the Casimir energy is then drastically changed, and comparison with the case of a flat boundary sheds some light on the key features of the Casimir energy in non-covariant gauges.