Showing papers on "Spherical shell published in 1980"

Hitting Spheres with Brownian Motion

Abstract: Let $X_t$ be standard Brownian motion in $R^d$ starting at fixed $X_0$, and let $T$ be the hitting time for a sphere or concentric spherical shell. Explicit formulas, in terms of a natural Laplace-Gegenbauer transform, are obtained for the joint distribution of $T$ and $X_T$.

Zero-point energy in bag models

Abstract: The zero-point (Casimir) energy of free vector (gluon) fields confined to a spherical cavity (bag) is computed. The result is quadratically divergent, but it is argued that this divergence may be absorbed by a suitable renormalization of a constant force parameter. If so, the result for eight gluons is E=+0.51/a. This result is substantially larger than that for a spherical shell (where both interior and exterior modes are present), and so affects Johnson's model of the quantum-chromodynamic vacuum. It is also smaller than, and of opposite sign to, the value used in bag-model phenomenology, so it will have important implications there.

Infinite Prandtl number thermal convection in a spherical shell

Abstract: A Galerkin technique is used to calculate the steady-state axisymmetric nonlinear convective motions in an infinite-Prandtl-number Boussinesq fluid in a relatively thick spherical shell heated from below. A reasonably complete study of the properties of the even and general axisymmetric steady states is carried out for a range of moderately supercritical Rayleigh numbers. In addition, stability analyses are conducted to determine which form of axisymmetric steady convection is the preferred one and whether the axisymmetric steady flows are unstable to azimuthal perturbations.

Thermal convection of an internally heated infinite Prandtl number fluid in a spherical shell

Abstract: A Galerkin technique is used to study the finite-amplitude axisymmetric steady convective motions of an infinite Prandtl number Boussinesq fluid in a spherical shell. Two types of heating are considered: in one case, convection is driven both by internal heat sources in the fluid and by an externally imposed temperature drop across the shell boundaries; in the other case, only internal heat sources drive convection and the lower boundary of the shell is adiabatic. Two distinct classes of axisymmetric steady states are found to be possible: states characterized by temperature and radial velocity fields that are symmetric about an equatorial plane; and a class of solutions that does not possess any symmetry properties about the equatorial plane.

Perturbation theory and the thermodynamic properties of fluids. II. The CRIS model

Abstract: This paper is the second of three articles describing a hard sphere perturbation theory of liquids and dense gases. The general theory presented in the preceding paper is used to derive a model for calculating thermodynamic properties. Three approximations are made. First, we assume that each molecule is located at the center of a spherical shell formed by its neighbors. The radius of this shell varies throughout the fluid according to a distribution function which is known for hard spheres. Second, the coordination number varies along with the nearest neighbor distance in such a way that the volume per molecule is constant and equal to the macroscopic value. Third, the potential energy of a molecule in the field of its neighbors depends only on the nearest neighbor distance and coordination number. Using this approximation, the energy of a liquid molecule can be calculated from the zero‐temperature isotherm of the solid at the same nearest neighbor distance. There are no adjustable parameters in the theory. All that is needed to apply the model is the cold curve of the solid, which can be obtained from either theory or experiment.

Buckled states of a spherical shell under uniform external pressure

Abstract: A method is outlined to obtain the “preferred” buckled states of a (complete) spherical shell under uniform external pressure. The shell model investigated is that of the John equations, a system of six nonlinear partial differential equations. Methods in bifurcation theory and group representations are used to reduce the problem to a finite-dimensional problem whose solutions generate buckled states that are “preferred” in a certain least-energy sense. Asymptotic methods and Newton's method are used in some special cases to relate the “preferred” buckled states obtained by the above approach to actual buckled states observed in experimental studies.

Method of manufacturing a shaft structure having a spherical bulb

Abstract: A shaft structure comprising a shaft and a hollow spherical shell having diametrically aligned holes which are of a diameter smaller than the outer diameter of the shaft. The shell is secured to the shaft at the aligned holes by radially deforming the shaft. The method for manufacturing the shaft structure includes steps of forming the shell from a tubular blank by swaging the blank so that the opposite ends of the blank bite into the shaft to secure it firmly to the shaft.

Late time optical spectra from the Ni/sup 56/ model for Type I Supernovae

Abstract: A numerical model has been created that produces self-consistent optical spectra, temperatures, and ionization states for a homologously expanding spherical shell which at t = 0 is assumed to consist of pure Nickel 56, and is further assumed to have density independent of radius within the shell. A brief summary is given of the model, followed by some results from the calculations. (GHT)

The failure of rigid shell models for rotationally inelastic LiH–He collisions

Abstract: A simple rigid‐body model for rotationally inelastic LiH–He collisions has been implemented. This treatment assumes impulsive collisions between a point particle and a smooth spherical shell whose center is displaced from the center of mass of the LiH molecule. For a given collision energy the radius and displacement of the shell are adjusted for a best fit to the equipotential contour at this energy on the ab initio surface of D. M. Silver [J. Chem. Phys. 72, 6445(1980)]. Cross sections for transitions from the rotationless j=0 state to all possible final j′ states have been computed in a classical trajectory approach and have been compared to more accurate quantum coupled‐states values at Ecol=0.3 eV [E. F. Jendrek and M. H. Alexander, J. Chem. Phys. 72, 6452(1980)]. The results from this simple model differ drastically both in magnitude and their j′ dependence from those obtained in the more sophisticated treatment. While such rigid‐body models have been used in the analysis of inelastic scattering exp...

Collective Aspects of Atomic Dynamics

Abstract: We give a brief review of the theories describing collective dynamics of atoms, and comment on the hydrodynamic approach as well as the manybody approach based on RPA In particular we put forward a unified approach, combining the hydrodynamical and single-particle aspects in a single theoretical framework Some general aspects of the theory are discussed as well as a simple application to the oscillations of a spherical shell

Surface currents and RCS of a spherical shell with a circular aperture

Abstract: The electromagnetic scattering behavior of a perfectly conducting, infinitesimally thin, spherical shell with a circular aperture is studied. A time-harmonic plane wave is symmetrically incident upon the aperture. The problem is formulated in terms of the E -field integral equation. This produces two coupled integral equations for the tangential components of the currents on the scatterer surface. The equations are cast into matrix form by application of the method of moments, and expressions for the matrix elements are derived. Calculated values of the surface currents and radar cross sections, not previously available in the open literature, are presented and discussed for several cases of interest.

On large axisymmetrical deflection states of spherical shells

Abstract: A boundary layer analysis is carried out to determine the possible form of large axisymmetrical deflection states for thin elastic spherical shells subjected to uniform external pressure. For the case of complete spheres it is shown that the governing equations admit boundary layer solutions corresponding to large deflections provided the pressure is sufficiently small. However, such solutions are found to exist for nonshallow clamped spherical caps for a much wider range of pressure. Numerical results are presented for the latter case.

Axisymmetric free vibration of a submerged spherical shell

Abstract: Previous studies of the title problem have produced only partial solutions for this classical configuration. The present study shows how complete solutions are readily obtained from simple polynomial expressions. Numerical results in graphical form are presented for a steel shell submerged in water as functions of a parameter related to the shell’s thickness‐to‐radius ratio. It is found that descriptions based upon added‐mass and added‐damping perturbations of the shell’s in vacuo free‐vibration characteristics can be misleading.

Nonlinear Stability of Thin Elastic Circular Shallow Spherical Shell under the Action of Uniform Edge Moment

Abstract: In this paper, nonlinear stability of thin elastic circular shallow spherical shell under the action of uniform edge moment is considered by the modified iteration method to obtain second and third approximations to decide the upper and lower critical loads. Results are plotted in curves for the engineering use and are compared with results of Hu Hai-chang's. We also investigate the neighbour situation of the critical point, i.e. the double points of the upper and lower critical loads and denote the range of validity of the second approximation. In the end, we obtain the special case, the design formulas of rigidity and stress as well as the corresponding curves as ν=0.3 of large deflection of circular plate under the same load. These results are also compared with Huang Tse-yen's.

On the Transverse Twisting of Shallow Spherical Ring Caps

Abstract: : The problem of transverse twisting of a shallow spherical shell with a small circular hole is solved, in generalization of the corresponding problem of a flat plate. The solution is of interest as a closed-form solution of an unsymmetrical stress concentration problem, with quantitative features depending on its boundary layer behavior for large values of a relevant parameter. The problem is also of interest as an example of the applicability of a previously proposed asymptotic procedure where interior contributions and edge-zone contributoins are determined in sequence rather than simultaneously. (Author)

Tube penetration in the region of a spherical security shield of a nuclear power plant

Abstract: 1. Piping penetration in the area of the spherical containment for a nuclear power plant, consisting of a sleeve nozzle (8) which is welded into the wall (7) of the containment, and a pipe nozzle (6a) welded into the sleeve nozzle, the associated piping (14) being connected to the two ends of the pipe nozzle (6a), characterized in that the sleeve nozzle is designed as part of a spherical shell (8) welded around its periphery to the wall (7) of the containment (1), and that the pipe nozzle (6a) is welded into the shell part (8) in such a way that its axis (12) passes through the center point (13) of this shell.

On the propagation and stability of wave motions in rapidly rotating spherical shells: I. The non-magnetic case

Abstract: The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius η, are studied in the small Prandtl number limit. When η = 0, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and 0 for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of con...

Dependence of the magnitude of the critical load for a spherical shell on the properties of the material

Abstract: Problems of stability of structural elements made of composite materials have been studied within the framework of refined (Timoshenko type) engineering theories as well as by three-dimensional analysis. Earlier studies ([1-4] and several others) have dealt with some general problems on the basis of the three-dimensional linearized theory, considering also the deformation stability of reinforced materials and structural elements (beams, plates, and cylindrical shells) made of such materials. Successive application of three-dimensional equations makes it possible to rationally construct a theory and to devise methods of calculation for the deformation stability of structural elements made of composite materials. Furthermore, solutions to problems based on three-dimensional equations provide a yardstick for engineering methods of calculation and a gauge for estimating their accuracy and also a reference for defining the ranges of applicability of classical and refined engineering theories of stability. With this approach it is possible to analyze, in the exact formulation of the problem, the dependence of the magnitude of critical loads on the properties of the material and to formulate recommendations for engineering design methods. Thus, the obtained specific results can then be useful for structural optimization of three-dimensionally reinforced composites in problems of stability involving elements of structures [5].

Oxidation preventing method in tank annealing process

Abstract: PURPOSE:To prevent oxidation due to intrusion of external air when lowering the temperature, by discharging the combustion gas in the tank by substituting with inert gas before and after stopping of annealing and heating to lower the temperature of and shrink the tank CONSTITUTION:The gas supplied from a gas pipe 6 is burned together with the external air intruded from a manhole duct 7 by a burner 5 provided in the lower part of a spherical shell 2 The combustion gas circulates almost completely in the spherical shell 2 as indicated by arrow A, heating and annealing the spherical shell 2 to the specified temperature, eg about 600 degC, and the gas is exhausted to the atmosphere from an upper manhole 8 sequentially by the quantity corresponding to the supplied gas capacity At the end of specified annealing, simultaneously with extinction of the burner 5, a valve 11 of the duct 7 is closed, and a valve 10 of N2 gas supply pipe 9 is opened The internal combustion residual gas P1 is exhausted properly outside of the system from the manhole 8, and the inside of the spherical shell 2 is gradually substituted with N2 gas P2, so that oxidation of the spherical shell 2 due to high temperature never occurs When the spherical shell 2 is cooled to ordinary temperature, the filling N2 gas is naturally substituted with external air, and the interior surface of the spherical shell 2 is painted

The darmstadt-heidelberg crystal ball

Abstract: A modularized NaI detector with close to 4π geometry can provide unique information on the decay γ-radiation from highly excited nuclei. GSI Darmstadt, the Max-Planck-Institute (MPI) for Nuclear Physics and the University of Heidelberg have joined in a collaboration to realize such a detector. The detector has the shape of a spherical shell with a free inner radius of 25 cm and a thickness of 20 cm and comprises 162 individual modules of equal solid angle. This contribution explains our special choice of configuration and gives an outline of the present status of the mechanical and electronic assembly.