Showing papers on "Spherical shell published in 2000"

Shell corrections of superheavy nuclei in self-consistent calculations

Abstract: Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nuclei are studied within the self-consistent Skyrme-Hartree-Fock and relativistic mean-field theories. As a result of the presence of a low-lying proton continuum resulting in a free particle gas, special attention is paid to the treatment of the single-particle level density. To cure the pathological behavior of the shell correction around the particle threshold, a method based on the Green's function approach has been adopted. It is demonstrated that for the vast majority of Skyrme interactions commonly employed in nuclear structure calculations, the strongest shell stabilization appears for Z=124 and 126, and for N=184. On the other hand, in the relativistic approaches the strongest spherical shell effect appears systematically for Z=120 and N=172. This difference probably has its roots in the spin-orbit potential. We have also shown that, in contrast to shell corrections which are fairly independent of the force, macroscopic energies extracted from self-consistent calculations strongly depend on the actual force parametrization used. That is, the A and Z dependence of the mass surface when extrapolating to unknown superheavy nuclei is prone to significant theoretical uncertainties. (c) 2000 The American Physical Society.

Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum

Abstract: We investigate the asymptotic properties of inertial modes confined in a spherical shell when viscosity tends to zero. We first consider the mapping made by the characteristics of the hyperbolic equation (Poincare's equation) satisfied by inviscid solutions. Characteristics are straight lines in a meridional section of the shell, and the mapping shows that, generically, these lines converge towards a periodic orbit which acts like an attractor. We then examine the relation between this characteristic path and eigensolutions of the inviscid problem and show that in a purely two-dimensional problem, convergence towards an attractor means that the associated velocity field is not square-integrable. We give arguments which generalize this result to three dimensions. We then consider the viscous problem and show how viscosity transforms singularities into internal shear layers which in general betray an attractor expected at the eigenfrequency of the mode. We find that there are nested layers, the thinnest and most internal layer scaling with $E^{1/3}$-scale, $E$ being the Ekman number. Using an inertial wave packet traveling around an attractor, we give a lower bound on the thickness of shear layers and show how eigenfrequencies can be computed in principle. Finally, we show that as viscosity decreases, eigenfrequencies tend towards a set of values which is not dense in $[0,2\Omega]$, contrary to the case of the full sphere ($\Omega$ is the angular velocity of the system). Hence, our geometrical approach opens the possibility of describing the eigenmodes and eigenvalues for astrophysical/geophysical Ekman numbers ($10^{-10}-10^{-20}$), which are out of reach numerically, and this for a wide class of containers.

Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

Abstract: The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, 32Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in 44 S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2+ excitation energy Ex = 1.46 MeV and the reduced transition probability B(E2;0+ gs→ 2+ 1)= 420 e 2 fm 4 obtained with our approach are in good agreement with experimental data.

Combined differential‐integral approach for the radiation field computation in a spherical shell atmosphere: Nonlimb geometry

Abstract: A new combined differential-integral approach (CDI) has been developed, which is more accurate than commonly used pseudospherical models but not so complicated and computer time-consuming as a fully spherical model. The radiative transfer equation is solved in its integral form. The multiple-scattering source function is obtained by solving the integrodifferential radiative transfer equation in a pseudospherical atmosphere. Relative differences between the new model and the pseudospherical model for a variety of solar zenith angles, viewing angles, and azimuth angles for a set of wavelengths are presented. Furthermore, the GDI model is compared with a Gauss-Seidel spherical model (GSS) and with MODTRAN. The difference between GDI and GSS is found to be less than 2% and between GDI and MODTRAN up to 12%.

Constitutive functions of elastic materials in finite growth and deformation

Abstract: The constitutive functions of soft biological tissues during growth are studied. A growth, treated as addition (often non-uniform) of material points, results in deformation, residual stresses, and evolution of the constitutive functions. A theory based on the concept of equivalent material points is developed with the current configuration taken as the reference. The residual stresses developed in a spherical shell undergoing spherical growths are studied.

Hemispherical dynamos generated by convection in rotating spherical shells

Abstract: At Taylor numbers of the order ${10}^{8}$ and Prandtl numbers of the order 1, dynamos generated by convection are found for which the magnetic field is essentially confined to either the northern or the southern hemisphere of a rotating spherical shell. The time dependence is typically chaotic, but latitudinal waves can be discerned that cause the magnetic field to change its polarity in a cyclical fashion. A possible relationship to a solar phenomenon is pointed out.

Geoelectromagnetic induction in a heterogeneous sphere:a new three‐dimensional forward solver using a conservative staggered‐grid finite difference method

Abstract: SUMMARY conservative staggered-grid finite diVerence method is presented for computing the electromagnetic induction response of an arbitrary heterogeneous conducting sphere by external current excitation. This method is appropriate as the forward solution for the problem of determining the electrical conductivity of the Earth’s deep interior. This solution in spherical geometry is derived from that originally presented by Mackie et al. (1994) for Cartesian geometry. The diVerence equations that we solve are second order in the magnetic field H, and are derived from the integral form of Maxwell’s equations on a staggered grid in spherical coordinates. The resulting matrix system of equations is sparse, symmetric, real everywhere except along the diagonal and illconditioned. The system is solved using the minimum residual conjugate gradient method with preconditioning by incomplete Cholesky decomposition of the diagonal sub-blocks of the coeYcient matrix. In order to ensure there is zero H divergence in the solution, corrections are made to the H field every few iterations. In order to validate the code, we compare our results against an integral equation solution for an azimuthally symmetric, buried thin spherical shell model (Kuvshinov & Pankratov 1994), and against a quasi-analytic solution for an azimuthally asymmetric configuration of eccentrically nested spheres (Martinec 1998).

Donor states in a multi-layered quantum dot

Abstract: The ground and excited state energies of a hydrogenic impurity located at the centre of a multi-layered quantum dot (MLQD) are calculated in the framework of the effective-mass approximation. The MLQD consists of a spherical core (e.g. GaAs) and a coated spherical shell (e.g. Ga1-xAlxAs). The whole dot is then embedded inside a bulk material (e.g. Ga1-yAlyAs). We solve the Schrodinger equation exactly. The eigenfunctions of the impurity are expressed in terms of Whittaker function and Coulomb wavefunction. The state energies are expressed in terms of the shell thickness, core radius, total dot radius and the potential heights. Our calculation shows that, as the dot radius approaches infinity, the state energies of an impurity located at the centre of a multi-layered or a single-layered QD approach -1/n2 Ry, where n is the principal quantum number, Ry = µe4/2e22, µ and e are the electronic effective mass and the dielectric constant of GaAs material. Thus it behaves like a three-dimensional free hydrogen atom. For very small dot radius, however, the state energy of the hydrogenic impurity of a MLQD behaves very differently from that of a single-layered QD. For a multi-layered QD with finite shell and bulk potential barrier heights, the state energies of the impurity are found to be dependent on the difference of the shell potential (V2) and the bulk potential (V3).

Casimir Effect for Spherical Shell in de Sitter Space

Abstract: The Casimir stress on a spherical shell in de Sitter background for massless scalar field satisfying Dirichlet boundary conditions on the shell is calculated. The metric is written in conformally flat form. Although the metric is time dependent no particles are created. The Casimir stress is calculated for inside and outside of the shell with different backgrounds corresponding to different cosmological constants. The detail dynamics of the bubble depends on different parameter of the model. Specifically, bubbles with true vacuum inside expand if the difference in the vacuum energies is small, otherwise they collapse.

Lighted ball toy

Abstract: A ball toy has an inner spherical shell within an outer spherical shell, a light source being mounted within the inner shell adjacent to a first end of a plurality of etched optical fibers having the other ends arrayed between the inner and outer shells. The outer shell is translucent while the inner shell has a coated outer surface that reflects light from the optical fibers. Between the light source and the first end of the optical fibers is a color chamber having different color elements through which light may be transmitted and which may move when the ball moves so as to vary the colors received by the optical fibers thereby effecting variation in the color seen as the ball rolls or is otherwise moved, the light seen at the translucent shell fluctuating according to the colors transmitted. A motion switch and/or a master switch may be used to turn the system on and off. A timer may deactivate the circuits if the ball is not moved after a period of time.

Modeling Foam Growth in Thermoplastics

Abstract: Foaming of thermoplastic polymers is a complex process. Here models are presented that address the viscoelastic character of the thermoplastic melt during the expansion phase of foam development. Each cell is described as consisting of a spherical gas bubble surrounded by a spherical shell of polymer containing dissolved gas (see Figure).

Magnetohydrodynamic flows in spherical shells

Abstract: After reviewing the derivation of the equations governing the evolution of magnetic fields in electrically conducting fluids, I consider two largely distinct classes of such phenomena in spherical shells. The first is kinematic dynamo theory, in which a flow is prescribed, and one searches for self-excited magnetic fields. The second is magnetic Couette flow, in which a magnetic field is imposed, and one solves for the flow and the induced field. In both cases existing results are reviewed; in the latter case some new results are also presented.

Ekman layers and the damping of inertial r-modes in a spherical shell: application to neutron stars

Abstract: Recently, eigenmodes of rotating fluids, namely inertial modes, have received much attention in relation to their destabilization when coupled to gravitational radiation within neutron stars. However, these modes have been known for a long time by fluid dynamicists. We give a short account of their history and review our present understanding of their properties. Considering the case of a spherical container, we then give the exact solution of the boundary (Ekman) layer flow associated with inertial r-modes and show that previous estimations all underestimated the dissipation by these layers. We also show that the presence of an inner core has little influence on this dissipation. As a conclusion, we compute the window of instability in the Temperature/rotation plane for a crusted neutron star when it is modeled by an incompressible fluid.

Stokes flow inside a porous spherical shell

Abstract: Stokes flow of a viscous, incompressible fluid inside a sphere with internal singularities, enclosed by a porous spherical shell, using Darcy's law for the flow in the porous region is discussed. The formulae for drag and torque are found by deriving the corresponding Faxen's laws. It is found that torque does not depend on the thickness of the spherical shell.

Mobility of a microgravity rover using internal electro-magnetic levitation

Abstract: A new type of mobility is discussed for space projects such as the MUSES-C aiming at small asteroid exploration. We propose the use of electro-magnetic levitation in order to integrate a mobility into the microgravity rover. The rover has a spherical shape and a smaller spherical shell inside. Four electromagnets are symmetrically located between the outer sphere surface and the inner sphere shell with one end of each directed to the center of the shell. With electromagnetic force of the magnets, a sphere iron ball inside the shell is controlled and levitated. When the rover lifts the ball inside with the electro-magnetic force, the rover is in return pressed down the ground by the reaction force, due to which the rover system not only gains upward momentum for floatation, but also obtains friction that enables its rolling on the ground. The prototype microgravity rover was developed and experimental results indicate effectiveness of the proposed mobility.

Axisymmetric dynamics of composite spherical shells with active piezoelectric/composite stiffeners

Abstract: The paper presents a theoretical formulation for spherical shells reinforced by meridional and circumferential stiffeners Active damping of the shell is introduced through control action of piezoelectric coupled pairs bonded to the meridional stiffeners The induced loads can include radial pressure and a thermal field that are independent of the circumferential coordinate Neglecting local deformations between adjacent meridional stiffeners, the response of the shell will be axisymmetric The analysis employs the Donnell-Mushtari-Vlasov version of Love's theory of shells together with a smeared stiffeners technique The paper also considers a particular case of shell mounted piezoelectic coupled pairs without conventional stiffeners A closed form solution is derived for spherical panels without conventional stiffeners within the range of the meridional coordinate between 75° and 90° using a version of the Geckeler approximation

Resonance suppression of a spherical electromagnetic shielding enclosure by using conductive dielectrics

Abstract: The resonance suppression for the electromagnetic shielding enclosure is theoretically investigated. A simple model of a double-layered spherical shell with a plane-wave illumination is assumed. When a spherical shell made of conductive dielectrics is covered with a thin metal layer, the conductivity of the dielectrics has an optimum value which minimizes the Q-factor at the fundamental resonant frequency. The optimum conductivity is shown to be a function of the resonant frequency and the thickness of the dielectric layer. The improvement of the shielding effectiveness by introducing the optimum conductivity is shown.

Stress distribution in a rotating elastic functionally graded material hollow sphere with spherical isotropy

Abstract: The stress distribution in a rotating, spherically isotropic, functionally graded material (FGM) spherical shell that has its elastic constants and mass density as functions of the radial coordinate is exactly investigated in the paper. Three displacement functions are employed to simplify the basic equations of equilibrium for a spherically isotropic, radially inhomogeneous elastic medium. By expanding the displacement functions in terms of spherical harmonics, the basic equations are finally turned into an uncoupled second-order ordinary differential equation and a coupled system of two such equations. Exact analysis of a steadily rotating spherical shell with the material constants being power functions of the radial coordinate is carried out and a numerical example is presented.

Nano-sized ceramics of coated alumina and zirconia analyzed with SANS

Abstract: The sintering behaviour of two new types of coated ceramics, made from alumina grains coated with a zirconia shell and from zirconia grains coated with an alumina shell, was analyzed with small angle neutron scattering (SANS). Measurements were performed both for the plain samples, and with contrast variation using D 2 O as immersion liquid. The size distribution and the volume fraction of grains and pores were determined from the corrected scattering curves using a direct model fitting, applying two different approaches, a sphere model and a combined sphere/spherical shell model. Results are discussed in context with the macroscopic density of the samples. The sintering behaviour of the two ceramics types was found to be very different.

Spherical Oscillatory α2 Dynamo Induced by Magnetic Coupling between a Fluid Shell and an Inner Electrically Conducting Core: Relevance to the Solar Dynamo

Abstract: A two-layer spherical α2 dynamo model consisting of an inner electrically conducting core (magnetic diffusivity λi and radius ri) with α = 0 surrounded by an electrically conducting spherical shell (magnetic diffusivity λo and radius ro) with a constant α is shown to exhibit oscillatory behavior for values of β = λi/λo and ri/ro relevant to the solar dynamo. Time-dependent dynamo solutions require ri/ro ≥ 0.55 and β ≤ O(1). For the Sun, ri/ro is about 0.8 and β ≈ 10-3. The timescale of the oscillations matches the 22 yr period of the sunspot cycle for λ0 = O(102 km2 s-1). It is unnecessary to hypothesize an α-ω dynamo to obtain oscillatory dynamo solutions; an α2 dynamo suffices provided the spherical shell region of dynamo action lies above a large, less magnetically diffusive core, as is the case for the solar dynamo.

Three-dimensional elasticity solutions of laminated annular spherical shells

Abstract: An asymptotic theory is presented for the analysis of laminated annular spherical shells by the perturbation method. By means of proper nondimensionalization, asymptotic expansion, and then successive integration of the basic equations through the thickness direction, we obtain the recursive sets of governing equations for the bending analysis of annular spherical shells. The method of differential quadrature is adopted for solving the problems of various orders. Illustrative examples are given to demonstrate the performance of the present asymptotic theory.