Showing papers on "Spherical shell published in 2007"

The tensor part of the Skyrme energy density functional. I. Spherical nuclei

Abstract: We perform a systematic study of the impact of the ${\mathbf{J}}^{2}$ tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate from both zero-range central and tensor forces. We build a set of 36 parametrizations, covering a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants with a fit protocol very similar to that of the successful SLy parametrizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of radii. The major findings of our study are as follows: (i) Tensor terms should not be added perturbatively to existing parametrizations; a complete refit of the entire parameter set is imperative. (ii) The free variation of the tensor terms does not lower the ${\ensuremath{\chi}}^{2}$ within a standard Skyrme energy functional. (iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead to instabilities of the spherical shell structure, or even to the coexistence of two configurations with different spherical shell structures. (iv) The standard spin-orbit interaction does not scale properly with the principal quantum number, such that single-particle states with one or several nodes have too large spin-orbit splittings, whereas those of nodeless intruder levels are tentatively too small. Tensor terms with realistic coupling constants cannot cure this problem. (v) Positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of spin-orbit splittings in chains of Ca, Ni, and Sn isotopes. (vi) For the same values of the tensor term coupling constants, however, the overall agreement of the single-particle spectra in doubly-magic nuclei is deteriorated, which can be traced back to features of the single-particle spectra that are not related to the tensor terms. We conclude that the currently used central and spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the presence of large tensor terms.

The design and simulated performance of a coated nano-particle laser

Abstract: The optical properties of a concentric nanometer-sized spherical shell comprised of an (active) 3-level gain medium core and a surrounding plasmonic metal shell are investigated. Current research in optical metamaterials has demonstrated that including lossless plasmonic materials to achieve a negative permittivity in a nano-sized coated spherical particle can lead to novel optical properties such as resonant scattering as well as transparency or invisibility. However, in practice, plasmonic materials have high losses at optical frequencies. It is observed that with the introduction of active materials, the intrinsic absorption in the plasmonic shell can be overcome and new optical properties can be observed in the scattering and absorption cross-sections of these coated nano-sized spherical shell particles. In addition, a “super” resonance is observed with a magnitude that is 103 greater than that for a tuned, resonant passive nano-sized coated spherical shell. This observation suggests the possibility of realizing a highly sub-wavelength laser with dimensions more than an order of magnitude below the traditional half-wavelength cavity length criteria. The operating characteristics of this coated nano-particle (CNP) laser are obtained numerically for a variety of configurations.

Collapse of the N=28 shell closure in (42)Si.

Abstract: The energies of the excited states in very neutron-rich Si-42 and P-41,P-43 have been measured using in-beam gamma-ray spectroscopy from the fragmentation of secondary beams of S-42,S-44 at 39A MeV. The low 2(+) energy of Si-42, 770(19) keV, together with the level schemes of P-41,P-43, provides evidence for the disappearance of the Z=14 and N=28 spherical shell closures, which is ascribed mainly to the action of proton-neutron tensor forces. New shell model calculations indicate that Si-42 is best described as a well-deformed oblate rotor.

Vibration analysis of spherical structural elements using the GDQ method

Abstract: This paper deals with the dynamical behaviour of hemispherical domes and spherical shell panels. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic. The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and the congruence relationships. The boundary conditions considered are clamped (C), simply supported (S) and free (F) edge. Numerical solutions have been computed by means of the technique known as the Generalized Differential Quadrature (GDQ) Method. These results, which are based upon the FSDT, are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Engineer, which also elaborate a three-dimensional analysis. The effect of different grid point distributions on the convergence, the stability and the accuracy of the GDQ procedure is investigated. The convergence rate of the natural frequencies is shown to be fast and the stability of the numerical methodology is very good. The accuracy of the method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions.

Negative axial radiation forces on solid spheres and shells in a Bessel beam.

Abstract: Prior computations predict that fluid spheres illuminated by an acoustic Bessel beam can be subjected to a radiation force directed opposite the direction of beam propagation. The prediction of negative acoustic radiation force is extended to the cases of a solid poly(methylmethacrylate) PMMA sphere in water and an empty aluminum spherical shell in water. Compared with the angular scattering patterns for plane wave illumination, the scattering into the back hemisphere is suppressed when the radiation force is negative. This investigation may be helpful in the development of acoustic tweezers and in the development of methods for manipulating objects during space flight.

At and below the chu limit: passive and active broad bandwidth metamaterial-based electrically small antennas

Abstract: The solution to the canonical problem of a radiating infinitesimal electric dipole antenna that is centred in a multilayered, concentric metamaterial-based spherical shell system is presented. It is demonstrated that when this system is electrically small, a specifically designed homogenous and isotropic epsilon-negative (ENG) layer can function as a distributed matching element to the antenna enabling a resonant radiation behaviour. A finite element model of the corresponding centre-fed cylindrical dipole antenna-based resonant system confirms that such designed ENG-based spherical layers can act as a distributed matching element, which can be optimised to produce a reactance free, resistively matched and, hence, efficient radiating system. Several limits on the dispersion properties of the homogenous and isotropic ENG media used in these matching layers are considered and their impact on the bandwidth of these resonant systems is established. Although the dispersionless resonant antenna-ENG system has a bandwidth substantially below the Chu limit, the bandwidths of the corresponding dispersive systems are shown to be at or just slightly below the Chu limit. An analytical model of an idealised gaseous plasma-based ENG layer sandwiched between two glass layers, a potential realisation of these metamaterial-based ENG spherical shell systems, is introduced and its solution is used to study these efficiency and bandwidth issues further. Resonant systems based on active ENG metamaterial layers realised with two types of idealised gain medium models are shown to have bandwidths that approach the idealised dispersionless medium values and, consequently, are substantially below the Chu limit

A Hybrid Optimization Method to Analyze Metamaterial-Based Electrically Small Antennas

Abstract: A model of an idealized radiating system composed of an electrically small electric dipole antenna enclosed in an electrically small multilayered metamaterial shell system is developed analytically. The far-field radiation characteristics of this system are optimized using a GA-MATLAB based hybrid optimization model. The optimized-analytical model is specifically applied to a spherical glass shell filled with a "cold plasma" epsilon-negative (ENG) medium. These analytical results are confirmed using ANSOFT HFSS and COMSOL Multiphysics simulations; these numerical results include input impedance and overall efficiency values not available with the analytical model. The optimized-analytical model is also used to achieve electrically small nonradiating metamaterial-based multilayered spherical shell designs. The optimized shell properties are exploited to obtain multiband radiating and nonradiating response characteristics. Dispersion properties of the ENG materials are also included in all the analytical models; the bandwidth characteristics of these systems are discussed

Kinematic dynamos with precession driven flow in a sphere

Abstract: Precession driven flow is investigated numerically in a spherical shell with an inner core of negligible size and at various angles between the axes of precession and rotation of the shell. For each angle and at an Ekman number of 5 ×10-4, there are always two values of retrograde precession at which the flow is particularly unstable. Dynamo action occurs in both cases. The generated magnetic fields have a relatively small dipole component and significant contributions from high multipoles.

Experimental and numerical studies of convection in a rapidly rotating spherical shell

Abstract: Thermal convection in a rapidly rotating spherical shell is investigated experimentally and numerically. The experiments are performed in water (Prandtl number P=7) and in gallium (P=0.025), at Rayleigh numbers R up to 80 times the critical value in water (up to 6 times critical in gallium) and at Ekman numbers E∼10−6. The measurements of fluid velocities by ultrasonic Doppler velocimetry are quantitatively compared with quasi-geostrophic numerical simulations incorporating a varying β-effect and boundary friction (Ekman pumping). In water, unsteady multiple zonal jets, weaker in amplitude than the non-axisymmetric flow, are experimentally observed and numerically reproduced at moderate forcings (R/Rc <40). In this regime, zonal flows and vortices share the same length scale. Gallium experiments and strongly supercritical convection experiments in water correspond to another regime. In these turbulent flows, the zonal motion amplitude U dominates the non-axisymmetric motion amplitude Ũ. As a result of the reverse cascade of kinetic energy, the characteristic Rhines length scale of zonal jets emerges, and the boundary friction becomes the main brake on the growth of the zonal flow. A scaling law U ∼ Ũ4/3 is then derived and verified both numerically and experimentally.

ŒDIPUS: a new tool to study the dynamics of planetary interiors

Abstract: SUMMARY We present a new numerical method to describe the internal dynamics of planetary mantles through the coupling of a dynamic model with the prediction of geoid and surface topography. Our tool is based on the simulation of thermal convection with variable viscosity in a spherical shell with a finite-volume formulation. The grid mesh is based on the ‘cubed sphere’ technique that divides the shell into six identical blocks. An investigation of various numerical advection schemes is proposed: we opted for a high-resolution, flux-limiter method. Benchmarks of thermal convection are then presented on steady-state tetrahedral and cubic solutions and time-dependent cases with a good agreement with the few recent programs developed to solve this problem. A dimensionless framework is proposed for the calculation of geoid and topography introducing two dimensionless numbers: such a formulation provides a good basis for the systematic study of the geoid and surface dynamic topography associated to the convection calculations. The evaluation of geoid and surface dynamic topography from the gridded data is performed in the spectral domain. The flow solver is then tested extensively against a precise spectral program, producing response functions for geoid as well as bottom and surface topographies. For a grid mesh of a reasonable size (6 × 64 × 64 × 64) a very good agreement (to within ∼1 per cent) is found up to spherical harmonic degree 15.

Acoustic beam scattering and excitation of sphere resonance: Bessel beam example

Abstract: The exact partial wave series for the scattering by a sphere centered on an ideal Bessel beam was recently given by Marston ["Scattering of a Bessel beam by a sphere," J. Acoust. Soc. Am. 121, 753-758 (2007)]. That series is applied here to solid elastic spheres in water and to an empty spherical shell in water. The examples are selected to illustrate the effect of varying the beam's conical angle so as to modify the coupling to specific resonances in the response of each type of sphere considered. The backscattering may be reduced or increased depending on properties of the resonance and of the specular contribution. Changing the conical angle is equivalent to changing the beamwidth. Some applications of the Van de Hulst localization principle to the interpretation of the partial wave series and to the interpretation of the scattering dependence on the beam's conical angle are discussed. Some potential applications to the analysis of the scattering by spheres of more general axisymmetric beams are noted.

Variational solutions for externally induced sloshing in horizontal-cylindrical and spherical vessels

Abstract: A mathematical model is developed for calculating linear sloshing effects in the dynamic response of horizontal-cylindrical and spherical liquid containers under external excitation, with emphasis on earthquake excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the configuration of the containers, the associated spatial functions are nonorthogonal and the problem is not separable, resulting in a system of coupled nonhomogeneous ordinary linear differential equations of motion. The solution can be obtained through either direct integration or modal analysis. Particular emphasis is given on the rate of convergence of the solution. The cases of half-full cylinders and spheres are examined in detail, where explicit expressions for the coefficients of the governing equations are derived. Using the proposed methodology, sloshing frequencies and masses are calculated rigorously for arbitrary liquid height of horizontal-cylindrical or spherical containers, and the response under two characteristic seismic events is obtained. The results describe the linear dynamic response of such containers and can be used for an efficient seismic analysis and design of industrial pressure vessels.

Elastic buckling of barrelled shell under external pressure

Abstract: The aim of the paper is to present a procedure for design of a family of shells of revolution of constant mass and, as a next step, of constant volume. As a reference a cylindrical shell is taken into consideration. By decreasing the value of the meridional radius of curvature R 1 , which for cylindrical shell equals infinity, barrelled shells are created up to the spherical shell for which both meridional and circumferential radii of curvature are equal ( R 1 = R 2 ). A numerical example of using the presented procedure is considered. Then for the family of shells of revolution of constant mass a buckling analysis using FEM method is carried out. Results of the analysis show the relationship between the radius of curvature of the shell R 1 and the critical load p cr in the case of uniform external pressure.

Equatorial wave attractors and inertial oscillations

Abstract: Three different approximations to the axisymmetric small-disturbance dynamics of a uniformly rotating thin spherical shell are studied for the equatorial region assuming time-harmonic motion. The first is the standard /3-plane model. The second is Stern's (Tellus, vol. 15, 1963, p. 246) homogeneous, equatorial β-plane model of inertial waves (that includes all Coriolis terms). The third is a version of Stern's equation extended to include uniform stratification. It is recalled that the boundary value problem (BVP) that governs the streamfunction of zonally symmetric waves in the meridional plane becomes separable only for special geometries. These separable BVPs allow us to make a connection between the streamfunction field and the underlying geometry of characteristics of the governing equation. In these cases characteristics are each seen to trace a purely periodic path. For most geometries, however, the BVP is non-separable and characteristics and therefore wave energy converge towards a limit cycle, referred to as an equatorial wave attractor. For Stern's model we compute exact solutions for wave attractor regimes. These solutions show that wave attractors correspond to singularities in the velocity field, indicating an infinite magnification of kinetic energy density along the attractor. The instability that arises occurs without the necessity of any ambient shear flow and is referred to as geometric instability. For application to ocean and atmosphere, Stern's model is extended to include uniform stratification. Owing to the stratification, characteristics are trapped near the equator by turning surfaces. Characteristics approach either equatorial wave attractors, or point attractors situated at the intersections of turning surfaces and the bottom. At these locations, trapped inertia-gravity waves are perceived as near-inertial oscillations. It is shown that trapping of inertia-gravity waves occurs for any monochromatic frequency within the allowed range, while equatorial wave attractors exist in a denumerable, infinite set of finite-sized continuous frequency intervals. It is also shown that the separable Stern equation, obtained as an approximate equation for waves in a homogeneous fluid confined to the equatorial part of a spherical shell, gives an exact description for buoyancy waves in uniformly but radially stratified fluids in such shells.

Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets

Abstract: Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in the flexure mechanism. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However local studies of gravity and topography data suggest large variations in the thickness of the lithosphere. In this article we obtain the scalar flexure equations governing the deformations of a thin spherical shell with variable thickness or variable Young's modulus. The resulting equations can be solved in succession, except for a system of two simultaneous equations, the solutions of which are the transverse deflection and an associated stress function. In order to include bottom loading generated by mantle convection, we extend the method of stress functions to include loads with a toroidal tangential component. We further show that toroidal tangential displacement always occurs if the shell thickness varies, even in the absence of toroidal loads. We finally prove that the degree-one harmonic components of the transverse deflection and of the toroidal tangential displacement are independent of the elastic properties of the shell and are associated with translational and rotational freedom. The flexure equations for a shell of variable thickness are useful not only for the prediction of the gravity signal in local admittance studies, but also for the construction of stress maps in tectonic analysis.

Photostrictive actuators for photonic control of shallow spherical shells

Abstract: Photostrictive materials, exhibiting light-induced strain, are of interest for the future generation of wireless remote control photo-actuators. Photostrictive actuators are expected to be used as the driving component in optically controlled flexible structures. In this paper, the photonic control of flexible spherical shells using discrete photostrictive actuators is investigated. This paper presents a coupled opto-piezothermoelastic shell theory that incorporates photovoltaic, pyroelectric and piezoelectric effects, and has the capability to predict the response of a spherical shell driven by the photostrictive actuators. In this study, the effects of actuator location as well as membrane and bending components on the control action have been analyzed. The results obtained indicate that the control forces are mode and location dependent. Analysis also shows that the membrane control action is much more significant than the bending control action.

The Solar Acoustic Simulator: Applications and Results

Abstract: It is important to understand the limits and accuracy of helioseismic techniques in their ability to probe the solar interior The availability of a method that is able to compute the solar acoustic wave eld in the presence of thermal or o w perturbations affords us a means to place bounds on detectability and accuracy of inferences of interior perturbations We describe the technique used to simulate wave propagation within a spherical shell that extends from a desired depth (not including the center) into the solar atmosphere and which possesses a solar like stratication

Spherical Couette flow in a dipolar magnetic field

Abstract: We consider numerically the flow of an electrically conducting fluid in a differentially rotating spherical shell, in a dipolar magnetic field. For infinitesimal differential rotation the flow consists of a super-rotating region, concentrated on the particular field line C just touching the outer sphere, in agreement with previous results. Finite differential rotation suppresses this super-rotation, and pushes it inward, toward the equator of the inner sphere. For sufficiently strong differential rotation the outer boundary layer becomes unstable, yielding time-dependent solutions. Adding an overall rotation suppresses these instabilities again. The results are in qualitative agreement with the DTS liquid sodium experiment.

Redshift spherical shell energy in isotropic universes

Abstract: We introduce the redshift spherical shell energy, which can be used to test in the redshift space the radial inhomogeneity of an isotropic universe, providing additional constraints for Lemaitre-Tolman-Bondi models, and a more general test of cosmic homogeneity.

Experimental and numerical studies of magnetoconvection in a rapidly rotating spherical shell

Abstract: Thermal magnetoconvection in a rapidly rotating spherical shell is investigated numerically and experimentally in electrically conductive liquid gallium (Prandtl number P = 0.025), at Rayleigh numbers R up to around 6 times critical and at Ekman numbers E ∼ 10 -6 . This work follows up the non-magnetic study of convection presented in a companion paper (Gillet et al. 2007). We study here the addition of a z-invariant toroidal magnetic field to the fluid flow. The experimental measurements of fluid velocities by ultrasonic Doppler velocimetry, together with the quasi-geostrophic numerical simulations incorporating a three-dimensional modelling of the magnetic induction processes, demonstrate a stabilizing effect of the magnetic field in the weak-field case, characterized by an Elsasser number A <(E/P) 1/3 . We find that this is explained by the changes of the critical parameters at the onset of convection as A increases. As in the non-magnetic study, strong zonal jets of characteristic length scales l β (Rhines length scale) dominates the fluid dynamics. A new characteristic of the magnetoconvective flow is the elongation of the convective cells in the direction of the imposed magnetic field, introducing a new length scale l o . Combining experimental and numerical results, we derive a scaling law U ∼(U s U o ) 2/3 ∼ U s 4/3 (l o /l β )2/3 where U is the axisymmetric motion amplitude, U s and U o are the non-axisymmetric radial and azimuthal motion amplitudes, respectively.

Convection in rotating spherical fluid shells with inhomogeneous heat flux at the outer boundary

Abstract: The Earth's core is subject to a laterally varying heat flux at the outer boundary, which may account for correlations between the geomagnetic field and lower mantle structure. Studies of nonmagnetic, rotating convection in a spherical shell with fixed temperature boundary conditions have revealed flows resonating with, or locked to, the boundary anomalies when the length scales of the convection are close to those of the boundary condition. Here we study a similar system but for fixed heat flux upper boundary conditions, as in the Earth's core. We first map out the onset of thermal instability in a rotating shell of aspect ratio 0.4 for uniform outer boundary cooling with both rigid and stress-free boundaries. A preference for large scale (azimuthal wavenumber m = 1) flows, not observed for the uniform temperature case, persists to Ekman numbers down to almost 10− 4. The preference for large scales is greatest for rigid boundaries and high (≥ 1) Prandtl numbers. Hemispheric asymmetry appears in the weakl...