Spherical Shell Research Articles

Lithospheric Stress Due to Mantle Convection and Mantle Plume over East Africa from GOCE and Seismic Data

The Afar and Ethiopian plateaus are in a dynamic uplift due to the mantle plume, therefore, considering the plume effect is necessary for any geophysical investigation including the estimation of lithospheric stress in this area. The Earth gravity models of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and lithospheric structure models can be applied to estimate the stress tensor inside the Ethiopian lithosphere. To do so, the boundary-value problem of elasticity is solved to derive a general solution for the displacement field in a thin elastic spherical shell representing the lithosphere. After that, general solutions for the elements of the strain tensor are derived from the displacement field, and finally the stress tensor from the strain tensor. The horizontal shear stresses due to mantle convection and the vertical stress due to the mantle plume are taken as the lower boundary value at the base of the lithosphere, and no stress at the upper boundary value of the lithospheric shell. The stress tensor and maximum stress directions are computed at the Moho boundary in three scenarios: considering horizontal shear stresses due to mantle convection, vertical stresses due to mantle plume, and their combination. The estimated maximum horizontal shear stresses’ locations are consistent with tectonics and seismic activities in the study area. In addition, the maximum shear stress directions are highly correlated with the World Stress Map 2016, especially when the effect of the mantle plume is solely considered, indicating the stress in the study area mainly comes from the plume.

Design and Manufacturing Process of a New Type of Deep-Sea Spherical Pressure Hull Structure

Spherical shell structures are the most suitable shape for deep-sea pressure hulls because they have ideal mechanical properties for handling symmetrical pressure. However, the shape accuracy requirement for a hull in a spherical shell structure subjected to deep-sea pressure is extremely high. Even minor asymmetry can significantly degrade its mechanical properties. In this study, a new type of spherical deep-sea pressure hull structure and its integral hydro-bulge-forming (IHBF) method are proposed. First, 32 flat metal plate parts are prepared and welded along their straight sides to form a regular polygonally shaped box. Next, water pressure is applied inside the preformed box to create a spherical pressure vessel. We performed a forming experiment using a spherical pressure vessel with a design radius of 250 mm as a verification research object. The radius of the spherical pressure vessel obtained from the forming experiment is 249.32 mm, the error from the design radius is 0.27%, and the roundness of the spherical surface is 2.36 mm. We performed a crushing analysis using uniform external pressure to confirm the crushing and buckling characteristics of the formed spherical pressure vessel. The results show that the work-hardening increased the crushing and buckling load of the spherical pressure vessel, above that of the conventional spherical shell structure. Additionally, it is established that local defects and the size of the weld line significantly and slightly affected the crushing and buckling load of the spherical pressure hull, respectively.

The Proxy-SU(3) Symmetry in Atomic Nuclei

The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated through Nilsson model calculations and its connection to the spherical shell model. The major role played by the highest weight-irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables β and γ for even–even nuclei in the explanation of the dominance of prolate over oblate shapes in the ground states of even–even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, and in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined.

Latitudinal regionalization of rotating spherical shell convection

Convection occurs ubiquitously on and in rotating geophysical and astrophysical bodies. Prior spherical shell studies have shown that the convection dynamics in polar regions can differ significantly from the lower latitude, equatorial dynamics. Yet most spherical shell convective scaling laws use globally-averaged quantities that erase latitudinal differences in the physics. Here we quantify those latitudinal differences by analysing spherical shell simulations in terms of their regionalized convective heat-transfer properties. This is done by measuring local Nusselt numbers in two specific, latitudinally separate, portions of the shell, the polar and the equatorial regions, $Nu_p$ and $Nu_e$ , respectively. In rotating spherical shells, convection first sets in outside the tangent cylinder such that equatorial heat transfer dominates at small and moderate supercriticalities. We show that the buoyancy forcing, parameterized by the Rayleigh number $Ra$ , must exceed the critical equatorial forcing by a factor of ${\approx }20$ to trigger polar convection within the tangent cylinder. Once triggered, $Nu_p$ increases with $Ra$ much faster than does $Nu_e$ . The equatorial and polar heat fluxes then tend to become comparable at sufficiently high $Ra$ . Comparisons between the polar convection data and Cartesian numerical simulations reveal quantitative agreement between the two geometries in terms of heat transfer and averaged bulk temperature gradient. This agreement indicates that rotating spherical shell convection dynamics is accessible both through spherical simulations and via reduced investigatory pathways, be they theoretical, numerical or experimental.

Multi-criterion optimization of invasive antenna applicators for Au@Fe3O4, Au@-Fe2O3 and Au@-Fe2O3 mediated microwave ablation treatment

ABSTRACT Magnetic nanoparticle (MNP) mediated microwave ablation has the great potential at present to address challenges associated with treatment planning such as maximum heat generation in the vicinity of targeted tissues in lesser penetration time. Further, the antenna applicators injected in human phantom must be rigid and thin. The derivative-free optimization algorithms are carried out for optimum design of monopole, slot, dipole, and tapered slot antenna applicators for ablation of tumour tissues invasively. It is found that in terms of input impedance matching, the used multi-criterion Nelder-Mead optimization performs efficiently for tapered slot applicator achieving S 11 value of –40 dB with much reduced antenna dimensions. In order to further escalate the performance of tapered slot antenna, gold (Au)-coated iron-based MNPs are suggested for tumor infusion. Spherical gold-coated shell material is preferrable for more sphericity of ablation zone, biocompatibility and due to high conductivity, heat generated in MNPs can be transferred to biological tissues more rapidly. The size, type, and shape of MNPs also influence the heat generation in tumor tissues. Thus, three different types of MNPs having high magnetization properties, Au@Fe3O4, Au@-Fe2O3 and Au@-Fe2O3 have been employed to study the performance in terms of maximum rise in temperature, specific absorption rate (SAR), and area of ablation zone by varying core size radius of MNPs. Results demonstrate that increase in radius of MNP core helps in increasing the temperature distribution and reduction in ablation zone. The optimized lesion is achieved for 20 nm core radius of Au@Fe3O4.

Acoustic radiation force of elastic spherical shell with eccentric droplet in plane wave acoustic field

Based on the application of acoustic waves in cell manipulation, a model consisting of an elastic spherical shell and eccentric droplet is established to simulate a eukaryotic cell and analyze the acoustic radiation force (ARF) on the cell. In this work, we derive an exact expression for the ARF on the liquid-filled spherical shell. The influence of eccentric distance, radius of the eccentric droplet and impedance of the medium inside the liquid-filled spherical shell on the ARF are analyzed numerically. The results show that the ARF is very sensitive to the position and size of the eccentric droplet. As the eccentricity of the eccentric droplet increases, the ARF becomes greater. In a low frequency region (<i>ka</i><3) the resonance peak point increases, and the position of the curve ventral point shifts to the high frequency region (<i>ka</i>>3) with the increase of the radius of the eccentric droplet. The effect of the position variation on the ARF is more significant than that of the radius change, and both of their effects will be superimposed on each other. The ARF, as a function of <i>ka,</i> is mainly affected by the variation of the nucleus characteristic impedance. The ARF amplitude around <i>ka</i> = 5 increases and the position of the ventral point tends to shift rightwards with the enlargement of the nucleus impedance. Therefore, the radiation response at a certain frequency or in a cell size range can be enhanced when the nucleus impedance increases. The results of this study provide theoretical basis for the cell sorting and targeted therapy.

Structural characterization of systems with competing interactions confined in narrow spherical shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. In fact, confinement has been proven to be a good strategy to induce the formation of novel ordered microphases that might be appealing to the development of functional nanomaterials. Using Grand Canonical Monte Carlo (GCMC) simulations, we study a model colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions under which the hexagonal phase is stable in bulk. We observe the formation of three parent ordered structures formed by toroidal clusters and two spherical clusters (Type I), toroidal clusters and one spherical cluster (Type II), and toroidal clusters alone (Type III), depending on the radius of the confining shell, that can often coexist with other related structures derived from these parent ones by a simple transformation, in which the system is divided into two hemispheres that are rotated with respect to each other by a given angle. We propose a general method to characterize and predict the structures obtained under confinement in spherical shells in systems able to self-assemble into a hexagonal phase in bulk. We also show that deforming the spherical shells into ellipsoidal ones affects the structure of the system in such a way that helical structures are favoured by prolate ellipsoids and toroidal structures by oblate ellipsoids.

Broadband near-perfect optical absorbers fabricated with complete spherical platinum shells with and without induced symmetry broken cracks using a simple colloidal route

Broadband perfect absorbers with an average absorptivity of 96.2% in the 200–1500 nm are proposed. Complete spherical Pt shells with induced cracks are fabricated from monolayer microspheres along with heating using conformal oxide and metal coating.

Interaction of a plane pressure wave with a spherical shell in an elastic medium

Interaction of a plane pressure wave with a spherical shell in an elastic medium

Exact solutions of one-dimensional steady heat conduction analysis for multi-layered mediums by tri-diagonal matrix algorithm (TDMA) applicable to Excel program (Analytical solutions of steady heat conduction for multi-layered symmetrical plat plate, solid cylinder, sphere, unsymmetric plat plate, pipe, and spherical shell, and these applications to engineering problems)

Exact solutions of one-dimensional steady heat conduction analysis for multi-layered mediums by tri-diagonal matrix algorithm (TDMA) applicable to Excel program (Analytical solutions of steady heat conduction for multi-layered symmetrical plat plate, solid cylinder, sphere, unsymmetric plat plate, pipe, and spherical shell, and these applications to engineering problems)

Stability conditions of plastic deformation of thin-walled plates and shells under complex stress state

Using examples of uniaxial and biaxial tension of thin-walled metal or composite elements, the main hypotheses allowing to estimate the conditions of unstable deformation are explained. Specific estimations are given for a basic equation relating stress and strain tensor intensities as applied to plates, cylindrical and spherical shells. The equipment for testing tubular specimens under proportional loading under various plane stress states is described.

Аналіз граничної рівноваги зігнутої сферичної оболонки з колінеарними тріщинами за локальним та інтегральним критеріями руйнування

The stressed-strain state and limit equilibrium of shallow spherical shell weakened by two cross-cutting meridional collinear cracks is studied in the two-dimensional formulation. The crack closure caused by bending deformation was taken into account based on the model of the crack edges contact along a line in one of the face surfaces of the shell. The boundary problem for equations of classical shell theory with interrelated conditions along the line of the cracks is formulated within the framework of such model. Singular integral equation for the unknown jump of normal rotation angle on the cracks edges has been elaborated. Based on numerical solutions of singular integral equation the stressed-strain state and limit equilibrium of the spherical shell depending on the parameters of shell curvature and distance between cracks are investigated. Using the local and integral through-the-thickness energy failure criteria of linear mechanics of fracture, the upper and lower values of limit load were established. It was found that the upper estimate of the limit load according to the integral criterion is approximately twice the magnitude of the lower estimate according to the local criterion.

О возможности создания крупногабаритных конструкций в условиях открытого космоса

The paper gives a brief overview of the history of the development of inflatable space struc-tures. Further development should be the use of inflatable shells that harden in space. The possibility of using this technology in the framework of the use of simple tasks is considered in the article. On the ex-ample of thick-walled spherical and cylindrical shells, using Lame's analytical solutions, it is shown that the thickness of the shell can be thin. The thin shell design is much easier to inflate. No high pressure is required for this. Using the classical heat conduction equation, the temperature distribution inside a cy-lindrical shell is determined. When setting the boundary conditions, the flux of rays incident both from the side of the Sun and from the side of the Earth was taken into account. The radiation on the surface of the cylinder was calculated according to the Stefan-Boltzmann law. It has been established that a tem-perature occurs in the shell, the maximum value of which is in the range from 150 to 200 degrees Celsi-us. Prepreg casings require the use of a high temperature resin suitable for hot curing.

Surface Structure Inspection System with Passive Rotating Spherical Shell UAV

Surface Structure Inspection System with Passive Rotating Spherical Shell UAV

Three Dimensional Coupling between Elastic and Thermal Fields in the Static Analysis of Multilayered Composite Shells

This new work aims to develop a full coupled thermomechanical method including both the temperature profile and displacements as primary unknowns of the model. This generic full coupled 3D exact shell model permits the thermal stress investigation of laminated isotropic, composite and sandwich structures. Cylindrical and spherical panels, cylinders and plates are analyzed in orthogonal mixed curved reference coordinates. The 3D equilibrium relations and the 3D Fourier heat conduction equation for spherical shells are coupled and they trivially can be simplified in those for plates and cylindrical panels. The exponential matrix methodology is used to find the solutions of a full coupled model based on coupled differential relations with respect to the thickness coordinate. The analytical solution is based on theories of simply supported edges and harmonic relations for displacement components and sovra-temperature. The sovra-temperature magnitudes are directly applied at the outer faces through static state hypotheses. As a consequence, the sovra-temperature description is assumed to be an unknown variable of the model and it is calculated in the same way as the three displacements. The final system is based on a set of coupled homogeneous differential relations of second order in the thickness coordinate. This system is reduced in a first order differential relation system by redoubling the number of unknowns. Therefore, the exponential matrix methodology is applied to calculate the solution. The temperature field effects are evaluated in the static investigation of shells and plates in terms of displacement and stress components. After an appropriate preliminary validation, new benchmarks are discussed for several thickness ratios, geometrical data, lamination sequences, materials and sovra-temperature values imposed at the outer faces. Results make evident the accordance between the uncoupled thermo-mechanical model and this new full coupled thermo-mechanical model without the need to separately solve the Fourier heat conduction relation. Both effects connected with the thickness layer and the related embedded materials are included in the conducted thermal stress analysis.

Comparative evaluation of design codes for buckling assessment of a steel spherical shell

Comparative evaluation of design codes for buckling assessment of a steel spherical shell

Natural vibrations of a cylindrical shell with the end cap. II. Analysis of the spectrum

Using numerical and asymptotic methods, the lowest natural frequencies and vibration modes of a structure consisting of a closed circular cylindrical shell with an end cap attached to it, having the shape of a shallow spherical segment, are studied in the paper. Three types of natural vibrations of the structure are described. Eigenfrequencies and modes of vibrations of the first type, close to the frequencies and modes of vibrations of a shallow spherical shell, were studied in previous works. In this paper, we study the forms and frequencies of the second type of vibrations (cylindrical shell) and the third type (cantilever beam with the load). An optimization problem is solved to determine the values of the structure parameters, the relative thickness of its elements and the curvature of the end cap, at which the minimum value of the natural frequency is maximum. A comparison of the asymptotic and numerical results reveals their good agreement.

Propagation of skew-symmetric unsteady shear waves from thick-walled shell in elastic space

Problems of propagation and diffraction of nonstationary waves in elastic bodies are of great theoretical and practical importance in such fields of science and technology as aircraft construction, shipbuilding, seismic exploration of minerals, seismic resistance of structures, and many others. The paper considers the problem of the propagation of skew-symmetric unsteady shear waves from a thick-walled spherical shell in elastic space. To solve the problem, the integral Laplace transforms in dimensionless time, and the method of incomplete separation of variables was used. In the image space, the problem is reduced to an infinite system of linear algebraic equations, the solution of which is sought in the form of an infinite exponential series. Formulas for the displacement vector components and the stress tensor are obtained. The transition to the originals is carried out using the theory of residues. Numerical experiments have been carried out, the results of which are presented in graphs. The obtained results of the work can be used in geophysics, seismology, and design organizations in the construction of structures and in the design of underground reservoirs.

Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches

The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within ΛCDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. This result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.

Synthesis of hypercrosslinked polymers with a spherical shell structure for highly effective cycloaddition of CO2 under ambient conditions

Hypercrosslinked polymers with a spherical shell structure were fabricated by controlling the monomer feed rate; for the CO2 cycloaddition reaction, they show a 52% higher catalytic yield than the bulk materials.