Challenging the dipolar paradigm for Proterozoic Earth

ABSTRACT A robust, geology-based Proterozoic continental assembly places the northern and eastern margins of the Siberian craton against the southwestern margins of Laurentia in a tight, spoon-in-spoon conjugate fit. The proposed assembly began to break apart in late Neoproterozoic and early Paleozoic time. Siberia then drifted clockwise along the Laurussian margin on coast-parallel transforms until suturing with Europe in late Permian time. The proposed drift path is permitted by a geocentric axial dipole (GAD) magnetic field from Silurian to Permian time. However, the Proterozoic reconstruction itself is not permitted by GAD. Rather, site-mean paleomagnetic data plot ted on the reconstruction suggest a multipolar Proterozoic dynamo dominated by a quadrupole. The field may have resembled that of present-day Neptune, where, in the absence of a large solid inner core, a quadrupolar magnetic field may be generated within a thin spherical shell near the core-mantle boundary. The quadrupole may have dominated Earth’s geomagnetic field until early Paleozoic time, when the field became erratic and transitioned to a dipole, which overwhelmed the weaker quadrupole. The dipole then established a strong magnetosphere, effectively shielding Earth from ultraviolet-B (UV-B) radiation and making the planet habitable for Cambrian fauna.

A fast approach for acoustic source localization on a thin spherical shell

Thin spherical shell structures are wildly used as pressure vessels in the industry because of their property of having equal in-plane normal stresses in all directions. Since very large pressure difference between the inside and outside of the wall exists, any formation of defects in the pressure vessel wall has a huge safety risk. Therefore, it is necessary to quickly locate the area where the defect maybe located in the early stage of defect formation and make repair on time. The conventional acoustic source localization techniques for spherical shells require either direction-dependent velocity profile knowledge or a large number of sensors to form an array. In this study, we propose a fast approach for acoustic source localization on thin isotropic and anisotropic spherical shells. A solution technique based on the time difference of arrival on a thin spherical shell without the prior knowledge of direction-dependent velocity profile is provided. With the help of “L”-shaped sensor clusters, only 6 sensors are required to quickly predict the acoustic source location for anisotropic spherical shells. For isotropic spherical shells, only 4 sensors are required. Simulation and experimental results show that this technique works well for both isotropic and anisotropic spherical shells.

Physical Characteristics of and Transient Response from Thin Cylindrical Piezoelectric Transducers Used in a Petroleum Logging Tool

We report on a transient response model of thin cylindrical piezoelectric transducers used in the petroleum logging tools, parallel to a recently established transient response model of thin spherical-shell transducers. Established on a series of parallel-connected equivalent-circuits, this model provides insightful information on the physical characteristics of the thin cylindrical piezoelectric transducers, i.e., the transient response, center-frequency, and directivity of the transducer. We have developed a measurement system corresponding to the new model to provide a state-of-the-art comparison between theory and experiment. We found that the measured results were in good agreement with those of theoretical calculations.

Magnetic Helicity and the Solar Dynamo

Solar magnetism is believed to originate through dynamo action in the tachocline. Statistical mechanics, in turn, tells us that dynamo action is an inherent property of magnetohydrodynamic (MHD) turbulence, depending essentially on magnetic helicity. Here, we model the tachocline as a rotating, thin spherical shell containing MHD turbulence. Using this model, we find an expression for the entropy and from this develop the thermodynamics of MHD turbulence. This allows us to introduce the macroscopic parameters that affect magnetic self-organization and dynamo action, parameters that include magnetic helicity, as well as tachocline thickness and turbulent energy.

Study and detection of relativistic Solar Neutrons at ground level with the Spherical Proportional Counter

A novel method of high energy solar neutron detection is proposed with the Spherical Proportional Counter (SPC), taking advantage of the 209Bi(n,f) reaction. This reaction, is considered as a standard for high energy neutron detection, due to large cross section values in the 100 MeV – 1 GeV energy interval, obtained in the n_TOF facility at CERN. A thin spherical shell of Bismuth will be situated in the large volume of the SPC, serving as target for high energy neutrons bombarding the detector, thus resulting in fission fragment emission. Detailed simulation of the 209Bi(n,f) reaction with the INCL++ model, coupled with the ABLA07 de–excitation code is performed (cross section, mass & atomic number distribution, kinetic energy per fragment) in the 100 MeV – 10 GeV energy interval, together with SRIM for the fragments’ projected range in 209Bi. Experimental data from a 252Cf source are obtained, in order to validate the SPC’s efficiency in fission fragment detection. Calculations for the expected reactions in the 209Bi shell have been performed in different atmospheric depths (700 & 1000 g/cm2), and various spherical detector radii.

Absorption of zero-mass planar waves by dirty black holes

Astrophysical black holes are often with companions, including other gravitating objects, accretion disks, electromagnetic fields, and others. Because of the nonlinear nature of general relativity, it is difficult to account for the gravitational effects of these companions, which can only be investigated analytically for very few cases. In this paper, we consider black holes with surrounding matter — often called dirty black holes — and analyze the absorption cross section of massless scalar fields. We start by laying out the generic setup for spherically symmetric scenarios and then specify for a simple model. We consider planar massless scalar waves impinging upon a Schwarzschild black hole surrounded by a thin spherical shell, and compute the absorption cross section. We present a selection of numerical results complementary to those presented in [C. F. B. Macedo, L. C. S. Leite and L. C. B. Crispino, Phys. Rev. D 93 (2016) 024027, arXiv:1511.08781 [gr-qc]] for arbitrary frequencies, considering different values of the shell position as well as its mass.

Buckling load prediction of an externally pressurized thin spherical shell with localized imperfections

A simple formula for buckling load was derived from the asymptotic analysis of nonlinear behavior of a thin spherical shell. Firstly, two asymptotic cases were studied: the initial post-buckling regime of a perfect structure with small (compared to shell thickness) deflections and equilibrium states with large deflections. Two asymptotic formulae were jointed to obtain the solution for the entire range of deflection amplitude. Then the solution was modified for an imperfect shell. Initial deflections were introduced by only one parameter: the slope of the load–deflection diagram at small pressure. This minimal information was enough to predict the buckling load of the structure with localized imperfections. The suggested asymptotic result was validated by the finite element method and by comparison with experimental data.

3D Characterization of corneal deformation using ultrasound speckle tracking

The three-dimensional (3D) mechanical response of the cornea to intraocular pressure (IOP) elevation has not been previously reported. In this study, we use an ultrasound speckle tracking technique to measure the 3D displacements and strains within the central 5.5[Formula: see text]mm of porcine corneas during the whole globe inflation. Inflation tests were performed on dextran-treated corneas (treated with a 10% dextran solution) and untreated corneas. The dextran-treated corneas showed an inflation response expected of a thin spherical shell, with through-thickness thinning and in-plane stretch, although the strain magnitudes exhibited a heterogeneous spatial distribution from the central to more peripheral cornea. The untreated eyes demonstrated a response consistent with swelling during experimentation, with through-thickness expansion overriding the inflation response. The average volume ratios obtained in both groups was near 1 confirming general incompressibility, but local regions of volume loss or expansion were observed. These results suggest that biomechanical measurements in 3D provide important new insight to understand the mechanical response of ocular tissues such as the cornea.

Free Vibration of Thin Spherical Shells

This research introduces a new approach to analytically derive the differential equations of motion of a thin spherical shell. The approach presented is used to obtain an expression for the relationship between the transverse and surface displacements of the shell. This relationship, which is more explicit than the one that can be obtained through use of the Airy stress function, is used to uncouple the surface and normal displacements in the spatial differential equation for transverse motion. The associated Legendre polynomials are utilized to obtain analytical solutions for the resulting spatial differential equation. The spatial solutions are found to exactly satisfy the boundary conditions for the simply supported and the clamped hemispherical shell. The results to the equations of motion indicate that the eigenfrequencies of the thin spherical shell are independent of the azimuthal coordinate. As a result, there are several mode shapes for each eigenfrequency. The results also indicate that the effects of midsurface tensions are more significant than bending at low mode numbers but become negligible as the mode number increases.