Axisymmetric buckling of a spherical shell embedded in an elastic medium under uniaxial stress at infinity

The problem of a thin spherical linearly-elastic shell, perfectly bonded to an infinite linearly-elastic medium is considered. A constant axisymmetric stress field is applied at infinity in the matrix, and the displacement and stress fields in the shell and matrix are evaluated by means of harmonic potential functions. In order to examine the stability of this solution, the buckling problem of a shell which experiences this deformation is considered. Using Koiter's nonlinear shallow shell theory, restricting buckling patterns to those which are axisymmetric, and using the Rayleigh–Ritz method by expanding the buckling patterns in an infinite series of Legendre functions, an eigenvalue problem for the coefficients in the infinite series is determined. This system is truncated and solved numerically in order to analyse the behaviour of the shell as it undergoes buckling, and to identify the critical buckling stress in two cases — namely where the shell is hollow and the stress at infinity is either uniaxial or radial

AE, D ST and their SuperMAG Counterparts : the effect of improved spatial resolution in geomagnetic indices

For decades, geomagnetic indices have been used extensively to parameterize space weather events, as input to various models and as space weather specifications. The auroral electrojet (AE) index and disturbance storm time index (DST) are two such indices that span multiple solar cycles and have been widely studied. The production of improved spatial coverage analogs to AE and DST is now possible using the SuperMAG collaboration of ground‐based magnetometers. SME is an electrojet index that shares methodology with AE. SMR is a ring current index that shares methodology with DST. As the number of magnetometer stations in the SuperMAG network increases over time, so does the spatial resolution of SME and SMR. Our statistical comparison between the established indices and their new SuperMAG counterparts finds that, for large excursions in geomagnetic activity, AE systematically underestimates SME for later cycles. The difference between distributions of recorded AE and SME values for a single solar maximum can be of the same order as changes in activity seen from one solar cycle to the next. We demonstrate that DST and SMR track each other but are subject to an approximate linear shift as a result of the procedure used to map stations to the magnetic equator. We explain the observed differences between AE and SME with the assistance of a simple model, based on the construction methodology of the electrojet indices. We show that in the case of AE and SME, it is not possible to simply translate between the two indices

Nearest neighbor - A new non-parametric test used for classifying spectral data

Nonparametric statistical interference program for spectral data classificatio

Inflation system for balloon type satellites Patent

Inflation system for balloon type satellite

Real-Time Cavity QED with Single Atoms

The combination of cold atoms and large coherent coupling enables investigations in a new regime in cavity QED with single-atom trajectories monitored in real time with high signal-to-noise ratio. The underlying “vacuum-Rabi” splitting is clearly reflected in the frequency dependence of atomic transit signals recorded atom by atom, with evidence for mechanical light forces for intracavity photon number <1. The nonlinear optical response of one atom in a cavity is observed to be in accord with the one-atom quantum theory but at variance with semiclassical predictions

Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.Comment: 18 pages, 10 figures, preprin