A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

Oscillating magnetic field current drive in a spherical plasma device

The continuous steady-state current drive in a spherical argon plasma by transverse oscillating magnetic field (OMF) is investigated. The experimental results reveal that a rotating magnetic field is generated, and its amplitude depends linearly on the external steady vertical magnetic field. It has been shown that steady toroidal currents of up to about 400 A can be driven by a 490 kHz OMF with an input power of 1.4 kW. The generation of steady toroidal magnetic fields directed oppositely in the upper and lower hemispheres have been recorded. The measurements of time-varying magnetic fields unveil a strong nonlinear effect of the frequency-doubled field harmonics generation. The electron number density and temperature of up to 6.2×1018 m-3 and 12 eV have been obtained. The observed effects validate the existing theory of the OMF current drive in spherical plasmas.

Series in vector spherical harmonics : an efficient tool for solution of nonlinear problems in spherical plasmas

The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses. © 2000 American Institute of Physics.

An adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In previous work we introduced a method to update the reference views in a topological map so that a mobile robot could continue to localize itself in a changing environment using omni-directional vision. In this work we extend this longterm updating mechanism to incorporate a spherical metric representation of the observed visual features for each node in the topological map. Using multi-view geometry we are then able to estimate the heading of the robot, in order to enable navigation between the nodes of the map, and to simultaneously adapt the spherical view representation in response to environmental changes. The results demonstrate the persistent performance of the proposed system in a long-term experiment.

Long-term experiments with an adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In this work, we introduce a method to update the reference views in a hybrid metrictopological map so that a mobile robot can continue to localize itself in a changing environment. The updating mechanism, based on the multi-store model of human memory, incorporates a spherical metric representation of the observed visual features for each node in the map, which enables the robot to estimate its heading and navigate using multi-view geometry, as well as representing the local 3D geometry of the environment. A series of experiments demonstrate the persistence performance of the proposed system in real changing environments, including analysis of the long-term stability.

A biomechanical study of spherical grip

Use of the hand is vital in working life due to the grabbing and pinching it performs. Spherical grip is the most commonly used, due to similarity to the gripping of a computer mouse. Knowledge of its execution and the involved elements is essential. Analysis of this exertion with surface electromyography devices (to register muscular activity) and accelerometer devices (to register movement values ) can provide multiple variables. Six subjects performed ball gripping and registered real-time electromyography (thenar region, hypothenar region, first dorsal interosseous, flexors of the wrist, flexor carpi ulnaris and extensors of the wrist muscles) and accelerometer (thumb, index, middle, ring, pinky and palm) values. The obtained data was resampled “R software” and processed “Matlab Script” based on an automatic numerical sequence recognition program. Electromyography values were normalized on the basis of maximum voluntary contraction, whilst modular values were calculated for the acceleration vector. After processing and analysing the obtained data and signal, it was possible to identify five stages of movement in accordance with the module vector from the palm. The statistical analysis of the variables was descriptive: average and standard deviations. The outcome variables focus on the variations of the modules of the vector (between the maximum and minimum values of each module and phase) and the maximum values of the standardized electromyography of each muscle. Analysis of movement through accelerometer and electromyography variables can give us an insight into the operation of spherical grip. The protocol and treatment data can be used as a system to complement existing assessments in the hand.

Foliar micromorphology and anatomy of Ugni molinae Turcz. (Myrtaceae), with particular reference to schizogenous secretory cavities

Background Ugni molinae Turcz. is one of the most studied species of South American Myrtaceae due to its edible fruits and foliar medicinal compounds. However, there is no anatomical study of the leaves or secretory cavities. This paper seeks to describe the leaf micromorphology and anatomy of the species using standard protocols for light and scanning electron microscopy. Secretory cavities were anatomically characterized in young and mature leaves. Histochemical staining of the cavities was performed. Results The leaves of U. molinae are hypostomatic, have a wavy surface and possess scattered hairs. Leaf anatomical features include dorsiventral mesophyll, two to three layers of palisade parenchyma with abundant chloroplasts, calcium oxalate crystals and internal phloem in vascular bundles. Schizogenous secretory cavities are present on the abaxial surface and are mainly located on the margins of the leaves. Histochemical tests of these cavities suggest the presence of lipophilic substances. Conclusions This is the first study of secretory cavities in Chilean Myrtaceae. In general, micromorphological and anatomical characters are similar to other species of the family. The present findings could provide valuable anatomical information for future research in South American Myrtaceae.

Time-temperature histories of spherical food products during bulk forced-air precooling

A general mathematical model for forced air precooling of spherical food products in bulk is developed. The food products are arranged inline to form a rectangular parallelepiped. Chilled air is blown along the height of the package. The governing equations for the transient two-dimensional conduction with internal heat generation in the product, simultaneous heat and mass transfer at the product-air interface and one-dimensional transient energy and species conservation equations for the moist air are solved numerically using finite difference methods. Results are presented in the form of time-temperature histories. Experiments are conducted with model foods in a laboratory scale air precooling tunnel. The agreement between the theoretical and experimental results is found to be good. In general, a single product analysis fails to predict the precooling characteristics of bulk loads of food products. In the range of values investigated, the respiration heat is found to have a negligible effect.

Porphyrins with multiple crown ether voids: novel systems for cation complexation studies

Porphyrins appended with crown ether, benzo-15-crown-5, at the methine positions have been synthesized and characterized. The fully and partially substituted porphyrins and their metallo (Co, Cu, and Zn) derivatives describe one or more ether cavities in the periphery that are capable of recognizing spherical cations. The ability of these macrocycles to complex cations (Na+, K+, Mg2+, Ca2+, Ba2', and NH4+) is investigated by use of visible, 'H NMR, ESR, and emission spectral studies. The tetrasubstituted crown porphyrin (TCP) exhibits very high selectivity for K+. The cations (K', Ba2+, and NH4+) that require two crown ether cavities for complexation promote dimerization of the porphyrins. The ESR study of the cation-induced porphyrin dimers reveals axial symmetry with the porphyrin planes separated by -4.2 A. This distance increases from the fully substituted to partially substituted porphyrins. The cations (K', Ba2+, and NH4') quench efficiently the fluorescence of the free base porphyrins and their metallo derivatives. The quenching process is attributed to the steric geometry of the dimers.

Stresses around reinforced curvilinear holes in spherical shells

A perturbation technique is used to determine the stress concentration around reinforced curvilinear holes in thin pressurized spherical shells. Starting from the governing differential equations for thin shallow spherical shells, a solution is first obtained for a circular hole. The solution for an arbitrary shaped curvilinear hole is then obtained as a first-order perturbation over the circular hole solution using the conformal mapping technique. The effects of a large number of parameters involved in the design of a reinforcement around cutouts in shells are studied. The problems of symmetric and eccentric reinforcements are also considered. The results obtained would be very helpful in the design of an efficient reinforcement for elliptical and square holes in thin shallow spherical shells.

Thermal stresses around circular holes in spherical shells

The thermal stress problem of a circular hole in a spherical shell of uniform thickness is solved by using a continuum approach. The influence of the hole is assumed to be confined to a small region around the opening. The thermal stress problem is converted as usual to an equivalent boundary value problem with forces specified around the cutout. The stresses and displacement are obtained for a linear variation of temperature across the thickness of the shell and presented in graphical form for ready use.

Plastic response of orthotropic spherical shells under blast loading

The plastic response of a segment of a simply supported orthotropic spherical shell under a uniform blast loading applied on the convex surface of the shell is presented. The blast is assumed to impart a uniform velocity to the shell surface initially. The material of the shell is orthotropic obeying a modified Tresca yield hypersurface conditions and the associated flow rules. The deformation of the shell is determined during all phases of its motion by considering the motion of plastic hinges in different regimes of flow. Numerical results presented include the permanent deformed configuration of the shell and the total time of shell response for different degrees of orthotropy. Conclusions regarding the plastic behaviour of spherical shells with circumferential and meridional stiffening under uniform blast load are presented.

Natural convection in rectangular cavities at high Rayleigh number

Natural convection in rectangular two-dimensional cavities with differentially heated side walls is a standard problem in numerical heat transfer. Most of the existing studies has considered the low Ra laminar regime. The general thrust of the present research is to investigate higher Ra flows extending into the unsteady and turbulent regimes where the physics is not fully understood and appropriate models for turbulence are not yet established. In the present study the Boussinesq approximation is being used, but the theoretical background and some preliminary results have been obtained[1] for flows with variable properties.

Laminar and turbulent natural convection in rectangular cavities

A computer program has been developed for the prediction of buoyancy-driven laminar and turbulent flow in rectangular air-filled two-dimensional cavities with differentially heated side walls. Laminar flow predictions for a square cavity and Rayleigh numbers from Ra = 10^3 up to the onset of unsteady flow have been obtained. Accurate solutions for Ra = 5 x 10^6, 10^7, 5 x 10^7 and 10^8 are presented and an estimate for the critical Rayleigh number at which the steady laminar flow becomes unsteady is given for this geometry. Numerical predictions of turbulent flow have been obtained for RaH~0(10^9 -10^11 ) and compared with existing experimental data. A previously developed second moment closure model (Behnia et al. 1987) has been used to model the turbulence. Results indicate that a second moment closure model is capable of predicting the observed flow features.