Images inside a reflecting spherical surface with possible application in astronomy

This report studies an algebraic equation whose solution gives the image system of a source of light as seen by an observer inside a reflecting spherical surface. The equation is looked at numerically using GeoGebra. Under the hypothesis that our galaxy is enveloped by a reflecting interface this becomes a possible model for many mysterious extra galactic observations.

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.

Is retinal shape different in Asians and Caucasians? Estimation from peripheral refraction and peripheral eye length methods

Purpose:Race appears to be associated with myopiogenesis, with East Asians showing high myopia prevalence. Considering structural variations in the eye, it is possible that retinal shapes are different between races. The purpose of this study was to quantify and compare retinal shapes between racial groups using peripheral refraction (PR) and peripheral eye lengths (PEL). Methods:A Shin-Nippon SRW5000 autorefractor and a Haag-Streit Lenstar LS900 biometer measured PR and PEL, respectively, along horizontal (H) and vertical (V) fields out to ±35° in 5° steps in 29 Caucasian (CA), 16 South Asian (SA) and 23 East Asian (EA) young adults (spherical equivalent range +0.75D to –5.00D in all groups). Retinal vertex curvature Rv and asphericity Q were determined from two methods: a) PR (Dunne): The Gullstrand-Emsley eye was modified according to participant’s intraocular lengths and anterior cornea curvature. Ray-tracing was performed at each angle through the stop, altering cornea asphericity until peripheral astigmatism matched experimental measurements. Retinal curvature and hence retinal co-ordinate intersection with the chief ray were altered until sagittal refraction matched its measurement. b) PEL: Ray-tracing was performed at each angle through the anterior corneal centre of curvature of the Gullstrand-Emsley eye. Ignoring lens refraction, retinal co-ordinates relative to the fovea were determined from PEL and trigonometry. From sets of retinal co-ordinates, conic retinal shapes were fitted in terms of Rv and Q. Repeated-measures ANOVA were conducted on Rv and Q, and post hoc t-tests with Bonferroni correction were used to compare races. Results:In all racial groups both methods showed greater Rv for the horizontal than for the vertical meridian and greater Rv for myopes than emmetropes. Rv was greater in EA than in CA (P=0.02), with Rv for SA being intermediate and not significantly different from CA and EA. The PEL method provided larger Rv than the PR method: PEL: EA vs CA 87±13 vs 83±11 m-1 (H), 79±13 vs 72±14 m-1 (V); PR: EA vs CA 79±10 vs 67±10 m-1 (H), 71±17 vs 66±12 m-1 (V). Q did not vary significantly with race. Conclusions:Estimates of Rv, but not of Q, varied significantly with race. The greater Rv found in EA than in CA and the comparatively high prevalence rate of myopia in many Asian countries may be related.

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.

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.

Singular perturbation analysis of spherical and cylindrical N waves

Using a singular perturbation analysis the nonplanar Burgers' equation is solved to yield the shock wave-displacement due to diffusion for spherical and cylindrical N waves, thus supplementing the earlier results of Lighthill for the plane N waves. Physics of Fluids is copyrighted by The American Institute of Physics.

High lithium storage in micrometre sized mesoporous spherical self-assembly of anatase titania nanospheres and carbon

Composite of anatase titania (TiO2) nanospheres and carbon grown and self-assembled into micron-sized mesoporous spheres via a solvothermal synthesis route are discussed here in the context of rechargeable lithium-ion battery. The morphology and carbon content and hence the electrochemical performance are observed to be significantly influenced by the synthesis parameters. Synthesis conditions resulting in a mesoporous arrangement of an optimized amount carbon and TiO2 exhibited the best lithium battery performance. The first discharge cycle capacity of carbon-titania mesoporous spheres (solvothermal reaction at 150 degrees C at 6 h, calcination at 500 degrees C under air, BET surface area 80 m(2)g(-1)) was 334 mAhg(-1) (approximately 1 Li) at current rate of 0.066 Ag-1. High storage capacity and good cyclability is attributed to the nanostructuring of TiO2 (mesoporosity) as well as due to formation of a percolation network of carbon around the TiO2 nanoparticles. The micron-sized mesoporous spheres of carbon-titania composite nanoparticles also show good rate cyclability in the range (0.066-6.67) Ag-1.

Spherical means with centers on a hyperplane in even dimensions

Given a real-valued function on R-n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with great simplicity and economy. We apply their method to derive an inversion formula for the even n case. A feature of our inversion formula, for the even n case, is that it does not require the Fourier transform of the mean values or the use of the Hilbert transform, unlike the previously known inversion formulas for the even n case. Along the way, we extend the isometry identity of Bukhgeim and Kardakov for odd n, for solutions of the wave equation, to the even n case.