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.

Particle size distribution effects on preferential deposition areas in metal foam wrapped tube bundle

This paper presents a numerical model for understanding particle transport and deposition in metal foam heat exchangers. Two-dimensional steady and unsteady numerical simulations of a standard single row metal foam-wrapped tube bundle are performed for different particle size distributions, i.e. uniform and normal distributions. Effects of different particle sizes and fluid inlet velocities on the overall particle transport inside and outside the foam layer are also investigated. It was noted that the simplification made in the previously-published numerical works in the literature, e.g. uniform particle deposition in the foam, is not necessarily accurate at least for the cases considered here. The results highlight the preferential particle deposition areas both along the tube walls and inside the foam using a developed particle deposition likelihood matrix. This likelihood matrix is developed based on three criteria being particle local velocity, time spent in the foam, and volume fraction. It was noted that the particles tend to deposit near both front and rear stagnation points. The former is explained by the higher momentum and direct exposure of the particles to the foam while the latter only accommodate small particles which can be entrained in the recirculation region formed behind the foam-wrapped tubes.

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.

A two-arm cluster randomized control trial to determine the effectiveness of a pressure ulcer prevention bundle for critically ill patients

Purpose This study tested the effectiveness of a pressure ulcer (PU) prevention bundle in reducing the incidence of PUs in critically ill patients in two Saudi intensive care units (ICUs). Design A two-arm cluster randomized experimental control trial. Methods Participants in the intervention group received the PU prevention bundle, while the control group received standard skin care as per the local ICU policies. Data collected included demographic variables (age, diagnosis, comorbidities, admission trajectory, length of stay) and clinical variables (Braden Scale score, severity of organ function score, mechanical ventilation, PU presence, and staging). All patients were followed every two days from admission through to discharge, death, or up to a maximum of 28 days. Data were analyzed with descriptive correlation statistics, Kaplan-Meier survival analysis, and Poisson regression. Findings The total number of participants recruited was 140: 70 control participants (with a total of 728 days of observation) and 70 intervention participants (784 days of observation). PU cumulative incidence was significantly lower in the intervention group (7.14%) compared to the control group (32.86%). Poisson regression revealed the likelihood of PU development was 70% lower in the intervention group. The intervention group had significantly less Stage I (p = 002) and Stage II PU development (p = 026). Conclusions Significant improvements were observed in PU-related outcomes with the implementation of the PU prevention bundle in the ICU; PU incidence, severity, and total number of PUs per patient were reduced. Clinical Relevance Utilizing a bundle approach and standardized nursing language through skin assessment and translation of the knowledge to practice has the potential to impact positively on the quality of care and patient outcome.

Reducing pressure injuries in critically ill patients by using a patient skin integrity care bundle (InSPiRE)

Purpose To test an interventional patient skin integrity bundle, InSPiRE protocol, on the impact of pressure injuries (PrIs) in critically ill patients in an Australian adult intensive care unit (ICU). Methods Before and after design was used where the group of patients receiving the intervention (InSPiRE protocol) was compared with a similar control group who received standard care. Data collected included demographic and clinical variables, skin assessment, PrI presence and stage, and a Sequential Organ Failure Assessment (SOFA) score. Results Overall, 207 patients were enrolled, 105 in the intervention group and 102 in the control group. Most patients were men, mean age 55. The groups were similar on major demographic variables (age, SOFA scores, ICU length of stay). Pressure injury cumulative incidence was significantly lower in the intervention group (18%) compared to the control group for skin injuries(30.4%) (χ2=4.271, df=1, p=0.039) and mucous injuries (t test =3.27, p=<0.001) . Significantly fewer PrIs developing over time in the intervention group (Logrank= 11.842, df=1, p=<0.001) and patients developed fewer skin injuries (>3 PrIs/patient = 1/105) compared with the control group (>3 injuries/patient = 10/102) (p=0.018). Conclusion The intervention group, recieving the InSPiRE protocol, had lower PrI cumulative incidence, and reduced number and severity of PrIs that developed over time. Systematic and ongoing assessment of the patient's skin and PrI risk as well as implementation of tailored prevention measures are central to preventing PrIs.

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.