Sphere Cap Research Articles

Design and implementation of I‐slot conformal circular patch antenna on sphere structure

In this article, an I-slot circular patch antenna conformed on a spherical structure is proposed. For the implementation of the proposed antenna, the polylactic acid (PLA) material is used with the help of a 3D printer. In accordance with this purpose, we determine the permittivity value of the PLA with a T-resonator method before the design process. Then, the geometrical design of the spherical patch antenna is optimized by means of a differential evolution algorithm. After the design and optimization process, the conformal spherical patch antenna is fabricated on a sphere cap. The main characteristics of the proposed antenna are given for both the simulations and the measurements. It is seen that the simulation results agree well with the measurement results. Furthermore, an experiment is performed in order to examine the application possibility of the presented spherical antenna. For this experiment, a spherical communication module with the proposed antenna and an inner wireless transmitter system is built. In this experiment, the spherical module is rolled down a slope while it continuously transmits pseudo-random numbers. The data are received by a receiver station at the top of the slope. The received data are evaluated in terms of the amount of received packets per unit of time. The numerical results indicate that the proposed antenna can be used for dynamic spherical systems such as throwable objects and spherical robots.

Ductile Fracture Analysis of Welded Hollow Spherical Joints Subjecting Axial Forces with Micromechanical Fracture Models

Two micromechanical fracture models, void growth model (VGM) and stress modified critical strain (SMCS) model, were adopted to distinguish the failure mechanism of welded hollow spherical (WHS) joints under axial load based on FE analysis. Ductile fracture was successfully predicted for WHS joints under axial tension. The predicted fracture location is at the weld toe between WHS joints and circular hollow section members, which is consistent with corresponding test results. The predicted fracture load is lower than the peak load on the load–displacement curve, which indicates that the failure mechanism of WHS joints under axial tension is fracture due to inadequate strength and the fracture load should be taken as the ultimate load bearing capacity of the joints. A simplified SMCS model was proposed and verified for ductile fracture prediction of WHS joints under axial tension. Micromechanical fracture analysis was also conducted on WHS joints under axial compression. It was obtained by both VGM and SMCS model that no fracture would occur before the load reached its peak value, the reason of which was discussed by tracing the variation of the equivalent plastic stain and stress triaxiality at the potential location of fracture. Therefore, the failure mechanism of WHS joints under axial compression is losing stability with the depression of the sphere cap and the peak load on the load–displacement curve should be taken as the ultimate load bearing capacity of WHS joints.

Numerical study on the single bubble rising behaviors under rolling conditions

The accurate prediction of bubbles rising characteristics is very important for the two-phase flow and heat transfer calculation, especially under the ocean conditions. The additional force will be introduced and applied on the bubbles and the bubble behaviors is different from that under the stationary conditions. In present work, two methods, the additional force and dynamic mesh of Arbitrary Lagrangian–Eulerian (ALE) method, are compared, the result shows these two methods are in accordance to calculate the effect of rolling. Then Volume of fluid (VOF) and ALE method have been used to calculate the single bubble rising characteristic under rolling conditions. Results show that sphere bubble, ellipsoidal bubble and sphere cap bubble exist during the whole rising process and the deformation is becoming larger with the increase of bubble size. The bubble tends to move laterally and periodically under rolling conditions. The period of lateral movement is in accordance with the rolling period and the amplitude of the bubble is proportional to the rolling amplitude. Also, larger bubbles have the higher rising velocity than the small ones. The bubble rising characteristics are determined by not only the rolling motion but also the surface oscillation under rolling conditions.

Design and numerical simulation of a new sandwiched sphere structure for ballistic protection

Sphere structures for ballistic protection have rarely been studied. In this paper a novel unit cell, called Square Based Pyramid Unit Cell (SBPUC), is created as a fundamental building block of sphere structures for the purpose of ballistic protection. Although it has been proved by the other authors that the arrangement of spheres in a tapered chain is an efficient way for impact energy absorption (Sokolow A, Pfannes JM, Doney RL, Nakagawa M, Agui JH. Absorption of short duration pulses by small, scalable, tapered granular chains. Appl Phys Lett 2005;87:1–3), it is very difficult to convert this 1D concept to 3D application in reality with arbitrary tapering angle. The adoption of SBPUCs may provide a good solution. In this research, the core of a sandwiched sphere structure is build with such SBPUCs and is characterized with increasing sphere diameter, decreasing sphere thickness, and increasing sphere cap thickness. From the numerical simulation results with ABAQUS/Explicit, the sandwiched sphere structure can absorb at least 11.6% more impact energy compared with the monolithic plate with the same area density. This study might provide a potential armor design platform which makes further performance improvement possible by optimizing the large parameter space associated with material selection and structure design.

Effect of the Insulating Shield Thickness on the Steady-State Diffusion-Limiting Current of Sphere Cap Microelectrodes

The effect of the insulating shield thickness on the steady-state diffusion-limiting current of sphere cap microelectrodes is investigated. Theoretical steady-state limiting currents are obtained by using a simulation procedure, which relies on the explicit finite difference method with a fixed time grid and an exponentially spatial grid. The results obtained indicate that the current increases by decreasing the thickness of the insulating sheath or by increasing the aspect ratio of the sphere cap (h/a, where h is the height of the sphere cap and a is the electrode basal radius), similarly to other types of microelectrodes with different electrode geometry, such as disks and finite cones. The simulated data are fitted to approximate analytical expressions to describe the dependence of the limiting current on both h/a and RG (RG=b/a, where b is the overall tip radius) parameter. Theoretical currents are also compared with experimental data, which are obtained with a range of mercury-coated platinum microelectrodes having different RG and h/a values. The measurements are performed by using cyclic voltammetry at 1 mVs(-1), in aqueous solutions containing Ru(NH3)6-Cl3 as electroactive species. A good agreement (within 3%) between theoretical and experimental steady-state currents is found. Finally, SECM operating in the feedback mode is used to assess the validity of the shape parameters found by voltammetry for sphere cap microelectrodes, whose insulating shields are of a thickness comparable to the electrode radius.

Application of Sphere Cap Mercury Microelectrodes and Scanning Electrochemical Microscopy (SECM) for Heavy Metal Monitoring at Solid/Solution Interfaces

AbstractIn this paper, a combination of anodic stripping voltammetry (ASV) at mercury microelectrodes and scanning electrochemical microscopy (SECM) was employed to establish the concentration profiles of heavy metal ions at the soil/water interface of a natural sediment and bauxitic‐soil sample. Air dried soil samples were equilibrated with aqueous solutions containing 0.5 M NaCl plus acetate buffers or HClO4 at different concentrations to allow the achievement of different pH either in the aqueous phase or in the soil slurry. It was verified that mixing acidified aqueous solution and the soil without stirring led to concentration profiles displaying a maximum at the water/soil interface. This was explained as due to pH gradients that originated at the soil/water interface and within the soil slurries. On the other hand, mixing the soils and water solutions, under stirring for 24–48 h, provided almost uniform pH throughout the system. This allowed obtaining uniform metal ion concentrations within the soil slurries. For the evaluation of the concentrations, the anodic charge involved in the stripping step was utilized. The mercury microelectrode was standardized in a 0.5 M NaCl aqueous solution by performing calibration plots over the concentration range 0.1–500 μM. To evaluate the concentrations of the metal ions in the soil slurries, a procedure was developed to obtain the apparent diffusion coefficients of the metal ions, which depended on the physical properties of the soil such as porosity and tortuosity. The microanalytical methodology proposed here can be utilized for predicting the mobilization of trace elements from soils that comes into contact with acid rain.

Scanning electrochemical microscopy imaging of rhodochrosite dissolution using gold amalgam microelectrodes

Gold/mercury amalgam (Au/Hg) microelectrodes with a diameter of 25 microm were developed for the detection of environmentally relevant analytes such as manganese and iron by scanning electrochemical microscopy (SECM), and applied to investigate the controlled dissolution of manganese carbonate (MnCO(3); rhodochrosite) in acidic conditions. Characterization of the amalgam electrode geometry via approach curves recorded during SECM experiments revealed Au/Hg microelectrodes with sphere cap geometry. Quantitative determination of Mn(2+) has been achieved by calibration of the Au/Hg microelectrode in bulk solution experiments. Subsequent SECM imaging experiments confirm the applicability of amalgam microelectrodes for imaging of Mn(2+) production during dissolution of MnCO(3) at pH 3.9. This study confirms feasibility and provides the fundamental basis of SECM imaging with amalgam microelectrodes to address biogeochemically relevant questions.

Sphere‐Cap Mercury Microelectrodes for Scanning Electrochemical Microscopy Above an Insulating Substrate

AbstractSphere‐cap mercury microelectrodes, fabricated onto platinum microdisks 1 and 10 μm radius, were employed as tips in scanning electrochemical microscopy (SECM). Experimental current vs distance curves were acquired above an insulating substrate with a series of sphere caps whose aspect ratio h/a (h is the height of mercury deposit, a is the disk basal radius) varied between 0.28 and 2.14. It was found that the hindered diffusion effect of the insulating surface was the less pronounced the higher was the h/a parameter of the sphere cap. Comparison of experimental and theoretical approach curves displayed a fairly good agreement for subhemisphere caps (h<a), and a less satisfactory agreement for hemispherical (h=a) and superhemispherical (h>a) caps. Preliminary coupled anodic stripping voltammetry and SECM measurements were also performed for the investigation on local chemical equilibria involving heavy metals at sediment/water interfaces.

Stability of mercury-coated platinum microelectrodes upon touching a solid surface in scanning electrochemical microscopy (SECM) experiments

The features of experimental approach curves, recorded in scanning electrochemical microscopy measurements, and acquired with a series of sphere-cap tips while approaching a solid insulating substrate, are examined in detail. Sphere-caps are prepared by electrodeposition of liquid mercury onto a platinum microdisk substrate 10 μm radius, and having RG= R/ a=10 ( R is total tip dimension, which includes the shield thickness and the electrode radius a). From the data obtained, it is established that sphere caps with aspect ratio h/ a>0.3 ( h is the sphere cap height) are able to touch, or even be squeezed against the surface of the solid substrate. Under these latter conditions, for the sphere caps, the negative feedback process at low tip–substrate distances, is more pronounced than that of the corresponding naked microdisk. A good tip stability and no mercury loss is observed upon touching the substrate for sphere caps with h/ a<1.3. This circumstance allows one to perform “contact” voltammetric measurements of lead ions adsorbed onto a thin layer chromatography plate.

Measurement and modeling of boundary shape and surface deformation of the Mongolian gerbil pars flaccida

The shape of the pars flaccida (PF) boundary and its pressure induced deformation was measured in five Mongolian gerbil ears, using an opto-electronic moiré interferometer. To determine the PF boundary, membranes were deformed by middle ear (ME) pressures of −2 kPa and +2 kPa. The boundary of the PF was defined as the locus of points where the pressure induced deformation begins. To a very high precision, this boundary was found to be a circle with the same radius for both over- and underpressure deformations. Between animals the radius varied from 0.760 mm to 0.778 mm. We show that the shape of the PF, while being deformed by static pressure in the ME, can be modeled as part of a sphere. Volume displacement can then be calculated as the volume enclosed by the sphere cap, delimited by the circular PF boundary plane. Volume displacement was calculated for membranes deformed by 400 Pa ME overpressure and −400 Pa ME underpressure. The agreement of the experimental data with the sphere cap model is shown to be very good, and results in a volume displacement measuring accuracy which is better than 10%.

Steady-State Currents at Sphere-Cap Microelectrodes and Electrodes of Related Geometry

Mercury microelectrodes, fabricated by electrodeposition on an inlaid disk, adopt the shape of a sphere cap. This article derives the steady-state diffusion-limited voltammetric current at such electrodes and correlates the current with the radius, area, and volume of the sphere cap. Also predicted are the steady-state currents at an entire sphere emerging from an insulating plane.

Simulating Natural Light

AbstractSimulating natural light is an interesting subject in computer graphics. Using the principles of meteorology, we build a sphere cap light source model. Unlike existing illumination or light source models, we consider the effects of both the ratio of direct light to diffuse light and the position of the sun under different weather conditions. We use an area light source to generate shadows and a point light source to generate the other effects. The ratio of the two types of light is adjusted by a brightness factor b while the position of the sun is determined by giving the light direction. In addition. a modifiable sphere cap is used to obtain modified penumbra which vary with illumination.

The polarizability of a truncated sphere on a substrate I

A general method for the calculation of the polarizability of a truncated spherical particle on a substrate is developed, assuming that this particle is much smaller than the wavelength of light. The relation between the polarizability and the optical properties of an assembly of such particles is discussed. The method is applied to the special cases of a sphere, hemisphere and thin spherical cap on a substrate.