Half Sphere Research Articles

Cylinder transition amplitudes in pure AdS3 gravity

A spacelike surface with cylinder topology can be described by various sets of canonical variables within pure AdS3 gravity. Each is made of one real coordinate and one real momentum. The Hamiltonian can be either H = 0 or it can be nonzero and we display the canonical transformations that map one into the other, in two relevant cases. In a choice of canonical coordinates, one of them is the cylinder aspect q, which evolves nontrivially in time. The time dependence of the aspect is an analytic function of time t and an “angular momentum” J . By analytic continuation in both t and J we obtain a Euclidean evolution that can be described geometrically as the motion of a cylinder inside the region of the 3D hyperbolic space bounded by two “domes” (i.e. half spheres), which is topologically a solid torus. We find that for a given J the Euclidean evolution cannot connect an initial aspect to an arbitrary final aspect; moreover, there are infinitely many Euclidean trajectories that connect any two allowed initial and final aspects. We compute the transition amplitude in two independent ways; first by solving exactly the time-dependent Schrödinger equation, then by summing in a sensible way all the saddle contributions, and we discuss why both approaches are mutually consistent.

Development of a 3D-printed Medication Label for the Blind and Visually Impaired.

This study explored the potential of three-dimensional printing (3DP) technology in producing a three-dimensional (3D) medication label for blind and visually impaired (BVI) patients to ease their drug administration. Different variations of label wordings, dosing instructions, and medication identifiers were designed with reference to guidelines by the American Foundation for the Blind. Shapes and symbols were used as dosing instructions and medication identifiers to the patient’s medical conditions. Prototype designs were created with common graphics computer-assisted drafting software and 3D-printed using acrylonitrile butadiene styrene as the polymer filament. Feedback was then obtained from five people with normal vision and four BVI persons. The initial prototype comprised four components, namely, medication name and strength, patient’s name, dosing instruction, and medication identifier. A revised label comprising the latter two components was developed after feedback by BVI persons. Words were in all uppercase and regular font type, with a 5-mm center-to-center letter spacing. Elevation heights of the letters alternated between 1 mm and 1.5 mm. A half sphere represented the medication dose unit, while vertical lines and a horizontal center line with alternating elevation of arrowheads represented the frequency of administration and the medication’s consumption in relation to food, respectively. Symbols based on target organs were used as medication identifiers. With rapid advancements in 3DP technologies, there is tremendous potential for producing 3D labels in patients’ medication management.

High-Speed Forming of Continuous Fiber Reinforced Thermoplastics

Forming processes of continuous fiber reinforced thermoplastic materials are oftentimes limited to high volume production due to the high costs for tooling and processing machines. This study suggests the combined use of a cold and simple tool and high forming speeds to reduce tooling and processing costs and enable the usage of common stamping machines. Half sphere samples are produced from single and two-layer polypropylene and glass fiber organo-sheets in a custom built drop tower and analyzed for their geometry, degree of re-consolidation, surface quality and potential fiber damage using a variety of microscopy techniques. While only mediocre degrees of re-consolidation and limited surface qualities can be achieved with the combination of a cold tooling and state-of-the-art forming speeds of 0–0.5 ms−1, the usage of a higher forming speed of 3 ms−1, vastly improves surface qualities and the degree of re-consolidation without any detectable fiber damage. This effect is more pronounced in the dual layer material. Extensive knowledge on the forming behavior of continuous fiber reinforced thermoplastics at high cooling rates and high speeds of deformation is required for sufficient process control and future studies need to further elaborate and quantify the influencing factors and limits of high-speed forming of continuous fiber reinforced thermoplastics.

Laser Surface Texturing of PECM Tools and the Validation

As a non-contact unconventional machining approach, Electrochemical Machining (ECM), it is widely used for the machining of modern high-strength materials in the automotive, aerospace, or medical industry. ECM is also considered as an effective approach to reproduce complex surface patterns on the workpieces with high geometrical precision. On the other hand, it becomes a practical demand to precisely produce the desired pattern molds on the ECM tools, i.e., cathodes. Compared to traditional cathode forming approaches, such as milling, a short-pulsed laser can shape or sculpture functional surfaces on the scale of micrometers. In this study, a nanosecond laser was implemented to produce several complex two- and three-dimensional patterns on the PECM cathodes, made of the stainless steel 1.4301, including grooves, half spheres, and hexagonal pyramids. The textured tools were tested and validated on an industrial PECM machine PEMCenter8000, by replicating those patterns on workpieces made of Ti-6Al-4V. In this paper, fabrication of the tool patterns using nanosecond laser and and the subsequent quality inspection are introduced, and the first results of the tool validation are presented by comparing the geometrical measurement of the tool patterns to those replicated on the workpieces. It is found that the tool patterns produced by the nanosecond laser have clear surface conditions, and the tool pattern shapes meet the initial design. The geometrical precision of the pattern replications on the workpieces could be strongly influenced by the pattern design, as those sharp edges could cause an anisotropic electric field and instable electrolyte flushing conditions. The molten materials staked on the sharp positions might also be an important factor.

Numerical Analysis of Under-Reamed Pile Subjected to Dynamic Loading in Sandy Soil

Under-reamed piles are piles with enlarged bases, which may be single bulb or multi bulbs. Such piles are suitable for resisting considerable soil movement of filed up ground, soft clay, and loose sand and have the advantages of increasing the soil strength and decreasing the displacement. In the present study, the finite element method was used to analyse the performance of a single pile with under-reamed bulbs of different shapes, that is, single cone, double cone, and half and full sphere, embedded in homogeneous, poorly graded sandy soil. The model of under-reamed pile was made of reinforced concrete and the bulb located at the middle of the embedded length of the pile. The dynamic load applied on the piles is a vertical harmonic load produced from the vibration of machine fixed on the pile cap and the results analysed using PLAXIS 3D software. The Moher-Coulomb model was used to simulate the behaviour of the soil and the linear elastic model was used for simulating the behaviour of the pile material. The load-settlement curve was obtained from the analysis of different patterns of the under-reamed pile, and the results showed a reduction in the settlement by 1,670% when using a single cone. The single cone gives the best results in comparison with other shapes of under-reamed bulbs.

Determining the tribological properties of different 3D printing filaments

The paper aims to determine the friction coefficient and wear behaviour of different 3D filaments in contact with a metallic disc. The method used for testing was the pin-on-disc method, where 3D half inch diameter pins with a half sphere end were printed out of the different filaments and rotated on the disc. The optimal time for measuring the friction coefficient was determined by observing when a sudden change in friction was recorded by the sensor as a result of material deposition on the disc. All filaments were tested for the same amount of time using the same normal loads. The friction behaviour was monitored and the mass wear was determined by weighting the spheres before and after each test. The research work of this paper was orientated to determine which 3D printing filament is most suitable for building different parts that come in contact with one another such as parts for creating an innovative 3D printed smart shoes sole.

Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications

Nonlocal gradient operators are prototypical nonlocal differential operators that are very important in the studies of nonlocal models. One of the simplest variational settings for such studies is the nonlocal Dirichlet energies wherein the energy densities are quadratic in the nonlocal gradients. There have been earlier studies to illuminate the link between the coercivity of the Dirichlet energies and the interaction strengths of radially symmetric kernels that constitute nonlocal gradient operators in the form of integral operators. In this work we adopt a different perspective and focus on nonlocal gradient operators with a non-spherical interaction neighborhood. We show that the truncation of the spherical interaction neighborhood to a half sphere helps making nonlocal gradient operators well-defined and the associated nonlocal Dirichlet energies coercive. These become possible, unlike the case with full spherical neighborhoods, without any extra assumption on the strengths of the kernels near the origin. We then present some applications of the nonlocal gradient operators with non-spherical interaction neighborhoods. These include nonlocal linear models in mechanics such as nonlocal isotropic linear elasticity and nonlocal Stokes equations, and a nonlocal extension of the Helmholtz decomposition.

On the thin-walled half sphere deep drawing on the hydraulic press with digital control

On the thin-walled half sphere deep drawing on the hydraulic press with digital control

On s-harmonic functions on cones

We deal with non negative functions which are s-harmonic on a given cone of the n-dimensional Euclidean space with vertex at zero, vanishing on the complementary. We consider the case when the parameter s approaches 1, wondering whether solutions of the problem do converge to harmonic functions in the same cone or not. Surprisingly, the answer will depend on the opening of the cone through an auxiliary eigenvalue problem on the upper half sphere. These conic functions are involved in the study of the nodal regions in the case of optimal partitions and other free boundary problems and play a crucial role in the extension of the Alt-Caffarelli-Friedman monotonicity formula to the case of fractional diffusions.

Making a Rhombicosidodecahedron: Mathematical Thinking Revisited

A rhombicosidodecahedron (an Archimedean solid with 30 square, 20 triangles, and 12 pentagon faces) was redeemed from 60 pieces by modular origami. This study used a qualitative research case study as it asked about how participants experienced this construction process of rhombicosidodecahedron. Preservice primary mathematics teachers from a mathematics and art course were participants of the study. Additionally, one student; the first student who came out with the totally symmetric and no damaged object was interviewed for the assembly process. Mathematical thinking throughout the process was noted. Student brought her/his previous experiences as much as specific aptıtudes. Student took this project as a creative writing piece so that the process gone through similar phases as intro, progress, and artifact. Deformations and sinking occurred but student investigated the specifics of the real mathematical object did it without a fault. To deal with problems occurred in the phases; students used a creative insight as using paperclips to attach modules and assembly of half spheres. Two main processes; organizational and structural took place in the creative model formation and assembly. Suggestions and future studies are also discussed.

“This Heavy Thing”: Catherine the Great’s Coronation Crown

After seizing power in 1762, Catherine II organized the most extravagant coronation money could buy. To add to the splendour, she placed a rush order for a crown. With carte blanche to use luxurious objects from the Russian treasury, jeweler Jérémie Pauzié designed “one of the richest objects that has ever existed in Europe”. Five thousand diamonds adorned the surface of the two half spheres; two rows of white pearls outlined the edges of the miters. The pièce de résistance was a nearly 400-carat ruby red spinel, removed from the crown of Empress Anna, niece of Peter the Great. The world’s second largest spinel had been acquired in Peking in 1676 by Russia’s envoy to China. Thrilled, Catherine declared that she’d somehow manage to hold “this heavy thing” on her head during the four-hour Kremlin ceremony. In the tradition of Byzantine emperors before and Napoleon after, Catherine placed the crown on her own head. It was worn by all of her successors, from her son Paul I to Nicholas II, Russia’s last tsar.

Rising bubbles as mechanism for scavenging and aerosolization of diatoms

Bubbles rising in saline water cause steady displacement of ions at the bubble boundaries which creates anionic upper half sphere and significantly stronger cationic vortex. Since viable diatoms as well as bacteria develop negative charge on outer membranes, these are attracted to the cationic bubble bottom vortex that forms a whirling collection pocket. When bubble bursts at the air/water interface the diatoms and bacteria are ejected into the air with initial or secondary jet droplets that are projected upward with a small water column derived from a sub-bubble cationic vortex. Laboratory experiments conducted in brackish and oceanic saline water on Nanofrustulum and Cyclotella cells indicate that their incorporation into jet droplets compared to original concentration in bulk water (here termed the enrichment factor) may range from 8 to 307.

Subcellular Quantification of Uptake in Gram-Negative Bacteria.

Infections by Gram-negative pathogens represent a major health care issue of growing concern due to a striking lack of novel antibacterial agents over the course of the last decades. The main scientific problem behind the rational optimization of novel antibiotics is our limited understanding of small molecule translocation into, and their export from, the target compartments of Gram-negative species. To address this issue, a versatile, label-free assay to determine the intracellular localization and concentration of a given compound has been developed for Escherichia coli and its efflux-impaired ΔTolC mutant. The assay applies a fractionation procedure to antibiotic-treated bacterial cells to obtain periplasm, cytoplasm, and membrane fractions of high purity, as demonstrated by Western Blots of compartment-specific marker proteins. This is followed by an LC-MS/MS-based quantification of antibiotic content in each compartment. Antibiotic amounts could be converted to antibiotic concentrations by assuming that an E. coli cell is a cylinder flanked by two half spheres and calculating the volumes of bacterial compartments. The quantification of antibiotics from different classes, namely ciprofloxacin, tetracycline, trimethoprim, and erythromycin, demonstrated pronounced differences in uptake quantities and distribution patterns across the compartments. For example, in the case of ciprofloxacin, a higher amount of compound was located in the cytoplasm than in the periplasm (592 ± 50 pg vs 277 ± 13 pg per 3.9 × 109 cells), but owing to the smaller volume of the periplasmic compartment, its concentration in the cytoplasm was much lower (37 ± 3 vs 221 ± 10 pg/μL for the periplasm). For erythromycin and tetracycline, differences in MICs between WT and ΔTolC mutant strains were not reflected by equal differences in uptake, illustrating that additional experimental data are needed to predict antibiotic efficacy. We believe that our assay, providing the antibiotic concentration at the compartment in which the drug target is expressed, constitutes an essential piece of information for a more rational optimization of novel antibiotics against Gram-negative infections.

Reconstruction of Solar Fuel Ultrathin Films via Periodically Microbending for Efficient Photoelectrochemical Water Splitting

Tackling the conflict between the optical and electronic properties of the ultrathin optoelectronic films is of critical importance for the development of highly efficient photoenergy conversion devices. We show in this report a proof of concept for designing an ultrathin photoelectrode film that compensates intrinsic low absorption coefficients and limited charge-carrier transport properties. To enhance light absorption under these conditions a light trapping structure using coupled optical properties was designed on the basis of an array of hollow half spheres generated by periodically microbending the deposited thin film, yielding well-defined two-dimensional ordered microspaces. Exemplified by α-Fe2O3, this film structure is able to generate an approximately 4.5-fold increase in photocurrent at a bias of 1.23 V versus RHE under simulated solar radiation conditions compared to that of a flat film with the same thickness. Both the experimental results and the theoretical simulations prove that modulatin...

Orthogonal polarization switchable lasing based on axial polarization pulling of SBS in polarization-maintaining fiber.

The axial polarization pulling, due to stimulated Brillouin scattering (SBS) in linear polarization maintaining fibers (PMFs), is proposed, simulated by vectored SBS equations, and demonstrated experimentally. The simulation shows that the SBS pulling is always towards one of principal axes of PMF, depending on the pump light projection of the input state of polarization (SOP) on the polarization vector of PMFs. Based on this principle, an SBS fiber laser with 20 m PMF is configured. Further, we observe that the SOP of lasing light switches between two orthogonal SOPs, as the pump light changes its SOP between two half spheres of the Poincaré sphere. Moreover, the orthogonal polarization switching (OPS) scenarios relating to different powers and SOPs of pump light are studied. We analyze and experimentally demonstrate the lasing conditions for the fully polarized OPS state, where only one of the principal polarization modes resonates, as well as the depolarization state, where two principal polarization modes resonate simultaneously.

On s-harmonic functions on cones

We deal with non negative functions satisfying \[ \left\{ \begin{array}{ll} (-\Delta)^s u_s=0 & \mathrm{in}\quad C, u_s=0 & \mathrm{in}\quad \mathbb{R}^n\setminus C, \end{array}\right. \] where $s\in(0,1)$ and $C$ is a given cone on $\mathbb R^n$ with vertex at zero. We consider the case when $s$ approaches $1$, wondering whether solutions of the problem do converge to harmonic functions in the same cone or not. Surprisingly, the answer will depend on the opening of the cone through an auxiliary eigenvalue problem on the upper half sphere. These conic functions are involved in the study of the nodal regions in the case of optimal partitions and other free boundary problems and play a crucial role in the extension of the Alt-Caffarelli-Friedman monotonicity formula to the case of fractional diffusions.

Characterization of the droplet formation phase for the H2O[sbnd]LiBr absorber: An analytical and experimental analysis

The poor heat and mass transfer occurring in the H2OLiBr absorber is one of the main limitations towards reducing the size of absorption chillers. Previous research shows that, as droplets form at the base of the absorber pipes, considerably large mass transfer coefficients can be obtained. However, modeling this phase of droplet formation has not been fully explored, as most of the research focuses on the film flow process preceding the droplet formation. The present study focuses on two aspects. Firstly, the dynamics of the droplet formation is investigated, with a focus on the effect of the solid surface shape on the droplet formation. A model to describe the droplet profile geometry was developed using the Euler-Lagrange equation and validated against experimental tests. Several pin geometries were tested and the results have shown that a 120° rhomboidal geometry is more suitable to increase the liquid-vapor interface area, while lowering the risk of droplet coalescence. Secondly, an analytical heat and mass transfer model based on the Fourier Series method has been developed to study the influence of pin size on the absorption process in an adiabatic absorber. The results show that the optimum width of the 120° rhomboidal pin is found at 6 mm, which maximizes the water absorbed during the droplet formation phase, without excessive use of material. The common assumption that treats the forming droplet as a half sphere fails to capture changes in the pin-droplet interaction which adversely affects the model accuracy. The proposed model shows that for pin widths smaller than 6 mm, the absorption process is impaired by the lower surface area exposed to the water vapor, resulting in up to 67% less mass absorbed obtainable and a decrease in the cooling power obtainable.In more practical terms, a rated 3 kW of cooling power is used as a case study with a 6 mm pin which reduces the absorber volume by 30% with respect to an absorber with 3 mm wide pins. This shows that by treating the droplet formation phase with a more physically-sound geometrical domain can improve the accuracy of the absorption models and can be easily implemented with any programming language to help in the design optimization of the absorber.

CFD simulation of hemispherical domes: structural flexibility and interference factors

The computational fluid dynamics (CFD) method is widely used today for determining the wind action on structures. Along with the CFD method the wind tunnel experiments are also employed to achieve this purpose. The cost and effort required for a wind tunnel test, however, is much higher than that of the CFD method; therefore, it is beneficial to extend and validate the use of CFD method to various classes and types of structures. This paper firstly compares the results of CFD method with the results of three series of wind tunnel tests available in the literature. Then, numerically the effect of structural flexibility and the neighbourhood of the objects on the wind pressure distribution coefficients are studied. Two and three half spheres are arranged sequentially and transversally. According to the CFD analysis, at a clear distance greater than 2.5 times the diameter of the (obstructing) dome, the wind dynamic interference effects on the reference hemisphere are diminished.

Nanoindentation of ion-irradiated reactor pressure vessel steels – model-based interpretation and comparison with neutron irradiation

Ion-irradiation-induced hardening is investigated on six selected reactor pressure vessel (RPV) steels. The steels were irradiated with 5 MeV Fe2+ ions at fluences ranging from 0.01 to 1.0 displacements per atom (dpa) and the induced hardening of the surface layer was probed with nanoindentation. To separate the indentation size effect and the substrate effect from the irradiation-induced hardness profile, we developed an analytic model with the plastic zone of the indentation approximated as a half sphere. This model allows the actual hardness profile to be retrieved and the measured hardness increase to be assigned to the respective fluence. The obtained values of hardness increase vs. fluence are compared for selected pairs of samples in order to extract effects of the RPV steel composition. We identify hardening effects due to increased levels of copper, manganese-nickel and phosphorous. Further comparison with available neutron-irradiated conditions of the same heats of RPV steels indicates pronounced differences of the considered effects of composition for irradiation with neutrons vs. ions.

Modeling and simulation of brain herniation caused by subdural hematoma using finite-element method

Brain shift and herniation are important signs of increased intracranial pressure (ICP) caused by hematomas or other types of intracranial mass. We propose a novel finite-element model that can be deformed in response to increased ICP. The half sphere model of the brain is partially divided into two compartments by the intact mid-sagittal plane, allowing subfalcine herniation. A 40 mm circle in the center of its equatorial plane allows transtentorial herniation. We perform a single load step, structural static analysis, simulating a left-sided subdural hematoma (SDH) compressing the cerebral hemispheres from the outer surface of the left hemisphere. Subfalcine and transtentorial brain herniations are reproduced and visualized. The Poisson’s ratio represents the tightness of the brain and the pressure load represents the ICP. There is a linear relationship between maximal deformation and the pressure load. The maximal deformation at the basal circumference and that at the basal midline closely resembles the maximal thickness of the SDH and the midline shift. We have developed a simple finite-element model that can simulate brain shift and herniation caused by pressure loads exerted on its surface by a mass. The experimental results correlate well with clinical observation on patients with acute and chronic SDH.