Spherical Geometry Research Articles

Synthesis and crystal structure of a mixed-ligand zinc(II) complex derived from ethyl (2,6-dimethylphenylcarbamoyl) formate and 1,10-phenanthroline

ABSTRACT. A mixed-ligand zinc(II) complex, [Zn(Hpma)(phen)Cl] (where Hpma– = N-(2,6-dimethylphenyl)oxamate and phen = 1,10-phenanthroline), has been prepared by the reaction of zinc chloride, ethyl (2,6-dimethylphenylcarbamoyl)formate (Hdmp) and 1,10-phenanthroline under basic conditions in dimethylformamide. The structure of the complex was characterised by elemental analysis, IR, 1H-NMR, UV-Vis absorption and X-ray crystallography. The metal complex crystallises in the monoclinic system (space group P21/c) and is composed of the five-coordinate zinc ion in a distorted spherical square pyramidal geometry. Stabilisation of single crystals occurs through hydrogen bonds and π-π stacking interactions.
 
 KEY WORDS: Zinc(II), N-(2,6-Dimethylphenyl)oxamate, 1,10-Phenanthroline, Crystal structure, Hydrogen bonding, π-π Stacking, Mixed-ligand
 Bull. Chem. Soc. Ethiop. 2023, 37(4), 891-900. 
 DOI: https://dx.doi.org/10.4314/bcse.v37i4.7

Light rings in static and extremal black holes

In this work we establish some results concerning the existence of external light rings in extremal black hole spacetimes through the Newman-Penrose formalism. Specifically, assuming flat or (anti)--de Sitter asymptotics, staticity and the null energy condition, we show that a sufficient condition for the existence of external light rings is $R<2{K}_{G}$, where $R$, the curvature scalar of the spacetime and ${K}_{G}$, the Gaussian curvature of a spacelike two-surface, are both evaluated at the outermost event horizon, which can be endowed with spherical, hyperbolic or planar geometry. Our results are valid for any metric gravity theory where photons follow null geodesics.

Emergent area laws from entangled matrices

We consider a wavefunction of large N matrices supported close to an emergent classical fuzzy sphere geometry. The SU(N) Gauss law of the theory enforces correlations between the matrix degrees of freedom associated to a geometric subregion and their complement. We call this ‘Gauss law entanglement’. We show that the subregion degrees of freedom transform under a single dominant, low rank representation of SU(N). The corresponding Gauss law entanglement entropy is given by the logarithm of the dimension of this dominant representation. It is found that, after coarse-graining in momentum space, the SU(N) Gauss law entanglement entropy is proportional to the geometric area bounding the subregion. The constant of proportionality goes like the inverse of an emergent Maxwell coupling constant, reminiscent of gravitational entropy.

Uncovering Conformal Symmetry in the 3D Ising Transition: State-Operator Correspondence from a Quantum Fuzzy Sphere Regularization

The $3D$ Ising transition, the most celebrated and unsolved critical phenomenon in nature, has long been conjectured to have emergent conformal symmetry, similar to the case of the $2D$ Ising transition. Yet, the emergence of conformal invariance in the $3D$ Ising transition has rarely been explored directly, mainly due to unavoidable mathematical or conceptual obstructions. Here, we design an innovative way to study the quantum version of the $3D$ Ising phase transition on spherical geometry, using the ``fuzzy (non-commutative) sphere" regularization. We accurately calculate and analyze the energy spectra at the transition, and explicitly demonstrate the state-operator correspondence (i.e. radial quantization), a fingerprint of conformal field theory. In particular, we have identified 13 parity-even primary operators within a high accuracy and 2 parity-odd operators that were not known before. Our result directly elucidates the emergent conformal symmetry of the $3D$ Ising transition, a conjecture made by Polyakov half a century ago. More importantly, our approach opens a new avenue for studying $3D$ CFTs by making use of the state-operator correspondence and spherical geometry.

Coordinate System Invariant Formulation of Fractional‐Dimensional Child‐Langmuir Law for a Rough Cathode

AbstractThis work presents an exact closed‐form analytical model of the space charge limited (SCL) current density for planar, cylindrical, and spherical geometries in fractional dimensional spaces (Fα) where α represents the fractional dimensions having a range 0 < α ⩽ 1. Decreasing value of α shows an increasing degree of surface roughness. This analytical model approaches Langmuir–Blodgett equations for sufficiently close anode (Ra) and cathode (Rc) radii for integer dimensions (α = 1). To calculate SCL current density for any geometry, variational calculus (VC) is used to derive the differential equations in fractional (α) dimensions. The effect of electrode radius ratios on space charge limited current is investigated here considering the surface roughness.

A neuromorphic bionic eye with filter-free color vision using hemispherical perovskite nanowire array retina

Spherical geometry, adaptive optics, and highly dense network of neurons bridging the eye with the visual cortex, are the primary features of human eyes which enable wide field-of-view (FoV), low aberration, excellent adaptivity, and preprocessing of perceived visual information. Therefore, fabricating spherical artificial eyes has garnered enormous scientific interest. However, fusing color vision, in-device preprocessing and optical adaptivity into spherical artificial eyes has always been a tremendous challenge. Herein, we demonstrate a bionic eye comprising tunable liquid crystal optics, and a hemispherical neuromorphic retina with filter-free color vision, enabled by wavelength dependent bidirectional synaptic photo-response in a metal-oxide nanotube/perovskite nanowire hybrid structure. Moreover, by tuning the color selectivity with bias, the device can reconstruct full color images. This work demonstrates a unique approach to address the color vision and optical adaptivity issues associated with artificial eyes that can bring them to a new level approaching their biological counterparts.

A Green’s Function Method based approach for effectiveness factor evaluation in two-dimensional spherical catalyst geometries with non-linear kinetics and partial wetting

The solution of the two-dimensional spherical diffusion equation inside the catalyst particle is proposed using Green’s Function Method (GFM). A Green’s Function was derived using Eigenfunction expansion in the polar direction and considering jump discontinuity in the radial direction. The advantage of using multi-precision arithmetic in the evaluation of Green’s Function has been demonstrated. A pre-computed value of Green’s Function at a selected precision level was used to calculate the concentration profile inside the fully and partially wetted spherical catalyst particle geometry. The non-linear kinetic rate expression-based formulation for concentration profile calculation gives rise to non-linear equations. These non-linear equations were solved in PETSc (Balay et al., 2017) using various combinations of linear pre-conditioners and Krylov methods. A comparison with the Finite Difference Method (FDM) formulation is presented, and the advantage of the proposed GFM-based formulation for convergence and reduction in computation time is demonstrated.

Study of Decoupled Cosmological Solutions in f(R,T)$f(\mathbb {R},\mathbb {T})$ Theory

AbstractIn this paper, we consider a non‐static spherical geometry and formulate its extension for the case of anisotropic matter configuration through minimal gravitational decoupling in theory. We apply a particular transformation only on the radial metric function that divides the modified field equations into two distinct sectors corresponding to their parent (original and additional) sources. The unknowns in the first (isotropic) set are reduced by taking the Friedmann‐Lemaitre‐Robertson‐Walker cosmic model. We then obtain the isotropic solution by employing a linear equation of state and power‐law form of the scale factor. The other set involves the decoupling function and components of an extra source, therefore we adopt a density‐like constraint to close it. Finally, we analyze the role of this modified gravity and the decoupling parameter on three different eras of the cosmos by graphically observing the developed extended solution. It is concluded that the resulting solutions fulfill all the physical requirements only for the matter and radiation‐dominated eras.

Rapid and precise tracking of water influx and efflux across cell membranes induced by a pulsed electric field.

Quantitative measurements of water content within a single cell are notoriously difficult. In this work, we introduce a single-shot optical method for tracking the intracellular water content, by mass and volume, of a single cell at video rate. We utilize quantitative phase imaging and a priori knowledge of a spherical cellular geometry, leveraging a two-component mixture model to compute the intracellular water content. We apply this technique to study CHO-K1 cells responding to a pulsed electric field, which induces membrane permeabilization and rapid water influx or efflux depending upon the osmotic environment. The effects of mercury and gadolinium on water uptake in Jurkat cells following electropermeabilization are also examined.

Research on discrete element simulation of slump test for fresh self-compacting concrete

A numerical computational modelling of slump tests for fresh self-compacting concrete (SCC) was developed in this investigation based discrete element method (DEM). The coarse aggregates in DEM model were characterized by using spherical shapes and 3D irregular geometries obtained by scanning real aggregates, respectively. By comparing the results of the slump simulation tests corresponding to the two geometric models, it was found that the average error of the latter was smaller, about 2.9%. The results of quantitative analysis of the rotational kinetic energy for both found that the motion of the real coarse aggregate model was more consistent with the actual situation. The effect of coarse aggregate gradation characteristics on the flow properties of fresh SCC was investigated based on the real coarse aggregate model. The results indicated that the increase in the content of large-size coarse aggregate or its replacement of small-size coarse aggregate both resulted in the deterioration of the flow properties of fresh SCC. During the lifting of the bucket at the beginning of the slump test, different velocity distribution patterns existed before and after the complete separation of the bucket from the concrete. The maximum flow velocity, about 0.8 m/s, occurred when the bucket was not completely separated from the SCC and was distributed in the top part of the inner bucket.

The first X-ray look at SMSS J114447.77-430859.3: the most luminous quasar in the last 9 Gyr

ABSTRACT SMSS J114447.77-430859.3 (z = 0.83) has been identified in the SkyMapper Southern Survey as the most luminous quasar in the last $\sim 9\, \rm Gyr$ . In this paper, we report on the eROSITA/Spectrum–Roentgen–Gamma (SRG) observations of the source from the eROSITA All Sky Survey, along with presenting results from recent monitoring performed using Swift, XMM-Newton, and NuSTAR. The source shows a clear variability by factors of ∼10 and ∼2.7 over time-scales of a year and of a few days, respectively. When fit with an absorbed power law plus high-energy cutoff, the X-ray spectra reveal a Γ = 2.2 ± 0.2 and $E_{\rm cut}=23^{+26}_{-5}\, \rm keV$ . Assuming Comptonization, we estimate a coronal optical depth and electron temperature of $\tau =2.5-5.3\, (5.2-8)$ and $kT=8-18\, (7.5-14)\, \rm keV$ , respectively, for a slab (spherical) geometry. The broadband SED is successfully modelled by assuming either a standard accretion disc illuminated by a central X-ray source, or a thin disc with a slim disc emissivity profile. The former model results in a black hole mass estimate of the order of $10^{10}\, \mathrm{ M}_\odot$ , slightly higher than prior optical estimates; meanwhile, the latter model suggests a lower mass. Both models suggest sub-Eddington accretion when assuming a spinning black hole, and a compact ($\sim 10\, r_{\rm g}$ ) X-ray corona. The measured intrinsic column density and the Eddington ratio strongly suggest the presence of an outflow driven by radiation pressure. This is also supported by variation of absorption by an order of magnitude over the period of $\sim 900 \ \rm d$ .

Chiral Chromonics Confined in Spherical Geometries

Chromonic liquid crystals have recently received a lot of attention due to their spontaneous self-assembly in supramolecular columnar structures that, depending on their concentration in water, align to form a nematic liquid crystalline phase. The chirality may be induced in chromonics by adding chiral moieties to the nematic phase or enhanced by confining them in curved geometrical constraints. This review summarizes the recent research developments on chiral chromonic liquid crystals confined in spherical geometry, relating the results to what was observed for thermotropic liquid crystals in the same conditions. The review focuses on the studies carried out on commercially available nematic chromonics, investigating the effects on their topologies in different anchoring conditions and different chiral dopants and suggesting an application in the sensor field.

Effect of overlapping laser beams and density scale length in laser-plasma instability experiments on OMEGA EP

Experiments have been conducted on the OMEGA EP laser facility to study the effect of density scale length and overlapping beam geometry on laser-plasma instabilities near and below the quarter-critical density. Experiments were conducted in both planar geometry (density scale length L n ∼ 190 to 300 μm) and spherical geometry ( L n ∼ 150 μm) with up to four overlapping beams and were designed to have overlapped intensities and density scale lengths comparable to OMEGA spherical experiments, but with many fewer beams. In comparison with previous experiments on OMEGA and National Ignition Facility, it is confirmed that shorter density scale lengths favor the two-plasmon decay (TPD) instability, while longer density scale lengths favor stimulated Raman scattering (SRS). In addition, for experiments at the same scale length and overlapped laser intensity, higher single-beam intensities favor SRS, while a larger number of overlapping beams favor TPD.

Improving Co(II) separation from Ni(II) by solvent extraction using phosphonium-based ionic liquids

The solvent extraction of Co(II) from its aqueous solutions free of acids or chloride salts at high concentration by the ionic liquids trihexyl(tetradecyl)phosphonium bis(2,4,4-trimethylpentyl)phosphinate ([P66614][C272]) and trihexyl(tetradecyl)phosphonium thiocyanate ([P66614][SCN]) was characterised at saturation of the organic phase with Co(II) using toluene as diluent. The ionic liquids’ cation participated in the formation of two ion-pairs in the organic phase, i.e., one with the complex anion containing cobalt, and the other with the cobalt counter anion, thus preserving electroneutrality in both the organic and aqueous phases. This was considered to be an example of bifurcated extraction.UV–visible spectral studies of the intensively blue organic phase after Co(II) extraction demonstrated that the Co(II) coordination sphere geometry in the case of both extractants was tetrahedral. The Co(II) extraction stoichiometry was experimentally determined for the first time by saturating the organic phase with Co(II). The [P66614][C272] to Co(II) stoichiometric mole ratio in the extracted adduct was found to be 2.8:1, suggesting that eight phosphinate anions acted as bridging ligands around three cobalt centres. For the [P66614][SCN], the stoichiometric mole ratio was found to be 2.5:1 with the Co(II)-thiocyanate adduct consisting of two Co(II)-thiocyanate tetrahedra linked by a bridging thiocyanate ion.The Co(II) extraction was enhanced when the aqueous phase contained an anion with high lipophilicity (e.g., nitrate, thiocyanate). [P66614][SCN] did not extract Ni(II) from nitrate or chloride solutions, thus demonstrating its potential for the separation of Co(II) from Ni(II) without requiring the addition of high concentrations of acids or chloride salts to the aqueous phase.

Variations in Biodistribution and Acute Response of Differently Shaped Titania Nanoparticles in Healthy Rodents

Titanium dioxide nanoparticles (TiO2 NPs) are one of the main sources of the nanoparticulate matter exposure to humans. Although several studies have demonstrated their potential toxic effects, the real nature of the correlation between NP properties and their interaction with biological targets is still far from being fully elucidated. Here, engineered TiO2 NPs with various geometries (bipyramids, plates, and rods) have been prepared, characterized and intravenously administered in healthy mice. Parameters such as biodistribution, accumulation, and toxicity have been assessed in the lungs and liver. Our data show that the organ accumulation of TiO2 NPs, measured by ICP-MS, is quite low, and this is only partially and transiently affected by the NP geometries. The long-lasting permanence is exclusively restricted to the lungs. Here, bipyramids and plates show a higher accumulation, and interestingly, rod-shaped NPs are the most toxic, leading to histopathological pulmonary alterations. In addition, they are also able to induce a transient increase in serum markers related to hepatocellular injury. These results indicate that rods, more than bipyramidal and spherical geometries, lead to a stronger and more severe biological effect. Overall, small physico-chemical differences can dramatically modify both accumulation and safety.

Theoretical and experimental study on vibration sensitivity of a transportable spherical optical reference cavity with multi-channel

Optical reference cavities have a significant role in optical and atomic physics. In this paper, we describe a multi-channel transportable spherical optical reference cavity that is rigidly mounted and vibration insensitive. The structure is built based on sphere geometry with four supports arranged symmetrically in a tetrahedral pattern around the optical axis. We theoretically calculate the vibration sensitivities of the multi-channel spherical optical reference cavity. We measure the vibration sensitivities of the spherical optical reference cavity with a simple method that is achieved by measuring the change in the cavity linewidth caused by vibration. The observed vibration sensitivities to accelerations along three directions for the optical reference cavity are approximately (5.1–8.4) × 10−10/g. The theory results of vibration sensitivities are in accordance with experiments. Despite having higher vibration sensitivity than a cubic optical reference cavity, our spherical optical reference cavity has a mass that is approximately half that of a cubic optical reference cavity with the same dimensions. This is beneficial for transportable ultra-stable lasers.

Application of GDQ method to large amplitude response of FGM joined spherical-conical shells under rapid surface heating

Geometrically non-linear thermally induced vibrations of functionally graded material (FGM) joined spherical-conical shells are analyzed in the current research. Thermo-mechanical properties of the shells are assumed to be temperature and position dependent. The system of joined spherical-conical shells is subjected to thermal shock on the ceramic-rich surface, whereas the metal-rich one is kept at reference temperature. The one-dimensional transient heat conduction equation is established and solved via the generalized differential quadrature (GDQ) and Crank-Nicolson methods. This equation is non-linear since the thermo-mechanical properties of the shells are temperature dependent. The total functional of the shells is obtained under the assumptions of uncoupled thermoelasticity laws, first order shear deformation shell theory, and the von Kármán type of geometrical non-linearity. Non-linear coupled equations of motion are solved via the iterative Picard method accompanied with the β-Newmark time approximation technique. Numerical results are well-validated with the available data for the case of single FGM spherical shell. Parametric studies are conducted to examine the influences of conical and spherical shell geometries, material composition, temperature dependence, in-plane and out-of-plane mechanical boundary conditions, various configuration of conical/spherical shell system, and thermal boundary conditions. It is highlighted that thermally induced vibrations indeed exists.

Spherical vector radiative transfer model for satellite ocean color remote sensing.

Atmospheric correction is the key step for satellite ocean color remote sensing. However, most of the existing atmospheric correction algorithms do not consider the effects of Earth curvature. In fact, Earth curvature has a significant impact on satellite observation signals under large solar zenith angles or large viewing zenith angles. In this study, based on the Monte Carlo method, a vector radiative transfer model with spherical shell atmosphere geometry (hereafter our SSA-MC model) considering the influence of Earth curvature was established, which can be applied to conditions with high solar zenith angles or high viewing zenith angles. Our SSA-MC model was first compared with the Adams&Kattawar model, and the results show that the mean relative differences are 1.72%, 1.36% and 1.28% for solar zenith angles of 0 ∘, 70.47 ∘ and 84.26 ∘, respectively. Moreover, our SSA-MC model was further validated by more recently benchmarks from Korkin's scalar and vector models, and the results show that the relative differences are mostly less than 0.5% even at extremely high solar zenith angles (84.26 ∘). Then, our SSA-MC model was verified with the Rayleigh scattering radiance calculated by the look-up tables (LUTs) in SeaDAS under low-to-moderate solar or viewing zenith angles, and the results show that the relative differences are less than 1.42% when solar zenith angles are less than 70 ∘ and viewing zenith angles are less than 60 ∘. Our SSA-MC model was also compared with the Polarized Coupled Ocean-Atmosphere Radiative Transfer model based on the pseudo-spherical assumption (PCOART-SA), and the results show that the relative differences are mostly less than 2%. At last, based on our SSA-MC model, the effects of Earth curvature on Rayleigh scattering radiance were analyzed for both high solar zenith angles and high viewing zenith angles. The result shows that the mean relative error between the plane-parallel (PP) geometry and spherical shell atmosphere (SSA) geometry is 0.90% when the solar zenith angle is 60 ∘ and the viewing zenith angle is 60.15 ∘. However, the mean relative error increases with increasing solar zenith angle or viewing zenith angle. When the solar zenith angle is 84 ∘ and the viewing zenith angle is 84.02 ∘, the mean relative error is 4.63%. Thus, Earth curvature should be considered in atmospheric corrections at large solar or viewing zenith angles.

NGC 4388: a test case for relativistic disc reflection and Fe K fluorescence features

ABSTRACT We present a new analysis of the Suzaku X-ray spectrum of the Compton-thin Seyfert 2 galaxy NGC 4388. The spectrum above ∼2 keV can be described by a remarkably simple and rather mundane model, consisting of a uniform, neutral spherical distribution of matter, with a radial column density of $2.58\pm 0.02 \times 10^{23} \ \rm cm^{-2}$, and an Fe abundance of $1.102^{+0.024}_{-0.021}$ relative to solar. The model does not require any phenomenological adjustments to self-consistently account for the low-energy extinction, the Fe Kα and Fe Kβ fluorescent emission lines, the Fe K edge, and the Compton-scattered continuum from the obscuring material. The spherical geometry is not a unique description, however, and the self-consistent, solar abundance MYTORUS model, applied with toroidal and non-toroidal geometries, gives equally good descriptions of the data. In all cases, the key features of the spectrum are so tightly locked together that for a wide range of parameters, a relativistic disc-reflection component contributes no more than $\sim 2{{\ \rm per\ cent}}$ to the net spectrum in the 2–20 keV band. We show that the commonly invoked explanations for weak X-ray reflection features, namely a truncated and/or very highly ionized disc, do not work for NGC 4388. If relativistically broadened Fe Kα lines and reflection are ubiquitous in Seyfert 1 galaxies, they should also be ubiquitous in Compton-thin Seyfert 2 galaxies. The case of NGC 4388 shows the need for similar studies of more Compton-thin AGN to ascertain whether this is true.

Greener microwave synthesized Se nanospheres for antioxidant, cell viability, and antibacterial effect.

Selenium nanocrystals (SeNPs) were developed using Coccinia grandis fruit (CGF) extract by green microwave approach. The morphological characters revealed that the quasi SeNPs with dimensions ranging from 12 to 24 nm have been arranged in encapsulated spherical geometries with dimensions ranging from 0.47 to 0.71 m. The DPPH assay revealed that SeNPs at a concentration of 70 µl of 99.2% had the greatest possible scavenging capacity. The nanoparticle concentrations were around 500 g/mL and the cellular uptake of SeNPs through living thing extracellular matrix cell lines in vitro was limited to 75.1 ± 3.8%. The biocidal activity was tested against E. coli, B. cereus, and S. aureus strains. Since it had the greatest MIC against B. cereus with 32 mm compared with the reference antibiotics. These incredible qualities of SeNPs suggest that attempting to manipulate multi-purpose nanoparticles for powerful and flexible wound and skin therapeutic innovations is very impressive.