Radius Of Sphere Research Articles

A novel gradient method for extracting elastoplastic properties of metals from spherical indentation force-contact radius data

A novel gradient method for extracting elastoplastic properties of metals from spherical indentation force-contact radius data

The Influence of Key Dimensions of the Swivel Hinge on the Mechanical Performance of Bridge Rotary Structure

To assess the influence of the spherical and supporting radius of swivel hinges on the anti-overturning capability of T-structures and the safety of lower turntables, this study focuses on large-tonnage rotary bridges spanning the South-to-North Water Diversion Project along the Jiaozuo to Tanghe Expressway. The research involved theoretical analysis and numerical simulations to evaluate the stability of the rotary structures and the load-bearing capacity of rotary platforms with varying spherical and supporting radii, and we generated 15 numerical models. The results indicate that the critical eccentricity for T-structure anti-overturning increases with larger supporting and spherical radii, with diminishing returns as the supporting radius decreases. The critical eccentricity for spherical hinges is consistently lower than that seen for flat hinges. The lower turntable’s failure characteristics divide it into four zones, as follows: main compressive stress failure at the bottom under the hinge, main tensile stress failure at the top around the hinge, and two other regions less prone to failure. The supporting radius significantly influences compressive and tensile stress failures, while the spherical radius mainly affects the tensile stress area. These results offer insights for the design and construction of large-tonnage rotational bridges.

Phase transitions, shadows, and microstructure of Reissner-Nordström-Anti-de-Sitter black holes from a geometrothermodynamic perspective

We study the thermodynamic properties of the Reissner-Nordström black hole with cosmological constant, expressed in terms of the curvature radius, using the approach of shadow thermodynamics and the formalism of geometrothermodynamics. We derive explicit expressions for the shadow radius in terms of the horizon, photon sphere, and observer radii. The phase transition structure turns out to strongly depend on the value of the curvature radius, including configurations with zero, one, or two phase transitions. We also analyze the black hole's microscopic structure and find differences between the approaches of thermodynamic geometry and geometrothermodynamics, which are due to the presence of the curvature radius. We impose the important condition that the black hole is a quasi-homogeneous thermodynamic system to guarantee the consistency of the geometrothermodynamic approach.

Plasma impact on black hole shadows and gravitational weak lensing in the Einstein–Maxwell-scalar theory

In this paper, we investigate the optical properties of a non-rotating charged black hole (BH) in the Einstein–Maxwell-scalar (EMS) theory, together with a plasma medium. We first consider the photon sphere and shadow radius under the impact of the plasma medium existing in the environment surrounding the BH in the EMS theory. We show that the radius of the photon sphere and the BH shadow decrease under the influence of the parameter β. We further study gravitational weak lensing in detail by adapting general methods and derive the light ray’s deflection angle around the BH together with the plasma environment. It is found that for uniform plasma, the deflection angle increases with the rise of the plasma parameter, whereas it decreases with the increase of the plasma parameter for non-uniform plasma. Besides, we also study the magnification of image brightness.

Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime

Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime

Thermal chaos of quantum-corrected-AdS black hole in the extended phase space

We briefly analyzed the equation of state and critical points of the quantum-corrected-AdS black hole and used the Melnikov method to study its thermal chaotic behavior in the extended phase space of flat, closed, and open universes. The results show that the black hole’s thermodynamic behavior is similar to that of the Van der Waals system. Although the critical ratios at the critical points in the three types of universes differ, they are all independent of the quantum correction parameter. Only an open universe can attain the critical ratio of 38\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{3}{8}$$\\end{document} corresponding to the Van der Waals system, while in the other two universes, the critical ratio is always greater than this value. For chaos, time perturbations will lead to chaotic behavior when their amplitude exceeds a critical value that depends on the quantum correction parameter and the radius of the dust sphere in the FRW model. Based on this, we found that the chaotic behavior of the black hole varies across different universes depending on the quantum correction parameter, but this parameter always makes chaos more likely. Using the value of the quantum correction parameter determined by Meissner, chaos is always more difficult to occur in an open universe compared to the other two types of universes. Which universe is most prone to chaos depends on the radius of the dust sphere. Finally, chaotic behavior is always present under spatial perturbations.

Open-source hardware and software for the measurement, characterization, reporting, and correction of geometric distortion in MRI.

Geometric distortion is a serious problem in MRI, particularly in MRI guided therapy. A lack of affordable and adaptable tools in this area limits research progress and harmonized quality assurance. To develop and test a suite of open-source hardware and software tools for the measurement, characterization, reporting, and correction of geometric distortion in MRI. An open-source python library was developed, comprising modules for parametric phantom design, data processing, spherical harmonics, distortion correction, and interactive reporting. The code was used to design and manufacture a distortion phantom consisting of 618 oil filled markers covering a sphere of radius 150mm. This phantom was imaged on a CT scanner and a novel split-bore 1.0 T MRI magnet. The CT images provide distortion-free dataset. These data were used to test all modules of the open-source software. All markers were successfully extracted from all images. The distorted MRI markers were mapped to undistorted CT data using an iterative search approach. Spherical harmonics reconstructed the fitted gradient data to 1.0±0.6% of the input data. High resolution data were reconstructed via spherical harmonics and used to generate an interactive report. Finally, distortion correction on an independent data set reduced distortion inside the DSV from 5.5±3.1 to 1.6±0.8mm. Open-source hardware and software for the measurement, characterization, reporting, and correction of geometric distortion in MRI have been developed. The utility of these tools has been demonstrated via their application on a novel 1.0 T split bore magnet.

Prediction of non-magnetic metal sphere radius using real part slope of inductance

The existing eddy current measurement thickness technology is mainly for one or more layers of metal plate. However, in real life, the radius of spherical metal is also a critical parameter, so using an eddy current sensor to measure it is also an important research topic. In this paper, real part slope of inductance is used as the characteristic value to characterize the radius of the non-magnetic metal sphere. Compared with the traditional real part of inductance, the addition of slope improves the accuracy and stability of detection data. The experimental results show that the maximum error rate of radius measurement is less than 2%, and the overall data stability is good, which can meet the measurement requirements.

Study on buckling characteristics of PC/PET spherical-cylindrical combined pressure cabin

The buckling characteristics of PC/PET spherical–cylindrical combined pressure cabins under uniform external pressure were studied via experimental and numerical methods. The material properties of the PC/PET plastic alloy were tested. Six spherical–cylindrical combined pressure cabins with different structures were designed and fabricated, and the thickness and geometry of each model were measured. The hydrostatic pressure experiment was carried out on all the pressure cabins, and the ultimate load of the pressure cabin was recorded. Linear buckling analysis and nonlinear buckling analysis of PC/PET spherical–cylindrical combined pressure cabins were carried out, and the numerical and experimental results were found to be consistent. Moreover, the effects of the spherical shell radius and the thicknesses of different combinations on the buckling load were studied.

Constrained cosmological simulations of the Local Group using Bayesian hierarchical field-level inference

We present a novel approach based on Bayesian field-level inference that provides representative initial conditions for simulation of the Local Group (LG) of galaxies and its neighbourhood, constrained by present-day observations. We extended the Bayesian Origin Reconstruction from Galaxies ( algorithm with a multi-resolution approach, allowing us to reach the smaller scales needed to apply the constraints. Our data model simultaneously accounts for observations of mass tracers within the dark haloes of the Milky Way (MW) and M31, for their observed separation and relative velocity, and for the quiet surrounding Hubble flow, represented by the positions and velocities of 31 galaxies at distances between one and four megaparsec. Our approach delivers representative posterior samples of realisations that are statistically and simultaneously consistent with all of these observations, leading to significantly tighter mass constraints than found if the individual datasets are considered separately. In particular, we estimate the virial masses of the MW and M31 to be $ (M_ 200c /M_ and $12.33 respectively, their sum to be $ 200c /M_ and the enclosed mass within spheres of radius $R$ to be $ (M(R)/M_ and $12.96 for $R=1$ Mpc and $3$ Mpc, respectively. The M31-MW orbit is nearly radial for most of our realisations, and most of them feature a dark matter sheet aligning approximately with the supergalactic plane, despite the surrounding density field not being used explicitly as a constraint. High-resolution, high-fidelity resimulations from initial conditions identified using the approximate simulations of our inference scheme continue to satisfy the observational constraints, demonstrating a route to future high-resolution, full-physics simulations of ensembles of LG look-alikes, all of which closely mirror the observed properties of the real system and its immediate environment.

Black holes, photon sphere, and cosmology in ghost-free [formula omitted] gravity

The improved version of ghost-free f(G) gravity introduced in Nojiri and Odintsov (2005) is proposed and investigated. It is demonstrated that improved ghost-free f(G) gravity may be consistently applied to describe the expanding universe (with horizon) as well as the static spacetime like black holes. Interestingly, such a theory looks like a close avatar of scalar-Einstein–Gauss–Bonnet gravity with the only difference that the scalar field is not a dynamical one so that many predictions of ghost-free f(G) gravity are very similar to that of sEGB gravity.We discuss the gravitational wave in the improved model with the condition that the propagating speed of the gravitational wave is identical to that of the propagation speed of light. A model that describes inflation in the early universe and could satisfy the observational constraints is also constructed. The solution of ghost-free f(G) gravity realising the given static spacetime with spherical symmetry is proposed. Some of such solutions realise explicitly the Reissner–Nordström black hole or the Hayward black hole, which is a regular black hole without curvature singularity, We also construct a black hole in our theory which contains the Arnowitt–Deser–Misner (ADM) mass, the horizon radius, and the radius of the photon sphere as independent parameters. The radius of the black hole shadow in this model as well as photon sphere radius are estimated. It is shown that there exists a parameter region which satisfies the constraints coming from Event Horizon Telescope observations. Furthermore, we construct model where the radius of the black hole shadow or photon orbit is smaller than the horizon radius supposed from the ADM mass.

X-ray diffraction and quasielastic neutron scattering studies of the structure and dynamic properties of water confined in ordered microporous carbon pores

The structure and dynamic properties of capillary-condensed water confined in ordered microporous carbon (OMC) of pores diameter 18.7 Å are investigated over a temperature range of 200–300 K by adsorption/desorption isotherms, X-ray diffraction (XRD), and quasielastic neutron scattering (QENS). The nitrogen adsorption/desorption isotherm of OMC pores at 77 K exhibits an I-type pattern. The water adsorption/desorption isotherm of OMC pores at 298 K is of type V. The XRD data on water confined in OMC reveal that the tetrahedral network structure of water is perturbed from the bulk water structure, but not to such an extent as found for water confined in MCM-41 and Ph-PMO previously reported. With decreasing the temperature, the ∼2.8 Å peak shifts to shorter distances, while the second-neighbor H2O– H2O interaction distances gradually increase from 3.95 Å and 4.49 Å to 4.43 Å and 4.84 Å, indicating a tendency to form a more tetrahedral-like hydrogen-bonded water structure at subzero temperatures. Below 230 K, the hexagonal ice Ih was partially formed in OMC pores. The QENS spectra were analyzed using a jump-diffusion model to translate water molecules. The translational diffusion of water molecules in OMC pores is comparable to that of bulk water at 300 K and higher than that in MCM-41, and the mobility slows as the temperature decreases. The elastic incoherent structure factor (EISF) analysis found evidence for immobile and mobile fractions of confined water. The mobile fraction exhibited jump diffusion, with a jump length consistent with a sphere of confinement radius of 4–8 Å. The results obtained in the present work are compared with those reported for MCM-41 with a hydrophilic interface and Ph-PMO with an amphiphilic interface, and the influence of interface effect on local structure and dynamic properties of confined water is discussed.

Backreaction in Numerical Relativity: Averaging on Newtonian gauge-like hypersurfaces in Einstein Toolkit cosmological simulations

We introduce a spatial averaging scheme and use it to study the evolution of spatial averages in large-scale simulations of cosmological structure formation performed with the Einstein Toolkit. The averages are performed on the spatial hypersurfaces of the simulation setup which, at least initially, represent the hypersurfaces of statistical homogeneity and isotropy. We find only negligible cosmic backreaction on these hypersurfaces even on very small scales, but find significant curvature fluctuations of up to 10% in ΩR for sub-volumes with radius ∼200 Mpc and even larger fluctuations in smaller sub-volumes. In addition, we quantify fluid flow in and out of these sub-volumes. We find this to be significant, up to a 5% change in the density between redshift z=1 and z=0 of a single sphere of radius ∼200 Mpc (and larger for smaller spheres). We suggest this may be important for studies basing averages on volumes co-moving with the simulation hypersurfaces.

Flame Front Model with the Clusters Condensation

The processes model in a flame during the n-alkanes air mixture combustion initiation is proposed, taking into account the supramolecular structures formation possibility in the peroxide clusters form. This approach is justified by the n-alkanes melting temperatures correlation with their autoignition temperatures and anti-knock indexes. The condensation possibility is provided for such high molecular structures. Boiling temperatures values at flame front pressures characteristic were evaluated. To predict the peroxide clusters melting temperatures, a formula developed earlier for the hydrocarbons condensed state was used, which takes into account the length and molecular weight of modeled clusters. Expected peroxide clusters melting temperatures were predicted for conditions of dimeric and tetrameric structures. A linear dependence was used to recalculation the obtained values in boiling temperatures. It is shown that the calculated clusters phase transitions characteristic temperatures can be realized in the flame front preparatory zone. Based on the condensation theory, the flame front thickness and the minimum non-extinguishing sphere radius during ignition were estimated: the obtained data closely coincide with these parameters known values.

Banakh spaces and their geometry

Following Will Brian, we define a metric space X to be Banakh if all nonempty spheres of positive radius r in X have cardinality 2 and diameter 2r. Standard examples of Banakh spaces are subgroups of the real line. In this paper we study the geometry of Banakh spaces, characterize Banakh spaces which are isometric to subgroups of the real line, and also construct Banakh spaces X which do not embed into the real line and have a prescribed distance set d[X2].

Study on the scattering characteristics of large double-spherical systems

To study the influence of multiple scattering factors on the scattering characteristics, the scattering properties of a sizable double-spherical system at random orientations were analyzed by comparison of the T matrix and simple addition in the S-, C-, and X-bands, including the backscatter section (Cbak), attenuation section (Cext) and scattering section (Csca), asymmetry factor (g), and single scattering albedo (w), with the change in the spherical distance (d) and particle radius (r). It was found that the spacing between the spheres is four times the sphere’s radius, which is a clear cut-off point for the influence of multiple scattering in a two-spherical system. Then, by fitting the relative difference multiples of the T matrix method and the simple addition method, the uniform expression of each optical parameter under multiple scattering conditions is obtained.

A New Retest-Stable Tortuosity Metric for Retinal Vessel Analyses.

Existing retinal vessel tortuosity metrics lack standardization and retest reliability, hindering their clinical utility. Our study addresses this gap by introducing a novel metric, coined as the "vascular curvature index" (VCI), to enhance accuracy and consistency in biomarkers associated with medical conditions. We assess VCI's performance in terms of retest reliability in healthy subjects to transform early detection and monitoring approaches for various diseases. We recruited 44 patients for a single-session study, capturing fundus images before and after a five-minute break. Using AutoMorph, we generated vessel segmentation maps and evaluated retest reliability using multiple tortuosity metrics. The VCI was introduced and statistically compared to existing metrics. We performed a paired one-sided t-test to test for significantly improved retest reliability of our newly proposed metric. We analyzed distribution histograms, Fisher-Pearson coefficient of skewness, and correlation matrices for further insights. VCI is the most retest-reliable metric, statistically surpassing other curvature metrics, except inverse spherical radius tortuosity. With a somewhat negatively distributed pattern (coefficient of skewness of -0.52), VCI exhibits the strongest correlation with the second most retest-reliable metric; inverse-radius-tortuosity (Pearson and Spearman correlation of 0.7 and 0.72, respectively). Its correlation with angle-tortuosity is lower (Pearson and Spearman correlation of 0.05 and 0.07, respectively). The VCI emerges as a highly retest-reliable metric with a relatively normal distribution in healthy patients. Further investigation is warranted to evaluate its clinical performance in real-world applications, potentially influencing proactive healthcare interventions and personalized treatment decision-making.

Quasinormal modes, thermodynamics and shadow of black holes in Hu–Sawicki f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{f(R)}$$\\end{document} gravity theory

We derive novel black hole solutions in a modified gravity theory, namely the Hu–Sawicki model of f(R) gravity. After obtaining the black hole solution, we study the horizon radius of the black hole from the metric and then analyse the dependence of the model parameters on the horizon. We then use the 6th order WKB method to study the quasinormal modes of oscillations (QNMs) of the black hole perturbed by a scalar field. The dependence of the amplitude and damping part of the QNMs are analysed with respect to variations in model parameters and the error associated with the QNMs are also computed. After that we study some thermodynamic properties associated with the black hole such as its thermodynamic temperature as well as greybody factors. It is found that the black hole has the possibility of showcasing negative temperatures and is thermodynamically unstable for feasible values of model parameters. Then we analyse the geodesics and derive the photon sphere radius as well as the shadow radius of the black hole. The photon radius is independent of the model parameters while shadow radius showed fair amount of dependence on the model parameters. We tried to constrain the parameters with the help of Keck and VLTI observational data and obtained some bounds on m and c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_{2}$$\\end{document} parameters.

Improving mimetic gravity with non-trivial scalar potential: Cosmology, black holes, shadow and photon sphere

It is not easy to treat the spacetime with horizon(s) in the standard mimetic gravity. The solution to this problem has been presented in Nojiri and Nashed (2022), where it was suggested to modify the Lagrange multiplier constraint.In this paper, by using the improved formulation, we investigate the cosmology and black holes in mimetic gravity with scalar potential and in the scalar mimetic F(R) gravity. The inflationary era and dark energy epoch for the above theories are presented as specific examples from the general reconstruction scheme which permits to realize any universe expansion history via the choice of the corresponding scalar potential or function F(R). Two black hole solutions including the Schwarzschild and Hayward ones are constructed. The shadow and the radius of the photon sphere for the above black holes are found. The explicit confrontation of the black hole shadow radius with the observational bounds from M87∗ and Sgr A∗ objects is done. It is demonstrated that they do not conflict with Event Horizon Telescope observations.

Optical pattern formation of laser fields in the Rydberg atomic gases

We study the phenomena of long-wave and short-wave modulation instabilities (LMI and SMI) in Rydberg atomic gases within the framework of the nonlocal nonlinear Schrödinger equations in the local and nonlocal regions (characterized by the ratio of beam radius to radius of Rydberg blockade sphere), respectively. We further reveal the rich soliton dynamics arising from interactions of nonlinear waves triggered by LMI. We also show the variety of spatial self-organization pattern formations and their active manipulation due to SMI. Through a synthesis of theoretical analysis and numerical simulations, the self-organized optical structures reported here provide a way for realizing what we believe to be novel optical patterns and solitons based on Rydberg atomic gases.