Radius Ratio Research Articles

Simulation of the optical caustics associated with the secondary rainbow for tilted oblate droplets illuminated by a Gaussian beam

In this study, vector ray tracing is used to compute optical caustic associated with the secondary rainbow for an oblate spheroidal droplet illuminated by a Gaussian beam. The optical caustics are classified as rainbow fringes and hyperbolic umbilical fringes. By comparing with the optical caustics for droplet with parallel beam illumination, the influence of the Gaussian beam on the optical caustics is studied. The curvature of the rainbow fringes and the horizontal and vertical location of the cusp caustics are discussed for droplets with different droplet-to-beam ratios (i.e. the ratio of the equatorial radius of the droplet to the waist radius of the Gaussian beam). Furthermore, the optical caustics of tilted droplets were investigated and compared with those of the aligned droplets, based on the boundary of outgoing rays. The long-term aim is to develop a novel method for measuring the aspect ratio of oblate droplets with arbitrary orientation.

Eu-Substituents-Induced Modifications in the Thermoelectric Properties of the Zintl Phase Ba1-xEuxZn2Sb2 System.

Four quaternary Zintl phase thermoelectric (TE) materials belonging to the Ba1-xEuxZn2Sb2 (x = 0.02(1), 0.04(1), 0.08(1), 0.15(1)) system were successfully synthesized using the molten Pb-flux or the conventional high-temperature reaction methods. Their crystal structures were characterized by both powder and single-crystal X-ray diffraction analyses, and all four isotypic title compounds adopted the orthorhombic BaCu2S2-type (Pnma, Z = 4, Pearson code oP20) structure. The radius ratio criterion, based on the cationic and anionic elements (i.e., r+/r-), was successfully verified in the title system, as in our previous reports, where r+/r- > 1 for the BaCu2S2-type structure. A series of density functional theory calculations were performed using a hypothetical model with the idealized compositions of Ba0.75Eu0.25Zn2Sb2, and the results were compared with the ternary parental compound BaZn2Sb2 to understand the influence of Eu substituents in the Ba1-xEuxZn2Sb2 system. A similar overall shape of the density of states (DOS) curves and the near-constant DOS values at EF before and after the cationic substitution suggest only marginal changes in the carrier concentration. Therefore, carrier mobility has a dominant role in rationalizing the observed variations in the electrical transport properties of the title system. Temperature-dependent TE property measurements proved that an increase in the Seebeck coefficient S and a decrease in electrical conductivity σ were observed as the Eu substituents gradually increased in the Ba1-xEuxZn2Sb2 system, although the overall S and σ values were lower than those in the parental compound BaZn2Sb2. The thermal conductivities of these title compounds were successfully lowered by phonon scattering, but due to the overall smaller electrical transport properties, the observed maximum ZT was 0.49 at 773 K for Ba0.98(1)Eu0.02Zn2Sb2.

Promise and Peril: Stellar Contamination and Strict Limits on the Atmosphere Composition of TRAPPIST-1 c from JWST NIRISS Transmission Spectra

Abstract Attempts to probe the atmospheres of rocky planets around M dwarfs present both promise and peril. While their favorable planet-to-star radius ratios enable searches for even thin secondary atmospheres, their high activity levels and high-energy outputs threaten atmosphere survival. Here we present the 0.6–2.85 μm transmission spectrum of the 1.1 R ⊕, ∼ 340 K rocky planet TRAPPIST-1 c obtained over two JWST NIRISS/SOSS transit observations. Each of the two spectra displays 100–500 ppm signatures of stellar contamination. Despite being separated by 367 days, the retrieved spot and facula properties are consistent between the two visits, resulting in nearly identical transmission spectra. Jointly retrieving for stellar contamination and a planetary atmosphere reveals that our spectrum can rule out hydrogen-dominated, ≲300× solar metallicity atmospheres with effective surface pressures down to 10 mbar at the 3σ level. For high mean molecular weight atmospheres, where O2 or N2 is the background gas, our spectrum disfavors partial pressures of more than ∼10 mbar for H2O, CO, NH3, and CH4 at the 2σ level. Similarly, under the assumption of a 100% H2O, NH3, CO, or CH4 atmosphere, our spectrum disfavors thick, >1-bar atmospheres at the 2σ level. These nondetections of spectral features are in line with predictions that even heavier, CO2-rich atmospheres would be efficiently lost on TRAPPIST-1 c given the cumulative high-energy irradiation experienced by the planet. Our results further stress the importance of robustly accounting for stellar contamination when analyzing JWST observations of exo-Earths around M dwarfs, as well as the need for high-fidelity stellar models to search for the potential signals of thin secondary atmospheres.

Starting Electroosmosis in a Fibrous Porous Medium with Arbitrary Electric Double-Layer Thickness

The transient electroosmotic response in a charged porous medium consisting of a uniform array of parallel circular cylindrical fibers with arbitrary electric double layers filled with an electrolyte solution, for the stepwise application of a transverse electric field, is analyzed. The fluid momentum conservation equation is solved for each cell by using a unit cell model, where a single cylinder is surrounded by a coaxial shell of the electrolyte solution. A closed-form expression for the transient electroosmotic velocity of the bulk fluid in the Laplace transform is obtained as a function of the ratio of the cylinder radius to the Debye screening length and the porosity of the fiber matrix. The effect of the fiber matrix porosity on the continuous growth of the electroosmotic velocity over time is substantial and complicated. For a fiber matrix with larger porosity, the bulk fluid velocity takes longer to reach a certain percentage of its final value. Although the final value of the bulk fluid velocity generally increases with increasing porosity, early velocities may decrease with increasing porosity. For a given fiber matrix porosity, the transient electroosmotic velocity is a monotonically increasing function of the ratio of the cylinder radius to the Debye length.

Axial length to corneal curvature radius ratio is negatively correlated with choroidal blood flow in myopic children.

The pathophysiologic mechanisms underlying early-onset myopia remain unclear; in this study, we investigate the pathogenesis by examining the interrelationships between axial length to corneal curvature radius ratio ( ) and choroidal blood flow. This cross-sectional study included 202 eyes from myopic children, categorized into 141 eyes with mild myopia, 47 eyes with moderate myopia, and 14 eyes with high myopia. Optical coherence tomography angiography (OCTA) was used to measure choroidal blood flow perfusion within a 6mm × 6mm area of the macular region, divided into nine subareas based on ETDRS partitioning: macular fovea, nasal side 1, superior 1, temporal side 1, inferior 1, nasal side 2, superior 2, temporal side 2, and inferior 2. Data on corneal curvature and ocular axial length were collected to calculate the , with equivalent spherical lens power, gender, and age gathered for group comparisons, and the correlation between AL/CR and choroidal blood flow perfusion volume was analyzed. was significantly negatively correlated with choroidal blood flow perfusion ( ). Linear regression and mediation analyses indicated that for each unit increase in choroidal blood perfusion volume in nasal region 1, decreased by an average of 0.421 units. This relationship is mediated by several factors, with axial length serving as a key mediator. correlates with choroidal blood flow perfusion, indicating a link between refractive biological parameters and ocular blood circulation. Myopia is an ischemic eye condition that warrants attention to fundus microcirculation changes in myopic children.

Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and Gaia DR3 parallaxes

Context. A recent investigation highlighted peculiar trends between the radii derived from surface brightness-colour relations (SBCRs) combined with Gaia DR3 parallaxes with respect to asteroseismic scaling relation radii from K2 data. Aims.Kepler data differ from K2 data in many aspects. We investigated on the robustness of the results based on Kepler data. Methods. We cross-matched asteroseismic and astrometric data for over 12 000 red giant branch and red clump stars from the end-of-mission Kepler catalogue with the Gaia DR3 and TESS Input Catalogue v8.2 to obtain precise parallaxes, V- and K-band magnitudes, and E(B − V) colour excesses. Two well-tested SBCRs from the literature were adopted to estimate stellar radii. Results. The analysis confirmed that SBCR and asteroseismic radii agree very well. The overall differences are only 1–2% depending on the adopted SBCR. The dispersion of 7% was about two-thirds of what was found for K2-based data. As a difference from the K2-based investigation, the ratio of SBCRs-to-asteroseismic radii did not depend on the metallicity [Fe/H]. Moreover, the intriguing decreasing trend with [α/Fe] of the radius ratio for massive stars that was observed in K2 data was absent in Kepler data. The SBCR radii are systematically higher than asteroseismic estimates by 5% for stars with masses below 1.0 M⊙. Conclusions. The SBCRs have proven to be a highly effective tool for estimating radii with a precision comparable to that obtained from asteroseismology, but at a significantly lower observational cost. Moreover, the superior concordance of Kepler-derived radii with SBCR measurements and the absence of the discrepancies observed in the K2-derived radii suggest the existence of underlying systematic errors that impact specific mass and metallicity regimes within the K2 dataset.

Experimental study on the translation behavior of an in-situ bubble pair in the ultrasonic field.

The dynamics of acoustic cavitation bubbles hold significant importance in ultrasonic cleaning, biomedicine, and chemistry. Utilizing an in-situ normal pressure bubble generation and observation system that was developed, this study examined the translational behavior of micrometer-scale normal pressure bubble pairs with initial radius ratio of 1:1 and 2:1 under ultrasonic field excitation. A velocity-distance curve was proposed to quantify the secondary Bjerknes forces during various interaction stages of the bubbles. The findings revealed that equal-sized bubbles underwent an acceleration phase, a deceleration phase, and a velocity jump phase during attraction in both strong and weak acoustic fields. In contrast, bubbles of unequal sizes, due to different oscillation frequencies, experienced multiple acceleration and deceleration phases, presenting asynchronous behaviors. The study further explored the effects of the initial bubble radius, shape oscillation, and volume oscillations on the attraction speed. Results showed that the velocity of the bubble's centroid decreased with an increase in the initial radius, while intensified volume oscillations increased the secondary Bjerknes force, thereby increasing the centroid's velocity. Moreover, strong acoustic fields were more likely to induce severe volume and shape oscillations in bubbles than weak fields. The irregular shape oscillations in twin bubbles resulted in shortened durations of acceleration and deceleration phases, reduced peak velocities of acceleration phase, and diminished acceleration during the velocity jump phase. The research provided some mechanical explanations for acoustic cavitation dynamics and its applications.

Increasing the durability of soldering wearresistant steel by regulating the redistribution of thermal stresses

Abstract. Problem. The tangential load has a significant influence on the stress state during pressure treatment of metals in the contact zone and on the nature of fatigue failure. As a result of plastic deformations, stresses are redistributed in places of concentration of defects. Since the amount of plastic displacements depends on the level of tangential stresses, the critical number of internal breaks in the material should increase with the increase in the intensity of stresses σ, as the quantity responsible for the formation of the material. Goal. The purpose of the work is to determine the critical values of external loads and the angle of initial propagation of cracks (crack-type defects) at which local or complete destruction of the body will occur. Methodology. Brazing with wear-resistant alloys of the Cr-MnTi-Si and Cr-Mn-Mo-Ti-Si systems was carried out on samples made of 50HNM steel according to the "slide" scheme with flux-cored wire. The effect of temperature on the strength and wear resistance of alloys was studied at elevated temperatures under the conditions of a volumetric stress state using the calculated criterion equations of fracture mechanics. Calculations were made using Mathcad software.Originality. It is theoretically substantiated that at temperatures of 673...873 K and large ratios of crack radii to their depth, mechanical and thermal stresses are responsible for the destruction of the investigated wear-resistant alloys, with an increase in temperature and a decrease in the ratio of the crack radius to its depth, a factor that affects their destruction, there is accumulated plastic deformation. Practical value. Analysis of the results of the influence of temperature stresses on the ultimate external load shows: – at T=673 K, the temperature stresses are 33% of the destructive load;– at T=793 K, the temperature stresses are 44% of the destructive load; – at T=893 K, temperature stresses are 50% of the destructive load

Research on Dynamic Modeling and Vibration Characterization of Integrated Bearings

Integrated bearings, characterized by their unique structure, feature an inner ring that is seamlessly integrated with the shaft. This study is based on the theoretical framework of rolling bearing dynamics and considers bearing friction, lubrication, and Hertz elastic contact theory. A dynamic simulation model considering the interaction between the components of the rolling bearing is established. Additionally, a subroutine for calculating the interaction forces between the bearing components was written in C and compiled into a dynamic link library, which was then integrated with the dynamic simulation software. To solve and simulate the dynamics of the integrated bearing model, a sophisticated combination of a refined integration method and the predictor-corrector Adams–Bashforth–Moulton multistep technique was employed. The theoretical analysis offers insights into the vibration characteristics of the integrated bearings across different structural and operational parameters. Results indicate that a judicious selection of parameters, such as the curvature radius ratio of the inner and outer grooves and the gap of the cage pockets, can significantly enhance the bearings’ vibration and noise reduction capabilities. Furthermore, the application of an appropriate axial preload effectively reduces bearing vibrations, and there exists an optimal range of rotational speeds that minimizes these vibrations.

Free-space propagation of double-ring perfect optical vortex beams

Abstract Single-ring perfect optical vortex (SR-POV) beams have received significant attention from the singular optics community due to their topological charge (TC)-independent ring radius, which offers certain advantages over conventional vortex beams such as Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) beams in applications like particle trapping, optical communication, and imaging. However, the generation of double-ring perfect optical vortices (DR-POVs), embedded with two TCs, offers greater advantages over SR-POVs in terms of robustness during propagation and enhanced channel capacity in communication networks. In our theoretical analysis, we first highlight the differences between true and approximated representations of DR-POV beams. We then investigate the propagation of DR-POV beams in free-space, demonstrating how their evolution is influenced by factors such as the TCs of the inner and outer rings, the ratio of the beam radius to beam width at the waist plane. Similar to SR-POV beams, DR-POV beams exhibit non-diffracting behavior over short propagation distances, with little to no impact on the beam’s propagation when the TCs of the inner and outer rings are altered. However, phase wandering characteristics are observed, even over short propagation distances. Our research could find potential applications in the field of free-space optical communication.

Ocular biometric parameters in Chinese preschool children and physiological axial length growth prediction using machine learning algorithms: a retrospective cross-sectional study

ObjectivesTo examine the ocular biometric parameters and predict the annual growth rate of the physiological axial length (AL) in Chinese preschool children aged 4–6 years old.MethodsThis retrospective cross-sectional study included...

A morphology of the distal medial femoral surface that should be considered when performing coronal osteotomy in medial closed wedge distal femoral varus osteotomy.

The aim of the present study was to evaluate the morphology of the distal medial femoral surface during coronal osteotomy in medial closed wedge distal femoral varus osteotomy (MCWDFO) using plain CT. Twenty knees (mean age, 55.3years) were included. Preoperative CT images were obtained prior to MCWDFO for valgus OA. In the cross-section depicting the starting position of the transverse cut, a curve was drawn that passed through the centre of the femoral cortex, and lines parallel and perpendicular to the surgical epicondylar axis (SEA) were drawn to analyse the medial side. Inflection points on the medial line were defined as P1-P4. The radii of circles passing through P1-P3 (PR, posterior radius) and P2-P4 (AR, anterior radius) were drawn. Values for the PR, AR, and radius ratio (PR/AR) were measured. Based on the PR/AR, the cross-sectional morphologies were classified into 5 triangular types (PR/AR < 0.5), 4 flat types (PR/AR > 0.8), and 11 convex types (PR/AR 0.6 to 0.7). The medial anteroposterior width and flange thickness were easier to assess in the flat type; however, these were difficult to assess in the triangular type with a gentle anterior slope. Surgeons should consider the differences in the anterior slope according to cross-sectional morphologies when performing coronal osteotomy in MCWDFO.

Weakly nonlinear analysis of the onset of convection in rotating spherical shells

A weakly nonlinear study is numerically conducted to determine the behaviour near the onset of convection in rotating spherical shells. The mathematical and numerical procedure is described in generality, with the results presented for an Earth-like radius ratio. Through the weakly nonlinear analysis a Stuart–Landau equation is obtained for the amplitude of the convective instability, valid in the vicinity of its onset. Using this amplitude equation we derive a reduced order model for the saturation of the instability via nonlinear effects and can completely describe the resultant limit cycle without the need to solve initial value problems. In particular the weakly nonlinear analysis is able to determine whether convection onsets as a supercritical or subcritical Hopf bifurcation through solving only linear 2D problems, specifically one eigenvalue and two linear boundary value problems. Using this, we efficiently determine that convection can onset subcritically in a spherical shell for a range of Prandtl numbers if the shell is heated internally, confirming previous predictions. Furthermore, by examining the weakly nonlinear coefficients we show that it is the strong zonal flow created through Reynolds and thermal stresses that determines whether convection is supercritical or subcritical.

Geometric rigidity of sections in the form of in torsion

This article is a generalization of known solutions to the problem of determining the reduced geometric stiffness of sections of elastic prismatic beams using geometric arguments: the shape coefficient and the ratio of conformal radii (internal to external). Analytical dependences are constructed for all considered sections (regular polygons, ellipses, rectangles, isosceles and right triangles): reduced geometric stiffness is the coefficient of shape and reduced geometric stiffness is the ratio of conformal radii. Formulas in the form of polynomials for determining the ratio of conformal radii are also constructed for these sections. An analysis of the changes in both arguments under various geometric transformations showed that the ratio of conformal radii has similar isoperimetric properties as the shape coefficient. This allows to determine the geometric torsional stiffness of the sections by interpolation.

An Algorithm for Determining Pith Position Based on Crown Width Size

To accurately estimate the pith position, a method was proposed for estimating the pith position by the crown width. The crown widths of 120 trees and radiuses of each disc extracted at the height of 1.3 m from these trees were measured in four directions. The crown and radius ratios of the length of each direction to the total length in that direction and the opposite direction were calculated. Using the crown ratio as an independent variable, as well as the radius ratio as a dependent variable, the linear, logarithmic, exponential, and polynomial models were built. The model with the highest R2 was selected as the radius ratio model. The geometric center method and the crown width method were applied to estimate the pith position, and the estimation errors were calculated, respectively. The R2 of the linear, logarithmic, exponential, and polynomial models were 0.405, 0.379, 0.403, 0.404, respectively, and the linear model was chosen as the radius ratio model. The prediction error based on the crown width was 7.6%, and that of the geometric center method was 10.1%. The findings indicate that the crown width method can improve the accuracy of estimating the pith position.

Longitudinal thermoelastic guided waves in functionally graded hollow cylinders with Green–Naghdi thermoelastic theory

Abstract At present, functional gradient material (FGM) pipelines are widely used in high-temperature environments, and the need for online inspection of such pipelines is becoming more and more urgent. Ultrasonic guided wave is undoubtedly one of the most promising methods for detection, but research on the propagation characteristics of thermoelastic guided wave in high-temperature FGM pipelines is still limited. In this paper, based on Green–Naghdi thermoelastic theory, a theoretical model of longitudinal thermoelastic guided wave in a hollow cylinder of FGM considering temperature effect is established by using the Voigt model, and the governing equations of thermoelastic guided wave are solved by the Legendre series method. The dispersion, displacement, and temperature distribution curves of guided waves in a hollow cylinder of FGM are plotted. The convergence of the method and the influence of the coupling of thermodynamic equations on the dispersion characteristics of guided waves are discussed. The influence of circumferential order, ratio of radius to thickness, gradient index, and temperature change on the dispersion characteristics of guided waves is analyzed. This study provides a theoretical basis for nondestructive testing and evaluation of high-temperature FGM pipelines.

Shear Stress Solutions for Curved Beams: A Structural Analysis Approach.

The shear stress on isotropic curved beams with compact sections and variable thickness is investigated. Two new solutions, based on Cook's proposal and the mechanics of materials approach, were developed and validated using computational finite element models (FEM) for four typical cross-sections (rectangular, circular, elliptical, and triangular) used in civil and mechanical structures, constituting a novel approach to predicting shear stresses in curved beams. They predict better results than other reported equations, are simpler and easier for engineers to use quickly, and join the group of equations found using the theory of elasticity, thereby expanding the field of knowledge. The results reveal that both equations are suitable to predict the shear stress on a curved beam with outer/inner radii ratios in the interval 1<b/a ≤ 5 aspect ratios. There is a maximum relative difference between the present solutions and finite element models of 8% within 1<b/a ≤ 2, and a maximum of 16% in 2<b/a ≤ 5. Additionally, the neutral axis of the curved beam can be located with the proposed solution and its position matches with that predicted by FEM. The displacement at the top face of the end of the curved beam induces a difference in the shear stress results of 8.0%, 7.0%, 6.5%, and 2.9%, for the circular, rectangular, elliptical, and triangular cross-sections, respectively, when a 3D FEM solution is considered. For small b/a ratios (near 1), the present solutions can be reduced to Collignon's formula.

A new method of shrink fit design for large-sized prestress die of hot extrusion: An example of large fan shaft

Due to the remarkable increase in the geometric size, interference fit amount and assembly difficulty of large-sized hot extrusion prestress die, the conventional methods (such as thick wall cylinder theory and empirical value method) of shrink fit design were inapplicable to the pre-stressed die for hot extrusion of fan shaft with a maximum radius of 255 mm. In this study, a new shrink fit design method for large-sized prestress die was proposed by using the finite element method, and two sets of the formulas and nomograms that were easy to use were obtained to determine the interference fit ratio β, the radius ratio of die and stress ring a21, a31. Finally, the shrink fit of the prestressed die for the hot extrusion of the large fan shaft was designed by adopting the introduced new approach, and the hot extrusion experiment was carried out. The results show that the prestressed die for hot extrusion of the large fan shaft designed by the new method not only reduced the material cost by 58.6% compared with the integral die, which had considerable economic advantages but also had outstanding stress-bearing capacity, which could be safely applied for the manufacture of large aero-engine fan shaft, which also verified the feasibility of the new shrink fit design method for large-sized hot extrusion prestress die.

Impact of Lorentz force on forced convective MHD Jeffrey fluid flow through annular sector duct

Present numerical simulation is to investigate the Lorentz force and constant axial pressure gradient effects on flow and heat transfer of electrically conducting magneto-hydrodynamic, [Formula: see text] Jeffrey fluid at fully developed region of annular sector duct. The law of conservation of energy is simulated by taking two thermally boundary conditions, known as [Formula: see text]1 thermally boundary condition (i.e. constant axial heat flux with uniform peripherally temperature in the annular sector duct’s cross section) and [Formula: see text] thermally boundary condition (i.e. constant temperature axially and peripherally). The numerical results are simulated in the following range of parameters: the ratio of radii, [Formula: see text], an apex angle of duct [Formula: see text] by using [Formula: see text] number of fins, Hartman number, [Formula: see text] and the ratio of relaxation time to retardation time, [Formula: see text]. During the simulation, it has been concluded that the other parameter corresponding to Jeffrey fluid (i.e. the retardation time, [Formula: see text]), has ignored due to minor attribution on flow and heat transfer by increasing the value from [Formula: see text] to [Formula: see text]. Hartman number, [Formula: see text], upgrades the [Formula: see text] up to 18.76% and 14.60%, while [Formula: see text] / [Formula: see text] up to 1.82% and 1.47%/1.55% and 1.29% for [Formula: see text] and [Formula: see text] respectively at [Formula: see text] and [Formula: see text] by increasing its value from 0 to 2. At higher [Formula: see text], the difference becomes ignored in the case of [Formula: see text] when we change the annular region along radial direction.

Properties of tsunami-generated electromagnetic variation observed on islands.

Electrically conductive seawater, moving in an ambient magnetic field, generates electromagnetic (EM) variations. Tsunamis are significant contributors to this phenomenon, inducing observable electric and magnetic fluctuations at seafloor and coastal observatories. While understanding of these occurrences in open oceans is robust, knowledge regarding their observation on islands remains limited. This article seeks, through the use of numerical experimentation, to enhance our understanding of tsunami-generated EM (TGEM) variations observed on islands. Utilizing simulations involving conical islands, we identify three key insights regarding EM intensity normalized by the height of incident tsunamis: (i) increased ocean depth surrounding the island amplifies tsunami EM signals, particularly for periods shorter than 20 min; (ii) magnetic field strength at the island is approximately comparable to that observed at the seafloor in the absence of the island when the island radius is smaller than 6 km; and (iii) electric field intensity at the island notably surpasses that observed at the seafloor, especially with smaller island radii ([Formula: see text] 6 km). Additionally, we establish that employing the ratio of island radius to tsunami wavelength near the island coast facilitates the derivation of empirical functions for this phenomenon.This article is part of the theme issue 'Magnetometric remote sensing of Earth and planetary oceans'.