Ring Radius Research Articles

Weak gravitational lensing and shadow cast by rotating black holes in axionic Chern–Simons theory

We investigate the impact of the axionic coupling parameter on the bending angle of light and the shadow cast by slowly rotating black holes in Chern–Simons modified gravity. We utilize the Ishihara et al. method to derive the deflection angle of light for an observer and source located at finite distances from a lens object in an asymptotically flat spacetime, using the Gauss–Bonnet theorem. The deflection angle exhibits an increasing trend up to a certain point, followed by a decrease as a function of the impact parameter, with the presence of the axion matter field causing the observed increase. Additionally, we calculate the Einstein ring radius as a direct application of the weak deflection angle. We also investigate the effect of the axion matter field on the time delay of light and analyze its impact on the shadow cast by slowly rotating black holes. Our findings reveal a significant effect of the axionic coupling parameter on the black hole’s shadow.

A novel method for age identification of mountain-cultivated ginseng.

Panax ginseng, a slow-growing perennial herb, is the most praised and popular traditional medicinal herb. Mountain-cultivated ginseng (MCG) and cultivated ginseng (CG) both belong to Panax ginseng C. A. Meyer. The market price and medical effects of this popular health product are closely related to its age. It is widely acknowledged that CG is typically harvested after 4-6 years of growth, but MCG is often collected after 10 years. Until now, the age identification of MCG or mountain wild ginseng (MWG) has remained a major challenge. In this study, we established a novel and rapid method for staining xylem vessels with phloroglucinol and identifying the "annual growth rings" of ginseng by utilizing a stereoscope, which serves as a reliable indicator of the age of MCG. Statistical analysis of the ring radius and the ring density of MCG aged from 1 to 20 years shows that the secondary xylem of MCG increases rapidly in the first 3 years but then gradually slows down from 4 to 10 years, and minor fluctuation is observed in the next 10 years. Meanwhile, the space between the growth rings (ring density) becomes increasingly small with age. This straightforward staining approach can reveal the age of MCG with remarkable clarity and can distinguish MCG from CG. RESEARCH HIGHLIGHTS: A novel rapid staining method for Panax ginseng was established. The age of mountain-cultivated ginseng (MCG) can be identified by microscopic techniques. MCG and cultivated ginseng (CG) can be discriminated by microstructure characteristics.

Experimental study of vortex ring impingement on concave hemispherical cavities

Discrete vortex rings impinging on concave hemispherical cavities were explored experimentally. Planar laser-induced fluorescence, two-dimensional particle image velocimetry and flow visualization techniques were employed. Five different ratios of vortex ring to hemisphere cavity radius ( $\gamma$ ) were investigated, namely, $\gamma = 1/4,1/3,2/5,$ $1/2, 2/3$ . For $\gamma = 1/4,1/3, 2/5$ , the geometric confinement of the primary ring due to the hemispherical cavity induced loop-like instabilities in the secondary ring, which led to head-on collision and ejection of the looped ends as they orbited the primary ring. As the hemispherical cavity decreased in diameter (increasing $\gamma$ ), the dynamics were altered significantly due to the increased generation of vorticity along the edge of the hemisphere. For $\gamma = 1/2$ , vorticity produced at the edge/lip of the hemisphere ultimately disrupted the classical formation of a secondary vortex ring from the wall-bounded vorticity. For $\gamma = 2/3$ , the primary ring and hemisphere radius were close enough in size that the interaction was dominated by direct impact of the primary ring with the lip of the cavity. The primary vortex ring produced a vortex ring at the lip of the hemisphere that ultimately separated from the cavity, orbited around the primary ring, and then self-advected in the direction opposite to the primary vortex ring trajectory. A detailed investigation of the dynamics provided.

Case Study: Optimizing Grading Ring Design for High Voltage Polymeric Insulators in Power Transmission Systems for Enhanced Electric Field and Voltage Distribution by Using a Finite Element Method

This research paper aims to investigate the optimal design of grading rings for high-voltage polymeric insulators in an actual power transmission system, with a focus on improving the electrical representation of the insulator strings. One such subsidiary accessory commonly used with porcelain and polymer insulator strings is the grading ring, which is employed to improve the electric field and voltage distribution surrounding the insulator string. The efficiency of insulator strings can be enhanced by grading rings, as they facilitate a more linear potential division along the strings. The design parameters of grading rings significantly influence their performance on insulator strings. In this study, we examine the optimal design of the grading rings of high-voltage polymer insulators, since no uniform design methodology has been developed for high-voltage polymer insulators, and their optimization is currently the subject of many research studies. The electric field on an outdoor polymeric insulator is examined using finite element method (FEM) software and COMSOL Multi-Physics program. A 2D model is utilized to simulate a 220 kV polymeric insulator. The effectiveness of high-voltage polymeric insulators greatly depends on the dimensions and locations of the grading rings. Therefore, the impacts of the radius of the grading ring and that of its tube and the tube’s vertical position are thoroughly investigated, under dry and humid conditions. To achieve this objective, a search algorithm is employed to adjust the dimensions and locations of the grading ring. The optimization approach in this study is based on determining the maximum electric field across the insulator surface, while ensuring that it remains below the corona initiation level.

Anodic growth of TiO2 nanotube arrays: Effects of substrate curvature and residual stress

We study anodic growth of TiO2 nanotubes on the surfaces of Ti rings of different thicknesses in a two-electrode cell under 50 V with an anodization time of 30 min at room temperature. The experimental results demonstrate that there are three factors controlling the growth of TiO2 nanotubes on the surfaces of Ti rings – ring radius, ring thickness and residual stress. The length of TiO2 nanotubes decreases with the increase of the radius of Ti rings and the decrease of the ring thickness. The residual stress hinders the growth of TiO2 nanotubes on the surfaces of Ti rings.

Tight-focusing evolution of linearly polarized auto-focusing circular Bessel-Gaussian vortex beam

In this paper, we analyzed the influence of on-axis and off-axis vortex on the intensity distribution of the linearly polarized auto-focusing Bessel-Gaussian vortex beam (LABGVB). By comparing its tight-focusing properties with that of the linearly polarized circular Airy beam, it is found that when transmitted in the tight-focusing system, the LABGVB not only generates multiple focusing, but also allows the focal points to be located away from the geometric focus of the high numerical aperture (HNA) lens. In addition, changing the focal length of the HNA lens not only causes the splitting and merging of the focal points, but also results in different control effects on the depth of focus and the distance between focal points due to different focusing times. In particular, the LABGVB can not only form multiple optical bottles for particle capture in the focusing region, but also exhibit two different distributions of the spin density vectors along the optical axis after choosing the appropriate scale factor and main ring radius, one being a circular line and the other being a helical line.

Liquid entrainment of the toroidal bubble crossing the interface between two immiscible liquids

We experimentally investigate the transport of liquid by a toroidal bubble that rises vertically and penetrates a horizontal interface between two immiscible liquids. Experiments are conducted with various strengths of vortex circulation in the bubble, and with different liquid densities and viscosities. In contrast to a spherical bubble, a rising toroidal bubble carries a great amount of the lower liquid by virtue of the self-induction of circulating flow. The lower liquid is entrained by the toroidal bubble and forms an ellipsoidal body enclosing the bubble after it penetrates the interface. The downward net force acting on the ellipsoidal body results in the radial contraction of the bubble, reducing the volume of the entrained lower liquid. As the entrained volume decreases, the nearby upper liquid eventually pierces the ellipsoidal body, making the bubble unstable. At this instant, the net force acting on the ellipsoidal body approaches zero, and the volume ratio of the entrained lower liquid and bubble converges to a specific value. For smaller vortex circulation and larger density difference between the liquids, the volume of the entrained lower liquid within the ellipsoidal body becomes smaller and the travel distance of the bubble from the initial interface until it becomes unstable decreases. The effective Froude number, which accounts for both the inertial effect of vortex circulation and the gravitational effect of liquid density difference, is found to characterise the temporal changes in the ring radius, propagation speed and entrained volume.

Generation of a spatially multiplexed perfect vortex beam for digital data transmission

A perfect vortex beam (PVB) has emerged as a potential candidate for optical communication as its intensity profile remains invariant for different orbital angular momenta being carried by the beam. The present study proposes a simple technique to enhance the data handling capacity of the beam through its spatial multiplexing. The variation of the ring radius of the PVB under Fourier transformation, with different focal lengths, has been used to generate multiple PVBs of different annular radii, and then combined into a single beam to produce a concentric PVB (CPVB). Each ring may represent one bit of digital data. A simple experimental setup was used to generate the beam, which has also been validated through theoretical simulation. Further studies confirm that each ring of the CPVB has the same phase profile, with impeccable spatial alignment. Spatial multiplexing of the PVB adds an additional degree which can multiply the data handling capacity of the PVB, as a result of which it can prove to be a potential candidate for optical data transmission.

Static and dynamic magnetic characteristics in concentric permalloy nanorings

Magnetic nanodisks and nanorings have been focus of attention for quite some time due to their applicability in magnetic memory devices. In this paper, static and dynamic magnetic properties of Permalloy concentric thin ring nanostructures are reported as a function of the number of rings by using micromagnetic simulations. The maximum outer radius (R) and thickness (t) of the concentric rings are fixed at 100 nm and 20 nm respectively. The distance between any two neighbouring rings is always maintained equal to the width of each ring while the number of nanorings is increased starting from one to five. In-plane magnetic hysteresis loops show that in all cases, the remanence and coercivity values are found to be almost zero while vortex state is exhibited with opposite helicity in adjacent nanorings. When the number of nanorings reach five, the narrowest hysteresis loop is observed with almost no hysteresis at all. Dynamic susceptibility spectra was computed by relaxing the system from a out of plane saturated state followed by an in-plane excitation using a small field pulse. In most of the cases, the in plane magnetic field pulse excites azimuthal spin wave modes. The resonance frequency corresponding to these excitation modes depends on the remanent configuration and the number of peaks increase with increment in the number of rings. The ferromagnetic resonance mode that is common for all the samples considered, moves towards lower frequency with increase in number of concentric rings.

Local dynamic behavior of dark beams in self-defocusing Kerr media

We study the local dynamic behavior of dark beams in self-defocusing Kerr media. In this, we are encouraged by the interesting results obtained in Refs. [1,2], although these papers are concerned with the bright beams in self-focusing Kerr media. Similar to these papers, we are interested in the two-dimensional (2D) necklace ring beams, but under certain circumstances. Different from these papers, we are interested in the dark necklace beams in self-defocusing media. When the dimensionless ring radius L is far greater than the ring thickness w, the 2D defocusing nonlinear Schrödinger equation in cylindrical coordinates can be simplified to the standard 1D defocused nonlinear Schrödinger (NLS) equation. Then, an approximate solution of the 1D NLS equation can be constructed by different means, for example by a simple combination of exponential and trigonometric functions. In general, such a necklace solution can be described by two parameters: the ring radius L and the topological charge m. Hence, we study the local dynamic behavior of dark beams with different topological charges m and different ring radii L when they are much larger that the ring thickness w. Different spatial distributions of dark beams are obtained for m zero, positive integer, and half-integer. We use direct numerical simulation to confirm the validity of our analytical approximate solution. Our results show that the structure of dark beams can be well controlled by adjusting the ring radius and the topological charge. Our procedure provides a new method for dealing with high-dimensional nonlinear equations of different origin.

Self-focusing effect analysis of a perfect optical vortex beam in atmospheric turbulence.

The correlation function and the detection probability of orbital angular momentum (OAM) of a perfect optical vortex beam (POVB) were obtained under atmospheric turbulence conditions and then used to estimate the POVB propagation model through atmospheric turbulence. The POVB propagation in a turbulence-free channel can be divided into anti-diffraction and self-focusing stages. The beam profile size can be well preserved in the anti-diffraction stage as the transmission distance increases. After shrinking and focusing the POVB in the self-focusing region, the beam profile size expands in the self-focusing stage. The influence of topological charge on the beam intensity and profile size differs depending on the propagation stage. The POVB degenerates into a Bessel-Gaussian beam (BGB)-like when the ratio of the ring radius to the Gaussian beam waist approaches 1. The unique self-focusing effect of the POVB enables higher received probability compared to the BGB when propagating over long distances in atmospheric turbulence. However, the property of the POVB that its initial beam profile size is not affected by topological charge does not contribute to the POVB achieving a higher received probability than the BGB in short-range transmission application scenarios. The BGB anti-diffraction is stronger than that of the POVB, assuming a similar initial beam profile size at short-range transmission.

Double slot micro ring resonators with inner wall angular gratings as ultra-sensitive biochemical sensors.

We simulate and demonstrate experimentally an inner-wall grating double slot micro ring resonator (IG-DSMRR) with a center slot ring radius of only 6.72 µm based on the silicon-on-insulator platform. This novel photonic-integrated sensor for optical label-free biochemical analysis boosts the measured refractive index (RI) sensitivity in glucose solutions to 563 nm/RIU with the limit of detection value being 3.7 × 10-6 RIU (refractive index units). The concentration sensitivity for sodium chloride solutions can reach 981 pm/%, with a minimum concentration detection limit of 0.02%. Using the combination of DSMRR and IG, the detection range is enlarged significantly to 72.62 nm, three times the free spectral range of conventional slot micro ring resonators. The measured Q-factor is 1.6 × 104, and the straight strip and double slot waveguide transmission losses are 0.9 dB/cm and 20.2 dB/cm, respectively. This IG-DSMRR combines the advantages of a micro ring resonator, slot waveguide, and angular grating and is highly desirable for biochemical sensing in liquids and gases offering an ultra-high sensitivity and ultra-large measurement range. This is the first report of a fabricated and measured double-slot micro ring resonator with an inner sidewall grating structure.

Electrical properties of a high-precision hexagonal spiral silicon drift detector

With the deepening and expansion of semiconductor technology and research, in order to continuously optimize the structure and performance of semiconductor detectors, a high-precision hexagonal spiral silicon drift detector (SDD) is proposed in this paper. In order to obtain a more accurate spiral ring structure, this paper goes beyond the first-order formula in the Taylor expansion for calculating the radius of the spiral ring. Based on the first-order formula, the second-order formula for calculating the radius of the spiral ring is further developed and derived. The point coordinates are obtained by combining the radius, angle, and ring spacing change formula to obtain a more accurate spiral ring structure. The actual number of turns is more accurate than that obtained from first-order approximation, which better solves the problem of accurate calculation of the number of spiral rings and the structure of the spiral SDD in the existing technology, that is, the accurate calculation of the radius of the spiral ring. In order to verify the abovementioned theory, we model this new structure and use Technology Computer-Aided Design to system simulate and study its electrical properties, including potential distribution, electric field distribution, and electron concentration distribution. According to the simulation results, compared with the first-order formula, the second-order formula has better electrical properties; more uniform distribution of potential, electric field, and electron concentration; and a clearer electron drift channel.

Cyclic vs Linear Bottlebrush Polymers in Solution: Side-Chain Length Effect

Bottlebrush polymers (BBPs) of different architecture are of considerable interest for a broad range of applications, including nanomedicine, electronics, and self-healing materials. Using atomistic molecular dynamics simulations, we investigate and compare the structural and hydration properties of cyclic and linear poly(vinyl alcohol)-graft-poly(ethylene oxide) (PVA-g-PEONsc) BBPs in aqueous solution as functions of PEO side-chain length, Nsc. We find that overall cyclic BBPs are smaller than the corresponding linear BBPs and their shape changes from donutlike to disklike to starlike with increasing side-chain length, while linear BBPs vary in shape from an expanded coil to a rod/cylinder. The radius of gyration of cyclic BBPs increases with an increase of the side-chain length at a somewhat slower rate than the linear BBPs but follows the same scaling Rg ∼ Nsc0.58 in the limit of long side chains. For short grafts, we determine that the persistence length, lp, for both cyclic and linear BBPs increases in a similar manner following an lp ∼ Nsc0.54 dependence. In the long side-chain limit, the persistence length (lp) of cyclic BBP saturates, while for linear BBPs lp strongly increases following the expected scaling relation lp ∼ Nsc15/8. We propose a scaling model that shows that the fraction of side-chains located inside the cyclic BBPs depends on the radius of the backbone ring and significantly decreases with an increase of graft length. For both cyclic and linear BBPs, the hydrogen bonding between PEO side chains and water is somewhat reduced near the backbone, where local chain stretching is observed, while reaching full hydration on the periphery. Overall, the hydration shell within 1 nm of the cyclic BBP backbone is found to be more dynamically stable compared to linear BBPs.

Key to an extension or shortening of focal length in the enhancement of autofocusing ability of a circular Airyprime beam caused by a linear chirp factor.

Researchers are puzzled whether the enhancement of the abruptly autofocusing ability caused by a linear chirp factor is accompanied by the shortening or the extension of the focal length. In this Letter, a circular Airyprime beam is chosen as the research object to reveal this mystery. Extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability depends on the exponential decay factor a and the dimensionless radius of the primary ring. When a is small enough, there exists a critical value for the dimensionless radius. If the dimensionless radius is greater than the critical value, the focal length is shortened in the enhancement of the abruptly autofocusing ability. If the dimensionless radius is less than the critical value, the focal length is extended in the enhancement of the abruptly autofocusing ability. As a increases, the critical value for the dimensionless radius decreases until it reaches zero. The physical mechanism of extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability is elucidated.

Quantum backflow for a massless Dirac fermion on a ring

We study the quantum backflow problem for a massless charged Dirac fermion constrained to move on a ring of radius R. Using the relativistic current operator for states of definite magnetic quantum number it is shown that quantum backflow takes place on the ring. We also study the backflow problem on the line and it is shown that unlike massive fermions, massless fermions do not exhibit quantum backflow.

Mechanical performance of an elastomeric bearing incorporated within steel ring restrainers

Unseating may be one of the most severe forms of damage to a bridge caused by an earthquake; such an event may lead to catastrophic span falling or collapse. A novel elastomeric bearing incorporated within steel ring restrainers (EB-SRRs) to prevent the unseating of bridges is therefore proposed. The EB-SRRs consists mainly of an elastomeric bearing in the center and multiple steel ring restrainers (SRRs) symmetrically distributed on both sides. The finite element (FE) model of the EB-SRRs is established, and its reliability is validated using data from earlier experiments. A parametric analysis of the EB-SRR performance is undertaken using the FE method. Finally, a method for the prediction of the mechanical behavior of the EB-SRRs is proposed. The results show that EB-SRRs can provide multi-level mechanical properties: compared with traditional EB, EB-SRRs has the same behavior under small horizontal load but provide a slight increase in strength and energy dissipation under moderate horizontal load and a greater increase in strength and energy dissipation under large horizontal load.The cross-section height h and cross-section width w mainly affect the ultimate bearing capacity Fu and the energy dissipation of the EB-SRRs; steel ring radius R, guide pulley diameter D, and straight part length a mainly affect the ultimate displacement δu; the straight part length a significantly affect the activation displacement δa. The method of predicting the force–displacement curves of the EB-SRRs proposed in this study is shown to be accurate.

Seismic Performance of Self-reset Piers Assembled with External Replaceable Energy Dissipation Rings

In order to improve the shear and energy dissipation capacity, this paper proposes a kind of external replaceable energy dissipation ring segment assembly self-reset pier. The ABAQUS platform is used to simulate the refined model of pier and energy dissipation device. Then the influence of different energy dissipation modes on the seismic performance of bridge piers is studied by pseudo-static analysis. Finally, the influence of different parameters of energy dissipation ring on the seismic behavior of bridge piers is analyzed. The results show that the capacity of shear resistance and energy dissipation of the pier with two energy dissipation lines is significantly higher than that of the pier without energy dissipation devices. Reducing the radius of energy dissipation ring can effectively improve the lateral bearing capacity and cumulative energy dissipation of bridge piers. The thickness of energy dissipation ring has little effect on the seismic performance of bridge piers. Increasing a pair of energy dissipation rings can increase the cumulative energy dissipation of bridge piers by 31.1%. Although the residual displacement of pier top increases, the residual displacement angle is still less than 0.5%.

Imaging the Inner Astronomical Unit of the Herbig Be Star HD 190073

The inner regions of protoplanetary disks host many complex physical processes such as star–disk interactions, magnetic fields, planet formation, and the migration of new planets. To study directly this region requires milliarcsecond angular resolution, beyond the diffraction limit of the world's largest optical telescopes and even too small for the millimeter-wave interferometer Atacama Large Millimeter/submillimeter Array (ALMA). However, we can use infrared interferometers to image the inner astronomical unit. Here, we present new results from the CHARA and VLTI arrays for the young and luminous Herbig Be star HD 190073. We detect a sub-astronomical unit (sub-AU) cavity surrounded by a ring-like structure that we interpret as the dust destruction front. We model the shape with six radial profiles, three symmetric and three asymmetric, and present a model-free image reconstruction. All the models are consistent with a near face-on disk with an inclination ≲20°, and we measure an average ring radius of 1.4 ± 0.2 mas (1.14 au). Around 48% of the total flux comes from the disk with 15% of that emission appearing to emerge from inside the inner rim. The cause of emission is still unclear, perhaps due to different dust grain compositions or gas emission. The skewed models and the imaging point to an off-center star, possibly due to binarity. Our image shows sub-AU structure, which seems to move between the two epochs inconsistently with Keplerian motion and we discuss possible explanations for this apparent change.

MOA-2020-BLG-208Lb: Cool Sub-Saturn-mass Planet within Predicted Desert

We analyze the MOA-2020-BLG-208 gravitational microlensing event and present the discovery and characterization of a new planet, MOA-2020-BLG-208Lb, with an estimated sub-Saturn mass. With a mass ratio , the planet lies near the peak of the mass-ratio function derived by the MOA collaboration and near the edge of expected sample sensitivity. For these estimates we provide results using two mass-law priors: one assuming that all stars have an equal planet-hosting probability, and the other assuming that planets are more likely to orbit around more massive stars. In the first scenario, we estimate that the lens system is likely to be a planet of mass and a host star of mass , located at a distance . For the second scenario, we estimate , , and . The planet has a projected separation as a fraction of the Einstein ring radius . As a cool sub-Saturn-mass planet, this planet adds to a growing collection of evidence for revised planetary formation models.