Symmetric Shape Research Articles

A new method development and validation for simultaneous estimation of ramipril and telmisartan by RP-HPLC method in combined dosage form

The present research work was development and validation of new RP-HPLC method for simultaneous estimation of Ramipril and Telmisartan in combined dosage form. In simultaneous RP-HPLC method development, Waters 2695 Separations Module with PDA Detector and column used is C8 SB ZORBAX (150 X 4.6mm) column with 3.5-micron particle size. Injection volume of 10 µL is injected and eluted with the mobile phase selected after optimization was Phosphate buffer and Acetonitrile in the ratio of 70:30 was found to be ideal. The optimized flow rate was at 1.0 mL/min. Detection was carried out at 230 nm. This system produced symmetric peak shape, good resolution and reasonable retention times of Ramipril and Telmisartan were found to be 2.275 and 4.261 minutes respectively. The Ramipril and Telmisartan showed linearity in the range of 20-60 µg/mL and 160-480 µg/mL respectively. The %RSD values for precision was found to be within the acceptable limit, which revealed that the developed method was precise. The developed method was found to be robust and the %RSD value for percentage recovery of Ramipril and Telmisartan was found to be within the acceptance criteria. The results indicate satisfactory accuracy of method for simultaneous estimation of the Ramipril and Telmisartan.

Solving Elliptic Curve Discrete Logarithm Problem on Twisted Edwards Curves Using Quantum Annealing and Index Calculus Method

Abstract This paper presents an approach to solving the elliptic curve discrete logarithm problem on alternative curve models over prime fields using a quantum annealing and index calculus method. Part of the algorithm, relation searching, is transformed into the Quadratic Unconstrained Boolean Optimization (QUBO) problem and then is efficiently solved using the D-Wave computer by quantum annealing. As Faugère et al. showed, twisted Edwards curves, because of their symmetric shape, allow us to obtain solutions of relations searching step using Groebner basis faster than in the case of Weierstrass curves. Because of symmetries, a system of equations of relations searching step for twisted Edwards curves has many symmetric solutions. Using the Groebner basis and having many system solutions makes it easier to find any of them. The same is true using quantum annealing - it is easier to find any solution to the QUBO problem if many are correct. In this paper, we used this observation to find out that a properly constructed QUBO problem for the relations searching step for twisted Edwards curves allows us to find a solution faster for the same size of the base field than in the case of Weierstrass curves. Using the presented approach, we solved the discrete logarithm problem using quantum annealing and index calculus method for elliptic curve discrete logarithm problem defined on twisted Edwards curve over a field 𝔽1021 with order equal to 4 · 241. It is now the biggest field and size of the group, where the elliptic curve discrete logarithm problem was solved using quantum methods.

An optimization DEM modelling method for soil-fibre undrained cyclic loading tests model based on the influence range of fibre

The computational cost of discrete element modelling is high owing to the limitations of particle size and contact in fibre modelling. This paper proposes an optimised discrete element method (DEM) for a hybrid model of soil and fibres based on the fibre influence range. First, a relative velocity state function is established based on the relative motion state between the fibres and soil particles under undrained cyclic loading. Subsequently, the influence range of the fibres is determined using the relative velocity function based on the first few cycles of the undrained cyclic loading numerical tests. Cluster and clump models of the fibre are then generated based on the influence range of the fibre. Finally, a symmetrical shape of the optimised model is developed by extracting the distribution length of the edge curve of the influence range along the vertical direction of the axis. In this study, the proposed optimised DEM was validated through a series of undrained cyclic loading numerical tests on fibre-reinforced soil. The results of the optimised model were highly consistent with those of the traditional model, and the computational time was significantly reduced. The cyclic loading timing for determining the range of influence of the fibre was analysed. The optimised model based on the influence range of the 15th cycles not only restored almost the same results but also saved the calculation cost by nearly eight times. The optimised model established based on the influence range after the 15th cycles had a slight influence on the results. In addition, the applicability of the optimised model is discussed. This paper provides new insights into the establishment of a hybrid model of soil and fibres.

Ponderomotive potential effects on strong field two-photon double ionization in neon

Abstract In the context of the recently reported experiment on photoionization in neon atom, we theoretically study the photoionization of neon atom at a comparatively intense laser field. The calculated photoelectron spectrum for a Gaussian laser pulse show an asymmetric double peak line shape at a pulse duration of 14.2 fs and peak intensity of 1x1015 W/cm2. A systematic study clearly indicates that the ponderomotive potential of the photoelectron released during photoionization of neon is instrumental in causing the visible asymmetry. 
 Interestingly, for similar laser parameters asymmetry in the the photoelectron spectrum gets significantly reduced for a Sech2
shaped laser pulse. Time resolved photoelectron spectrum reveals that even for a Sech2 shaped laser pulse the two peak photoelectron spectrum is initially asymmetric and evolves into a symmetric line shape with increase in time. The results clearly indicate that irrespective of laser pulse shape asymmetry shows a non-linear decrease as a function of time. Our study also shows the possibility of controlling the asymmetry by varying the pulse duration. The calculations establishes a correlation between the effects of direct double ionization and ponderomotive potential on the asymmetry of the photoelectron spectrum at different pulse durations.

Chiral Symmetry Breaking in Colloidal Metal Nanoparticle Solutions by Circularly Polarized Light.

Shape symmetry breaking in the formation of inorganic nanostructures is of significant current interest. It was typically achieved through the growth of colloidal nanoparticles with adsorbed chiral molecules. Photochemical processes induced through asymmetric plasmon excitation by circularly polarized light in surface immobilized nanostructures also led to symmetry breaking. Here, we show that chiral symmetry breaking can be achieved by randomly rotating gold@silver core-shell nanobars in colloidal solution using circularly polarized illumination, where orientational averaging does not eliminate the symmetry breaking of an asymmetric plasmon-induced galvanic replacement reaction. Different morphological effects that are produced by circularly vs linearly polarized light illumination demonstrate the intricate effect of light polarization on the localized plasmonic-induced photochemical response. The essential features of this symmetry breaking, such as illumination wavelength dependence, were reproduced by simulations of circularly polarized light-excited-plasmon-induced hot-electron generation as the source for asymmetric metal deposition. The symmetry breaking becomes smaller in more symmetric geometrical shapes, such as triangular nanoprisms and nanocubes, and down to zero in spherical ones. The degree of symmetry breaking rises when the nanobars are immobilized on a substrate and illuminated from a single direction.

Determination of multiple restricted and prohibited ingredients in hair dyes using a novel 3D stationary phase coupled with gas chromatography-mass spectrometry

Hair dyes (HDs) are mainly composed of various benzene series, amines, and phenolic compounds. These ingredients are well known to have allergenic, teratogenic, and carcinogenic properties. As such, the presence of these ingredients in HDs has received increased attention in recent years. At present, the applications of traditional analytical and detection methods and commercial chromatographic columns are limited by problems such as poor qualitative analysis and inaccurate quantification. Thus, the development of new analytical and detection technologies and stationary phases is an urgent endeavor. Moreover, HDs contain complex compounds and exhibit significant matrix interference. Hence, appropriate sample pretreatment methods are necessary to analyze HDs. In this study, the 3D nonpolar rigid structure of triptycene (TP) was combined with the polar flexible chains of polyethylene glycol (PEG) to design and synthesize a TP derivative, TP-PEG, as a stationary phase for chromatographic columns. The stationary phase enabled the expansion of the selection range for polar and nonpolar analytes. Subsequently, gas chromatography-mass spectrometry (GC-MS) was used to quantitatively analyze 22 ingredients in HDs. The experimental results demonstrated that analytes with different polarities exhibited sharp and symmetrical peak shapes on the stationary phase, and all 22 analytes achieved baseline separation on the chromatographic column. The 22 ingredients in HDs showed good linear relationships within their respective ranges, with correlation coefficients greater than 0.9985. The average recovery rates at three spiked levels were in the range of 89.2%-103.2%, and RSDs were less than 5%. Compared with traditional methods, the proposed method has higher efficiency and better accuracy, thus verifying the excellent separation performance of the new stationary phase and the effectiveness of the established GC-MS detection method. The findings indicated the applicability of the developed method to the detection and analysis of various compounds in HDs.

Quantifying the Wind‐Induced Bias of Rainfall Measurements for the Thies CLIMA Optical Disdrometer

AbstractThe wind‐induced bias of rainfall measurements obtained from non‐catching instruments is addressed in this work with reference to the Laser Precipitation Monitor (LPM) optical disdrometer manufactured by Thies CLIMA. A numerical simulation approach is adopted to quantify the expected bias, involving three different models with increasing complexity. Computational Fluid‐Dynamics simulation of the airflow field around the instrument with an embedded Lagrangian particle‐tracking module to obtain raindrop trajectories are performed by solving the Unsteady Reynolds Averaged Navier‐Stokes (URANS) equations and a Large Eddy Simulation (LES) model. URANS‐uncoupled, LES‐uncoupled, and LES‐coupled approaches are tested to assess the impact of modeling the airflow turbulent fluctuations in detail. Due to the non‐radially symmetric external shape of the instrument, various combinations of the wind speed and direction are considered. Catch ratios for monodisperse rain are obtained as a function of the particle Reynolds number and the wind direction and fitted to obtain site‐independent curves to support application of the simulation results. Based on literature expressions to link the drop size distribution of real rainfall events with the rainfall intensity (which instead depend on the local rainfall climatology at the measurement site), sample collection efficiency curves are obtained from the catch ratios of monodisperse rain. The resulting adjustment curves allow rainfall measurements to be corrected using either a real‐time or post‐processing approach. However, at high wind speed and assuming that the wind blows parallel to the instrument sensing area, the instrument may fail to report precipitation altogether.

Finding The Relationship between Pulsation Motion and Hα Emission Lines on γ Cas using Photometric and Spectroscopic Data

Abstract Pulsating stars show variability in brightness due to changes in their volume. There are two types of pulsation/oscillation: radial and non-radial. Radial oscillation keeps the symmetrical shape of the star, while non-radial oscillation does not. We study a pulsating star: γ Cas, classified as a B0.5 IVe variable star because of its pulsations and also an emission star due to the emission lines in its spectra. When a star pulsates, its atmosphere expands and contracts, potentially leading to the formation of shock waves. Observational features such as discontinuities in the radial velocity curve and emission lines support this phenomenon. In this study, we analyse the relationship between pulsation motion and the H α emission lines of γ Cas using photometric and spectroscopic data. Photometric data is obtained from the BRIght Target Explorer (BRITE) catalog, while spectroscopic data comes from the Be Star Spectra (BeSS) catalog. Both datasets cover the same observational dates: August 28 to October 26, 2015. Confirming the pulsation period of γ Cas at 1.21 days, we also discover an added pulsation period of 10 days from photometric data. To confirm this, we examine spectroscopic data from three specific dates: August 28, September 7, and 27, 2015. Notably, the relative flux of the H α emission lines continue to increase, leading us to conclude that these lines are indeed caused by the pulsation of γ Cas.

A Novel Nano-Spherical Tip for Improving Precision in Elastic Modulus Measurements of Polymer Materials via Atomic Force Microscopy.

Micro-nano-scale mechanical properties are vital for engineering and biological materials. The elastic modulus is generally measured by processing the force-indentation curves obtained by atomic force microscopy (AFM). However, the measurement precision is largely affected by tip shape, tip wear, sample morphology, and the contact model. In such research, it has been found that the radius of the sharp tip increases due to wear during contact scanning, affecting elastic modulus calculations. For flat-ended tips, it is difficult to identify the contact condition, leading to inaccurate results. Our research team has invented a nano-spherical tip, obtained by implanting focused helium ions into a silicon microcantilever, causing it to expand into a silicon nanosphere. This nano-spherical tip has the advantages of sub-micro size and a smooth spherical surface. Comparative tests of the elastic modulus measurement were conducted on polytetrafluoroethylene (PTFE) and polypropylene (PP) using these three tips. Overall, the experimental results show that our nano-spherical tip with a consistent tip radius, symmetrical geometric shape, and resistance to wear and contamination can improve precision in elastic modulus measurements of polymer materials.

The role of uncertain perspective information in recovering 3D symmetrical shapes

The role of uncertain perspective information in recovering 3D symmetrical shapes

[formula omitted]-space physics-informed neural network (k-PINN) for compressed spectral mapping and efficient inversion of vibrations in thin composite laminates

The vibrational response of structural components carries valuable information about their underlying mechanical properties, health status and operational conditions. This underscores the need for the development of efficient physics-based inversion algorithms which, given a limited set of sensing data points and in the presence of measurement noise, can reconstruct the response at locations where measurement data is not available and/or identify the unknown mechanical properties. Addressing this challenge, Physics-Informed Neural Networks (PINNs) have emerged as a promising approach. PINNs seamlessly integrate governing equations into their architecture and have gained significant interest in solving inversion problems. In the context of learning and inversion of multimodal, multiscale vibrational responses, this paper introduces a novel spectral extension of PINNs, utilizing Fourier basis functions in the wavenumber domain, commonly known as k-space. The proposed method, referred to as k-space PINN (k-PINN), offers a robust framework for adjusting complexity and wavenumber composition of the response. Notably, the spectral formulation of k-PINN, coupled with the generally sparse representation of vibrations in k-space, facilitate efficient reconstruction and learning of broadband vibrations and alleviate the spectral bias associated with standard PINN. Additionally, the spectral solution space introduced by k-PINN substantially reduces the computational cost associated with computing physics-informed loss terms. We evaluate the effectiveness of the proposed methodology on reconstructing the bending vibrational mode shapes of a thin composite laminate and identifying its effective bending stiffness coefficients. Mode shapes are initially obtained from finite element simulation, and virtual test data with added noise are generated for evaluation purposes. It is shown that the proposed k-PINN methodology outperforms the standard PINN in terms of both learning and computational efficiency. The performance of k-PINN is further demonstrated by show casing its capability in learning different selections of symmetric, anti-symmetric and asymmetric mode shapes.

Bayesian inference for unit Gamma distribution

In this article, we develop Bayesian inference for the unit-Gamma (GU) distribution, initially introduced by Grassia (1977). This distribution is highly flexible, allowing it to take various forms within the interval (0,1), encompassing both symmetric and asymmetric shapes. Such flexibility makes it an attractive alternative to traditional distributions in this range, like the Kumaraswamy and beta models. We propose a parameterization based on quantiles, a particularly advantageous approach when dealing with datasets that include outliers, since the median, for instance, is a more robust estimator compared to the mean in such cases. Our work covers parameter estimation, model fit assessment, model comparison, and influence analysis. All procedures were implemented using Markov Chain Monte Carlo (MCMC) methods via Just Another Gibbs Sampling (JAGS) through the R2jags package in R, an open-source software. Furthermore, we demonstrate the effectiveness of this methodology by applying it to a real-world dataset, highlighting its practical utility.

Chromatographic evaluation and application of nitrogenous heterocyclic ring-bonded stationary phase in hydrophilic interaction liquid chromatography

Hydrophilic interaction liquid chromatography (HILIC) based on polar stationary phases has vital research significance in the separation of polar compounds. Numerous HILIC stationary phases with different structures have been developed, which do not have universal properties and broad selectivity, making it a challenge to select the suitable column based on the properties of the samples. Consequently, it is particularly important to develop a bonded phase capable of separating a wide variety of samples, while having enhanced retention, improved selectivity, symmetric peak shape and good stability. Herein, a novel nitrogen-containing heterocyclic bonded phase with multiple functionalities, such as thioether, amino and hydroxyl groups (named AMTA) was employed as HILIC stationary phase. Detailed chromatographic evaluations were carried out, and the results showed that it was superior to other hydrophilic chromatographic columns in terms of selectivity, peak shapes and practical sample separation. Lastly, it has been verified that AMTA exhibited high orthogonality with the XBridge C18 column of reversed-phase liquid chromatography (RPLC) mode. In summary, we anticipate our assay to be instructive to other researchers in developing the HILIC stationary phase.

Removal of ceftriaxone and cefotaxime antibiotics from industrial wastewater via complexation with Cu(II).

A high-performance liquid chromatographic method (HPLC) with UV detection is described for determination of ceftriaxone sodium (CFX) and cefotaxime sodium (CFM) content in pharmaceutical industrial wastewater. These methods are based on the detection of these antibiotics via the formation of chelate complexes with Cu(II). The developed Liquid Chromatographic method offers symmetric peak shape, good resolution and reasonable retention time for both drugs. The removal percentage reached about 100 and 92.1% at pH 7.2 for CFX and CFM, respectively. In UV detection, the removal of the chelating antibiotics were based on forming of chelate complexes with Cu(II) which detected at λmax = 253 and 244nm for CFX and CFM, respectively. Linearity, accuracy and precision were found to be acceptable over the concentration range of 5.99-59.86µgmL-1 for CFX and 14.33-71.63 µgmL-1 for CFM. The proposed method can be used for the quality control of industrial wastewater containing CFX and CFM.

Influence of beam polarization on underwater femtosecond laser machining of silicon wafer

This paper investigates the effect of polarization directions on underwater femtosecond laser machining of silicon wafer. Firstly, laser ablation in liquids produces laser-induced periodic surface structures (LIPSS) on both edges of the groove. The direction of LIPSS has direct correlation with the polarization of the laser beam. Secondly, the electric field intensity distribution within the groove is analyzed by numerical simulation employing the finite-difference-time-domain (FDTD) method. The simulation and experimental results reveal that the distribution of the inter electric field intensity within the grooves varies with polarization direction. As the angle between the polarization and scanning directions decreases, the peak electric field strength and groove depth gradually increase. Finally, changing the direction of polarization of the beam affects the symmetry of the groove profile. The groove profile produced by ablation is symmetrical when the beam polarization direction is parallel to the scanning direction. By modulating and optimizing the direction of polarization, grooves with large depth and symmetrical shape can be obtained.

Hybrid organic monolithic column containing MIL-68(Al) for the separation of small molecules by capillary HPLC

A hybrid organic monolithic column made of poly(lauryl methacrylate-co-1,6-hexanediol dimethacrylate) and the metal-organic framework MIL-68(Al) was prepared for the first time. The column was used in capillary liquid chromatography, both in isocratic and gradient elution modes. Separation performance towards small molecules of different chemical nature (polycyclic aromatic hydrocarbons, alkylbenzenes, phenols, etc.) was studied. Monte Carlo simulations were made to both select the proper precursors to obtain empty metal-organic framework micropores in the monolithic polymer and also, to analyze the potential free access of the studied analytes into the micropores (necessary to improve mass transfer and column efficiency). The hereby synthesized metal-organic framework microcrystals allowed obtaining homogeneous hybrid monolithic columns. Adding of MIL-68(Al) (1030 m2 g-1 BET specific surface area) increased the surface area from 3.9 m2 g-1 for the parent monolith to 18.2 m2 g-1 for the hybrid column containing 8 mg mL-1 of the microcrystals. Chromatographic performance of this new column was evaluated by studying retention factors, resolution, and plate counts at room temperature. Different compounds, not completely resolved in the parent monolith, were partially or completely separated after metal-organic framework addition. Using the monolithic column with only 2 mg mL-1 of MIL-68(Al), five alkylbenzenes were completely separated with very symmetrical peak shapes, resolution factors up to 3.60 and plate counts of 4300 plates m-1 for n-hexylbenzene. This value is higher than those obtained by other authors who used organic monolithic columns with embedded metal-organic frameworks to perform separations at room temperature. Additionally, nine polycyclic aromatic hydrocarbons were partially or completely resolved in gradient elution mode. The hybrid monolithic columns exhibited very good intra-day (%RSD=1.9), inter-day (%RSD=2.6), and column-to-column (%RSD=4.3) reproducibility values. Easy and fast column preparation, and versatility to efficiently separate several compounds of different chemical nature in isocratic and gradient mode, makes this new hybrid column a very good option for the analysis of small molecules in capillary (or nano) HPLC.

Easy-to-design wide stop-band multi-layer metamaterial filter based on symmetrical modified circular resonators for terahertz communication applications and electromagnetic interference shielding

Terahertz filters represent an essential element in modern communications system engineering. Designing a stopband filter with unique electrical qualities remains a relatively complicated task to achieve. In this context, the present paper suggests an easy-to-design bandstop filter to exploit it in terahertz communications and electromagnetic interference (EMI) shielding. The proposed filter is based on the multi-layer metamaterials stacking technique; it is constituted by a five-layer metal-insulator-metal-insulator-metal (MIMIM) microstructure. The two dielectric layers in polyimide with the three metallic layers in gold represent a total thickness of 43 μm. Each metallic layer is represented by a modified metamaterial resonator (MTMR) of the same symmetrical circular shape. The filter cell dimensions are optimized as 120 × 120 μm2 to have the desired stopband feature. The electrical qualities of the proposed filter have been analyzed by the finite element method (FEM) via the ANSYS high-frequency structure simulator software (HFSS). Through the simulation outcomes, salient filter features were highlighted. A wide −20 dB bandwidth of the order of 1.062 THz centered at 1.872 THz with a low transmission rate in the stopband which is less than 0.87 %, a significant square ratio of 0.86 and a relative bandwidth of around 57 %. Moreover, the absorption rate of the stopband has reached more than 97 % with excellent flat-top characteristics. To give more credibility to our results, we have presented a parametric analysis that included several components. In addition, the designed filter was insensitive to the polarization angle thanks to the symmetrical metamaterial resonators. Based on all these results and due to the simplicity of its design combined with all these unique features, our filter can be a prominent contender in the field of THz communications. It can be also required for terahertz imaging and EMI shielding.

A New Generalization of the Inverse Generalized Weibull Distribution with Different Methods of Estimation and Applications in Medicine and Engineering

Limitations inherent to existing statistical distributions in capturing the complexities of real-world data often necessitate the development of novel models. This paper introduces the new exponential generalized inverse generalized Weibull (NEGIGW) distribution. The NEGIGW distribution boasts significant flexibility with symmetrical and asymmetrical shapes, allowing its hazard rate function to be adapted to many failure patterns observed in various fields such as medicine, biology, and engineering. Some statistical properties of the NEGIGW distribution, such as moments, quantile function, and Renyi entropy, are studied. Three methods are used for parameter estimation, including maximum likelihood, maximum product of spacing, and percentile methods. The performance of the estimation methods is evaluated via Monte Carlo simulations. The NEGIGW distribution excels in its ability to fit real-world data accurately. Five medical and engineering datasets are applied to demonstrate the superior fit of NEGIGW distribution compared to competing models. This compelling evidence suggests that the NEGIGW distribution is promising for lifetime data analysis and reliability assessments across different disciplines.

Investigation the behavior of different fullerenes on graphene surface

In the present study, the regime of motion of fullerene molecules on graphene substrate in a specific temperature range is investigated. The potential energy of fullerene molecules is analyzed using classical molecular dynamics methods. Fullerene molecules C36, C50, C60, C76, C80, and C90 are selected due to spherical shapes of different sizes and good motion performance in previous studies. Analysis of the motion regime at different temperatures is one of the main objectives of this study. To achieve this aim, the translational and rotational movements of fullerene molecules are studied independently. In the first step of the investigation, Lennard-Jone's potential energy of fullerene molecules is calculated. Subsequently, the motion regime of different fullerenes is classified based on their displacement and diffusion coefficient. Findings indicate C60 is not appropriate in all conditions. However, C90 and C76 molecules are found to be appropriate candidates in most cases in different conditions. As far as a straight-line movement is considered, the deviation of fullerene molecules is compared by their angular velocities. Although C60 has a lower angular velocity due to its symmetrical shape, it may not move well due to its low diffusion coefficient. Overall, our study helps to understand the performance of different fullerene molecules on graphene substrate and find their possible applications, especially as wheels in nanomachine or nanocarrier structures.

Multi‐Concentric Generalized Perfect Vortex Beams by Hybrid Phase Metasurfaces

AbstractMetasurface‐based vortex beams are expected to overcome the current communication challenges of massive data and limited bandwidth by their theoretical infinite and mutually orthogonal states. However, limited by the spatial extension of array vortices, only finite orbital angular momentum (OAM) eigenstates are available, of which the expansion will boost the bandwidth toward an inexhaustible stage. In this manuscript, multi‐concentric generalized perfect vortex beams (G‐PVBs) are experimentally generated by the fabricated hybrid phase metasurfaces integrating generalized focusing phases and circular domain function into vortex phases. Diverse vortex shapes and helical lobes within beam patterns and spiral interferograms are both arranged in a non‐overlapping concentric manner instead of spatial arrays, respectively, breaking the limitation of symmetric shape while avoiding inter‐modal cross‐talk. The vortex shape, topological charge and vortex number are decoupled mutually in orthogonal polarization states, realizing both space and polarization multiplexing. Furthermore, shaped into anomalous profiles with asymmetric states of polarization, multi‐concentric vector G‐PVBs are experimentally generated to transmit parallelly stable order information with high robustness in turbulence environments. The proposed multi‐concentric G‐PVBs simultaneously expanded the novel vortex dimension by anomalous shapes and information channels of multi‐concentric OAM modes, providing potential application in high‐capacity vortex optical communication and information encryption.