Angular Function Research Articles

Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma

We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole’s exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton–Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.

MIFAD-Net: Multi-Layer Interactive Feature Fusion Network With Angular Distance Loss for Face Emotion Recognition.

Understanding human emotions and psychology is a critical step toward realizing artificial intelligence, and correct recognition of facial expressions is essential for judging emotions. However, the differences caused by changes in facial expression are very subtle, and different expression features are less distinguishable, making it difficult for computers to recognize human facial emotions accurately. Therefore, this paper proposes a novel multi-layer interactive feature fusion network model with angular distance loss. To begin, a multi-layer and multi-scale module is designed to extract global and local features of facial emotions in order to capture part of the feature relationships between different scales, thereby improving the model's ability to discriminate subtle features of facial emotions. Second, a hierarchical interactive feature fusion module is designed to address the issue of loss of useful feature information caused by layer-by-layer convolution and pooling of convolutional neural networks. In addition, the attention mechanism is also used between convolutional layers at different levels. Improve the neural network's discriminative ability by increasing the saliency of information about different features on the layers and suppressing irrelevant information. Finally, we use the angular distance loss function to improve the proposed model's inter-class feature separation and intra-class feature clustering capabilities, addressing the issues of large intra-class differences and high inter-class similarity in facial emotion recognition. We conducted comparison and ablation experiments on the FER2013 dataset. The results illustrate that the performance of the proposed MIFAD-Net is 1.02–4.53% better than the compared methods, and it has strong competitiveness.

Correlation symmetry analysis of electron nanodiffraction from amorphous materials

Angular symmetry in diffraction reflects rotational symmetry in the sample. We introduce the angular symmetry coefficient as a method to extract local symmetry information from electron nanodiffraction patterns of amorphous materials. Symmetry coefficients are the average of the angular autocorrelation function at the characteristic angles of a particular rotational symmetry. The symmetry coefficients avoid non-structural features arising from Fourier transformation and Friedel symmetry breakdown that affect the angular power spectrum approach to determining angular symmetries in amorphous nanodiffraction. Both methods require thin samples to avoid overlapping diffraction from clusters of atoms separated in the thickness of the sample, but symmetry coefficients are more forgiving. Electron nanodiffraction experiments on a Pd-based metallic glass sample demonstrate both potentially misleading information in angular power spectrum and the utility of symmetry coefficients.

Calibrating the Davis–Chandrasekhar–Fermi Method with Numerical Simulations: Uncertainties in Estimating the Magnetic Field Strength from Statistics of Field Orientations

Abstract The Davis–Chandrasekhar–Fermi (DCF) method is widely used to indirectly estimate the magnetic field strength from the plane-of-sky field orientation. In this work, we present a set of 3D MHD simulations and synthetic polarization images using radiative transfer of clustered massive star-forming regions. We apply the DCF method to the synthetic polarization maps to investigate its reliability in high-density molecular clumps and dense cores where self-gravity is significant. We investigate the validity of the assumptions of the DCF method step by step and compare the model and estimated field strength to derive the correction factors for the estimated uniform and total (rms) magnetic field strength at clump and core scales. The correction factors in different situations are cataloged. We find the DCF method works well in strong-field cases. However, the magnetic field strength in weak-field cases could be significantly overestimated by the DCF method when the turbulent magnetic energy is smaller than the turbulent kinetic energy. We investigate the accuracy of the angular dispersion function (ADF; a modified DCF method) method on the effects that may affect the measured angular dispersion and find that the ADF method correctly accounts for the ordered field structure, the beam smoothing, and the interferometric filtering, but may not be applicable to account for the signal integration along the line of sight in most cases. Our results suggest that the DCF methods should be avoided to be applied below ∼0.1 pc scales if the effect of line-of-sight signal integration is not properly addressed.

Deriving the angular response function for backscattering sensors.

We derived the angular response function (WN) for scattering sensors that automatically satisfies the normalization criterion and its corresponding weight (WT). WN's, derived for two commercial sensors, HydroScat-6 (HOBI Labs) and ECO-BB (Sea-Bird Inc.), agrees well with the Monte Carlo simulation and direct measurements. The backscattering measured for microbeads of known sizes agrees better with Mie calculation when the derived WN was applied. We deduced that the reduction of WT with increasing attenuation coefficient is related to path length attenuation and showed that this theoretically derived correction factor performs better than the default methods for the two commercial backscattering sensors. The analysis conducted in this study also leads to an estimate of uncertainty budget for the two sensors. The major uncertainty for ECO-BB is associated with its angular response function because of its wide field of view, whereas the main uncertainty for the HydrScat-6 is due to attenuation correction because of its relatively long path length.

On the rotation repetitions of Mathieu beams angular spectrum in frequency space

In the recent works on Mathieu beams, the angular spectrums commonly used are even and odd angular Mathieu functions with an angular variation vary between 0 to 2π. In this work, we propose to introduce a new index m characterizing the rotation repetitions (m-times) of the structure of the original angular spectrum of Mathieu beams on the total circle in the frequency space. With this index, the angular spectrum of Mathieu beams rotation can be controlled to change the beam symmetry. We study the effect of these repetitions of the angular spectrum on the even and odd Mathieu modes features when they propagate through a paraxial optical system. We show that rotated repetitions of the angular spectrum does not affect the nondiffracting property of the beams. To illustrate the rotation repetitions of the angular spectrum, the Fourier transform of the beam is calculated in the focal plane of a thin lens. From the obtained results, we can conclude that the rotation repetitions of the angular spectrum can be used to produce others Mathieu beams shapes and can enrich the applications of these kinds of beams.

SIMULATION OF NEUTRON RESPONSE FUNCTIONS OF SILICON SENSOR APPLIED TO REAL-TIME PERSONAL ALBEDO NEUTRON DOSEMETER IN THE ENERGY RANGE BETWEEN 0.01EV AND 10KEV.

Neutron response functions of a silicon sensor, which is applied to a new real-time personal albedo neutron dosemeter, have been simulated for low energy neutrons from 0.01eV to 10keV using the Monte Carlo technique. The angular neutron response functions were obtained by multiplying simulated neutron energy spectra crossing the neutron sensor and the cross-section of the 6Li(n,t)4He reaction. The neutron response functions have been closed to the dose conversion coefficient of personal doses, Hp(10) recommended by the International Commission on Radiological Protection by selecting neutrons incident from angles of 105° to 180° with respect to an axis perpendicular to an acrylic phantom surface. From these simulation results, the neutron energy response function has been improved by shielding the sensor with cadmium box without a face toward the phantom. The neutron sensor provides a good conformance to the Hp(10) conversion coefficients within 15% for low energy neutrons.

Quantum Theory of Massless Particles in Stationary Axially Symmetric Spacetimes.

Quantum equations for massless particles of any spin are considered in stationary uncharged axially symmetric spacetimes. It is demonstrated that up to a normalization function, the angular wave function does not depend on the metric and practically is the same as in the Minkowskian case. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms, which depend in a unique way on time and space curvatures. In agreement with the principle of equivalence, these terms vanish locally, and the radial equations reduce to the same homogeneous equations as in Minkowski spacetime.

Polarised emission from aligned dust grains in nearby galaxies: Predictions from the Auriga simulations

Context. Polarised emission from non-spherical dust grains contains information about the alignment of these dust grains and traces the structure of the interstellar magnetic field. Methods. We post-processed a set of Milky-Way-like galaxies from the Auriga project, assuming a dust mix consisting of spheroidal dust grains that are partially aligned with the model magnetic field. We constrained our dust model using Planck 353 GHz observations of the Milky Way. This model was then extrapolated to shorter wavelengths that cover the peak of interstellar dust emission and to observations of arbitrarily oriented nearby Milky-Way-like galaxies. Results. Assuming an intrinsic linear polarisation fraction that does not vary significantly with wavelength for wavelengths longer than 50 micron, we predict a linear polarisation fraction with a maximum of 10 − 15% and a median value of ≈7% for face-on galaxies and ≈3% for edge-on galaxies. The polarisation fraction anti-correlates with the line of sight density and with the angular dispersion function which expresses the large-scale order of the magnetic field perpendicular to the line of sight. The maximum linear polarisation fraction agrees well with the intrinsic properties of the dust model. The true magnetic field orientation can be traced along low density lines of sight when it is coherent along the line of sight. These results also hold for nearby galaxies, where a coherent magnetic field structure is recovered over a range of different broad bands. Conclusions. Polarised emission from non-spherical dust grains accurately traces the large-scale structure of the galactic magnetic field in Milky-Way-like galaxies, with expected maximum linear polarisation fractions of 10 − 15%. To resolve this maximum, a spatial resolution of at least 1 kpc is required.

Angular Multiplexing Nanoprinting with Independent Amplitude Encryption Based on Visible-Frequency Metasurfaces.

Two-dimensional (2D) metasurfaces hold great promise to enable multiplexing and multifunctional optical devices due to their artificial freedom in design, device miniaturization, etc. Various multiplexing and multifunctional metasurfaces have been extensively studied, including polarization multiplexing, wavelength multiplexing, and orbit angular momentum (OAM) multiplexing. However, due to the lack of angular encoding freedom, angular multiplexing switchable nanoprinting has rarely been studied or demonstrated yet to the best of our knowledge. Here, we realize angular multiplexing switchable nanoprinting functionality with independent amplitude encryption based on visible-frequency metasurfaces. By screening a large number of structural designs and breaking the angular correlation, we eventually obtain optimal metasurface designs to realize dual-channel arbitrary image encryption. Furthermore, we illustrate that the proposed scheme would serve as an optical information concealment/retrieval strategy by combining the structural color and amplitude modulation. Overall, we believe that angular multiplexing metasurfaces would easily find promising applications, including optical information encryption/concealment, multifunctional switchable devices, and advanced eyeglass-free three-dimensional (3D) stereoscopic displays.

Modelling the visual world of a velvet worm.

In many animal phyla, eyes are small and provide only low-resolution vision for general orientation in the environment. Because these primitive eyes rarely have a defined image plane, traditional visual-optics principles cannot be applied. To assess the functional capacity of such eyes we have developed modelling principles based on ray tracing in 3D reconstructions of eye morphology, where refraction on the way to the photoreceptors and absorption in the photopigment are calculated incrementally for ray bundles from all angles within the visual field. From the ray tracing, we calculate the complete angular acceptance function of each photoreceptor in the eye, revealing the visual acuity for all parts of the visual field. We then use this information to generate visual filters that can be applied to high resolution images or videos to convert them to accurate representations of the spatial information seen by the animal. The method is here applied to the 0.1 mm eyes of the velvet worm Euperipatoides rowelli (Onychophora). These eyes of these terrestrial invertebrates consist of a curved cornea covering an irregular but optically homogeneous lens directly joining a retina packed with photoreceptive rhabdoms. 3D reconstruction from histological sections revealed an asymmetric eye, where the retina is deeper in the forward-pointing direction. The calculated visual acuity also reveals performance differences across the visual field, with a maximum acuity of about 0.11 cycles/deg in the forward direction despite laterally pointing eyes. The results agree with previous behavioural measurements of visual acuity, and suggest that velvet worm vision is adequate for orientation and positioning within the habitat.

Deep Morphological Anomaly Detection Based on Angular Margin Loss

Deep anomaly detection aims to identify “abnormal” data by utilizing a deep neural network trained on a normal training dataset. In general, industrial visual anomaly detection systems distinguish between normal and “abnormal” data through small morphological differences such as cracks and stains. Nevertheless, most existing algorithms emphasize capturing the semantic features of normal data rather than the morphological features. Therefore, they yield poor performance on real-world visual inspection, although they show their superiority in simulations with representative image classification datasets. To address this limitation, we propose a novel deep anomaly detection algorithm based on the salient morphological features of normal data. The main idea behind the proposed algorithm is to train a multiclass model to classify hundreds of morphological transformation cases applied to all the given data. To this end, the proposed algorithm utilizes a self-supervised learning strategy, making unsupervised learning straightforward. Additionally, to enhance the performance of the proposed algorithm, we replaced the cross-entropy-based loss function with the angular margin loss function. It is experimentally demonstrated that the proposed algorithm outperforms several recent anomaly detection methodologies in various datasets.

A temperature-dependent critical Casimir patchy particle model benchmarked onto experiment.

Synthetic colloidal patchy particles immersed in a binary liquid mixture can self-assemble via critical Casimir interactions into various superstructures, such as chains and networks. Up to now, there are no quantitatively accurate potential models that can simulate and predict this experimentally observed behavior precisely. Here, we develop a protocol to establish such a model based on a combination of theoretical Casimir potentials and angular switching functions. Using Monte Carlo simulations, we optimize several material-specific parameters in the model to match the experimental chain length distribution and persistence length. Our approach gives a systematic way to obtain accurate potentials for critical Casimir induced patchy particle interactions and can be used in large-scale simulations.

Angular Airy function: a model of Fabry-Perot etalons illuminated by arbitrary beams.

Fabry-Perot (FP) etalons are used as filters and sensors in a range of optical systems. The reflected and transmitted fields associated with an FP etalon have traditionally been predicted by the Airy function, which assumes a plane wave illumination. FP etalons are, however, often illuminated by non-collimated beams, rendering the Airy function invalid. To address this limitation, we describe the angular Airy function which calculates the reflected and transmitted fields for arbitrary illumination beams, using angular spectrum decomposition. Combined with realistic models of the experimental illumination beams and detection optics, we show that the angular Airy function can accurately predict experimental wavelength resolved intensity measurements. Based on the angular Airy function, we show that the fundamental operating principle of an FP etalon is as an angular-spectral filter. Based on this interpretation we explain the asymmetry, broadening and visibility reduction seen on wavelength resolved intensity measurements from high Q-factor FP etalons illuminated with focused Gaussian beams.

Massless particle of any spin in static uncharged spherically symmetric curved spacetimes

Quantum equations for massless particles of any spin in static spherically symmetric spacetimes, namely, the Minkowski, FRW and Schwarzschild spacetimes are considered. The metrics of all three are diagonal and their corresponding E2 2 and E3 3 inverse veirbein fields are identical. Thus the angular wave functions are spherical harmonics spinors corresponding to simple modes specified by orbital angular momenta and their z component. By applying consistently a procedure based on variables separation it is shown that the radial wave functions are second order ordinary differential equations sharing the same homogeneous equation though nonhomogeneous terms are different depending on the characteristic E0 0 and E1 1 of each spacetime.

WEB-ORIENTED SYSTEM FOR MONITORING AND MANAGEMENT OF AGILE METHODOLOGY PROJECTS

The work is devoted to the development of a web-based support system for monitoring the implementation and management of small projects implemented according to the agile methodology (in particular, in the field of information technologies). Monitoring the implementation of projects is an important factor in their success, which in turn has a positive impact on the company's profits and the economy as a whole. Existing solutions in the field of project management were analyzed: the main models of project management were considered, as well as the main software tools for their implementation, their advantages and disadvantages. The task of developing a web-based system for monitoring and project management according to the Agile methodology was formed. The software tools for the system implementation were selected and the database structure was designed. The software of the server part was implemented using the architecture "model - view - controller", for which UML-diagrams of the relevant components of the system were developed. The developed server software uses a software interface with response to requests in JSON format, which allows you to further develop in addition to the web interface and mobile applications. The web interface implemented by the Angular framework implements basic functions for users and system administrators, such as entity management, authorization and registration, and includes an analytical tool for monitoring project performance, namely the burn-out chart. The developed software will be useful for small projects that use Agile methodologies, both partially and completely, and which do not require complex tools that require a long setup process. Implementing this system as a web-based application allows you to use it from both desktop computers and mobile devices.

Theoretical and experimental study of wind turbine drivetrain fault diagnosis by using torsional vibrations and modal estimation

This paper provides an analytical proof and the theoretical development of the idea of using the torsional vibration measurements for a system-level condition monitoring of the drivetrain system. The method relies on modal parameter estimation of the drivetrain system by using the torsional measurements and subsequent monitoring of the variations in the system eigenfrequencies and normal modes. Angular velocity error function extracted from encoder outputs at both input and output of drivetrain is used to estimate modal parameters including natural frequencies and damping coefficients. In the proposed condition monitoring approach, it is shown that any abnormal deviation from the reference values of the drivetrain system dynamic properties can be translated into the progression of a specific fault in the system. In order to extract the condition monitoring features, local sensitivity analysis is engaged to establish a relationship between different categories of drivetrain faults with the system dynamic properties and the amplitude of torsional response, which helps with both to identify the state of the progressive faults and to localize them. Local sensitive analysis shows that abnormal deviations in stiffness and moment of inertia due to the presence of faults result in considerable changes in natural frequencies and modal responses which can be measured and used as fault detecting features by using the proposed analytical approach. Sensitivity analysis is also employed along with the estimated modal frequency for estimation of modal damping from the amplitude of response at the natural frequencies and their subsequent use for estimation of undamped natural frequencies which are later used in the proposed condition monitoring approach. The proposed approach is computationally inexpensive and can be implemented without additional instrumentation. Two test cases, using 10 MW simulated and 1.75 MW operational drivetrains have been demonstrated.

Concept for composition of hybrid flying multi-rotor platforms with distributed load and its experimental justification

This paper discusses the main approaches to the development and construction of hybrid flying multi-rotor platforms with separation of lift control functions and angular stabilization functions, called by the authors “distributed load”. A significant factor that limits flight time for majority of multi-rotor platforms is the energy density limit of lithium polymer batteries, which are most commonly used. To solve this problem we analyzed possible ways to increase flight time: replacing the main type of energy carrier for a more energy-intensive one and use of hybrid systems with combination of popular lithium-polymer batteries and a more energy-intensive energy carrier. The analysis was supported by experimental data.

Face Recognition Based on Lightweight Convolutional Neural Networks

Face recognition algorithms based on deep learning methods have become increasingly popular. Most of these are based on highly precise but complex convolutional neural networks (CNNs), which require significant computing resources and storage, and are difficult to deploy on mobile devices or embedded terminals. In this paper, we propose several methods to improve the algorithms for face recognition based on a lightweight CNN, which is further optimized in terms of the network architecture and training pattern on the basis of MobileFaceNet. Regarding the network architecture, we introduce the Squeeze-and-Excitation (SE) block and propose three improved structures via a channel attention mechanism—the depthwise SE module, the depthwise separable SE module, and the linear SE module—which are able to learn the correlation of information between channels and assign them different weights. In addition, a novel training method for the face recognition task combined with an additive angular margin loss function is proposed that performs the compression and knowledge transfer of the deep network for face recognition. Finally, we obtained high-precision and lightweight face recognition models with fewer parameters and calculations that are more suitable for applications. Through extensive experiments and analysis, we demonstrate the effectiveness of the proposed methods.

Nonlinear dynamics of the rotating beam with time-varying speed under aerodynamic loads

In this research, the bifurcation analysis is inspected for a rotatory pre-twisted beam which is subjected to the time varying angular velocity and aerodynamic forces. Aerodynamic loads are obtained by the Piston and Whitehead theories. It is assumed that a time-dependent periodic component is superposed on the angular velocity. The extended Hamilton's principle is utilized to derive the dynamic equations of motion in flapwise and chordwise directions. Then a combination of the Galerkin and multiple scales methods is established to obtain the modulation equations describing amplitude and phases of the interacting modes. Eigen value analysis is performed on the linear part of the equations and the possibility of 1:1 internal resonance condition is examined. The evolution of amplitudes is obtained versus the amplitude and frequency of the periodic angular velocity function. Primary and subharmonic resonance conditions are tuned between the angular velocity frequency and natural frequencies of the beam. Numerical simulations indicate that the nonlinear phenomena such as jump, saturation, and double jumping appear in nonlinear vibration of rotating beam with varying speed.