Angular Coordinates Research Articles

Kerr/CFT correspondence for the extremal accelerating Kerr–Taub–NUT black hole

In this paper, we explore the application of Kerr/CFT correspondence to the accelerating Kerr–Taub–NUT spacetime. We demonstrate that the correspondence can be maintained if the near-horizon angular coordinate is appropriately rescaled. This rescaling allows the Cardy formula to accurately reproduce the extremal Bekenstein–Hawking entropy, a departure from the typical direct recovery of extremal Bekenstein–Hawking temperature in Kerr/CFT literature. This discrepancy is attributed to the presence of multiple sources of conic singularity in the spacetime, specifically the acceleration and NUT parameters. To support the Kerr/CFT holography, we investigate the hidden conformal symmetry in the near-horizon region of the extremal black hole geometry. Our findings confirm that the angular coordinate rescaling does not introduce inconsistencies within the Kerr/CFT framework, as evidenced by the preserved hidden conformal symmetry and consistent entropy matching calculations in the near-horizon geometry of the extremal accelerating Kerr–Taub–NUT black hole.

Synthesis of a four-point model of an airplane

The modeling of echo signals from distributed radar objects taking into account the noise of their angular coordinates is considered. Relationships are presented that allow the transition from a multipoint model of an arbitrary object containing tens, hundreds and even thousands of emitting points to a model composed of four emitting points located at the vertices of a square. As an example, we synthesized an airplane model containing only four points. It is obtained on the basis of a multipoint model composed of 56 points. Using numerical modeling methods, it has been shown that angular noise generated by multi-point and four-point aircraft models have identical correlation functions and similar parameters of the probability density distribution of angular coordinate noise. The obtained result is also confirmed by semi-natural modeling methods using a matrix simulator.

ANALYTICAL DESCRIPTION AND ALGORITHM OF CALCULATIONS OF MECHANICS OF STRUCTURES WITH BERNOULLI – EULER BEAMS USING SCAS KIDY

The problems of developing a universal analytical description and algorithm for automatic computer calculations of dynamics, statics and kinetostatics of mechanical models of structures including a beam lattice are considered. This can be calculations of transient processes, steady-state free and forced oscillations, determination of equilibrium positions and stress-strain states under static and dynamic loads, etc. The structure itself can be flat or spa- tial, stationary or moving on a plane or in space. Various instruments and devices can be attached to it. Arbitrary connections can be taken into ac- count. It is shown how it is possible to succinctly, using a special language for preparing computer data, analytically describe a part of a structure rep- resenting a beam lattice. Based on the theory of elasticity of Bernoulli-Euler beams, 2 forms of the canonical representation of the potential energy of an elastic beam are obtained. This makes it possible to introduce into the language of description of mechanical models of the special computer algebra system KiDyM (SCAS KiDyM) a new beam element, for which the position of the coordinate systems associated with the extreme sections is indi- cated. The positions of these sections are determined by lattice nodes, like solid bodies. Angular and linear coordinates of such solid bodies give gen- eralized coordinates of the mechanical model. An algorithm has been developed for the formation of elements adopted to describe mechanical models in SCAS KiDyM. Thus, the elastic structure of the mechanical model is formed. Using the available tools in this program, equations of dynamics and statics are automatically constructed, that is, a mathematical model is formed, and dynamic and static calculations can be carried out. The proposed method is demonstrated in detail on the example of calculating the deformation of an elastic lattice, with is the basis of a UAV (unmanned aerial vehi- cle). The results are compared with calculations using the ANSYS program

Зависимость величины сигнала от смещения функции рассеяния точки, вписанной в четыре пиксела матрицы

An algorithm has been developed for calculating changes in the signal level of a matrix pixel when the point scattering function is shifted at an angle of 45º relative to the joining point of 4 matrix pixels. In the initial state of the point spread function, the point is inscribed in four pixels. The spectral sensitivity of a pixel is constant within the pixel area. The distribution of pixel irradiance in the point spread function in the form of uniform irradiance is considered. Method. The calculation is based on the method of dividing the point spread function on each pixel of the matrix into separate areas for which the signal is calculated. The displacement of the point scattering function by Δx along the X axis and by Δy along the Y axis is taken in a form normalized to the radius of the spot. To create a two-dimensional graph of the dependence of the pixel signal on the displacement of the point scattering function along the X, Y axes, we introduce the relative displacement of the point scattering function η. Main results. An algorithm has been developed for calculating changes in the signal level of a matrix pixel when the point scattering function is shifted relative to the matrix pixels for the case of pixel irradiation in the lens scattering circle in the form of uniform irradiance. The dependence of the normalized matrix pixel signal on the relative displacement of the point scattering function η at an angle of 45º has been plotted for the above case of irradiation. Practical significance. Matrix photodetectors are widely used in guidance and tracking systems for space objects and astronomical sensors. For a defocused optical system, uniform distribution is used. When the point scattering function shifts relative to the joining point of the four pixels of the matrix, the matrix signal drops, which, with a low signal-to-noise ratio, can lead to a breakdown in tracking or an increase in the error in measuring the angular coordinates of a space object. The results of these studies can be used to model a target guidance system and determine target coordinates.

Conical bodies with star-shaped transverse contour having the minimum wave drag

The problem of constructing the transverse contour of a conical body having the minimum wave drag in the range of supersonic velocities provided that the length and the volume are preserved is considered. A cone is taken as the initial body, an assumption about locality of the relation between variations in the geometric parameters and the pressure on the surface is made, and the quadratic approximation of this relation is used. The found solution is compared with the results obtained within the framework of the Newton model. These solutions are proposed to combine being based on the assumption of the power-law relation between the radius and the derivative of radius with respect to the angular coordinate. In this case, a class of contours in which half of the cycle consists of the element with monotonic variation in the radius and arc of the circle is distinguished. These contours can be described by specifying a single geometric parameter, namely, the exponent. Using the inviscid perfect gas model, direct numerical optimization of the shape of transverse contour is carried out and the possibility of reducing the wave drag as compared to the star-shaped bodies with plane faces is demonstrated.

Mechanical optimization of skateboard pumping

Skateboarders perform a reciprocating motion on a curved ramp, called pumping, by moving their bodies up and down perpendicular to the ramp surface. We propose a simple mechanical model for this pumping motion and solve the equation of motion explicitly in angular coordinates. This allows us to derive an optimal control strategy to maximize amplitude by dynamically adjusting the center of mass of the skateboarder. This optimal strategy is compared to experimental results for the motion of a skilled and an unskilled skateboarder in a half-pipe, validating that a skilled skateboarder follows the optimal control strategy more closely. Published by the American Physical Society 2024

Uni-variable cross-spectral densities

We introduce a novel class of planar, scalar sources whose cross-spectral density is a function of a single complex variable. For a typical pair of source points, the modulus and argument of such a variable equal the product of their radial coordinates and the difference of their angular coordinates, respectively. As functions of a single complex variable, the corresponding cross-spectral densities (CSD) are expandable in power series in their convergence domain, and a virtually infinite number of source models can be devised. All such sources are shown to have vortex fields as modes. The closed analytical form of these uni-variable CSDs makes it possible to evaluate in a simple way the significant quantities characterizing the sources and the ones of the fields they radiate. The basic tool leading to the definition of the uni-variable CSDs are the reproducing-kernel Hilbert spaces. As an example, the CSD derived from the so called Szegö kernel is studied in some detail, and its features are derived, together with of those of the radiated field in the far zone.

Послідовне встановлення двох двигунів внутрішнього згоряння на автомобілі як метод зниження нерівномірності крутного моменту

An analysis of studies on the possibility of reducing fuel consumption of cars by replacing their power plants with two internal combustion engines installed in series is carried out. It has been determined that it is possible to reduce fuel consumption by reducing the unevenness of torque at the transmission input shaft, which in turn depends on the relative angular orientation of the crankshafts of the installed internal combustion engines. The study has determined that when installing two consecutive internal combustion engines, each of which generates an indicator torque that obeys the harmonic law, it makes it possible to shift the curves of the indicator torque and the crankshaft angle so that both engines operate in opposite phases. It is proposed to use a method of increasing the energy efficiency of cars by using two consecutive internal combustion engines, the crankshafts of which are installed relative to their initial angular position with the difference in the angular coordinates (angles of rotation) of the crankshafts of both engines relative to the initial position, which allows to reduce unproductive energy losses. Approximating the actual curves of change of the indicator torque by the harmonic law, taking into account the angle of rotation of the crankshaft, graphs of dependence of the indicator torque on the angle of rotation of the crankshaft of four-stroke internal combustion engines with different numbers of cylinders are constructed. It has been determined that with an increase in the number of cylinders of an internal combustion engine and the coefficient of the share of torque on the drive wheels, there is a decrease in the coefficient of unproductive energy consumption, which takes into account the influence of the unevenness of the indicator torque. The problem of ensuring the operation of the second engine in the counterphase of the first engine is solved, which should be fulfilled by the ratio of the angles of rotation of the crankshafts of the first and second engines relative to the initial (zero) position with the difference in the angular coordinates (angles of rotation) of the crankshafts of both engines relative to the initial position. The results of calculating the angle of the crankshafts' relative position when two internal combustion engines are installed sequentially in the opposite phase indicate a decrease in this angle with an increase in the number of cylinders.

A space/time interchange symmetry of rotating AdS black holes in general dimensions

We revisit the previously known local inversion symmetry of the five-dimensional Kerr-AdS metric that relates the over-rotating black hole to the under-rotating one and reinterpret it as an interchanging symmetry between time and the longitudinal angular coordinates. We generalize this to all D dimensions, including D=4, thereby enlarging the trivial linear ZN symmetry of the N=⌊(D−1)/2⌋ longitudinal angular coordinates to the nonlinearly realized ZN+1 symmetry that involves time.

Модифицированная методика расчета характеристик дискриминатора угломера в моноимпульсном радиолокаторе методом амплитудного мгновенного сравнения

A modified technique for determining the characteristics of the goniometer discriminator in a monopulse radar using the method of amplitude instantaneous comparison is proposed. Its distinctive features from the generalized technique are: in determining the minimum number of intermediate points of the interpolating function of the discriminatory characteristic of the discriminator, followed by calculating its maximum deviation from the theoretical discriminatory characteristic; in estimating the steepness of the discriminatory characteristic at each intermediate point; in calculating the fluctuation characteristic of the discriminator by estimating the variance of the error signal of angular coordinates at intermediate points of the discriminatory characteristic; in using the interpolating steepness function and the fluctuation characteristic of the discriminator for mismatches smaller than the step of change of intermediate points. The results of mathematical modeling of the discriminatory and fluctuation characteristics of the discriminator of the goniometer using the proposed technique are presented.

Compensation States Approach in the Hybrid Diabatization Scheme: Extension to Multidimensional Data and Properties.

The diabatization of reactive systems for more than just a couple of states is a very demanding problem and generally requires advanced diabatization techniques. Especially for dissociative processes, the drastic changes in the adiabatic wave functions often would require large diabatic state bases, which quickly become impractical. Recently, we addressed this problem by the compensation states approach developed in the context of our hybrid diabatization scheme. This scheme utilizes wave function as well as energy data in combination with a diabatic potential model. In regions where the initial diabatic state basis becomes insufficient for an appropriate representation of the adiabatic states, new model states are generated. The new model states compensate for the state space not spanned by the initial diabatic basis. Such a compensation state is obtained by projecting the initial diabatic state space out of the adiabatic wave function. This yields a very efficient basis representation of the electronic Hamiltonian. The present work presents two new aspects. First, it is shown how other operators like the spin-orbit operator in the framework of the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) can be evaluated in this compact model state space without losing the correct wave function information and accuracy. Second, the extension of the approach to multidimensional potential energy surface models is presented for methyl iodide including the C-I dissociation coordinate and the angular H3C-I bending coordinates.

Polar-vision1: A Novel Collinearity Equation of Perspective Projection in Polar Coordinate System

Abstract. Progress has been made in the community of photogrammetry and 3d computer vision in addressing the mathematical challenge posed by the collinearity equation. We introduce a new method for establishing the coordinate reference for 2d pixels and 3d landmarks using 'angular coordinates'. The mathematical relationships required for converting 3d landmarks, expressed in angular coordinates, to the camera framework are presented. The landmarks are then projected using perspective projection to obtain 2d pixels represented in angular coordinates. This framework is formally nominated as the 'Polar-vision1', which has been developed and integrated into the commercial software G3D-Cluster. Its application to pinhole camera image processing has demonstrated superior efficiency and admission rates of tie points, as well as reconstruction detail capabilities, compared to OpenMVG, achieving approximately a 1.4× improvement. The project 'Key Technologies and Tool System for Realistic 3D Modeling through Integration of Multi-Source Information in the Space-Air-Ground Domain' was awarded First Prize at the 2023 Surveying Science and Technology Awards, with Polar-vision1 as one of the innovative points.

Modeling the dispersion measure—redshift relation for fast radio bursts

This theoretical work investigates different models to predict the redshift of fast radio bursts (FRBs) from their observed dispersion measure (DM) and other reported properties. We performed an extended revision of the FRBs with confirmed galaxy hosts in the literature and built the most updated catalog to date. With this sample of FRBs, we propose four models that relate the DM and z: a linear trend (inspired by the Macquart relation), a log-parabolic function, a power law, and an interpolation for DM that includes z and the position of the host galaxy of the transient. The latter model has the highest success rate according to the metrics implemented: likelihood, median of the z difference, and the Akaike and Bayesian information criteria. Although the performance of model D is closely followed by the power law and linear models, the former has the advantage of accounting for anisotropies in the dispersion measure due to the angular coordinates. Conversely, the log-parabolic formula performs poorly in this task but provides a good prediction for FRBs with low DM at a low redshift. Additionally, we use the reported galaxy properties of the hosts to establish a connection between the observed DM with the star formation rate (SFR) and stellar mass (Ms) of the galaxies where the FRBs reside. In both cases, we find a weak correlation. Although the studied correlations are well-motivated, the sample of FRBs is not statistically significant enough to draw solid conclusions in this second part of our work. With the advent of new facilities devoted to studying the localization and nature of these transients, we will get access to new data that will enrich the proposed models and give us hints on the astrophysical origin and evolution of FRBs.

Image processing algorithm in the spatial navigation system for the visually impaired

The algorithm for processing the image generated by the webcam of the spatial navigation system for the blind and visually impaired is proposed. Image processing includes selecting and identifying objects located in four sectors of the frame, shifting the center of the frame to the selected objects and determining the angular coordinates of the objects' location, forming an indication for turning the user's head towards the selected objects, measuring the distance to the object using LiDar, highlighting foreground objects, determining the speed of its movement and ensuring safe navigation visually impaired in accordance with the information voiced by the speech synthesizer. The proposed image processing algorithm is designed to form information support for the blind and visually impaired in spatial navigation systems.

Improving the systems for controlling ground-based sun orientation devices

The control system for terrestrial two-axis devices for orientation to the Sun has been improved with a high-speed microcontroller operation algorithm. A geomagnetic sensor was introduced into the system to increase the reliability of monitoring the positioning of solar cells. The basis of the algorithm is a simplified astronomical and geographical model of the movement of the Sun in the celestial sphere. The control system automatically tracks the trajectory of the Sun and calculates its angular coordinates for the current moment of time on any day of the year and for any point on the globe. The derived equations of the simplified mathematical model are suitable for calculations of orientation angles to the Sun in real time on 8-bit microcontrollers with low computing power. The control system by AVR-328 microcontrollers was studied. It was established that the use of the algorithm when programming microcontrollers for two-axis orientation systems ensures high stability and reliability of the tracker`s functioning process. The technical parameters of the AVR-328 microcontrollers in the case of using the developed algorithm ensure that the control system performs one reorientation step in a time interval of less than 2 seconds, which ensures the minimum technical period of the reorientation process by the tracker drive mechanisms which is about 5 seconds. Deviations of the calculated orientation angle from the exact value do not exceed 3°, which corresponds to the relative accuracy of recording the solar radiation intensity, which is less than 0.3 %. The microcontroller program written according to the developed simplified algorithm occupies about 35 % of its memory. Therefore, the use of the developed algorithm frees up the resources of AVR-328 microcontrollers for performing additional data processing operations and automatic control over various additional devices related to the process of orientation to the Sun. In the case of solar energy, the algorithm ensures the use of about 98 % of the power of solar radiation

Spout geometry of fine particle conical spouted beds equipped with internal devices

The size and geometry of the spout are crucial parameters for the design and scaling-up of spouted beds because they condition heat and mass transfer rates. It is well-established in the literature that spouted beds without draft tube show axisymmetric spout shape, but this does not occur with open-sided draft tubes. Particle velocity has been measured at several bed heights and angular coordinates, under different geometric parameters and operating conditions, to determine the location of the spout-annulus interface in beds provided with open-sided draft tubes. Narrow draft tube wall slits and low air velocities lead to spouts of small size and triangular shape. The greatest spout expansion (high air velocities and wide draft tube wall slits) leads to a Reuleaux triangle shape, in which the spout swallows the tube. The results allow a better understanding of fine particle hydrodynamics in conical spouted beds, which is essential information for their scaling-up.

Generalized molecule-like structure in atomic nuclei

Starting from a |ϕ|4 field theory with universal pn interacting angular and distance coordinates (θ,r) to depict nuclear long-range correlations, we have derived a cubic Schrödinger equation for NpNnpn interacting virtual bosons, which are believed to dominate the generic evolution of nuclear structure from spherical multi-nucleon shell-model states to deformed collective rotational states. It is shown that two-soliton solution in θ space manifests two opposite pn-type Ising-like chains existing in ground states and their gradual alignment responsible for nuclear rotational excitations. Of particular prominence is two-soliton solution with respect to r: the mutual relative motion of valence protons and neutrons around valence-nucleon mass centers considered as the dynamic equilibrium positions of a non-linear Schrödinger breather. And the resulting non-vanishing root mean square 〈r2〉 divides half the valence nucleons belonging to a chain into four local mass centers and proposes two chain-corresponding molecule-like tetrads outside inert cores pairwise hidden in ground states. Such solitons turn out to be an analogue of opposite axion fluids around a local mass center in the galactic dark-matter halo outside the soliton core (Garnier et al. (2021) [67]) and the present study facilitates making the latter more clear. The generalized molecule-like structure arouses a requisite to the addition of cluster-interior and cluster-to-core electric dipole moments in particular to pear-shaped nuclei, whose variants Schiff moments play an important role in measuring diamagnetic atomic electric dipole moments and therefore understanding CP-violating new physics beyond the standard model. We put additional parts in evidence by befitting the NpNn scheme verified already by electric quadrupole moments in same nuclei.

Polygonal Laguerre-Gauss beams

We demonstrate that Laguerre-Gauss (LG) beams can have a polygonal distribution with the radial and azimuthal components, the so-called polygonal Laguerre-Gauss beams. These light beams are generated with a linear and trigonometric phase function of the angular coordinate which transform the Perfect LG beams with a lens. The polygonal Laguerre-Gauss beams preserve their distribution within a maximum propagation distance without diffraction similar to that used in the propagation-invariant light fields. We expect that these polygonal Laguerre-Gauss beams will be a method for creating any distribution controlling the radial and azimuthal components; moreover, they can be a proposal to control the number of the ring structures of the light beams.

Integral Transform Solution for Natural Convection Within Horizontal Concentric Annular Cavities

Abstract Natural convection inside horizontal concentric annular cavities is dealt with through the generalized integral transform technique (GITT), offering a hybrid numerical-analytical solution of the continuity, Navier–Stokes, and energy equations in cylindrical coordinates. The flow is in steady-state, laminar regime, two-dimensional, buoyancy-induced, and the governing equations are written in the streamfunction-only formulation. Two strategies of integral transformation are adopted to verify the best computational performance, namely, the usual one with eigenvalue problems for both streamfunction and temperature defined in the radial variable, and a novel alternative with eigenvalue problems defined in the azimuthal angular coordinate. First, the eigenfunction expansions convergence behavior is analyzed to critically compare the two integral transform solution strategies. Then, test cases for different aspect ratios and Rayleigh numbers are validated with experimental data from the classical work of Kuehn and Goldstein. A maximum relative deviation of 5% is found comparing the GITT results for the average Nusselt number against the experimental data, while an 8% maximum relative deviation is found comparing against an empirical correlation by the same authors. It is concluded that the GITT solution with the eigenvalue problem in the angular coordinate yields better convergence rates than the more usual eigenfunction expansion in the radial variable. This is due to the originally homogeneous boundary conditions in the angular direction, which do not require filtering for convergence enhancement, as opposed to the required filter in the radial direction that introduces a source term in the filtered equation for the streamfunction.

Generating a full spherical view by modeling the relation between two fisheye images

Full spherical views provide advantages in many applications that use visual information. Dual back-to-back fisheye cameras are receiving much attention to obtain this type of view. However, obtaining a high-quality full spherical view is very challenging. In this paper, we propose a correction step that models the relation between the pixels of the pair of fisheye images in polar coordinates. This correction is implemented during the mapping from the unit sphere to the fisheye image using the equidistant fisheye projection. The objective is that the projections of the same point in the pair of images have the same position on the unit sphere after the correction. In this way, they will also have the same position on the equirectangular coordinate system. Consequently, the discontinuity between the spherical views for blending is minimized. Throughout the manuscript, we show that the angular polar coordinates of the same scene point in the fisheye images are related by a sine function and the radial distance coordinates by a linear function. Also, we propose employing a polynomial as a geometric transformation between the pair of spherical views during the image alignment since the relationship between the matching points of pairs of spherical views is not linear, especially in the top/bottom regions. Quantitative evaluations demonstrate that using the correction step improves the quality of the full spherical view, i.e. IQ MS-SSIM, up to 7%. Similarly, using a polynomial improves the IQ MS-SSIM up to 6.29% with respect to using an affine matrix.