Radius Vector Research Articles

Can nonstandard neutrino interactions explain the XENON1T spectral excess?

We perform a constrained spectral fit analysis of the excess observed in the electron recoil energy spectrum by XENON1T with neutrino magnetic moment, charge radius, neutrino millicharge and new light vector and scalar mediators. Within limits allowed by other laboratory experiments we find that the excess can be explained in the range (2−4)×10−11μB for the magnetic moment, (2−6)×10−31 cm2 for the charge radius, (1.7−2.3)×10−12e for the millicharge and (10−100) keV masses of light mediators with couplings of 3.5×10−7 for vector/axial-vector, 1×10−6 and 4×10−6 for scalar and pseudo-scalar mediators respectively. Among all neutrino millicharge, magnetic moment and vector mediators fit better to the observed spectrum. We also derive constraints on all new physics parameters considered here.

Central Field Motion with Perturbing Acceleration Varying According to the Inverse Square Law in the Reference Frame Associated with the Radius Vector

The motion of a point with zero mass under the action of attraction to the central body $$\mathcal{S}$$ and perturbing acceleration $${\mathbf{P}}{\kern 1pt} ' = {\mathbf{P}}{\text{/}}{{r}^{2}}$$ , inversely proportional to the square of the distance to $$\mathcal{S}$$ , is considered. It is assumed that $${\mathbf{P}}{\kern 1pt} '$$ is small in absolute value compared to the main acceleration, caused by the attraction of the central body. Further, the vector $${\mathbf{P}}$$ components are constant in the reference frame used in astronomy, with the origin in the central body and the axes directed along the radius vector, the transversal (perpendicular to the radius vector in the osculating plane in the direction of motion), and the binormal (directed along the area vector). Earlier, we performed an averaging transformation of Euler-type equations of motion in osculating elements and obtained mean element evolutionary differential equations of motion in the first approximation in a small parameter. This article is devoted to solving the averaged equations, which are integrated completely. Moreover, the quadratures were expressed via elementary functions. The solution found has singularities at zero eccentricity and in the absence of the transverse acceleration. These and some other special cases are considered separately. There are at least two applications of the problem considered which are: an asteroid’s motion with allowance for the Yarkovsky–Radzievsky effect and a spacecraft’s motion with a solar sail. In both cases, the perturbation is inversely proportional to the squared distance from the Sun.

Method of preliminary solution of the problem of space robot navigation by onboard astronomical measurements using the butterworth filter

A method of preliminary solution of the problem of space robot navigation based on the results of measurements carried out using its onboard optronic equipment is presented. The initial data of the navigation problem are the directional cosines of the space robot orientation vector in the absolute geocentric equatorial coordinate system with reference to time during one revolution. Analytical expressions are obtained for determining unknown parameters of the motion of the space robot center of mass in the form of Keplers elements of the orbit. It is shown that to determine the right ascension of the ascending node, the inclination and the semi-major axis of the orbit of the space robot, information about the orientation of its radius vector at various times is used, and to determine the perigee argument, the moment of passing the perigee and the eccentricity of the orbit, the angular orbital speed of the space robot is used, which is determined by the results of evaluating the speed of change in the orientation of its radius vector over time. The presented results can be used in the development of software for navigation systems that allow autonomous determination of the parameters of the space robots orbit using onboard electro-optical sensors in the absence of a priori information about the parameters of the reference orbit or signals from satellite radio navigation systems.

Singularity radius gradient-based rapid singularity-escape steering law for SGCMGs

In order to visualize singularity of SGCMGs in gimbal angle space, a novel continuous bounded singularity parameter--Singularity Radius, whose sign can distinctly determine singularity type, is proposed. Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary, and quickly escape elliptic singularities. Finally, simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.

Model of multi-criteria evaluation of functional efficiency of navigation complex used as a part of mobile military purpose products

The main aspects of systems efficiency are considered. It is shown that evaluating the efficiency of the functioning of systems can be both a single-criterion and a multi-criterion task depending on the objectives of the study. The correct statement of the problem of evaluating the effectiveness as an integral character in the general case allows only a multicriteria interpretation since in this case a combination of various factors affecting the system is taken into account. Information is provided on existing approaches to assessing the effectiveness of systems that use a large number of criteria for evaluating, which differ in their functional composition. A methodology for multicriteria functional efficiency assessment is proposed, which allows modeling the multifactorial dependence of performance indicators based on integral indicators expressed as radius vectors in multidimensional subject space, and forming a spectrum of various managerial actions and decisions based on the results obtained. The application of the presented assessment model for determining the options for navigation complex with the best and worst implementation for a set of technical parameters is shown.

Investigation on the Polymer Drawing Model of the Centrifugal Spinning.

Some patents have reported the centrifugal spinning method which utilizes the centrifugal force produced by a high speed rotating device to fabricate fibers from polymer melts or solutions. Recently, with the development of technologies, centrifugal spinning was employed to produce ultrafine fibers and nanofibers. In order to improve the equipment and technology of centrifugal spinning and obtain finer fibers, it is important to model the polymer drawing of the centrifugal spinning. The polymer drawing in the centrifugal spinning is modeled and simulated. The force balance equation and heat transfer balance equation are established after analyzing the motion and heat transfer of the polymer melts. These nonlinear equations are solved based on the least square method to obtain the radius of excircle and the shape of streamline. A fourth order Runge-Kutta method is utilized to obtain the diameter and temperature of the threadline because there are initial value problems of first order ordinary differential equations. Streamlines and diameter of polymer melts at different viscoelasticities and different spinning temperatures are obtained. The simulation results are compared with the measured results to verify the polymer drawing model. The viscoelastic force in the centrifugal spinning changes constantly at a fixed rotation speed of the rotating spinneret. As the spinneret is rotating, the radius of excircle R1 increases slowly when the time passes, which means the viscoelastic force decreases slowly. The change of the viscoelastic force accelerates the increase of the radius vector. The simulation results show that the threadline diameter under the condition of changing viscoelastic forces is smaller than that under the condition of fixed visoelastic forces. The temperature of the polymer melts decreases faster under the condition of changing viscoelastic forces than that under the condition of fixed visoelastic forces. The threadline diameter decreases with the increase of the rotation speed. Higher initial polymer temperatures yield smaller fiber diameters. The polymer drawing in the centrifugal spinning is modeled and simulated. The simulation results tally with the measured results confirming the effectiveness of the polymer drawing model. The simulation results show that the change of the viscoelastic force is favorable to the polymer drawing and both larger rotation speeds and higher initial polymer temperatures can produce finer fibers, which lays a good foundation for the computer-assisted design of the centrifugal spinning.

The technique of calculating the profile of a mirror reflector for discharge lamps of cylindrical shape and its testing on the example of design of an industrial lamp type ZhSP-250

Current scientific trends are developments - methodological, theoretical and experimental, related to increasing the efficiency of some categories of lamps with discharge lamps. One such category is the powerful industrial spotlight class luminaires. This work is aimed at solving the urgent scientific task of finding ways to improve the design efficiency of industrial luminaires with deep and concentrated light distribution. At present, there are practically no works related to the task of calculating the geometry of the profiles of mirrored round-symmetric reflectors, which, in the presence of a light source of a fixed type and power, would provide the necessary light distribution of the luminaires. The elemental reflection method described in classical works does not determine the geometry of the reflector correctly, which provides the necessary balance in the equation that relates the light power of the lamp to the light power of the source and the reflector. The considerable time of calculation by the classical method and obtaining inaccurate decisions leads to rethinking the solution of the problem of calculating the geometry of the the reflector profile of the lamp with rigidly regulated light distribution. This task was first formulated by us in previous works. The purpose of this work is to approve the technique of solving the inverse problem of determining the geometry of a round-symmetric mirror reflector on the example of an industrial lamp type ZhKU-250 with light distribution type G-2. As the output of the calculation we used the light source and technical characteristics of the light source - DNAT-250 lamps, the required light distribution of the light fixture, the reflectance of the reflector, and the requirements for the efficiency of the designed luminaire and its gain. As a result of the performed work, it is possible to note the efficiency of the method both in terms of the accuracy of the calculations and the simple geometry of the reflector, obtained in the calculation method, which will allow to use simplified technological schemes for the serial production of such lamps. Keywords - industrial luminaires, DNaT discharge lamps, reflector LPC (Light Power Curve) required, zone LPCs of the reflector, radius vector array, luminaire gain and efficiency, elemental reflection method, reflector profile, rotary extrusion method.

Norm of the Position Shift of a Celestial Body in a Dynamical Astronomy Problem

The averaging method is widely used in celestial mechanics, in which a mean orbit is introduced and slightly deviates from an osculating one, as long as disturbing forces are small. The difference $$\delta {\mathbf{r}}$$ in the celestial body positions in the mean and osculating orbits is a quasi-periodic function of time. Estimating the norm $$\left\| {\delta {\mathbf{r}}} \right\|$$ for deviation is interesting to note. Earlier, the exact expression of the mean-square norm for one problem of celestial mechanics was obtained: a zero-mass point moves under the gravitation of a central body and a small perturbing acceleration $${\mathbf{F}}$$. The vector $${\mathbf{F}}$$ is taken to be constant in a co-moving coordinate system with axes directed along the radius vector, the transversal, and the angular momentum vector. Here, we solved a similar problem, assuming the vector $${\mathbf{F}}$$ to be constant in the reference frame with axes directed along the tangent, the principal normal, and the angular momentum vector. It turned out that $${{\left\| {\delta {\mathbf{r}}} \right\|}^{2}}$$ is proportional to $${{a}^{6}}$$, where $$a$$ is the semi-major axis. The value $${{\left\| {\delta {\mathbf{r}}} \right\|}^{2}}{{a}^{{ - 6}}}$$ is the weighted sum of the component squares of $${\mathbf{F}}$$. The quadratic form coefficients depend only on the eccentricity and are represented by the Maclaurin series in even powers of $$e$$ that converge, at least for $$e < 1$$. The series coefficients are calculated up to $${{e}^{4}}$$ inclusive, so that the correction terms are of order $${{e}^{6}}$$.

Continuos Parameterization of the Median Surface of an Ellipsoidal Shell and Its Geometric Parameters

When analyzing the stress-strain state of thin-walled structural elements that have the shape of an ellipsoid, it becomes necessary to calculate the geometric characteristics of the ellipsoidal surface. When using the canonical ellipsoid equation, regions of uncertainty appear in the Cartesian coordinate system at the intersection points of the ellipsoid surface with the horizontal coordinate plane. To exclude these areas of uncertainty, we propose an expression of the radius vector of an ellipsoidal surface whose projections are functions of two parametric representations in mutually perpendicular planes. One of the planes is the vertical plane XOZ, and the other plane is the plane perpendicular to the axis O at the point with the x coordinate. The parameter T of the ellipse obtained from the intersection of the ellipsoid with the XOZ plane was chosen as the argument of the first parametric function. The argument of the second parametric function t is the parameter of an ellipse formed as a result of the intersection of an ellipsoidal surface with a plane perpendicular to the abscissa axis at a distance of x from the origin. The proposed representation of the ellipsoidal surface allowed us to exclude uncertainties at the intersection points of the ellipsoid with the HOWE coordinate plane. By differentiating the proposed radius-vector expression at an arbitrary point on an ellipsoidal surface, we obtain relations for the basis vectors of an arbitrary point and their derivatives represented by components in the same local basis. These relations are necessary for the development of algorithms for numerical analysis of deformation processes of engineering structures that have ellipsoidal surfaces.

The Calculation of the Ellipsoidal Shell Based FEM with Vector Interpolation of Displacements When the Variable Parameterisation of the Middle Surface

The algorithm for the formation of the stiffness matrix of a four-sided finite element, which is a fragment of an ellipsoidal shell, the middle surface of which was represented by two variants of parametrization, is presented. In the first variant of parametrization of the middle surface of the ellipsoidal shell, the axial coordinate and the angle measured from the applicate axis to the radius vector of the cross-section of the shell are used. In the second version of the representation of the middle surface, the ellipse parameter of the cross section of the ellipsoidal shell was used instead of the angle. The components of the displacement vector and their first derivatives were taken as nodal unknowns of the four-sided finite element. The approximation of the required quantities was carried out in a vector formulation using Hermite polynomials of the third degree. The approximating relations for individual components were obtained using matrix expressions between the basis vectors of the nodal points of a finite element and the basis vectors of its arbitrary point. On the example of calculation of the elliptical cylinder the advantage of the second variant of parametrization of the middle surface of the ellipsoidal shell is shown, as well as the efficiency of the vector formulation of obtaining approximating expressions of the required quantities by the finite element method in curvilinear coordinate systems is demonstrated.

Exploring the Polymer Drawing of the Air Centrifugal Spinning.

The air-flow field of the air centrifugal spinning is simulated and measured. The simulated air velocities coincide well with the measured ones, confirming the correctness of the air-flow field model. The polymer drawing in the air-flow field of the air centrifugal spinning is modeled and simulated. Effects of the rotation speed and initial air velocity on the diameter and radius vector of the threadline are investigated. The air velocity is found to decrease with the increase of the distance away from the nozzle exit. Simulation results show that both larger rotation speed and higher initial air velocity can reduce the threadline diameter. The radius vector of the threadline increases rapidly with the increase of the initial air velocity, which is helpful to reduce the threadline diameter.

Dynamics of a System of Two Connected Bodies Moving along a Circular Orbit around the Earth

Symbolic–numeric methods are used to investigate the dynamics of a system of two bodies connected by a spherical hinge. The system is assumed to move along a circular orbit under the action of gravitational torque. The equilibrium orientations of the two-body system are determined by the real roots of a system of 12 algebraic equations of the stationary motions. Attention is paid to the study of the conditions of existence of the equilibrium orientations of the system of two bodies refers to special cases when one of the principal axes of inertia of each of the two bodies coincides with either the normal of the orbital plane, the radius vector or the tangent to the orbit. Nine distinct solutions are found within an approach which uses the computer algebra method based on the algorithm for the construction of a Gröbner basis.

Application of Computer Algebra Methods to Investigation of Stationary Motions of a System of Two Connected Bodies Moving in a Circular Orbit

Computer algebra and numerical methods were used to investigate the properties of a nonlinear algebraic system determining the equilibrium orientations of a system of two bodies connected by a spherical hinge that move in a circular orbit under the action of a gravitational torque. Primary attention was given to equilibrium orientations of the two-body system in the special cases when one of the principal axes of inertia of both the first and second body coincides with the normal to the orbital plane, the radius vector, or the tangent to the orbit. To determine the equilibrium orientations of the two-body system, the set of stationary algebraic equations of motion was decomposed into nine subsystems. The system of algebraic equations was solved by applying algorithms for constructing Grobner bases. The equilibrium positions were determined by numerically analyzing the roots of the algebraic equations from the constructed Grobner basis.

Radius and concurrent vector fields in spray and Finsler geometry

Radius and concurrent vector fields in spray and Finsler geometry

Acoustic wind speed meter in the atmospheric boundary layer

A method of measurement is proposed, based on the measurement of the motion of an acoustic pack under the influence of wind. The described meter refers to the field of applied meteorology and can be used in several sectors of the economy: in aviation for remote measurement of wind speed over runway, in the locations of metallurgical and chemical enterprises for forecasting wind emission zones of harmful emissions, as well as in justifying the location of windmills in wind power systems. The results of research and development of the acoustic sounding system for measuring the parameters of the wind situation in the boundary atmospheric layer are presented. The structural diagram of the system of the atmosphere acoustic sounding is given. The analysis of the wind situation in the boundary atmospheric layer is carried out. The signal-to-noise ratios for different heights are calculated. The location of the acoustic package for changing the length of the radius vector is calculated. The wear rate of the acoustic package at different heights and the dependence of the measurement error on the signal-to-noise ratio were analyzed. Errors are calculated for wind speed components in different planes, as well as correlated error values for different signal / noise ratios. The calculated data completely satisfy the requirements set in the research and development of this system of acoustic sounding of the atmosphere and measurement of wind speed in the boundary layer of the atmosphere by the method of acoustic location.

GEOMETRICAL MODELING OF A SLEEVE GALAXY FORM BY METHODS OF DESCRIPTIVE GEOMETRY

Graphical modeling of the sleeves of galaxies by spirals is considered. It is shown that the sleeves of the galaxies have the form of logarithmic spirals, with the angle between the radius vector and the tangent remains constant for one and the same galaxy, but different for other galaxies.

Vector analysis of pole–pole array for determining the 3D boundary of object

ABSTRACTAn algorithm is proposed for the interpretation of resistivity data that allows the 3D parameters (the boundary in plan view and the depth range) of an anomalous resistivity object in a heterogeneous medium to be determined. The proposed method is based on a vector analysis of the apparent resistivity of soil obtained by a pole–pole survey within the measurement window. In the first stage of the algorithm, in each measurement window, the radius vector is calculated, and as a result, vector images of the main directions of change in the resistivity of the medium are constructed. This allows us to estimate the location of a local anomalous object and to correlate the resistivity of the object with that of the background medium. With a consistent variation in the effective depth of investigation, a set of vector images is formed that characterizes the apparent resistivity distribution in the soil layers. Mathematical analysis of the vector images by using the scalar product allows us to estimate the depth range of the anomalous object. The effectiveness of the proposed algorithm has been proven on synthetic models and in comprehensive investigations of archaeological sites. The proposed method does not allow the true resistivity of an anomalous object to be determined, which is a disadvantage. However, this simple algorithm for processing and analysing shallow electrical prospecting data can be directly used at the preliminary data processing stage during a field survey. First, a pole–pole array can be rapidly operated by a single person; second, the user does not need special knowledge in the field of electrical resistivity data processing. The estimated 3D boundaries of local objects will make it possible to determine the area of interest for further detailed surveying and to justify all the parameters of the measurement technique (distance between electrodes, depth range etc.).

Defect-driven rotating system based on a double-walled carbon nanotube and graphene

A nanoscale rotating system that consists of a double-walled carbon nanotube (DWCNT) and graphene and is driven by a defect in the graphene is proposed, and its rotating dynamics and driving mechanism are investigated through molecular dynamics simulations. A potential energy difference caused by the presence of the vacancy defect on the graphene substrate causes the outer tube in the DWCNT to stably rotate in a specific direction. The rotational speed of the outer tubem initially increases before reaching a stable speed. This phenomenon indicates that the driving torque is a difference between the sides of the outer tube in the van der Waals potential; this difference in potential is caused by the presence of the defect in the graphene. In addition, the effects of the system temperature, the radius and chiral vectors of the DWCNT, and the location of the defect in the graphene are investigated. The theoretical work reported here should provide a reference for the design of motion systems based on carbon nanotubes and graphene and their applications.

Application of Computer Algebra Methods for Investigation of the Stationary Motions of the System of Two Connected Bodies Moving along a Circular Orbit

Computer algebra and numeric methods are used to investigate properties of a nonlinear algebraic system that determines the equilibrium orientations for a system of two bodies connected by a spherical hinge that moves along a circular orbit under the action of gravitational torque. The main attention is paid to study the conditions of existence of the equilibrium orientations for the system of two bodies for special cases, when one of the principal axes of inertia both the first and second body coincides with the normal to the orbital plane, with radius vector or tangent to the orbit. To determine the equilibrium orientations for the system of two bodies, the system of 12 stationary algebraic equations is decomposed into 9 subsystems. The computer algebra method based on the algorithm for the construction of a Grobner basis applied to solve the stationary motion system of algebraic equations. Depending on the parameters of the problem, the number of equilibria is found by numerical analysis of the real roots of the algebraic equations from the Grobner basis constructed.

Криволинейное радиальное течение сжимаемой вязкопластичной нефти со свободной текучестью в однородном пласте

The paper presents a solution to a steady-state hydrodynamic problem dealing with one-dimensional free-surface radial flow of compressible viscoplastic oil in a horizontal homogeneous circular formation. A vertical producing oil well is located in the centre of the formation, penetrating the pay zone fully, with no well casing or perforation present. We used generalised Darcy's law and equations of state for a compressible fluid to determine mass flow rate of the compressible viscoelastic oil and derive equations for current density, oil flow rate, current pressure distribution in the drainage area, and current pressure gradient. The equations take into account oil compressibility and initial pressure gradient. We also determined the time it takes an oil particle to reach the well starting from the current radius vector and from the external boundary. This is the case when the oil deposit lies close to the earth surface. This depth range features no shale beds or interbedded formations. Since subsurface mining is possible with shallow oil deposits, both wells and tunnels may be used for production.