Coordinate Curves Research Articles

Some Regularities of Life Time and Damage for the New Structural Material MoNiCa during Sliding Friction and Mechano-Sliding Fatigue

The results of an experimental study of damage for the structural material MoNiCa (it is high-strength cast iron VCHTG – patent of the Republic of Belarus № 15617) on sliding friction and mechano-sliding fatigue are analyzed in the report. Tests of the mechanical system shaft (a sample with a working part diameter of 10 mm made of 0.45 % carbon steel) - an insert (a prismatic counter sample with a cross section of 10 ´ 10 mm made of MoNiCa) were carried out. The kinetics of the change in average wear at 8 local points along the perimeter of the dangerous area of the sample is given for contact loads FN from 20 to 92 N of the mechanical system under study with MoNiCa inserts without heat treatment and with heat treatment. The test results of the system under study are also presented in the form of sliding friction and mechano-sliding fatigue curves in coordinates of the contact load FN – the number of cycles N until the limit state.

APLIKASI INTEGRAL UNTUK MEMBUKTIKAN RUMUS KELILING LINGKARAN

Integral can be used to determine several quantities, one of them is to determine the length of a curve in the plane. It can be applied to prove the circumference formula of a circle. This research aims to explain how to prove the circumference formula of a circle using a single integral expressed in both cartesian and polar coordinates. The method used in this research is a study of literature. The result of this research shows that proving the circumference of a circle can be done by determining the implicit derivative of the circle equation. Then, the circle equation and its implicit derivative are substituted into the integral formula for determining the length of the curve in both cartesian and polar coordinates so that the circumference formula of a circle is obtained.

Surface Discharge Status Diagnosis Based on Optical Image Chromaticity Coordinates

The physical and chemical processes of surface discharge are more complicated than other discharge forms due to the influence of gas composition and dielectric properties. Spectral diagnosis can be used to analyze the main species in the discharge process. However, the chromaticity characteristics are the comprehensive representation of all emission spectra. This article presents a new method to diagnose the state of surface discharge using chromaticity coordinates in color space. It is observed that the chromaticity coordinates slide along a straight line between the equal energy white point and a specific spectral color with the development of surface discharge. The relative position of the chromaticity coordinates on the line indicates the different states of the surface discharge. The slope of the line is affected by the material characteristics while external factors such as the camera's exposure time and the color of materials have no effect on it. It is found that the slope of the chromaticity coordinate curve has a fixed range, which means that there exists a specific color space of surface discharge. Finally, the effects of the ambient noise are corrected. This method uses the chromaticity coordinates in a long time scale to diagnose the microscopic process of surface discharge and it can be extended to other state diagnoses of partial discharge phenomena. From the point of view of potential application, this method also provides a new simple method to meet the requirement of long time scale state monitoring in industrial application.

STUDI KOORDINASI OCR DAN GFR SALURAN DISTRIBUSI PENYULANG SANDA UNTUK MENINGKATKAN KONTINUITAS PELAYANAN

The Sanda feeder is supplied by Antosari Substation through transformer unit II and ithas 3 reclosers, they are pempatan recloser,bangsing recloser and palisan recloser. Based onthe 2017 disturbance fault recapitulation data from PT PLN (Persero) Bali, it has been phasephaseand 1-phase ground short circuit in Sanda feeders almost every month. One of theproblems that often occurs in Sanda Feeders is when a phase-phase and 1-phase ground faultoccurs at the end of the feeder network and causes simultaneous trips to the recloser at thebase of feeder network, causing the Sanda feeder relay to blackout. This shows the systemneed to analyze the evaluation of the coordination settings for the OCR and GFR protectionsystem on the recloser and Sanda Feeder relays to minimize disturbances so as to improveservice continuity. The analysis and simuation results represent that, the existing settingconditions of OCR and GFR has coincide coordination curves and the grading time is still below0.3 seconds. The calculation and simulation of OCR and GFR that are carried out show that theprotection system works selectively in the absence of coincide coordinating curves and a timegrading value above 0.3 seconds according to the IEC 60255 standard.

Four equivalent properties of integrable billiards

By a classical result of Darboux, a foliation of a Riemannian surface has the Graves property (also known as the strong evolution property) if and only if the foliation comes from a Liouville net. A similar result of Blaschke says that a pair of orthogonal foliations has the Ivory property if and only if they form a Liouville net. Let us say that a strictly geodesically convex curve on a Riemannian surface has the Poritsky property if it can be parametrized in such a way that all of its string diffeomorphisms are shifts with respect to this parameter. In 1950, Poritsky has shown that the only closed plane curves with this property are ellipses. In the present article we show that a curve on a Riemannian surface has the Poritsky property if and only if it is a coordinate curve of a Liouville net. We also recall Blaschke’s derivation of the Liouville property from the Ivory property and his proof of Weihnacht’s theorem: the only Liouville nets in the plane are nets of confocal conics and their degenerations. This suggests the following generalization of Birkhoff’s conjecture: If an interior neighborhood of a closed strictly geodesically convex curve on a Riemannian surface is foliated by billiard caustics, then the metric in the neighborhood is Liouville, and the curve is one of the coordinate lines.

Synthesis, structural and photoluminescence properties of novel red emitting Ba5(B2O5)2F2:xEu3+phosphors

A series of Ba5(B2O5)2F2:xEu3+ (x = 0, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18 and 0.20) phosphors were synthesized for the first time by the high-temperature solid-state reaction method. The polycrystalline powder samples of Ba5(B2O5)2F2 and Ba5(B2O5)2F2:0.14Eu3+ were determined by the X-ray powder diffraction measurement. The optical properties of Ba5(B2O5)2F2:xEu3+ were detected by photoluminescence excitation and emission spectra, CIE chromaticity coordinate, quantum efficiency and attenuation curve. Under near-UV excitation (λex = 394 nm), the phosphors exhibit dominant emission peak at 616 nm and generate bright red light, with the calculated R/O value is 2.65 in Ba5(B2O5)2F2:0.14Eu3+ phosphor. The optimal doping amount of Eu3+ in Ba5(B2O5)2F2:xEu3+ phosphors is x = 0.14 for the maximum emission. With a relatively high quantum efficiency of 40.83%, Ba5(B2O5)2F2:0.14Eu3+ red emitting luminescent material is probably a promising candidate for near-UV-based white LEDs application.

Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning

As a floating system connecting hydraulic support and scraper conveyor, the path planning of pushing mechanism is of great significance for their coordinated movement. In this paper, a method for path planning of hydraulic support pushing mechanism based on extreme learning machine (ELM) and Descartes path planning is proposed. According to the motion characteristics of moving mechanism, it is transformed into industrial robot model, based on the characteristics of the coordinates of the key points on the ear seat of the scraper conveyor when advancing, a prediction method of the key points coordinates based on ELM is proposed, so the target location of the end-effector is obtained. The path of the joint is determined by polynomial path partition and Descartes path planning method. The path is modified by Gaussian filtering method, and the peak value of path obtained by planning is filtered out, and the path correction is realized. Finally, the virtual simulation test is carried out in Unity3D. The planned coordinate curve has Poisson-like distribution and approximately around the target coordinate curve, and local error and correction error are within 2 cm and 0.1 cm, respectively. The coordinate curve obtained by combining planning and correction has a better effect.

A method of finding stress solutions for a general plastic material under plane strain and plane stress conditions

AbstractA general plastic material under plane strain and plane stress is classified by a yield criterion that depends on both the first and second invariants of the stress tensor. The yield criterion together with the stress equilibrium equations forms a statically determinate system. This system is investigated in the principal lines coordinate system (i.e. the coordinate curves of this coordinate system coincide with trajectories of the principal stress directions). It is shown that the scale factors of the principal lines coordinate system satisfy a simple equation. Using this equation, a method for constructing the principal stress trajectories is developed. Therefore, the boundary value problem of plasticity theory reduces to a purely geometric problem. It is believed that the method developed is useful for solving a wide class of boundary value problems in plasticity.

A Variational Method for Analyzing Vortex Flows in Radar-Scanned Tornadic Mesocyclones. Part I: Formulations and Theoretical Considerations

AbstractA variational method is formulated with theoretical considerations for analyzing vortex flows in Doppler radar–scanned tornadic mesocyclones. The method has the following features. (i) The vortex center axis (estimated as a continuous function of time and height in the four-dimensional space) is used as the vertical coordinate, so the coordinate system used for the analysis is slantwise curvilinear and nonorthogonal in general. (ii) The vortex flow (VF), defined by the three-dimensional vector wind minus the horizontal moving velocity of vortex center axis, is expressed in terms of the covariant basis vectors (tangent to the coordinate curves), so its axisymmetric part can be properly defined in that slantwise-curvilinear coordinate system. (iii) To satisfy the mass continuity automatically, the axisymmetric part is expressed by the scalar fields of azimuthally averaged tangential velocity and cylindrical streamfunction and the remaining asymmetric part is expressed by the scalar fields of streamfunction and vertically integrated velocity potential. (iv) VF-dependent covariance functions are formulated for these scalar variables and then deconvoluted to construct the square root of background error covariance matrix analytically with the latter used to transform the control vector to precondition the cost function. (v) The deconvoluted covariance functions and their transformed control variables satisfy two required boundary conditions (i.e., zero vertical velocity at the lower rigid boundary and zero cross-axis velocity along the vortex center axis), so the analyzed VF satisfies not only the mass continuity but also the two boundary conditions automatically.

Generalized model for conic-V-shaped flexure hinges.

This paper presents a new class of flexure hinges, namely, conic-V-shaped flexure hinges (CFHs), which can be used as a generalized model for flexure hinges with profiles such as parabolic-V-shape, elliptical-V-shape, and hyperbolic-V-shape. Compliance and precision equations for the CFHs were derived as a set of nonlinear equations using Castigliano's second theorem. The parameters of the nonlinear equations inputted to the compliance and precision matrices were based on the generalized equations used for conic curves in polar coordinates. Furthermore, the compliance equations were verified by means of finite element analysis and experiments. The errors in the finite element and experimental results were within 10% and 8% compared to the analytical results, respectively. Finally, the effects of dimensional parameters on the analytical model could be effectively analyzed by numerical simulations and comparisons.

СТРУКТУРА И СВОЙСТВА ДЕТАЛЕЙ, ПОЛУЧЕННЫХ СЕЛЕКТИВНЫМ ЛАЗЕРНЫМ СПЛАВЛЕНИЕМ ПОСЛЕ ИСПЫТАНИЯ НА МАЛОЦИКЛОВУЮ УСТАЛОСТЬ

Results of low cycle fatigue (LCF) testing, investigation of microstructure, and fractures of specimens, which was, obtain by selective laser melting process (SLM) of the powders from Inconel 718 alloy have been carried out in the present article. Chemical composition of the considered specimens, microstructure before and after testing, results at room and elevated temperatures, which were built in XY direction (horizontal), were carrying-out. The specimens in the as-build state were exposed by hot isostatic pressing (HIP) with subsequent inherent Inconel 718 heat treatment. It was established that in specimens in as-built state observe accurately expressed zones of layer-by-layer smelting with 100 μm height. After HIP with subsequent heat treatment strengthening of the considered alloy provides by intermetallic γ'' – Ni3Nb phase, γ'-phase and carbides, also was identified lamellar δ-phase in the microstructure. LCF-testing was conducted in a so-called «soft» cycle of loading with a predetermined interval of the strain for providing of fatigue life in 103, 5х103, 104 cycles. The obtained data was built logarithmic curve in coordinates «Strain σ – Number of cycles N», that allows, with sufficient reliability, determine a rational strain level at LCF-testing for providing a predetermined number of cycles. The following ratios of σ – N were established (Rσ=0, υ=1 Hz): for providing N=103, σ≤1020 МPа, N=5х103, σ=931…961 МPа, N= 104, σ≤941 МPа. Results of the fractures investigation after LCF-testing at 20°С and 550°С shows that during the cyclic elastoplastic deformation at room temperature multicentricity of crack initiations zones observes. Mainly fixed a viscous pattern of fracture with a fatigue grooves presence, which size increases in the process of crack advance to the zone of fracture area. At elevated temperature in the zones of fatigue crack initiation and spreading quasi-brittle character of destruction observes, and turns in viscous in the zone of fracture area. Authors should be pointed out that the application of additive technologies in the manufacture of aerospace parts requires extensive R&D works, and testing efforts to confirm the repeatability of alloy characteristics.

Analytical approach for the tunneling process in double well potentials using IRC calculations

A novel strategy to applying the analytical solution of the Schrödinger equation via angular prolate spheroidal (APS) function was developed. It provides a simple and accurate approach to calculating the energy levels, splitting and tunneling frequency in symmetrical double well potentials. The strategy consists of modeling the potential energy surface (PES) with an appropriate intrinsic reaction coordinate (IRC) curve, and its fitting to the solvable symmetric trigonometric potential. The parameter L is solved via the variation method. The accuracy was tested against using the same steps with the WKB method and the instanton-soliton approach to NH3, ND3 and methyl substituted amines. For NH3, the tunneling frequencies were 2.56,3.67 and 1.12×1010 s−1, using the APS function, WKB and instanton approaches respectively, while the experimental is 2.38×1010 s−1. The results show that it produced the most accurate results with a straightforward calculation, and in regions where the semi-classical fails.

Algorithms and complexity evaluation of 3- and 5-isogeny calculation of super singular Edwards curves

The properties and existence conditions of 3- and 5-isogenies for complete and quadratic super singular Edwards curves over the fields of p>3 odd characteristic are analyzed. It is proposed to use the minimum odd degrees 3- and 5-isogenies for the task of keys encapsulation based on the SIDH algorithm of post quantum cryptography, which allows bypassing the problem of special points of the 2nd and 4th orders. These points always arise on 2-isogenies for the classes of noncyclic Edwards curves. A review of the main properties of the Edwards curve classes is given. An analysis of the properties of isogenies of odd degrees of Edwards curves with one parameter d in affine coordinates and examples of their calculation are given The known formulas of 3- and 5-isogeny in affine coordinates are transformed into projective coordinates. To increase the rate of isogeny calculation, only the x-coordinate of the affine point of the curve is used. Formulas for the coordinates and complexity evaluation for 3-isogeny calculations in the classes of complete and quadratic Edwards curves in projective coordinates are obtained. The parameter d of the curve was expressed in terms of the x-coordinates of the points of the nucleus for the 5th order nucleus, which allowed us to obtain formulas independent of d for the coordinates of 5-isogenies. A comparative analysis of the complexity of 4 algorithms for calculating the coordinates of 5 isogenies is carried out. Algorithms for computing 3- and 5-isogenies in the classes of complete and quadratic super singular Edwards curves are constructed. Some requirements for the parameters of the cryptosystem are considered.

Constructing a method for the geometrical modeling of the lame superellipses in the oblique coordinate systems

The elliptic curves possess a certain disadvantage related to that at the point of intersection with the coordinate axes the ellipses have tangents perpendicular to these axes. However, such a situation is undesirable for some practical applications of ellipses. It can be prevented by modeling the specified curves in oblique coordinates, which, in turn, are related to a certain original Cartesian coordinate system. The Lame superellipses are understood to be the curves whose equations include the exponents that differ from those inherent in regular ellipses. Variating these exponents can produce a wide range of different curves. This paper has proposed a method for the geometric modeling of superellipses in the oblique coordinate systems. The source data for modeling are the coordinates of the two points with the known angles of the tangent slope. The accepted axes of the oblique coordinate system are the straight lines drawn as follows. Through the first point, a line parallel to the tangent at the second point is built, and at the second point, a line parallel to the tangent at the first point is constructed. It has been shown that these operations could yield the desired values of tangent angles at intersection points of the superellipse with axial lines. It has been proven that the superellipse arc could be drawn through a third given point with the required angle of the tangent; that, however, would require determining the exponents in the superellipse equation by a numerical method. Such a situation occurs, for example, when designing the projected profiles of axial turbine blades. Based on the proposed method of modeling the superellipse curves, a computer code has been developed that could be used in describing the contours of components applied in the technologically complex industries

Geometry of principal stress trajectories for piece‐wise linear yield criteria under axial symmetry

AbstractRigid‐ and elastic‐ plastic solids obeying quite a general yield criterion represented by linear functions of the principal stresses are considered. A general axisymmetric state of stress satisfying the hypothesis of Haar and von Karman is analyzed in quasi‐static flow. The circumferential velocity vanishes. A superimposed restriction on the yield criterion is that the system of stress equations is hyperbolic. The primary objective of this study is to select optimal coordinates and unknowns for deriving the integrable differential relations in their most convenient form for numerical treatments. It is shown that there exists a simple relation between the scale factors of the principal lines coordinate system (the coordinate curves of this coordinate system coincide with the trajectories of the principal stresses). Another simple relation exists between the scale factors and the principal stresses. The mapping between the principal lines and cylindrical coordinates is determined by a system of hyperbolic differential equations.

Metasurfaces homogenization technique based on the computation of the average value of the contravariant tensors elements

The purpose of this paper is to present a 2D metasurfaces homogenization based on the computation of the average value of the contravariant tensors elements. A simple semi-analytical model for the comprehension of the extraordinary optical transmission (EOT) through a 2D array of periodic subwavelength metasurface is analyzed through the proposed method. In this single mode model, the mono layer of the metasurface film is considered as homogeneous medium. Therefore, the electromagnetic response of this structure to a plane wave excitation is equivalent to that of a slab with homogeneous equivalent properties. In a coordinates system where the coordinate curves xj coincide with the physical discontinuity of the material, the covariant formalism involving contravariant components of density flux and covariant components of the electromagnetic field, allows to efficiently handle the continuity properties of the electromagnetic field. By averaging all these quantities involving local fields over the periods of the unit cell, and assuming that, these macroscopic fields and densities satisfy a constitutive relationship, the electromagnetic parameters such as averaged permittivity and permeability can be defined.

3- AND 5-ISOGENIES OF SUPERSINGULAR EDWARDS CURVES

An analysis is made of the properties and conditions for the existence of 3- and 5-isogenies of complete and quadratic supersingular Edwards curves. For the encapsulation of keys based on the SIDH algorithm, it is proposed to use isogeny of minimal odd degrees 3 and 5, which allows bypassing the problem of singular points of the 2nd and 4th orders, characteristic of 2-isogenies. A review of the main properties of the classes of complete, quadratic, and twisted Edwards curves over a simple field is given. Equations for the isogeny of odd degrees are reduced to a form adapted to curves in the form of Weierstrass. To do this, use the modified law of addition of curve points in the generalized Edwards form, which preserves the horizontal symmetry of the curve return points. Examples of the calculation of 3- and 5-isogenies of complete Edwards supersingular curves over small simple fields are given, and the properties of the isogeny composition for their calculation with large-order kernels are discussed. Equations are obtained for upper complexity estimates for computing isogeny of odd degrees 3 and 5 in the classes of complete and quadratic Edwards curves in projective coordinates; algorithms are constructed for calculating 3- and 5-isogenies of Edwards curves with complexity 6M + 4S and 12M + 5S, respectively. The conditions for the existence of supersingular complete and quadratic Edwards curves of order 4·3m·5n and 8·3m·5n are found. Some parameters of the cryptosystem are determined when implementing the SIDH algorithm at the level of quantum security of 128 bits

On the determination of fully conjugate hypoid tooth flanks

Presented is a procedure to individually specify fully conjugate hypoid gear tooth flanks. Cartesian coordinates for the hypoid tooth flanks are derived in terms of a planar rack with a specified constant pressure angle. These coordinates define a “coordinate curve” on the tooth flank. Each coordinate curve depends on an axial coordinate and the entire tooth flank is established as a family of these coordinate curves. This process results in global interference between locally conjugate hypoid tooth flanks if the pressure angle is constant. A differential equation is established for the axial variation in the rack’s pressure angle to avoid global interference. The resulting axial variation in normal pressure angle is combined with the determination of coordinate curves to obtain fully conjugate tooth flanks. An automotive hypoid gear pair is presented to showcase the process. Unloaded Ease-off (UEO) topography is used to quantify conjugate action for the example hypoid gear pair. Subsequently, axial and transverse profile modifications are applied individually to the ideal tooth flanks to accommodate generalized loading conditions. Loaded Transmission Error (TE) and maximum contact pressure are reported for a set of input torques.

On one method of approach reconstruction table form function to analytical form in domain point vicinity

Mathematical model researches data is in numeric matrices or numeric data tables, as usual. Functions reconstruction when it is in table numeric data form is made on parameter mesh. Density parameter mesh reducing for reconstruction function problem will be urgency in spite of temporary computer speed operates.Experimental data research allows obtaining the general algorithm for analytical form model reconstruction. The algorithm allow in high power reduce computer time waste for resultant function reconstruction but in point vicinity was proposed. So, instead of doing parameter mesh function values calculating, it is done in coordinate curves and as a result the resultant function number calculates are high reduced. The new sequence approximation method (SAM) allow to do analytical function form reconstruction (in univariable function product form) when it exist in table form in point vicinity. As experience is demonstrated, solutions of real tasks allow representing them in whole domain. In spite of the fact that the errors of the function representation raised up to domain boundary errors do not exceed 5-7%.. Thus influence parameter evaluating method consists of approximate solution reconstruction in form of exponent functions and its index exponent comparisons. Greater index value, stronger function parameter influence.For testing the accuracy limits we make the reconstruction of some analytical form functions. Graphic dependencies are present.

A 2D analysis of correlations between the parameters of the Gompertz–Makeham model (or law?) of relationships between aging, mortality, and longevity

When mortality (μ), aging rate (γ) and age (t) are treated according to the Gompertz model μ(t) = μ0eγt (GM), any mean age corresponds to a manifold of paired reciprocally changing μ0 and γ. Therefore, any noisiness of data used to derive GM parameters makes them negatively correlated. Besides this artifactual factor of the Strehler-Mildvan correlation (SMC), other factors emerge when the age-independent mortality C modifies survival according to the Gompertz-Makeham model μ(t) = C+μ0eγt (GMM), or body resources are partitioned between survival and protection from aging [the compensation effect of mortality (CEM)]. Theoretical curves in (γ, logμ0) coordinates show how μ0 decreases when γ increases upon a constant mean age. Within a species-specific range of γ, such "isoage" curves look as nearly parallel straight lines. The slopes of lines constructed by applying GM to survival curves modeled according to GMM upon changes in C are greater than the isoage slopes. When CEM is modeled, the slopes are still greater. Based on these observations, CEM is shown to contribute to SMC associated with sex differences in lifespan, with the effects of several life-extending drugs, and with recent trends in survival/mortality patterns in high-life-expectancy countries; whereas changes in C underlie differences between even high-life-expectancy countries, not only between high- and low-life-expectancy countries. Such interpretations make sense only if GM is not merely a statistical model, but rather reflects biological realities. Therefore, GM is discussed as derivable by applying certain constraints to a natural law termed the generalized Gompertz-Makeham law.