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We introduce an initial orbit determination technique that uses only sequential range-rate measurements along fixed lines of sight and time between measurements. Compared to existing velocity-based initial orbit determination methods which impose additional requirements such as concurrent observations, our method may reduce the number of sensors required for a spacecraft to perform autonomous, or onboard, initial orbit determination. The measurements required may be obtained by a single range-rate sensor, such as an X-ray detector observing X-ray pulsars, and an onboard clock. The accuracy of our algorithm is compared with existing techniques for a variety of orbits. Orbit determination errors, in terms of estimated position, are characterized with Monte Carlo simulation techniques. Results indicate that our method achieves better performance compared to an initial orbit determination method utilizing velocity vectors and time of flight. The position error of our technique increases for lower velocities and shorter measurement times, which is consistent with existing velocity-based initial orbit determination methods. [ABSTRACT FROM AUTHOR]

By a fractional quadratic transformation, an indirect-PH curve can have rational offsets. In this paper, I study properties of planar sextic indirect-PH curves, in terms of their Bézier control polygon legs. With our results, sextic Bézier curves can be efficiently tested whether they are indirect-PH curves. The main strategy to achieve our results is using complex representation of planar parametric curve. Sextic indirect-PH curves can be classified into three classes according to different factorizations of their hodographs. Necessary and sufficient conditions for all classes of sextic indirect-PH curves can be described by non-linear complex systems. By analyzing these non-linear systems, algebraic conditions for a sextic Bézier curve to be an indirect-PH curve are first discussed, then geometric characteristics in terms of legs of its control polygon are revealed.

The study of the "bifurcation memory" effect plays an important role in the study of dynamic features of real systems. Practical interest lies in studying the possibility of predicting a temporary decrease in response to control, which can significantly improve navigation safety. The effect of "bifurcation memory" is a temporary decrease in the phase velocity of the imaging point when passing through a certain area ("phase spot") on the phase plane. A "phase spot" appears near the equilibrium state that disappeared during bifurcation. Over the almost half-century history of studying this dynamic feature, very few methods have been proposed that make it possible to unambiguously and with sufficient accuracy identify the "bifurcation memory" effect. This article proposes an improved phase plane method, which consists in constructing a phase velocity hodograph. A distinctive feature of the proposed method is not only that it surpasses previously developed methods in accuracy, but also covers both phase coordinates, and also gives an adequate result for any initial conditions. The method is quite universal and can be used to study the effect of "bifurcation memory" in various dynamic systems. Information about the boundary values of the parameter - the rudder angle, at which the effect of "bifurcation memory" begins (ends) to manifest itself can be used, for example, in the problem of optimizing the design of the hull and rudders or when creating control algorithms. [ABSTRACT FROM AUTHOR]

At the first stage of research, the experimental transmission functions and optimal two-channel automatic adjustment system (ARS) of the residual moisture content during convection drying of apples were developed. As a result of the analysis of the structural synthesis of the ARS, the advantage of the optimal dual-channel ARS compared to the single-channel system was established. At the second stage of research, with a view to improving the quality of the single-channel speed ARS of the residual moisture content of apples, the robust ARS was developed by the method of parametric synthesis and root hodograph. Based on the research, the advantages of the speed singlechannel robust system compared to the dual-channel system were established, which will significantly improve the quality of the products and reduce energy consumption for drying. [ABSTRACT FROM AUTHOR]

Flexible flatfoot has demonstrated biomechanical linkages between distal and proximal lower extremities. However, supporting evidence is required to investigate the benefits of short foot exercise (SF) and short foot exercise in combination with lower extremity training (SFLE) on dynamic foot function. This study aimed to determine the effects of a 6-week SF, 6-week SFLE, or control condition (no intervention) on dynamic foot function during gait in individuals with flexible flatfoot. Forty-five individuals with flexible flatfoot were randomly assigned into three conditions: (1) SF, (2) SFLE, and (3) control conditions. Participants in two intervention programs performed daily training via telerehabilitation and a home-based exercise program. Foot kinematics and center of pressure excursion index (CPEI) during the gait, intrinsic foot muscle test, and navicular drop test were assessed at baseline and after the 6-week intervention program. Post-intervention participants in the SF and SFLE conditions showed a shorter time to the lowest medial longitudinal arch (MLA) and improved MLA motion during the stance phase compared with the baseline. In addition, participants in the SFLE conditions showed greater changes in CPEI than in the SF and control conditions. Improvements in intrinsic foot muscle and navicular drop tests were also observed in participants in both intervention programs post-intervention. A major finding of the study was the improvement in dynamic foot function during gait in individuals with flexible flatfoot after the six weeks of the SF and SFLE intervention programs. Both intervention programs appear to have the potential for inclusion in a corrective program for individuals with flexible flatfoot. • Short foot exercises can be done online. • Short foot exercises improved medial longitudinal arch and dynamic gait. • Short foot with lower extremity exercise changed the center of pressure index. [ABSTRACT FROM AUTHOR]

Copyright of Eurasian Physical Technical Journal is the property of E.A. Buketov Karaganda University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The earlier solutions of the problem of groundwater flow in an inundated rock massif with vertically drains (drain trenches) are represented by extremely complex mathematical relationships in complex variables which make them difficult to use in applied problems. A new approximate-hydromechanical solution of the problem was obtained with the use of velocity hodograph and the presentation of model relationships in elementary functions, which coincides with the exact data in boundary points and which are in almost complete agreement (⪡1%) with the results of exact calculations by V.V. Vedernikov for special cases. For the first time, a picture of the field of full flow velocities was analytically constructed in the form of an isotach family for the given inundated massif with drains, showing the heterogeneous character of velocity distribution in it at the presence of water in the drain. Groundwater flow diagrams are also presented for boundary lines (in particular, in comparison with the case when there is no water in the drain), along with plots of flow functions and heads. [ABSTRACT FROM AUTHOR]

Indirect Pythagorean hodographs (IPH) spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a fractional quadratic transformation. In this paper, the authors provide an algorithm to interactively design a cubic IPH spline curve from any given control polygon. The method has the same friendly interface and properties as those for B-splines, meanwhile facilitates intuitive and efficient construction of open and closed IPH spline curves. The key idea is to solve the ratios of a set of auxiliary points associated with the edges and then construct a piecewise cubic IPH spline curve which has as high as possible continuity, i.e., the absolute curvature value of the adjacent curve segments are the same. A very interesting observation is that for any open control polygon, a quadratic B-spline curve can have continuous absolute curvature by carefully choosing the knots as the function of the control points. [ABSTRACT FROM AUTHOR]

Background and Objectives: The purpose of the study carried out in the article is to obtain analytical expressions for calculating the gas (liquid) flow rate in the turbulent gas (liquid) flow regime. A method is presented for the mathematical description of a three-dimensional profile (hodograph) of the flow velocity in a turbulent flow regime based on two known velocity values in the pipeline cross section. The article analyzes the physical processes occurring in the turbulent flow. In the cross section of the pipeline, characteristic areas are distinguished: the core of the turbulent flow and the laminar near-wall layer. Materials and Methods: To simulate the velocity distribution in the core of the flow, a power law was used, in the near-wall region, a linear law of change in the modulus of the velocity vector. The exponent is determined depending on the value of the Reynolds number, the algorithm is given. The approach used does not require significant computational costs, in contrast to a number of well-known grid methods based on the Navier–Stokes system of differential equations. Results: Based on the analysis of physical processes, a method for mathematical modeling of the turbulent gas flow in a round pipe has been proposed in the form of fairly simple engineering formulas. The geometric view of the three-dimensional velocity hodograph is a combination of a round truncated cone and a figure of rotation formed on the basis of a power function. The boundary of the near-wall region has been determined on the basis of the Reynolds number, and an engineering formula has been obtained. The results of calculations have been presented; two-dimensional velocity profiles have been plotted for a number of velocity values. Conclusions: Analysis of the results allows us to determine the limits of applicability of the model. So, with significant deviations of the velocity modules on the axis of the pipeline and near the wall, i.e. as the Reynolds number decreases, the velocity hodograph undergoes a kink in the apex region. This is explained by the approach of the gas flow to the laminar flow regime and the need to use a parabolic velocity profile according to the Poiseuille law.

The aim of this work was to comprehensively study the effect of the variable atomic composition and structural-phase state of Cox(MgF2)100-x nanocomposites on their nonlinear transport and magnetic/magneto-optical properties. Micrometer-thick nanocomposite layers on glass substrates were obtained by means of ion-beam sputtering of a composite target in the argon atmosphere in a wide range of compositions (x = 16–59 at.%). Using a low metal content in the nanocomposite, magnesium fluoride was kept in the nanocrystalline state. As the metal content increased, nanocrystalline cobalt was formed. The value of the resistive percolation threshold, xper = 37 at.%, determined from the concentration dependences of the electrical resistance of the nanocomposites coincided with the beginning of nucleation of the metallic nanocrystals in the MgF2 dielectric matrix. The absolute value of the maximum negative magnetoresistive effect in the nanocomposites was 5% in a magnetic field of 5.5 kG at a Co concentration of x = 27 at.%. [ABSTRACT FROM AUTHOR]

The formation of waviness on the working surfaces of bearing parts is associated with fluctuations in the size of the cut layer of metal and changes in the components of the cutting force. Laplace operators were used to model the centerless grinding system based on the construction of the transfer function and the characteristic equation. It was found that the formation of waviness depends on the position of the hodograph of the movement of the vector of the center of the part in the complex plane, which in turn depends on the geometric parameters of the rigid supports of the centerless grinder machine. This makes it possible, based on hodographs and the angular orientation of their asymptotes, to determine the geometric stability of the process depending on the angles of adjustment of the rigid supports of the grinder machine. Two methodological approaches were used to confirm the correctness of the hypotheses. The first one is a multiplication of wave’s hodographs. The second one is regeneration displacement and the coincidence of the combined hodograph of regeneration and waviness displacement mechanisms with the hodograph of infinitely rigid machine displacement. The diagrams which allow choosing geometry of adjustment of rigid support that allows to increase or decrease parameters of certain harmonics are developed. The 3D diagram allows setting the local minima, characterized by acceptable geometric adjustment conditions, providing regulated waviness of the working surfaces of bearing parts.

In this paper, we analyze planar parametric sextic curves to determine conditions for Pythagorean hodograph (PH) curves. By expressing the curves to be analyzed in the complex form, the analysis is conducted in algebraic form. Since sextic PH curves can be classified into two classes according to the degrees of their derivatives' factors, we introduce auxiliary control points to reconstruct the internal algebraic structure for both classes. We prove that a sextic curve is completely characterized by the lengths of legs and angles formed by the legs of their Bézier control polygons. As such conditions are invariant under rotations and translations, we call them the geometric characteristics of sextic PH curves. We demonstrate that the geometric characteristics form the basis for an easy and intuitive method for identifying sextic PH curves. Benefiting from our results, the computations of the parameters of cusps and/or inflection points can also be simplified. [ABSTRACT FROM AUTHOR]

The use of input devices of resonance-type in flaw detectors is advisable at frequencies above 100–200 kHz. However, in the practice of non-destructive testing by eddy currents, it is often necessary to use lower frequencies. In this case, one should connect the eddy current probes to devices with a non-resonant interface such as a bridge circuit. The functioning of bridge circuits used in eddy current sensors is significantly different from its functioning when used for components measurement because eddy current sensors operate under linear parametric modulation. In this case, it is advisable to perform the measurements by the self-comparison method, when a pair of closely located identical probes are placed in adjacent arms of the bridge. In this article, we first provide a detailed mathematical analysis of the operation of such a bridge circuit used as a flaw detector interface device. We use impedances of arbitrary finite values as disturbances. It is shown that despite the non-resonant character of the bridge circuit, it exhibits good selectivity for different loading (insertion) impedances. The isolines of the output signal and the probe's complex impedance diagram (hodograph) in balanced and imbalanced bridge circuits are jointly built. In this way, it is possible, for the first time, to construct hodographs in the complex plane for both selective signal suppression, and maximum sensitivity. Although this method is already used in series flaw detectors designed for aircrafts testing, the theory behind this method is presented here for the first time. [ABSTRACT FROM AUTHOR]

Lupa ş q-Bernstein operator is the first proposed qinteger based qanalogue Bernstein operator in rational form. By using the recurrence formulas in reverse as a pyramid algorithm, the nth degree Lupaş q-Bernstein basis function sequence is generated via discrete convolution. Owing to the commutativity of discrete convolution, for each Lupaş q-Bézier curve of degree n, the hodograph and the collection of n! recursive evaluation algorithms are derived. Unlike the tangent point obtained by de Casteljau algorithm of Bézier curve, de Casteljau algorithm of Lupa ş q-Bézier curve obtains a point on the curve being one of the two cut points where the line intersects the curve. For quadratic Lupa ş q-Bézier curve, sufficient and necessary conditions for computing left and right cut points are obtained. In addition, the left and right cut points can be computed simultaneously by proposing a dual cut point algorithm. [ABSTRACT FROM AUTHOR]

In the past few decades polynomial curves with Pythagorean hodograph (PH curves) have received considerable attention due to their usefulness in various CAD/CAM areas, manufacturing, numerical control machining, and robotics. This work deals with classes of PH curves built upon exponential-polynomial spaces (EPH curves). In particular, for the two most frequently encountered exponential-polynomial spaces, we first provide necessary and sufficient conditions to be satisfied by the control polygon of the Bézier-like curve in order to fulfill the PH property. Then, for such EPH curves, fundamental characteristics like parametric speed or arc length are discussed to show the interesting analogies with their well-known polynomial counterparts. Differences and advantages with respect to ordinary PH curves become commendable when discussing the solutions to application problems like the interpolation of first-order Hermite data. Finally, a new evaluation algorithm for EPH curves is proposed and shown to compare favorably with the celebrated de Casteljau–like algorithm and two recently proposed methods: Woźny and Chudy’s algorithm and the dynamic evaluation procedure by Yang and Hong. [ABSTRACT FROM AUTHOR]

This paper deals with the construction of the Algebraic Trigonometric Pythagorean Hodograph (ATPH) cubic-like Hermite interpolant. A characterization of solutions according to the tangents at both ends and a global free shape parameter α is performed. Since this degree of freedom can be used for adjustments, we study how the curve evolves with respect to α. Several examples illustrating the construction process and a simple fitting method to determine the unique ATPH curve passing through a given point are proposed. [ABSTRACT FROM AUTHOR]

An explicit analytical solution is derived for a problem of steady, saturated seepage behind an earth retaining wall. Seepage occurs in a semi-infinite strip bounded by a vertical drain simulated as a seepage face. We use the singular point method of Chaplygin and Zhukovsky to map both the physical plane and the hodograph plane onto a common reference plane to obtain a solution. The total discharge to the drain and the pore-pressure field required to assess the thrust of the soil mass on the wall are evaluated. An alternate solution to the same problem was derived earlier by P.L. Barros as a Fourier series expansion. [ABSTRACT FROM AUTHOR]

Background: Computer use is associated with poor postures and increased risk of developing neck pain. Evaluating differences in working posture of individuals with and without chronic neck pain may assist the development of strategies to lessen or prevent pain.Objective: To identify if upper body kinematics differs between individuals with and without chronic idiopathic neck pain during four conditions (tablet, laptop, and desktop computer sitting and standing).Methods: Three-dimensional (3D) motion capture measured upper body kinematics in 44 individuals with chronic idiopathic neck pain > 90 days (Cases n = 22) and without pain (Control n = 22), during a typing task under four conditions: tablet, laptop, desktop computer (sitting and standing). Differences between groups were evaluated using generalised linear mixed models.Results: Across all conditions and compared to controls, cases had significantly less flexion between their head-neck and upper trunk segments (between group mean difference 7.15°, 2.1, 12.2, p = .006), greater upper trunk flexion relative to the laboratory (-6.15°, -10.9, -1.3, p = .012), greater shoulder flexion bilaterally (left 12.35°, 6.7, 17.9, p < .001; right 13.49°, 7.9, 19.1, p < .001) and less right elbow flexion (-6.87°, -12.1, -1.7, p = .010). Approaching significance, the case group had less left elbow flexion (between group mean difference -5.36°, -10.9, 0.1, p = .056) and a smaller mean craniocervical angle for the seated desktop condition (group x condition interaction -6.37°; 95% CI -12.7, -0.1, p = .052).Significance: Individuals with neck pain consistently used different upper body postures compared to individuals without pain when working on computerised devices under varying workstation conditions. This finding suggests that people with neck pain work in potentially aggravating postures that may be associated with their pain. [ABSTRACT FROM AUTHOR]

Introduction. Cylindrical and spherical shells are extensively used in engineering. They face internal and/or external pressure and heat. Stresses and strains distribution in elastoplastic shells has been studied by many scientists. Numerous works involve the use of the von Mises yield conditions, maximum shear stress, maximum reduced stress. These condi- tions do not include the dependence on the first invariant of the stress tensor and the sign of the third invariant of the stress deviator. In some cases, it is possible to obtain numerical-analytical solutions for stresses, displacements and de- formations for bodies with spherical and cylindrical symmetry under axisymmetric thermal and force action.Materials and Methods. The problem on the state of a thick-walled elastoplastic shell is solved within the framework of the theory of small deformations. A plasticity condition is proposed, which takes into account the dependence of the stress tensor on three independent invariants, and also considers the sign of the third invariant of the stress deviator and translational hardening of the material. A disconnected thermoelastoplastic problem is being solved. To estimate the stresses in the region of the elastic state of a spherical shell, an equivalent stress is introduced, which is similar to the selected plasticity function. The construction of the stress vector hodograph is used as a method for verification of the stress state.Results. The problem has an analytical solution for linear plasticity functions. A solution is obtained when the strength- ening of the material is taken into account. Analytical and graphical relationships between the parameters of external action for the elastic or elastoplastic states of the sphere are determined. For a combined load, variants are possible when the plastic region is generated at the inner and outer boundaries of the sphere or between these boundaries.Discussion and Conclusions. The calculation results have shown that taking into account the plastic compressibility and the dependence of the plastic limit on temperature can have a significant impact on the stress and strain state of a hollow sphere. In this case, taking into account the first invariant of the stress tensor under the plasticity condition leads to the fact that not only the pressure drop between the outer and inner boundaries of the spherical shell, but the pressure values at these boundaries, can vary within a limited range. In this formulation of the problem, when there is only thermal action, the hollow sphere does not completely pass into the plastic state. The research results provide predicting the behavior of an object (a hollow sphere) that experiences centrally symmetric distributed power and thermal external influences.

An exact two-parameter solution of the Cauchy problem of the flow of two-layer shallow water under a solid cover, i.e., two infinite contacting layers of liquid with a small density difference moving at different velocities in a horizontal channel with solid walls, is constructed. The distortion of the layer interface occurs due to the Kelvin–Helmholtz instability. The problem is described by a system of two quasi-linear first-order partial hyperbolic differential equations. The solution is constructed using a version of the hodograph method based on the conservation law. This method makes it possible to transform a system of first-order quasi-linear partial differential equations to a linear second-order partial differential equation with variable coefficients, for which the Riemann–Green function is known. A method is proposed for reconstructing the explicit solution of the Cauchy problem on the level lines of the implicit solution, which ultimately reduces the solution of the original problem to the solution of a certain Cauchy problem for a system of ordinary differential equations. The results of calculations for spatially periodic initial data are presented as an example. [ABSTRACT FROM AUTHOR]

В работе представлен метод построения траектории движения группы беспилотных летательных аппаратов (БПЛА) апроксимацией годографа Пифагора составными многочленами Бернштейна-Безье на плоскости.

The aim of this work was to comprehensively study the effect of the variable atomic composition and structural-phase state of Cox(MgF2)100-x nanocomposites on their nonlinear transport and magnetic/magneto-optical properties. Micrometer-thick nanocomposite layers on glass substrates were obtained by means of ion-beam sputtering of a composite target in the argon atmosphere in a wide range of compositions (x = 16–59 at.%). Using a low metal content in the nanocomposite, magnesium fluoride was kept in the nanocrystalline state. As the metal content increased, nanocrystalline cobalt was formed. The value of the resistive percolation threshold, xper = 37 at.%, determined from the concentration dependences of the electrical resistance of the nanocomposites coincided with the beginning of nucleation of the metallic nanocrystals in the MgF2 dielectric matrix. The absolute value of the maximum negative magnetoresistive effect in the nanocomposites was 5% in a magnetic field of 5.5 kG at a Co concentration of x = 27 at.%.

In this paper, we analyze planar parametric sextic curves to determine conditions for Pythagorean hodograph (PH) curves. By expressing the curves to be analyzed in the complex form, the analysis is conducted in algebraic form. Since sextic PH curves can be classified into two classes according to the degrees of their derivatives’ factors, we introduce auxiliary control points to reconstruct the internal algebraic structure for both classes. We prove that a sextic curve is completely characterized by the lengths of legs and angles formed by the legs of their Bézier control polygons. As such conditions are invariant under rotations and translations, we call them the geometric characteristics of sextic PH curves. We demonstrate that the geometric characteristics form the basis for an easy and intuitive method for identifying sextic PH curves. Benefiting from our results, the computations of the parameters of cusps and/or inflection points can also be simplified.

The frequency dependence of the thallium sulfide (TlS) crystal impedance is analyzed in wide frequency and temperature range for the hopping and superionic conduction mechanisms. It has been established that in weak alternating electric fields, there is a hopping mechanism of charge transfer. The use of impedance spectroscopy methods in TlS crystals, at temperatures of 300, 350 and 400 K in the frequency range of 2*106 Hz and subjected to γ -irradiation doses 0, 0.25 and 0.75 MGy charge transfer processes, has been investigated. Hodographs constructed from the data of experimental measurements of 400 K, in the low-frequency region (> 1 0 3 Hz) and regardless of the absorbed gamma quanta, indicating additional contributions to the conductivity, presumably corresponds to the fact that in the frequency range of the applied signal, carrier diffusion does not reach the diffuse layer. This type of hodographs at low frequencies is characteristic of the Warburg impedance. [ABSTRACT FROM AUTHOR]

Seepage through a zoned earth-filled dam with a vertical clay core, two permeable shoulders and toe drain are studied. Seepage through the core and the downstream shoulder are coupled. The flow rate and phreatic surface are found. The hodograph method is used, viz. a conformal mapping of a rectangle in the complex potential plane onto a circular triangle. Numerically, MODFLOW 2005 simulated seepage with the refraction of the streamlines at the interfaces between the core and both shoulders. [ABSTRACT FROM AUTHOR]

The impedance of the RC circuit in which the active resistance depends on the applied dc voltage is considered. It is shown that in this case, the dependence of the impedance on the applied voltage is described by a hodograph of a new type, namely, a semicircumference pressed to the imaginary axis. The calculated and experimental hodographs that confirm the above assumptions are shown. It is demonstrated that the similarity and differences in the form of hodographs for cases R(U)C and RC (R = const) reflect the relationship between the functionally related values presented on the complex plane. [ABSTRACT FROM AUTHOR]

The paper presents studies of the system “induction generator-induction motor” with parametric asymmetry on a mathematical model to determine the quality of generated electricity in load operating modes. A mathematical model of the “induction generator-induction motor” system has been developed taking into account losses in steel and parametric asymmetry. The analysis of the transient characteristics of an induction generator when a motor load is connected in symmetrical and asymmetrical modes of operation is carried out. The results of changes in the main characteristics of an induction motor at various degrees of parametric asymmetry in the generator are presented. The quality of the generated electricity was analyzed based on the calculations of the unbalance coefficients for each of the operating modes. The assessment of the thermal state in steady-state conditions was carried out using an equivalent thermal equivalent circuit. Thermal transients were investigated when starting an induction motor from an autonomous energy source based on an induction generator. On a thermal mathematical model, the study of the effect of the output voltage asymmetry on the heating of the connected induction motor was carried out. It is shown that the asymmetry of the output voltage of an induction generator reaches 3–10 % and causes overheating of the windings in excess of the permissible values. A regression model has been developed for studying the operating conditions of an induction motor when powered by an induction generator with an asymmetry of the stator windings. The use of the obtained equations will make it possible to determine the most rational combination of factors affecting the heating of the stator windings of induction machines, in which they will not overheat above the maximum permissible temperature values of the corresponding insulation classes. [ABSTRACT FROM AUTHOR]

Relevance. Transient electromagnetic soundings is the method in-demand of electric survey applied for mineral deposits prospecting. Modern geoelectric problems require the usage of multichannel devices. For such devices the processing and interpretation problem becomes very resource intensive. Thus, the further development of interpretation methods is highly recommended. One of the possible ways of such development is the usage of wavefield transformation for transient electromagnetic data. The main aim of the research is to apply the wavefield transformation to the transient electromagnetic data measured in multireceivers systems in conductive media with inclined boundary for obtaining new qualitative estimations for the geological media on study. Method of research is based on new numerical algorithms for the stable wavefiled transformations of transient electromagnetic soundings data. Input data for transformation checkout (calculated three-dimensional curves of transient electromagnetic field response) was received using MODEM3D software package, which is designed for direct modeling of transient electromagnetic fields. Results. Pseudowave transformations of transient electromagnetic soundings for the conductive media with inclined boundary were obtained. These pseudowave transformations are used to plot travel-time curves. The resulting sets of transformations allow allocating the outcrop of the inclined contact on the surface. It is established that overlapping sediments weaken the maxima of pseudowave transformations and reduce the possibility of exact localization of the outcrop of the inclined contact. The behavior of toroidal vertical currents depending on time in the media with inclined boundary was considered.

We implement and verify for the first time four Weather Research and Forecasting model urban configurations, focused on the coastal metropolitan area of Tel‐Aviv (MTA) using updated landuse and morphological maps. We analyze the mesoscale summertime flow and the urban canopy (UC) role in the occurrence of different hodograph dynamics observed within MTA at night. These events may be significant in air quality research. The four configurations—bulk (MM), single‐layer (SLUCM), multilayer (BEP), and BEP coupled with the building energy model—reproduce the observed diurnal temperature and wind cycles, with similar 10‐m wind direction bias and RMSE (≲15° and ∼30°, respectively), with preference for MM and SLUCM at night. However, the SLUCM shows the lowest skill for the 10‐m wind speed (WS) (bias and RMSE ≥1 m s−1), and the BEP shows the largest underestimation of the 2‐m temperature, ∼−2.5 °C. In the SLUCM, the WS increases over an UC and with increasing building heights. These results call for a reexamination of the SLUCM WS parameterization. The simulations show that at night, a convergence line (CL) builds up with the urban heat island, downstream of the NW flow. West of the CL, the wind continues flowing from the sea, and rotates anticlockwise to form a nonelliptical sea‐breeze hodograph. Removing MTA UC restores an elliptical hodograph. East of the CL, the UC supports an elliptical hodograph with a clockwise rotation through the NE sector, previously reported as dynamically unstable. We expect such wind hodograph dynamics within similar coastal metropolitan areas. Key Points: We verify WRF‐urban configurations and analyze summertime flow dynamics over the coastal metropolitan area of Tel‐AvivSensitivity tests for the single‐layer UCM 10m WS suggest that its parameterization be reexaminedA nighttime urban convergence suggests a mechanism for nonelliptical hodographs and supports a flow pattern previously reported unstable [ABSTRACT FROM AUTHOR]

• Analytical solution is obtained for flow towards systematic drains placed on a horizontal bedrock. • Potential 2-D phreatic flow towards submerged line sinks or Zhukovskii slits is analyzed with the help of hodograph. • Hilbert's boundary value problem is solved in an integral form. • HYDRUS2D FEM package is used for empty/filled drains including ones with backpressure. • Position of the phreatic surface, isobars, isotachs and streamlines in saturated-unsaturated flows are determined. An explicit analytical solution is obtained to an old problem of a potential steady-state 2-D saturated Darcian flow in a homogeneous isotropic soil towards systematic drains modeled as line sinks (submerged drains under an overhanging of a phreatic surface), placed on a horizontal impervious substratum, with a constant-rate infiltration from the vadose zone. The corresponding boundary-value problem brings about a quarter-plane with a circular cut. A mathematical clue to solving the Hilbert problem for a two-dimensional holomorphic vector-function is found by engaging a hexagon, which has been earlier used in analytical solution to the problem of phreatic flow towards Zhukovsky's drains (slits) on a horizontal bedrock. A hodograph domain is mapped on this hexagon, which is mapped onto a reference plane where derivatives of two holomorphic functions are interrelated via a Polubarinova-Kochina type analysis. HYDRUS2D numerical simulations, based on solution of initial and boundary value problems to the Richards equation involving capillarity of the soil, concur with the analytical results. The position of the water table, isobars, isotachs, and streamlines are analyzed for various infiltration rates, sizes of the drains, boundary conditions imposed on them (empty drains are seepage face boundaries; full drains are constant piezometric head contours with various backpressures). [ABSTRACT FROM AUTHOR]

Copyright of Technical Diagnostics & Nondestructive Testing / Tekhnicheskaya Diagnostika I Nerazrushayushchiy Kontrol is the property of International Association Welding (Paton Publishing House) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The calculation of water permeability through a system of defects (long narrow slits in the junctions) in the screen is considered based on the filtration model. Its structural layout and description of the model main elements are given. The solution is carried out for the plane formulation of the problem by the methods of the filtration theory using the method of conformal mappings and the velocity hodograph method. A distinctive feature is the study of free filtration through a system of screen slits (the isolated standard fragment with a single defect), characterized by a pressure movement of the filtration flow in the protective layer and pressure/pressure-free movement at the bottom of the screen, taking into account the mutual influence of the slits on each other. We obtained the calculated dependences for the determination of the specific filtration flow through the screen slit, as well as the total flow through the system of slits and the averaged screen filtration factor, the results of the calculations are compared to the known formulas for the defect system. For practical use, a table of averaged screen filtration factors and a graph of the change in the reduced flow rate through the screen, considering and not considering the influence of the underlying base are made.

This paper deals with Pythagorean hodograph curves of the spaces of algebraic trigonometric functions and trigonometric polynomials, span 1 , t , cos k t , sin k t k = 1 m and span 1 , cos k t , sin k t k = 1 m , respectively. First, we propose a general characterization of planar PH curves in these spaces. Next, we consider the particular cases m = 1 and m = 2. For each of them, we give the general form of the control polygon of the PH curves, the implicit relations defining these curves, and their geometrical interpretations. Some examples and particular cases complete this study. [ABSTRACT FROM AUTHOR]

Classical techniques for initial orbit determination (IOD) require the analyst to find a body's orbit given only observations such as bearings, range, and/or position. In these cases, one of the goals is often to solve for the unknown velocity vector at one or more of the observation times to fully define the orbit. Recently, however, a new class of IOD problems has been proposed that switches the knowns and unknowns in these classic IOD problems. Specifically, the objective is to find the unknown position vectors given only velocity measurements. This paper presents a detailed assessment of the geometric properties of this new family of velocity-only IOD problems. The primary tool for this geometric analysis is Hamilton's orbital hodograph, which is known to be a perfect circle for all orbits obeying Keplerian dynamics. This framework is used to produce intuitive and efficient algorithms for IOD from three velocity vectors (similar structure to Gibbs problem) and for IOD from two velocity vectors and time-of-flight (similar structure to Lambert's problem). Performance of these algorithms is demonstrated through numerical results. [ABSTRACT FROM AUTHOR]

Objective: To investigate the effects of external ankle support (EAS) on lower extremity joint mechanics and vertical ground-reaction forces (VGRF) during drop landings. Design: A 1 × 3 repeated-measures, crossover design. Setting: Biomechanics research laboratory. Patients: 13 male recreationally active basketball players (age 22.3 ± 2.2 y, height 177.5 ± 7.5 cm, mass 72.2 ± 11.4 kg) free from lower extremity pathology for the 12 mo before the study. Interventions: Subjects performed a 1-legged drop landing from a standardized height under 3 different ankle-support conditions. Main Outcome Measures: Hip, knee, and ankle angular displacement along with specific temporal (TGRFz1, TGRFz2; s) and spatial (GRFz1, GRFz2; body-weight units [BW]) characteristics of the VGRF vector were measured during a drop landing. Results: The tape condition (1.08 ± 0.09 BW) demonstrated less GRFz1 than the control (1.28 ± 0.16 BW) and semirigid conditions (1.28 ± 0.21 BW; P < .0001), and GRFz2 was unaffected. For TGRFz1, no-support displayed slower time (0.017 ± 0.004 s) than the semirigid (0.014 ± 0.001 s) and tape conditions (0.014 ± 0.002 s; P < .05). For TGRFz2, no-support displayed slower time (0.054 ±.006 s) than the semirigid (0.050 ± 0.006 s) and tape conditions (0.045 ± 0.004 s; P < .05). Semirigid bracing was slower than the tape condition, as well (P < .05). Ankle-joint displacement was less in the tape (34.6° ± 7.7°) and semirigid (36.8° ± 9.3°) conditions than in no-support (45.7° ± 7.3°; P < .05). Knee-joint displacement was larger in the no-support (45.1° ± 9.0°) than in the semirigid (42.6° ± 6.8°; P < .05) condition. Tape support (43.8° ± 8.7°) did not differ from the semirigid condition (P > .05). Hip angular displacement was not affected by EAS (F2,24 = 1.47, P = .25). Conclusions: EAS reduces ankle- and knee-joint displacement, which appear to influence the spatial and temporal characteristics of GRFz1 during drop landings. [ABSTRACT FROM AUTHOR]

The aim of this work is to provide new characterizations of planar quintic Pythagorean-hodograph curves. The first two are algebraic and consist of two and three equations, respectively, in terms of the edges of the Bézier control polygon as complex numbers. These equations are symmetric with respect to the edge indices and cover curves with generic as well as degenerate control polygons. The last two characterizations are geometric and rely both on just two auxiliary points outside the control polygon. One requires two (possibly degenerate) quadrilaterals to be similar, and the other highlights two families of three similar triangles. All characterizations are a step forward with respect to the state of the art, and they can be linked to the well-established counterparts for planar cubic Pythagorean-hodograph curves. The key ingredient for proving the aforementioned results is a novel general expression for the hodograph of the curve. • An algebraic characterization consisting of two equations covering all possible cases. • An algebraic characterization with three equations in geometric progression. • A geometric characterization based on the similarity of two quadrilaterals. • A geometric characterization based on the similarity of two triples of triangles. • Connections to the existing results for planar PH cubics. [ABSTRACT FROM AUTHOR]

• ATPH curves with polynomial parametric speed are constructed by solving different geometric Hermite interpolation problems. • Interpolation to both spatial G 1 Hermite data equipped with curvature values and spatial G 2 Hermite data is considered. • The Hermite ATPH interpolants are obtained by solving simple linear systems. • The obtained Hermite ATPH interpolants have C 0 -continuous curvature at least. In this paper we focus on the class of Algebraic-Trigonometric Pythagorean Hodograph curves (ATPH for short) that is characterized by a purely polynomial parametric speed. Within such a class of ATPH curves, we first construct interpolants to spatial G 1 Hermite data equipped with curvature values. With respect to the solutions proposed in [24], the G 1 Hermite ATPH interpolants we here propose are characterized by C 0 - and C 1 -continuous curvature plots. Secondly, we investigate the existence of ATPH interpolants to spatial G 2 Hermite data and show that solutions exist under some restrictions on the Hermite input data. [ABSTRACT FROM AUTHOR]

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Featured Application: Cooperative task allocation and path planning problems of multi-UAV are becoming more and more important. The proposed mission planning method can be easily applied to some civilian scenarios, such as multi-UAV cooperative forest fire fighting and some military scenarios. A hierarchical mission planning method was proposed to solve a simultaneous attack mission planning problem for multi-unmanned aerial vehicles (UAVs). The method consisted of three phases aiming to decouple and solve the mission planning problem. In the first phase, the Pythagorean hodograph (PH) curve was used in the path estimation process for each UAV, which also served as the input for the task allocation process. In the second phase, a task allocation algorithm based on a negotiation mechanism was proposed to assign the targets. Considering the resource requirement, time-dependent value of targets and resource consumption of UAVs, the proposed task allocation algorithm can generate a feasible allocation strategy and get the maximum system utility. In the last phase, a path planning method was proposed to generate a simultaneous arrival PH path for each UAV considering UAV's kinematic constraint and collision avoidance with obstacles. The comparison simulations showed that the path estimation process using the PH curve and the proposed task allocation algorithm improved the system utility, and the hierarchical mission planning method has potential in a real mission. [ABSTRACT FROM AUTHOR]

Linear tool path segments of computer numerical control (CNC) machine tools need to be smoothed and interpolated in order to guarantee continuous and steady machining. However, because of the highly nonlinear relation between arc lengths and spline parameters, it is difficult to develop algorithms to simultaneously achieve real-time corner smoothing and interpolation with high-order continuity, although it is important to guarantee both high calculation efficiency and good dynamic performance of high-speed CNC machining. This paper develops a computationally efficient real-time corner smoothing and interpolation algorithm with C³ continuous feature. The corners at the junction of linear segments are smoothed by inserting Pythagorean-hodograph (PH) splines under the constraints of user-defined tolerance limits. Analytical solutions of the arc length and curvature of the smoothed tool path are obtained by evaluating a polynomial function of the spline parameter. The smoothed tool path is interpolated in real time with continuous and peak-constrained jerk. Simulations and experimental results show that the proposed tool path smoothing and interpolation algorithm can be executed in real time with 0.5 ms control period. Acceleration and jerk continuity of each axis are achieved along the tool path. Comparisons with existing corner smoothing algorithms show that the proposed method has lower jerk than existing C² algorithms and the real-time interpolation algorithms based on the Taylor series expansion. [ABSTRACT FROM AUTHOR]