Spiral Segments Research Articles

Piecewise Reconstruction of 3D Euler Spirals From Planar Polygonal Curves

In this article, we propose a method for reconstructing approximate piecewise 3D Euler spirals from planar polygonal curves. The method computes the 3D coordinates of approximate Euler spiral such that its orthogonal projection onto the 2D plane is the closest possible to the input curve. To achieve this, a dataset is created, comprising Euler spiral segments and their orthogonal projections. Given an input curve, it is sampled and split into segments. Each segment is matched with the closest Euler spiral segments from the dataset, forming a pool of candidates. The optimal set of connected Euler spiral segments is then selected to reconstruct the approximate piecewise 3D Euler spiral. The selection prioritizes smoothness continuity at connecting points while minimizing the distance between the orthogonal projection and the input curve. We evaluate our method against synthetic 3D Euler spirals by applying our reconstruction to the orthogonal projection of the synthetic Euler spirals.

Why the Golden Spiral is Golden

Summary It is shown that there is a logarithmic spiral that segments a straight line through its pole in the golden ratio ϕ . This is the same spiral that is often referred to in the literature as the “Golden Spiral” Using the tools of analytic geometry and parametric vector equations, it is shown that the golden spiral is actually a member of a family of spirals defined by a generalized equation. The spirals exist as a continuum defined by a real number q > 1. When q = ϕ , the spiral segments a line through its pole in the golden ratio. That is the characteristic feature that sets it apart from all the other spirals in the continuum.

Circularly polarized differential intra-oral antenna design validation and characterization for tongue drive system

Assistive devices are becoming increasingly popular for physically disabled persons suffering tetraplegia and spinal cord injuries. Intraoral tongue drive system (iTDS) is one of the most feasible and non-invasive assistive technology (AT), which utilises the transferring and inferring of user intentions through different tongue gestures. Wireless transferring is of prime importance and requires a suitable design of the intra-oral antenna. In this paper, a compact circularly polarized differential intra-oral antenna is designed, and its performance is analysed within heterogeneous multilayer mouth and head models. It works at 2.4 GHz in the Industrial, Scientific, and Medical (ISM) band. The footprint of the differential antenna prototype is 0.271 λgtimes 0.271 λgtimes 0.015 λg. It is achieved using two pairs of spiral segments loaded in diagonal form near the edges of the central rotated square slot and a high dielectric constant substrate. Its spiral-slotted geometry further provides the desired swirling and miniaturization at the desired frequency band for both mouth scenarios. Additionally, corner triangular slits on the radiating patch assist in tuning the axial ratio (< 3 dB) in the desired ISM band. To validate the performance of the proposed in-mouth antenna, the measurement was carried out using the minced pork and the saline solution for closed and opened mouth cases, respectively. The measured − 10 dB impedance bandwidth and peak gain values in the minced pork are from 2.28 to 2.53 GHz (10.39%) and − 18.17 dBi, respectively, and in the saline solution, are from 2.3 to 2.54 GHz (9.92%) and − 15.47 dBi, respectively. Further, the specific absorption rate (SAR) is estimated, and the data communication link is computed with and without a balun loss. This confirms that the proposed differential intraoral antenna can establish direct interfacing at the RF front end of the intraoral tongue drive system.

Analiza konstrukcyjno-materiałowa innowacyjnego bębna mieszalnika o pojemności 12 m³

A structural and material analysis of individual elements of the mixing-unloading spiral and shell segments of the innovative mixer drum of the hydraulic truck concrete mixer with a capacity of 12 m3 was developed. A complex CAD design process of individual elements in terms of the developed manufacturing technology was carried out. The construction of the mixer components was verified in the 3D-CAD system and a numerical analysis of stress distribution using the finite element method (FEM) was carried out for key segments of the spiral, which directly determines the implementation of the correct and efficient concrete mixing process. The research resulted in the development of comprehensive technical documentation of the original mixer structure, including executive drawings of the components along with a description of the manufacturing technology and the choice of the initial material–steel with increased abrasion resistance. The results of the completed research process were used in the next stage of research, i.e. bench tests of the innovative design of the 12 m3 mixer drum.

The trophoblast giant cells of cricetid rodents.

Giant cells are a prominent feature of placentation in cricetid rodents. Once thought to be maternal in origin, they are now known to be trophoblast giant cells (TGCs). The large size of cricetid TGCs and their nuclei reflects a high degree of polyploidy. While some TGCs are found at fixed locations, others migrate throughout the placenta and deep into the uterus where they sometimes survive postpartum. Herein, we review the distribution of TGCs in the placenta of cricetids, including our own data from the New World subfamily Sigmodontinae, and attempt a comparison between the TGCs of cricetid and murid rodents. In both families, parietal TGCs are found in the parietal yolk sac and as a layer between the junctional zone and decidua. In cricetids alone, large numbers of TGCs, likely from the same lineage, accumulate at the edge of the placental disk. Common to murids and cricetids is a haemotrichorial placental barrier where the maternal-facing layer consists of cytotrophoblasts characterized as sinusoidal TGCs. The maternal channels of the labyrinth are supplied by trophoblast-lined canals. Whereas in the mouse these are lined largely by canal TGCs, in cricetids canal TGCs are interspersed with syncytiotrophoblast. Transformation of the uterine spiral arteries occurs in both murids and cricetids and spiral artery TGCs line segments of the arteries that have lost their endothelium and smooth muscle. Since polyploidization of TGCs can amplify selective genomic regions required for specific functions, we argue that the TGCs of cricetids deserve further study and suggest avenues for future research.

Spiral arms and the angular momentum gap in Milky Way Cepheids

ABSTRACT The angular momentum distribution of classical Cepheids in the outer Milky Way disc is bimodal with a gap at $L_\mathrm{gap}=2950\, \rm{km\,s^{-1}}$ kpc, corresponding to $R=13\,$ kpc, while no similar feature has been found in the general population of disc stars. We show that star formation in multiple spiral arm segments at the same azimuth leads to such multimodality that quickly dissolves and only shows in young stars. Unlike other explanations, such as a 1:1 orbital resonance with the Galactic bar, this also accounts for the observed steepening of the stellar warp at Lgap, since the adjacent spiral arms represent different parts of the warped gas disc, and for the predominance of the gap at negative Galactic longitude (ℓ &amp;lt; 0°), since for complex spiral structure this mechanism is limited in azimuth. In this scenario, the gap is clearly present only in young stars, as observed, while most purely stellar dynamical origins would affect all disc populations, including older disc stars.

Analytical Aircraft State and IMU Signal Generator From Smoothed Reference Trajectory

Generating aircraft position, velocity, and attitude along a reference trajectory is useful in many path and mission planning applications. In applications simulating an inertial navigation system the body-frame accelerations and angular rates are also required. This work presents a method for generating a smoothed continuous-curvature reference trajectory from a series of waypoints using line, arc, clothoid, and Fermat spiral segments in a fillet smoothing framework. The geometry of the segments are used to generate the position, velocity, and attitude of an aircraft following the reference trajectory. A primary contribution of this article is the use of the path geometry, coordinated turn model, and curvilinear motion theory to obtain analytical solutions for the body-frame accelerations and angular rates of the aircraft along the reference trajectory.

Single shot spiral TSE with annulated segmentation.

To develop, optimize, and implement a single shot spiral turbo spin echo (TSE) sequence at 3T and to demonstrate its feasibility to acquire artifact free images of the central nervous system with 1 mm spatial resolution in <200 ms. Spiral TSE sequences with annulated spiral segmentation have been implemented with different acquisition modes. In fixed mode, the duration of each spiral segment is fixed to fill the available acquisition time tacq . In tangential mode, the beginning of each spiral segment is reached via a straight tangential trajectory. Tangential mode allows faster transition and thus longer tacq for a given echo spacing (ESP), but less data points can be acquired per acquisition interval. Alternating between spiral-in and spiral-out readout in alternating echoes leads to a somewhat different point spread function for off-resonant spins. Images of the brain with 1 mm spatial resolution acquired with a variable density spiral with ∼40% undersampling can be acquired in a single shot. All acquisition modes produce comparable image quality. Only mild artifacts in regions of strong susceptibility effects can be observed for ESP of 10 ms and below. The use of variable flip angle schemes allows seamless acquisition of consecutive slices and/or dynamic scans without waiting time between consecutive acquisitions. Comparison with images acquired at 1.5T shows reduced susceptibility artifacts within the brain and facial structures. Single shot spiral TSE has been demonstrated to enable highly efficient acquisition of high-resolution images of the brain in <200 ms per slice.

A Mathematical Model for the Prediction of the Scale Layer Formation on ASTM A510/A853 Cold-Drawn Hypoeutectoid Steel Wire After Batch Annealing

Annealed hypoeutectoid ASTM A510/A853 steel wire is widely used in the construction industry due to its mechanical properties, which makes it a very versatile material to work with. This work concerns the prediction of the thickness of the scale layer of the hypoeutectoid steel wire once subjected to a batch annealing process. We propose a mathematical model to approach oxidation occurring during the process. The model treats this phenomenon as a non-isothermic instance; it takes as input a heating curve, a cooling curve, and a holding time that corresponds to the heating and cooling cycles and a heating holding cycle. We assume the temperature of material outer spiral segments as the furnace atmosphere temperature. With the aid of this model, it is possible to predict the oxide scale layer of the outer spirals segments of the annealed drawn wire coils after batch annealing with reasonable accuracy. We did not find visible evidence of decarburization; the steels of the study in this work do not decarburize. As an approximation, we assumed that the temperature of the outside of the drawn wire coils equals the furnace atmosphere.

Superposing the Magnetic Spiral Structure of the Milky Way, on the Stellar Spiral Arms—Matching the Unique Galactic Magnetic Field Reversal Zone with Two Galactic Spiral Arm Segments

To pinpoint the peak location of the synchrotron total intensity emission in a spiral arm, we use a map of the spiralarm locations (from the observed arm tangent). Thus In a typical spiral arm in Galactic Quadrant I, we find the peak of the synchrotron radiation to be located about 220 +/-40 pc away from the inner arm edge (hot dust lane) inside the spiral arm. While most of the galactic disk has a clockwise largescale magnetic field, we make a statistical analysis to delimitate more precisely the smaller reverse annulus wiith a counterclockwise galactic magnetic field. We find an annulus width of 2.1 +/-0.3 kpc (measured along the Galactic radius), located from 5.5 to 7.6 kpc from the Galactic Center). The annulus does not overlay with a single spiral arm -- it encompasses segments of two different spiral arms. Using a recent delineation of the position of spiral arms, the field-reversed annulus is seen to encompass the Crux-Centaurus arm (in Galactic Quadrant IV) and the Sagittarius arm (in Galactic Quadrant I).

The Construction of Polynomial Spiral Segment Using Cubic Ball Basis Functions

B-splines, Bezier, Ball curves and NURBS (non-uniform rational B-splines) are commonly used in CADand CAGD applications. Unfortunately their fairness is not guaranteed. Spiral segments help us in designingimproved form of curves called fair curves. Such fair curves are useful in sophisticated applications such asdesign of routes of high ways and railways and mobile robot trajectories. In this paper we have developed thepolynomial cubic Ball spiral segment with degree of freedom. The effect of shape parameters is also observed.In the end results are represented in graphical form.

New Cubic Trigonometric Bezier-Like Functions with Shape Parameter: Curvature and Its Spiral Segment

This work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been proved. The C 3 and G 3 continuity conditions between two curve segments have also been achieved. To check the applicability of proposed functions, different types of open and closed curves have been constructed. The effect of shape parameter and control points has been observed. It is observed that, by decreasing the value of shape parameter, the curve moves toward the control polygon and vice versa. The CT-Bézier curve is closer to the cubic Bézier curve for a fixed value of shape parameter. The proposed CT-Bézier curve can be used to represent ellipse. Using proposed basis functions, we have constructed the spiral segment which is very useful to construct fair curves and desirable to design trajectories of mobile robots, highway, and railway routes’ designing.

Galactic spiral structure revealed byGaiaEDR3

Using the astrometry and integrated photometry from theGaiaEarly Data Release 3, we map the density variations in the distribution of young upper main sequence (UMS) stars, open clusters, and classical Cepheids in the Galactic disc within several kiloparsecs of the Sun. We derive maps of relative over- and under-dense regions for UMS stars in the Galactic disc using both bivariate kernel density estimators and wavelet transformations. The resulting overdensity maps exhibit large-scale arches that extend in a clumpy but coherent way over the entire sampled volume, indicating the location of the spiral arm segments in the vicinity of the Sun. Peaks in the UMS overdensity are well matched by the distribution of young and intrinsically bright open clusters. By applying a wavelet transformation to a sample of classical Cepheids, we find that their overdensities possibly extend the spiral arm segments on a larger scale (≃10 kpc from the Sun). While the resulting map based on the UMS sample is generally consistent with previous models of the Sagittarius-Carina spiral arm, the geometry of the arms in the III quadrant (galactic longitudes 180° &lt;l &lt; 270°) differs significantly from that suggested by many previous models. In particular, we find that our maps favour a larger pitch angle for the Perseus arm, and that the Local Arm extends into the III quadrant at least 4 kpc past the position of the Sun, giving it a total length of at least 8 kpc.

Screwed up: Spirality of segments and other iterated structures suggest an underlying principle of seriality in bilaterians.

This review deals with helicomery, that is, the specific malformation of a spiral arrangement of segments and other serial structures. Helicomery was first described in annelid and arthropod body segments. However, corresponding patterns occur in arthropod appendages and other bilaterians with serially arranged body parts, such as tapeworms, nematodes, vertebrates, and probably chitons. The specifics of the spirals such as length, orientation, and handedness are described. Most spirals are dorsal and comprise only a few loops. Helicomery is formed by a shift of cells during development or in adults caused by changes in cell adhesion or mechanical impacts such as lesions. A model for the formation of helicomery is proposed, which is based on medieval church labyrinths. These complex spiral structures are derived from concentric lines by the shift of relatively few tiles. This principle of "small causes, great effect" also applies to "spiral segments," because helicomery dissolves segmental patterns and questions the concept of segments as distinct structures. The widespread occurrence of helicomery in nonhomologous serial structures might indirectly indicate an underlying principle of seriality among Bilateria.

“Perfect” Terahertz Vortex Beams Formed Using Diffractive Axicons and Prospects for Excitation of Vortex Surface Plasmon Polaritons

Transformation of a Bessel beam by a lens results in the formation of a “perfect” vortex beam (PVB) in the focal plane of the lens. The PVB has a single-ring cross-section and carries an orbital angular momentum (OAM) equal to the OAM of the “parent” beam. PVBs have numerous applications based on the assumption of their ideal ring-type structure. For instance, we proposed using terahertz PVBs to excite vortex surface plasmon polaritons propagating along cylindrical conductors and the creation of plasmon multiplex communication lines in the future (Comput. Opt. 2019, 43, 992). Recently, we demonstrated the formation of PVBs in the terahertz range using a Bessel beam produced using a spiral binary silicon axicon (Phys. Rev. A 2017, 96, 023846). It was shown that, in that case, the PVB was not annular, but was split into nested spiral segments, which was obviously a consequence of the method of Bessel beam generation. The search for methods of producing perfect beams with characteristics approaching theoretically possible ones is a topical task. Since for the terahertz range, there are no devices like spatial modulators of light in the visible range, the main method for controlling the mode composition of beams is the use of diffractive optical elements. In this work, we investigated the characteristics of perfect beams, the parent beams being quasi-Bessel beams created by three types of diffractive phase axicons made of high-resistivity silicon: binary, kinoform, and “holographic”. The amplitude-phase distributions of the field in real perfect beams were calculated numerically in the approximation of the scalar diffraction theory. An analytical expression was obtained for the case of the binary axicon. It was shown that a distribution closest to an ideal vortex was obtained using a holographic axicon. The resulting distributions were compared with experimental and theoretical distributions of the evanescent field of a plasmon near the gold–zinc sulfide–air surface at different thicknesses of the dielectric layer, and recommendations for experiments were given.

Characterization and quantification of railroad spiral-joint discontinuities

In this study, a new approach is proposed for the characterization and quantification of the spiral transitions in railroad vehicle system algorithms. Definitions of the super-elevation and balance speed are provided in order to have a better understanding of their variations within the space curve of the spiral segment. In order to develop this understanding, three different curves which have fundamentally different geometries are considered; a super-elevated constant-curvature curve with zero twist and zero vertical elevation, a vertically-elevated helix curve with a constant curvature and twist and zero super-elevation, and a spiral curve with non-zero varying-curvature, twist, super-elevation, and vertical elevation. The curve equations are developed in terms of Euler angles used by the rail industry to describe the track geometry in the computer simulations. Because the geometry of the spiral space curve can be completely defined in terms of two Euler angles only, the horizontal-curvature and the vertical-development angles; a third Euler angle referred to as the Frenet bank angle is written in terms of these two angles using an algebraic equation. The fact that, for given curvature and elevation angles, the Frenet bank angle cannot be treated as an independent geometric parameter is used to obtain accurate quantification of the spiral-intersection discontinuities. The severity of the twist and elevation discontinuities at the spiral intersections with the tangent and curve segments demonstrates the need for the adjustments used in practice by the rail engineers to achieve a higher degree of smoothness. In order to properly define the direction of the centrifugal force, a distinction is made between the super-elevation of a surface and the bank angle of a curve on the surface.

Segments of spiral arms of the Galaxy traced by classical Cepheids: effects of age heterogeneity

We investigated the dependence of the parameters of the segments of spiral arms of the Galaxy on the age of classical Cepheids. The catalog of Cepheids (Mel’nik et al.) was divided into two samples— relatively young (P > 9d) and relatively old (P < 9d) objects. The parameters of the spiral structure were determined both for two samples separately and jointly for the combination of two systems of segments traced by young and old objects. For most of the segments, their parameters for young and old objects differ significantly. Taking into account the difference between the two segment systems, we obtained the estimate R 0 equal to kpc, which in the modern Large Magellanic Cloud (LMC) calibration corresponds to the value of kpc. It is shown that the displacement between the segments is not reduced to the effect of differential rotation only. To interpret this displacement for objects of Perseus and Sagittarius-2 segments, we carried out a dynamic modeling of the change in the position of the segment points when moving in the smooth gravitational field of the Galaxy. At the angular velocity of rotation of the spiral pattern Ωp = 25.2 ± 0.5 km s−1 kpc−1 (Dambis et al.) the observed displacement between segments on young and old objects can be explained by the amplitude of spiral perturbations of the radial velocity of u = 10 ± 1.5 km s−1. For the constructed double system of spiral segments, it is demonstrated that the assumption of constancy of the pitch angles within each segment and the assumption that the pole of the spiral pattern is in the direction of the nominal center of the Galaxy do not contradict the data within the range of uncertainty.

Iron Calcium Carbonate Instability: Structural Modification of Siderite Corrosion Films.

Corrosion research related to CO2-containing environments has focused over the past few decades on siderite formation (FeCO3) as a main corrosion product on carbon steel, yet the influence of Ca and other ions on its chemical and structural characteristics is not fully understood. Metal-localized corrosion is the biggest industrial challenge because of the unknown and unpredictable character of this phenomenon that frequently leads to failure. We report here the role of Ca and formation of iron-calcium carbonate (FexCayCO3) through a spiral growth model as in the calcite system and quantify the replacement of Fe2+ by Ca2+ ions in the structure of FeCO3 to form FexCayCO3. The incorporation of Ca2+ inhibits the completion of spiral segments on the growth of the rhombohedral crystals of FeCO3, promoting an enlargement of its structure along the c-axis. This leads to distortions in the chemical structure and morphology affecting the chemical and mechanical properties. Under flow conditions over time in an undersaturated environment, Ca is leached out from the expanded structure of FexCayCO3 increasing the solubility of the crystals, weakening the mechanical properties of the resulting corrosion films and stimulating localized corrosion.

Manifold spirals in barred galaxies with multiple pattern speeds

In the manifold theory of spiral structure in barred galaxies, the usual assumption is that the spirals rotate with the same pattern speed as the bar. Here, we generalize the manifold theory under the assumption that the spirals rotate with a different pattern speed than the bar. More generally, we consider the case in which one or more modes, represented by the potentialsV2,V3, etc., coexist in the galactic disk in addition to the bar’s modeVbar, but the modes rotate with pattern speeds, Ω2, Ω3, etc., which are incommensurable between themselves and with Ωbar. Through a perturbative treatment (assuming thatV2,V3, etc. are small with respect toVbar), we then show that the unstable Lagrangian pointsL1andL2of the pure bar model (Vbar, Ωbar) are continued in the full model as periodic orbits, in the case of one extra pattern speed, or as epicyclic “Lissajous-like” unstable orbits, in the case of more than one extra pattern speeds. We useGL1andGL2to denote the continued orbits around the pointsL1andL2. Furthermore, we show that the orbitsGL1andGL2are simply unstable. As a result, these orbits admit invariant manifolds, which can be regarded as the generalization of the manifolds of theL1andL2points in the single pattern speed case. As an example, we computed the generalized orbitsGL1,GL2, and their manifolds in a Milky-Way-like model in which bar and spiral pattern speeds were assumed to be different. We find that the manifolds produce a time-varying morphology consisting of segments of spirals or “pseudorings”. These structures are repeated after a period equal to half the relative period of the imposed spirals with respect to the bar. Along one period, the manifold-induced time-varying structures are found to continuously support at least some part of the imposed spirals, except at short intervals around specific times at which the relative phase of the imposed spirals with respect to the bar is equal to ±π/2. The connection of these effects to the phenomenon of recurrent spirals is discussed.

Upper bound stability analysis of slurry-supported trenches in layered soils

Abstract A stability analysis of slurry-supported trenches in horizontally layered cohesive-frictional soils by using the kinematical approach of limit analysis is presented. To ensure the kinematical admissibility, the failure surface in the formulated multi-block rotational mechanism was composed of several segments of logarithmic spirals with a same rotation center. To account for varying soil properties among different layers, both toe and above-toe failure patterns were considered. The associated factor of safety was determined by the shear strength reduction technique and was verified by comparison with the shear strength reduction finite element method (SSRFEM). It was found that the results obtained from the simplified approach by using weighted average soil parameters were not reliable and sometimes led to significantly overestimated safety factors on trench stability in layered soils, which deserves more attention in practice.