Coaxial Circles Research Articles

Tribological behaviour of laser textured Ti3AlV 2.5V alloy under simulated body fluid

The use of lasers to fabricate micro-textures on the surface of medical implants is an effective method to improve their bio-tribological properties. In the present study, three distinct configurations of micro-textures, namely, co-axial circles, hexagon, and line with varying spacing of 300 µm, 400 µm, and 500 µm, were fabricated on Ti3Al2.5V alloy using Nd:YAG fibre lasers. The influence of micro-textured geometries on microhardness, coefficient of friction (COF), and wear rate was estimated. The tribological properties of the polished and textured samples were investigated using a linear reciprocating tribometer against silicon nitride (Si3N4) balls under simulated body fluid (SBF) lubricant. Orthogonal results indicate that the co-axial circles with a spacing of 305 µm prove to be the most efficient in enhancing the tribological performance of textured surfaces. This configuration demonstrates a significant improvement, with a 33.62 % reduction in friction coefficient and a 61.81 % reduction in wear rate compared to polished samples. The decrease in spacing appears to enhance the anti-friction and anti-wear properties of the textured surfaces. The working mechanism behind the reduction in the friction coefficient and wear rate lies in the capacity of the textures to trap particles.

Stability of surfaces with constant mean curvature bounded by two coaxial circles

Consider two coaxial round circles with the same radius. A mathematical model of a tiny liquid drop trapped between them are constant mean curvature (CMC) surfaces because a CMC surface is a critical point of the area for all variations that preserve the enclosed volume and satisfy given boundary condition. A CMC surface is said to be stable if the second variation of the area for any such variation is nonnegative. In this paper, we judge the stability of one period of the so-called unduloid between two consecutive bulges rigorously for the first time.

Calibration of Double-Plane-Mirror Catadioptric Camera Based on Coaxial Parallel Circles

A catadioptric camera with a double-mirror system, composed of a pinhole camera and two planar mirrors, can capture multiple catadioptric views of an object. The catadioptric point sets (CPSs) formed by the contour points on the object lie on circles, all of which are coaxial parallel. Based on the property of the polar line of the infinity point with respect to a circle, the infinity points in orthogonal directions can be obtained using any two CPSs, and a pole and polar pair with respect to the image of the absolute conic (IAC) can be obtained through inference of the Laguerre theorem. Thus, the camera intrinsic parameters can be solved. Furthermore, as the five points needed to fit the image of a circle are not easy to obtain accurately, only sets in which five points can be located can be obtained, whereas the points on the line of intersection between the two plane mirrors and the ground plane can easily be obtained accurately. An optimization method based on the analysis of neighboring point sets to compare the intersection points with an image of the center of multiple circle images fitted using the point sets is proposed. Bundle adjustment is then applied to further optimize the camera intrinsic parameters. The feasibility and validity of the proposed calibration methods and their optimization were confirmed through simulation and experiments. Two primary innovations were obtained from the results of this study: (1) by applying coaxial parallel circles to the double-plane-mirror catadioptric camera model, a variety of calibration methods were derived, and (2) we found that the overall model could be optimized by analyzing the features of the neighboring point set and bundle adjustment.

A Survey of Delaunay Surfaces with Applications in Capillary Surfaces

In this paper we survey Delaunay surfaces in $\mathbb{R}^{3}$ spanning two coaxial circles which appear as capillary surfaces supported on different solid supports in the absence of gravity. We classify these surfaces based on contact angles and the geometry of the support. Numerical solutions of the Euler Lagrange equation are provided using numerical methods.

The Doubly Connected Minimal Surfaces Between Two Circles in Parallel Planes

In this article, we revisit some results published by several mathematicians regarding existence and non-existence of doubly connected minimal surfaces between two circles in parallel planes. In particular, we propose new analytical interpretations and results for catenoidal solutions formed between two coaxial circles in parallel planes of arbitrary radii. We conclude by discussing the nature of the pair of the catenoidal solutions that arise from our proposed algorithm.

Tube-Based DBD Plasma Treatment for Improving the Performance of the Slippery Coating Layers on Medical Catheters

This work develops a tube-based dielectric barrier discharge (DBD) plasma treatment for improving the performance of the slippery coating layers on medical catheters. The raw materials of the polymer catheters usually exhibit hydrophobic surface property and need a hydrophilic slippery coating layer for reducing the friction during catheter insertion. However, the high friction force may cause an uncomfortable feeling or even the infective or thrombosis injuries on the epithelium. This study develops an atmospheric tube-based DBD plasma for treating the surface of the plastic catheter for enhancing the coating performance of the slippery layer coating on medical catheters. The tube-based DBD plasma system is a semiclose and co-axial concentric circles system composed of a glass tube as the DBD layer and the inner supporting hook for catheter production as the center electrode for DBD discharges. The treatment for the inner and outer catheter tube can be achieved simultaneously with a small carrier flow rate of 30–100 sccm. Results show that the contact angles of these catheter tubes are significantly reduced after plasma treatment and the hydrophilicity of the treated surface maintains 57% for more than 30 min after the treatments. The catheters with different plasma treatments are coated with the commercial slippery layer and tested the kinetic friction under the ASTM D1894 standard. The kinetic friction test indicates that the catheters with plasma treatment exhibit lower kinetic friction force, indicating that lower friction during catheter medical insertion operations. The experimental results have shown that the medical catheter treated by the developed tube-based DBD plasma can be effectively modified and facilitated in the subsequent coating process.

Application of an Inertial Measurement Unit for quantitative assessment of Single Leg Squat in recreational runners

In 3-dimensional Lorentz-Minkowski space we determine the number of catenoids connecting two coaxial circles in parallel planes. This study is separated according to the types of circles and the causal character (spacelike and timelike) of the catenoid.

The number of catenoids connecting two coaxial circles in Lorentz-Minkowski space

In 3-dimensional Lorentz-Minkowski space we determine the number of catenoids connecting two coaxial circles in parallel planes. This study is separated according to the types of circles and the causal character (spacelike and timelike) of the catenoid.

Bifurcation and symmetry breaking of nodoids with fixed boundary

Abstract We prove bifurcation results for (compact portions of) nodoids in ℝ3, whose boundary consists of two fixed coaxial circles of the same radius lying in parallel planes. Degeneracy occurs at an infinite discrete sequence of instants, that are divided into four classes. Different types of bifurcation and break of symmetry occur at each instant of three of the four classes; bifurcation does not occur at the degeneracy instants of the fourth class.

Self-calibrated visual servoing with respect to axial-symmetric 3D objects

A self-calibrated approach to visual servoing with respect to non-planar targets modeled through a pair of coaxial circles plus one point is discussed. Full calibration data (fixed internal parameters) are obtained from two views, and used to recover the Euclidean structure of an auxiliary virtual plane associated to the target, together with the relative pose of the camera. Pose disambiguation is achieved without requiring any real third view of the target. The approach benefits of an off-line planning strategy by which the camera follows a 3D helicoidal path around an arbitrarily chosen axis. A convenient choice for the helicoidal axis is found to be that of the target axis itself. Simulation results demonstrate that the approach is robust with respect to noise both in the off-line and on-line control phases.

VISUAL SERVOING WITH A PAIR OF COAXIAL CIRCLES

An uncalibrated approach to visual servoing with respect to non planar targets modeled through a pair of coaxial circles plus one point is discussed. Full calibration data (fixed internal parameters) are obtained from two views, and used to recover Euclidean target structure and camera relative pose. Pose disambiguation is achieved without requiring any real third view of the target. The approach benefits of an off-line planning strategy by which the camera follows a 3D helicoidal path around the target axis. Simulations results demonstrate that the approach is robust with respect to a noisy calibration.

Coaxial circles and complex intersections

The family G of orthogonal trajectories of the family F of circles x 2 + y 2 - 2ay = 1 is found and a simple application is considered.

Coaxial circular spherical array for ultrasonic imaging

A new type of receiving array has been designed and constructed for the purpose of visualizing an object by using the ultrasonic wave at low frequency. The array consists of 24 receiving elements around three coaxial circles on a spherical surface. The multiplication of three additive outputs, each of which is the sum of the eight element outputs on a circle, is performed for the signal processing of the array. After theoretical and experimental studies, it has been proven that the array proposed is appropriate for the high-directional receiver in the ultrasonic visualization system. A preliminary experiment on imaging the object in the air has been carried out.

Magnetostatics of axially symmetric structures

Relations are obtained for the magnetic potentials and magnetostatic energies of single circles of charge and systems of coaxial parallel circles. Results obtained by direct integration (as elliptic integrals) correlate with solutions of Laplace's equation (Bessel function form). Applications to the calculation of the fields from and the forces between magnets and the behaviour of cylindrical domain structures are indicated, and other extensions proposed.

Complex iterated radicals

We prove the convergence of the sequence S defined by Z+1 = (Z_-c) 2, c real, for any choice of z,. Let k=j-i_cj2. If c L, S has the fixed points w,=i+ik and w2=1-ik and converges to w1 if Re(zD)>O and to w2 otherwise. We show that convergence is strictly monotone when the neighborhood system is the pencil of coaxial circles with w1 and w2 as limiting points, and give rates of convergence. The purpose of this paper is to prove that the sequence of complex numbers defined by Zn+,=(z-C)12, c real, converges for any choice of z0, i.e. globally, and to discuss the limit and rate of convergence. This problem was posed by C. S. Ogilvy [1]. As a guide to global convergence we first investigate local convergence. The following facts are known about the sequence defined by zn?+=f(zn) for some choice of z0. LEMMA 1. If limrn,, z=w and f is continuous at w then f(w)=w, i.e. w is a fixed point. PROOF. W4=1imn--joo Zn+1=1im.oDf(z.)=f(w)Suppose w is a fixed point off. If ZN=W for some N, then z,,=w for all n_N and we call the sequence trivial. We define q(n, w)=jz,.+j-wj1jzn-w|. LEMMA 2. Suppose w is afixedpoint off andf '(w) exists. If If'(w)I 1, then the sequence cannot converge to w except trivially. Received by the editors June 15, 1972 and, in revised form, February 13, 1973. AMS (MOS) subject classifications (1970). Primary 40A05, 41A25; Secondary 39A10, 50D45.

A supplement to the condition of J. Douglas

While a Jordan curve in Euclidean 3-space always spans a minimal surface of the type of the circular disc, the existence of a minimal surface of the type of the circular annulus, bounded by a system of two disjoint Jordan curves, very much depends on the configuration of these curves. A sufficient criterion for the existence has been given by J. Douglas in a famous paper [3] and, in different form, by R. Courant (see [2], esp. chapter IV). Roughly speaking, this condition guarantees the existence of a minimal surface of the type of the circular annulus, bounded by two Jordan curves Pi and P~ without common points, provided that these curves span a doubly-connected surface whose area is smaller than the sum of the areas ot the two simply-connected surfaces of least area bounded by P i and P~, respectively. Douglas' condition can be verified in many concrete cases. Nevertheless, even if Douglas' condition is violated, the problem of finding a minimal surface of the type of the annulus, bounded by two Jordan curves, may still be solvable. This fact is illustrated with the classical experiment where the curves Pi and P2 are coaxial unit circles in parallel planes, say the planes z = h and z = h (h ~ 0). (See for instance the presentation in (i. A. Bliss [1]). For h < ht : 0 . 5 2 7 7 . Douglas' condition is fulfilled. For ht ~< h ~ h~ = 0.6627... Douglas' condition is violated, but the circles Pi and r~ still span a doubly-connected minimal

Generalized Circle Diagrams and Their Application to Protective Gear

The common underlying theory of generally used systems of protection involving comparison of two vector quantities is derived by coaxial (bipolar) circles in the complex plane, where amplitude or phase comparison can be used interchangeably to produce any desired circle or straight line characteristic. Practical departure from ideal comparison, resulting from relay power consumption, is considered, and the relationship between this analysis and two currently used methods of distance relaying is pointed out. The basic circuit of a commonly used pilot wire scheme is analyzed and its characteristic considered, and the effect of long pilots with distributed constants is indicated.

Extension of Howard's Circle Theorem to Adiabatic Jets

L. N. Howard proved an inequality concerning the complex velocity of the propagation of waves disturbing the laminar, unidirectional flow of an incompressible stratified fluid. It is shown that this theorem is closely related to the virial theorem of hydrodynamics. It can be generalized for the steady motion of a compressible fluid, provided the streamlines are either parallel straight lines or coaxial circles. The connection of the circle and virial theorems provides an interpretation of the former in terms of the energy of the perturbation. A positive potential energy always exerts a stabilizing influence, as does the angular velocity in the case of circular streamlines. This latter is diminished for short waves; it is also complicated by the fact that radial variations of the angular velocity may contribute negative terms to the potential energy. Zonal flow, such as the jet stream of the Earth's atmosphere, is generally baroclinic. In the barotropic case, the potential energy of the perturbation is simply proportional to the Väisälä-Brunt frequency. In the baroclinic case, this frequency cannot be usefully defined, and the more elaborate formulae are derived.

The Use of Current Sheets in the Design of Magnets to give Bounded Fields of Required Form, free from Edge Distortion

The use of current sheets to produce static magnetic fields of required form, with freedom from edge or fringing distortion and with no stray flux, is discussed. Two types of magnet winding are considered. The first, or field-terminating type, encloses a tube of force and serves as a sharp boundary to the field. The second, or iron-shrouded type, is wound against the inner surface of an iron shroud and, with a suitable distribution of turns, can generate any required shape of field in the iron enclosure. In both types stray field can be avoided if the iron return-path is infinitely permeable, or if it is covered with an `anti-reluctance' winding. A discussion is given of (a) the uniform field, (b) the field whose lines of force are coaxial circles, (c) the synchrotron field, and (d) the prolate spheroidal field, whose lines are confocal ellipses

1185. A group of coaxial circles ; generalization of the orthopole-theorem

1185. A group of coaxial circles ; generalization of the orthopole-theorem