Non-concentric Circles Research Articles

Influence of Surface Effects in the Problems of the Theory of Elasticity for Domains Bounded by Non-Concentric Circles

The article deals with some problems of the theory of elasticity for domains bounded by non-concentric circles by taking into account surface effects such as surface elasticity and surface stresses. The solutions are obtained by expanding variables written in a bipolar coordinate system into Fourier series. The values of surface stresses and stress concentrations that are of our interest are obtained using recurrence relations. The contribution made by surface effects is considered.

Analytical Study on Inter-Cell Handover via Non-Concentric Circles in Wireless Heterogeneous Small Cell Networks

In this paper, we propose a novel inter-cell handover approach from a new perspective in dense Heterogeneous and Small Cell Networks (HetSNets). We first devise a cell selection mechanism to choose a proper candidate small cell for the UEs that tend to implement inter-small cell handover (ICH). By exploiting the property of a typical non-concentric circle, i.e., circle of Apollonius, we then propose a novel analytical method for modeling inter-cell handover regions and present mathematical derivation to prove that the inter-small cell handover issues fit the property of the circle of Apollonius. We design an inter-cell handover algorithm (ICHA) by means of our proposed handover model to dynamically configure hysteresis margin and properly implement handover decision in terms of UE’s mobility. Simulation results demonstrate that the proposed ICHA yields lower call drop rate and radio link failure rate than the conventional methods and hence achieve high Handover Performance Indicator (HPI).

Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves

ABSTRACTIn this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function , with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields.

The Constructions of Egg-Shaped Surface Equations using Hugelschaffer’s Egg-Shaped Curve


 
 
 Hugelschaffer’s egg-shaped curve is egg-shaped curve that is constructed by two non-concentric circles using Newton’s transformation known as hyperbolism. This study has goals to construct the egg-shaped surface equations using Hugelschafer’s egg-shaped curve that is rotated on x-axis, y-axis and z-axis; to get the volume formula of the egg-shaped solid and the egg-shaped surface area and also to visualize the egg-shaped surface equations using GeoGebra. Hugelschaffer’s egg-shaped curve is selected because its equation is simple. The procedures of the construction of the egg-shaped surface equations are done by drawing the curve on xy-plane and xz-plane, then it is rotated on axes of the coordinate. Whereas, the volume formula of the egg-shaped solid is gotten by using the disk method of the volume integral. The egg-shaped surface area is attained by using the integral of surface area. Visualisation of the egg-shaped surface equations are done by choosing vary of parameter values of the equations that aims to know the effect of the parameter values with the shaped surface.
 
 

The projected circle centres and polar line for camera self-calibration

Epipolar geometry is an important concept in projective geometry, and it has been applied to camera calibration only gradually. In this study, using three non-concentric circles as a calibration pattern to ascertain the coordinates of the projected circle centres, the vanishing line could be computed by taking advantage of the linear relationship between the pole and the polar line to determine the camera's intrinsic parameters. In the image plane, the line passing through the two projected circle centres is a degenerate conic section, so it can be written in the form of a linear combination of two projected circles. In addition, the projected circle centre can be obtained by solving a linear equation. Because the relationship between the centre of a circle and the vanishing line is similar to the relationship between the pole and the polar line, the vanishing line can be determined by solving a linear equation. The results of our experiments show that this approach is effective and has high precision.

Pythagorean hodograph spline spirals that match [formula omitted] Hermite data from circles

A construction is given for a G3 piecewise rational Pythagorean hodograph convex spiral which interpolates two G3 Hermite data associated with two non-concentric circles, one being inside the other. The spiral solution is of degree 7 and is the involute of a G2 convex curve, referred to as the evolute solution, with prescribed length, and composed of two PH quartic curves. Conditions for G3 continuous contact with circles are then studied and it turns out that an ordinary cusp at each end of the evolute solution is required. Thus, geometric properties of a family of PH polynomial quartics, allowing to generate such an ordinary cusp at one end, are studied. Finally, a constructive algorithm is described with illustrative examples.

A Fast and Accurate Circular Segmentation Method for Iris Recognition Systems

With the development of the identification methods, an iris recognition system is expected to be one of the basic elements of modern society, with many application areas such as access control, national ID cards, etc. Any iris recognition system follows four functioning steps: Segmentation, Normalization, Encoding, and Matching. Iris segmentation is a key step in any iris recognition system and it directly affects the accuracy of matching. Several methods have been suggested to assess iris regions with two non-concentric circles. The circle model was investigated to find a tradeoff between modeling complexity, accuracy of the algorithm and computational time. In this paper, we propose an enhancement in the form of a modified Masek approach and a comparative study of the performance of three methods: radial segmentation, Masek approach and ours which are all parts of circle model approaches. Using CASIA Iris Database V3.0, our experimental results reveal that the proposed method provides a high performance in time and accuracy

Rotation indices related to Poncelet’s closure theorem

AbstractLet C

On the design of inscribed triangle non-concentric circular fractal antenna

This article presents the new ultra-wideband fractal antenna with CPW-fed.The fractal antenna has been fabricated on substrate εr = 4.3 mm and thickness h = 1.53 mm with 15-mm radius. This antenna inscribed triangles in non-concentric circles with varied radius offers the excellent bandwidth around 13.54 GHz (span from 1.335 to 14.88 GHz) corresponding to 167% impedance bandwidth at S11 < −10 dB. The first resonant frequency of fractal antenna shifted to 1.51 GHz by the application of fractal geometry in comparison to solid circular disc monopole first resonant frequency 2.215 GHz. This indicates the size reduction of the antenna. The experimental radiation patterns of the antenna are nearly omni directional. The proposed antenna is useful for mobile communication and UWB communication system. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52:2696–2699, 2010; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25555

Simulated cup/disc ratio: a tool for ophthalmologists

To evaluate and compare the observers' ability to measure simulations of cup/disc ratios (CDR) as concentric and non-concentric circles. In a prospective, random, and masked setting, 43 images representing the CDR spectrum from 0.2 to 0.9 for vertical and horizontal CDR measurements were developed and presented on a computer screen to 171 participants. There were satisfactory agreements according to the kappa coefficient (0.755 and 0.730 for horizontal and vertical cup disc ratios, respectively) and Lin's concordance correlation (R=0.88 and R=0.86 for horizontal and vertical measurements, respectively). However, very poor agreement was found for intermediate CDR values. The worst agreement occurred when the CDR was between 0.4 and 0.6 for both the horizontal and vertical values. The kappa coefficient was 0.37 and 0.39 for 0.4 CDR (horizontal and vertical, respectively), 0.39 and 0.38 for 0.5 CDR (horizontal and vertical, respectively) and 0.45 and 0.41 for 0.6 CDR (horizontal and vertical, respectively). Despite a good general agreement between the gold standard and the participants' responses, the absolute agreement for intermediate CDR values was very poor for both horizontal and vertical values.

O tempo das partes. Temporalidade e perspectiva em Espinosa

A filosofia espinosista foi freqüentemente associada com a imagem do círculo, como metáfora alusiva a um ser atemporal e a um saber eterno. Concretamente, Hegel utilizou essa associação para celebrar a concepção do infinito em ato de Espinosa; e interpretou a ilustração geométrica da Carta 12 nos termos dessa conexão entre infinitude verdadeira e circularidade. No presente trabalho, questionamos essa leitura, e utilizamos o exemplo espinosano dos círculos não concêntricos para tematizar a singular concepção espinosana da determinação e do limite. Graças à compreensão das coisas finitas como durações singulares é possível entender em que sentido o “tempo” é, para Espinosa, uma realidade imaginária que, enquanto tal, tem sua própria efetividade.

On PH quintic spirals joining two circles with one circle inside the other

The paper derives a spiral condition, for a single Pythagorean hodograph quintic transition curve of G 2 contact, between two circles with one circle inside the other. A spiral is free of local curvature extrema, making spiral designs an interesting mathematical problem with importance for both physical and aesthetic applications. In the construction of highways or railway routes in particular, it is often desirable to have a transition curve from circle to circle. Here, we treat an open problem on planar quintic spiral segments, called transition curve elements, examine techniques for curve design using the new results, and derive lower and upper bounds for the distance between the two circles. The proposed method is applicable for non-tangent and non-concentric circles.

Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section

The diffraction of an electromagnetic wave by a cylindrical object with arbitrary cross section is studied by taking advantage of recent progress in grating theories. The fast Fourier factorization method previously developed in Cartesian coordinates is extended to cylindrical coordinates thanks to the periodicity of both the diffracting object and the incident wave with respect to the polar angle theta. Thus Maxwell equations in a truncated Fourier space are derived and separated in TE and TM polarization cases. The new set of equations for TM polarization is resolved numerically with the S-matrix propagation algorithm. Examples of elliptic cross sections and cross sections including couples of nonconcentric circles show fast convergence of the results, for both dielectric and metallic materials, as well as good agreement with previous published results. Thus the method is suitable for an extension to conical (out-of-plane) diffraction, which will allow studying mode propagation along microstructured fibers.

NUMERICAL BIFURCATION OF EQUILIBRIA OF NEMATIC CRYSTALS BETWEEN NON-CO-AXIAL CYLINDERS

Calculations are presented giving the stable equilibrium states of nematic liquid crystals confined between non-co-axial circular cylinders subject to the condition that the director be normal to the bounding surfaces. The one-constant theory of nematics is employed and emphasis is laid on cases for which the minimizing director field does not lie in the plane perpendicular to the cylinders. Calculations are made of the force that the nematic exerts on the cylinders, tending to make them co-axial. The numerical problem faced is that of finding, for the Dirichlet energy, minimizing maps to S2, from a region in ℝ2 bounded by non-concentric circles. The method employed is a finite-element implementation of a projected gradient method for which the energy decreases at each iteration.

Modal dispersion curves for annular waveguides with core cross section bounded by conducting and dielectric nonconcentric circles

We study the modal characteristics of a waveguide of annular cross section with nonconcentric circular boundaries. In this study, either both or one of the cladding regions is taken as highly conducting. The bipolar coordinate system is introduced for the analysis, and the characteristic equations are derived. Results show that the absence of concentricity of the two boundaries reduces the number of sustained modes. Dispersion curves show that two types of modes are propagated simultaneously through the waveguide in which either of the claddings is metallic. One type shows an anomalous dispersion behavior. For the waveguide with both of the boundaries conducting, dispersion curves have the expected shape as in the case of standard annular waveguides of concentric circular boundaries. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 129–134, 2000.

Running in nonconcentric circles: Why environmental management isn't being integrated into business management

To manage effectively, you have to communicate. But before you can communicate, you have to speak a common language. In the past, business managers and environmental professionals spoke in different jargons—and went their separate ways. Fortunately, that situation is now beginning to change. © 2000 John Wiley & Sons, Inc.

Running in nonconcentric circles: Why environmental management isn't being integrated into business management

To manage effectively, you have to communicate. But before you can communicate, you have to speak a common language. In the past, business managers and environmental professionals spoke in different jargons—and went their separate ways. Fortunately, that situation is now beginning to change. © 2000 John Wiley & Sons, Inc.

Global coupling effects on spatiotemporal patterns on a ring electrode

Experimental results on spatiotemporal pattern formation on a ring electrode during the oscillatory electrodissolution of cobalt in 1.0 M phosphoric acid are reported; the ring is the area between two non-concentric circles and its width thus varies continuously with angle. The experiments were controlled potentiostatically with the tip of the capillary of the reference electrode placed in the center of the ring 1 mm above the surface. Under these conditions rotating waves, with and without modulation, occur. The influence of positive global coupling (in the form of an external resistor of variable size in series with the working electrode) on the pattern formation is investigated. A small added global coupling smoothes variations in speed and size of a rotating active area which are caused by the deformation of the ring and surface heterogeneities. A larger global coupling leads to non-traveling patterns including complete synchronization of the ring and also synchronization within subsections or smaller areas of the ring; these subsections themselves oscillate in a phase-locked or quasiperiodic fashion.

Correction to ?Modal dispersion curves of an optical waveguide with an annular core cross section separated by two nonconcentric circles from two cladding regions?

Correction to ?Modal dispersion curves of an optical waveguide with an annular core cross section separated by two nonconcentric circles from two cladding regions?

Modal dispersion curves of an optical waveguide with an annular core cross section separated by two nonconcentric circles from two cladding regions

An optical fiber with an annular cross section bounded by two nonconcentric circles is analytically studied with a view to obtaining the modal characteristics. Using the characteristic equation derived from the matching of fields at the core–cladding boundaries expressed in terms of bipolar coordinates, dispersion curves are obtained on the basis of numerical computations. The curves corresponding to some modes are similar to the standard dispersion curves for waveguides. However, the dispersion curves of other modes show some unexpected behavior; one mode even shows no dispersion at all. These points are qualitatively discussed. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 280–283, 1997.