Spherical Curves Research Articles

On the characterization of spherical curves in 3-dimensional Sasakian spaces

In this paper, we give the spherical characterization of a regular curve in 3-dimensional Sasakian space. Furthermore the differential equation which expresses the mentioned characterization is solved.

Tsunami propagation modelling – a sensitivity study

Abstract. Indian Ocean (2004) Tsunami and following tragic consequences demonstrated lack of relevant experience and preparedness among involved coastal nations. After the event, scientific and forecasting circles of affected countries have started a capacity building to tackle similar problems in the future. Different approaches have been used for tsunami propagation, such as Boussinesq and Nonlinear Shallow Water Equations (NSWE). These approximations were obtained assuming different relevant importance of nonlinear, dispersion and spatial gradient variation phenomena and terms. The paper describes further development of original TUNAMI-N2 model to take into account additional phenomena: astronomic tide, sea bottom friction, dispersion, Coriolis force, and spherical curvature. The code is modified to be suitable for operational forecasting, and the resulting version (TUNAMI-N2-NUS) is verified using test cases, results of other models, and real case scenarios. Using the 2004 Tsunami event as one of the scenarios, the paper examines sensitivity of numerical solutions to variation of different phenomena and parameters, and the results are analyzed and ranked accordingly.

Solution for Best Fitting Spherical Curvature Radius and Asphericity of Off-Axis Aspherics of Optical Aspheric Surface Component

This study aimed to establish the coordinate transformation between the off-axis aspherics coordinate system σ and the axial symmetry aspherics coordinate system σ by transforming coordinates and present the computation models of asphericity in rectangular coordinate system and cylindrical coordinate system respectively. The asphericity expressions in both coordinate systems were applicable to the comparative sphere calculation of Off-axis aspherics with different figures. We selected an Initiation sphere in view of technology, along with equations in a right coordinate system for certain caliber and structure. Then, by numerical computation, we selected the best fitting sphere and simplifed the complex models by choosing a right coordinate system. At last, the solution for asphericity and the best fitting sphere curvature radius of off-axis aspherics were introduced by examples.

Determination of plastic yield stress from spherical indentation slope curve

The indentation slope curve from a spherical indentation on elastic-plastic materials is examined. By comparing it with that of an linear elastic material of the same elastic properties, we found that the start point of plastic yielding for an elastic-plastic material can be easily located from the indentation slope curve. Based on this analysis, a simple but effective method is proposed to measure the plastic yield stress of very small samples from a spherical nano-indentation slope curve.

A Characteristic of Spherical Indentation Curve and its Application in Measuring Material Properties

The spherical indentation obeys Hertz contact theory when the applied load is within the elastic limit. Once the applied load is over the elastic limit, the indentation curve starts to deviate from the original purely elastic indentation curve. This deviation point, which indicates the start of the nonlinear deformation, is an important characteristic of a spherical indentation curve. The indentation force corresponding to the deviation point is related to a basic material constant, which is the yield stress for an elastic-plastic material or the transformation stress for a shape memory alloy. This relationship can be applied to measure the yield stress or the transformation stress from a simple spherical indentation curve. Detailed discussion on the relationship and the method is presented in this short paper.

On Rectifying Dual Space Curves

We give some characterizations of the rectifying curves in the dual space and show that rectifying dual space curves can be stated with the aid of dual unit spherical curves. Thus, we have a link between rectifying dual space curves and classical surfaces in the Euclidean three-space.

A CHARACTERIZATION OF DUAL LORENTZIAN SPHERICAL CURVES IN THE DUAL LORENTZIAN SPACE

A differential equation characterizing the dual Lorentzian spherical curves and an explicit solution of this differential equation are given. Also, without the precondition on the dual torsion is nowhere pure-dual, a necessary and sufficient condition for a curve to be dual Lorentzian spherical is presented. In addition, thanks to dual geodesic trihedron, torsion and curvature of dual Lorentzian curve $\overset{\rightarrow}{\hat{x}(s)}$ have been calculated.

Holographic confinement/deconfinement phase transitions of AdS/QCD in curved spaces

Recently Herzog has shown that deconfinement of AdS/QCD can be realized, in the hard-wall model where the small radius region is removed in the asymptotically AdS space, via a first order Hawking-Page phase transition between a low temperature phase given by a pure AdS geometry and a high temperature phase given by the AdS black hole in Poincare coordinates. In this paper we first extend Herzog's work to the hard wall AdS/QCD model in curved spaces by studying the thermodynamics of AdS black holes with spherical or negative constant curvature horizon, dual to a non-supersymmetric Yang-Mills theory on a sphere or hyperboloid respectively. For the spherical horizon case, we find that the temperature of the phase transition increases by introducing an infrared cutoff, compared to the case without the cutoff; For the hyperbolic horizon case, there is a gap for the infrared cutoff, below which the Hawking-Page phase transition does not occur. We also discuss charged AdS black holes in the grand canonical ensemble, corresponding to a Yang-Mills theory at finite chemical potential, and find that there is always a gap for the infrared cutoff due to the existence of a minimal horizon for the charged AdS black holes with any horizon topology.

Specifics of the design of the optical system of an astrograph for the Interplanetary Solar Stereoscopic Observatory Project

The requirements on the optical system of the astrograph for the Interplanetary Solar Stereoscopic Observatory are determined. Versions of orthoscopic optical systems of telescope objectives are considered, and a technique is presented for designing three-mirror objectives with corrected spherical aberration, coma, astigmatism, image curvature, and distortion. Screening in the resulting systems is determined. The results of a design of the astrograph with a focal length of 5 m, an f number of 10, and an angular field in object space of 1° are presented as an example.

On the stability index of hypersurfaces with constant mean curvature in spheres

In (2) Barbosa, do Carmo and Eschenburg characterized the to- tally umbilical spheres as the only weakly stable compact constant mean cur- vature hypersurfaces in the Euclidean sphere Sn+1. In this paper we prove that the weak index of any other compact constant mean curvature hyper- surface Mn in Sn+1 which is not totally umbilical and has constant scalar curvature is greater or equal to n + 2, with equality if and only if M is a constant mean curvature Cliord torus

Structure reconstruction with Ewald sphere curvature considerations

An approach is proposed to determine the structure of a three-dimensional non-crystallineobject from a single two-dimensional x-ray scattering image. If x-ray absorption is ignored,this method, unlike what has been reported in the literature, always generates a structureof real electron density, even in the case that the Ewald sphere curvature is large. Inaddition, if the original object is thin, the reconstructed object is the integrated electrondensity of the original one along a path which makes an angle with the incoming x-rays(z-axis) in proportion to the maximum x-ray wavevector transfer magnitude along the axis,revealing the object’s depth information. It is demonstrated mathematically that the blursor ripples associated with a reconstructed object are due to a resolution function effect.Reconstructed structures of a hypothetical three-dimensional object are shown to agreewith the theoretical predictions.

Spherical submanifolds in a Euclidean space

In this paper, we are interested in extending the study of spherical curves in R3 to the submanifolds in the Euclidean space Rn+p. More precisely, we are interested in obtaining conditions under which an n-dimensional compact submanifold M of a Euclidean space Rn+p lies on the hypersphere Sn+p−1(c) (standardly imbedded sphere in Rn+p of constant curvature c). As a by-product we also get an estimate on the first nonzero eigenvalue of the Laplacian operator Δ of the submanifold (cf. Theorem 3.5) as well as a characterization for an n-dimensional sphere Sn(c) (cf. Theorem 4.1).

실안의 수정체 굴절률 분포를 갖는 정밀모형안 설계

젊은 한국인 정시안에 대한 임상 자료를 가지고 구면수차 이외에 비축수차인 비점수차, 상면만곡과 왜곡수차들을 포함하는 실안의 광학적 성능과 유사한 정밀모형안을 설계하였다. 또한 수정체가 갖는 Gradient index 형태의 매질을 광학적으로 조사하였고, GRIN 매질을 수정체에 도입하여 정밀모형안을 설계하였다. In this study, clinical data for emmetopia in young Koreans was taken in order to design the finite schematic eye, which had optical properties of real eyes including spherical aberration, astigmatism, field curvature and distortion. Furthermore, the crystalline lens with GRIN medium was optically analyzed, and the finite schematic eye with the GRIN crystalline lens was designed.

Constructing spherical curves by interpolation

Based on a composite conical surface patch, we develop new simple methods for up to G 2 continuous interpolation of an arbitrary sequence of points on a sphere with a specified tangent direction and curvature vector at every point. The resulting interpolation curve is the intersection of the given sphere and the composite conical surface patch. Unlike some existing methods, introduced into the method are several free parameters that can be used in subsequent interactive modification such that the resulting curve’s shape hits our demand, and the resulting curve can be expressed explicitly. Experiments demonstrate the method is effective and potentially useful in pattern design on sphere, sphere trim, robot, and other industrial and research fields.

Communication modes in large-aperture approximation

Simplified versions of the communication modes in the Fresnel domain are derived when the system apertures are large. The approximate modes, which are in the form of spherical waves and sinc functions with a spherical curvature, give physical insight into the communication modes approach and the basic limits of free-space optical communication systems. They also show that Gabor's information theory is readily derived from the communication modes.

Medindo o poder refrativo de lentes de contato gelatinosas personalizadas

Soft contact lenses with spherical base curves have been used for many years. The computation of the refractive powers of these lenses is easy, requiring only that one uses the lens maker equation for thick lenses. Nevertheless, for customized contact lenses, there is yet no reliable method for measuring the higher order optical aberrations. In this study we have developed in the Center for Visual Sciences of the University of Rochester an optical apparatus that allows for precise measurement of low and high order aberrations of customized soft contact lenses. An optical apparatus was mounted on a conventional optical bench. This apparatus consists of a wet cell where the contact lenses are placed, a series of relay lenses, mirrors, beam splitters, and a Hartmann-Shack sensor. Bausch & Lomb manufactured the lenses used in this study. The root mean square error (RMSE) of the instrument was 0.04 microns. Given that the RMSE of the customized lens is between 4 and 6 microns, i.e., the precision of the instrument is approximately 1%. This precision is more than sufficient for the type of measurements necessary for manufacturing customized contact lenses. The instrument developed is extremely precise for measuring high order aberrations--up to the 10th order Zernike polynomials, that is, up to the 66th term. This technology is important for the development of new methods of optical corrections for patients that usually do not adapt to normal sphere-cylinder spectacles or that cannot undergo refractive surgery, such as those which have keratoconus, for example.

A CHARACTERIZATION OF DUAL LORENTZIAN SPHERICAL CURVES IN THE DUAL LORENTZIAN SPACE

A differential equation characterizing the dual Lorentzian spherical curves and an explicit solution of this differential equation are given. Also, without the precondition on the dual torsion is nowhere pure-dual, a necessary and sufficient condition for a curve to be dual Lorentzian spherical is presented. In addition, thanks to dual geodesic trihedron, torsion and curvature of dual Lorentzian curve $\overset{\rightarrow }{\hat{x}(s)}$ have been calculated.

First order hermite interpolation with spherical Pythagorean-hodograph curves

The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the Pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatialC1 Hermite data, we construct a spatial PH curve on a sphere that is aC1 Hermite interpolant of the given data as follows: First, we solveC1 Hermite interpolation problem for the stereographically projected planar data of the given data in ℝ3 with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in ℝ3 using the inverse general stereographic projection.

On areas of regions bounded by closed Lorentz spherical curves

On areas of regions bounded by closed Lorentz spherical curves

Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves

We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane $\boldsymbol{C}^2$ by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in terms of simple properties of the curvature of the generating curves. As applications, we provide explicitly conformal parametrizations of known and new examples of minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in $\boldsymbol{C}^2$.