Structured eigenvalue problems for rational gauss quadrature
NASA Astrophysics Data System (ADS)
Fasino, Dario; Gemignani, Luca
2007-08-01
The connection between Gauss quadrature rules and the algebraic eigenvalue problem for a Jacobi matrix was first exploited in the now classical paper by Golub and Welsch (Math. Comput. 23(106), 221?230, 1969). From then on many computational problems arising in the construction of (polynomial) Gauss quadrature formulas have been reduced to solving direct and inverse eigenvalue problems for symmetric tridiagonals. Over the last few years (rational) generalizations of the classical Gauss quadrature formulas have been studied, i.e., formulas integrating exactly in spaces of rational functions. This paper wants to illustrate that stable and efficient procedures based on structured numerical linear algebra techniques can also be devised for the solution of the eigenvalue problems arising in the field of rational Gauss quadrature.
Composite Gauss-Legendre Quadrature with Error Control
ERIC Educational Resources Information Center
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
Two-frequency-dependent Gauss quadrature rules
NASA Astrophysics Data System (ADS)
Kim, Kyung Joong
2005-02-01
We construct two-frequency-dependent Gauss quadrature rules which can be applied for approximating the integration of the product of two oscillatory functions with different frequencies [beta]1 and [beta]2 of the forms,yi(x)=fi,1(x) cos([beta]ix)+fi,2(x) sin([beta]ix), i=1,2,where the functions fi,j(x) are smooth. A regularization procedure is presented to avoid the singularity of the Jacobian matrix of nonlinear system of equations which is induced as one frequency approaches the other frequency. We provide numerical results to compare the accuracy of the classical Gauss rule and one- and two-frequency-dependent rules.
Gauss Legendre Quadrature Formulae for Tetrahedra
NASA Astrophysics Data System (ADS)
Rathod, H. T.; Venkatesudu, B.; Nagaraja, K. V.
2005-09-01
In this paper we consider the Gauss Legendre quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)|0 = x, y, z = 1, x + y + z = 1} in the Cartesian three-dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (?, ?, ?) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2-cube: {(?, ?, ?)| - 1 = ?, ?,? = 1} in the (?, ?, ?) space. This overcomes the difficulties associated with the derivation of new weight co-efficients and sampling points. The effectiveness of the formulae is demonstrated by applying them to the integration of three nonpolynomial and three polynomial functions.
Gauss Quadratures - the Keystone of Lattice Boltzmann Models
NASA Astrophysics Data System (ADS)
Piaud, Benjamin; Blanco, Stéphane; Fournier, Richard; Ambruş, Victor Eugen; Sofonea, Victor
2014-01-01
In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss-Hermite quadrature. The second one is the SLB(N;K,L,M) family, derived by using the spherical coordinate system and the Gauss-Laguerre, as well as the Gauss-Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.
Gauss-Laguerre interval quadrature rule
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Cvetkovic, Aleksandar S.
2005-10-01
In this paper we prove the existence and uniqueness of the Gaussian interval quadrature formula with respect to the generalized Laguerre weight function. An algorithm for numerical construction has also investigated and some suitable solutions are proposed. A few numerical examples are included.
Some new applications of truncated Gauss-Laguerre quadrature formulas
NASA Astrophysics Data System (ADS)
Mastroianni, G.; Monegato, G.
2008-12-01
We show how truncated Gauss-Laguerre quadrature formulas can be used to produce accurate approximations and high rates of convergence, also when they are applied to integrand functions having only an algebraic type decay to zero at infinity. The approach presented in the paper is proposed for the computation of integrals and for the construction of Nyström type interpolants for some second kind integral equations.
On the remainder term of Gauss-Radau quadratures for analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2008-09-01
For analytic functions the remainder term of Gauss-Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ±1 and a sum of semi-axes [varrho]>1 for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209-226] is proved.
Error analysis in some Gauss-Turan-Radau and Gauss-Turan-Lobatto quadratures for analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.
2004-03-01
We consider the generalized Gauss-Turan quadrature formulae of Radau and Lobatto type for approximating . The aim of this paper is to analyze the remainder term in the case when f is an analytic function in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses (cf. SIAM J. Numer. Anal. 80 (1983) 1170). Sufficient conditions on the convergence for some of such quadratures, associated with the generalized Chebyshev weight functions, are found. Using some ideas from Hunter (BIT 35 (1995) 64) we obtain new estimates of the remainder term, which are very exact. Some numerical results and illustrations are shown.
A note on the bounds of the error of Gauss-Turan-type quadratures
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.
2007-03-01
This note is concerned with estimates for the remainder term of the Gauss-Turan quadrature formula,where is the Gori-Michelli weight function, with Un-1(t) denoting the (n-1)th degree Chebyshev polynomial of the second kind, and f is a function analytic in the interior of and continuous on the boundary of an ellipse with foci at the points +/-1 and sum of semiaxes [varrho]>1. The present paper generalizes the results in [G.V. Milovanovic, M.M. Spalevic, Bounds of the error of Gauss-Turan-type quadratures, J. Comput. Appl. Math. 178 (2005) 333-346], which is concerned with the same problem when s=1.
Rational Gauss-Chebyshev quadrature formulas for complex poles outside [-1,1
NASA Astrophysics Data System (ADS)
Deckers, Karl; van Deun, Joris; Bultheel, Adhemar
2008-06-01
In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [-1,1] to arbitrary complex poles outside [-1,1] . The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside [-1,1] .
Variable transformations and Gauss-Legendre quadrature for integrals with endpoint singularities
NASA Astrophysics Data System (ADS)
Sidi, Avram
2009-09-01
Gauss-Legendre quadrature formulas have excellent convergence properties when applied to integrals int^1_0f(x) dx with fin C^infty[0,1] . However, their performance deteriorates when the integrands f(x) are in C^infty(0,1) but are singular at x=0 and/or x=1 . One way of improving the performance of Gauss-Legendre quadrature in such cases is by combining it with a suitable variable transformation such that the transformed integrand has weaker singularities than those of f(x) . Thus, if x=psi(t) is a variable transformation that maps [0,1] onto itself, we apply Gauss-Legendre quadrature to the transformed integral int^1_{0}f(psi(t))psi'(t) dt , whose singularities at t=0 and/or t=1 are weaker than those of f(x) at x=0 and/or x=1 . In this work, we first define a new class of variable transformations we denote widetilde{mathcal{S}}_{p,q} , where p and q are two positive parameters that characterize it. We also give a simple and easily computable representative of this class. Next, by invoking some recent results by the author concerning asymptotic expansions of Gauss-Legendre quadrature approximations as the number of abscissas tends to infinity, we present a thorough study of convergence of the combined approximation procedure, with variable transformations from widetilde{mathcal{S}}_{p,q} . We show how optimal results can be obtained by adjusting the parameters p and q of the variable transformation in an appropriate fashion. We also give numerical examples that confirm the theoretical results.
The generation of arbitrary order, non-classical, Gauss-type quadrature for transport applications
Spence, Peter J.
2015-09-01
A method is presented, based upon the Stieltjes method (1884), for the determination of non-classical Gauss-type quadrature rules, and the associated sets of abscissae and weights. The method is then used to generate a number of quadrature sets, to arbitrary order, which are primarily aimed at deterministic transport calculations. The quadrature rules and sets detailed include arbitrary order reproductions of those presented by Abu-Shumays in [4,8] (known as the QR sets, but labelled QRA here), in addition to a number of new rules and associated sets; these are generated in a similar way, and we label them the QRS quadrature sets. The method presented here shifts the inherent difficulty (encountered by Abu-Shumays) associated with solving the non-linear moment equations, particular to the required quadrature rule, to one of the determination of non-classical weight functions and the subsequent calculation of various associated inner products. Once a quadrature rule has been written in a standard form, with an associated weight function having been identified, the calculation of the required inner products is achieved using specific variable transformations, in addition to the use of rapid, highly accurate quadrature suited to this purpose. The associated non-classical Gauss quadrature sets can then be determined, and this can be done to any order very rapidly. In this paper, instead of listing weights and abscissae for the different quadrature sets detailed (of which there are a number), the MATLAB code written to generate them is included as Appendix D. The accuracy and efficacy (in a transport setting) of the quadrature sets presented is not tested in this paper (although the accuracy of the QRA quadrature sets has been studied in [12,13]), but comparisons to tabulated results listed in [8] are made. When comparisons are made with one of the azimuthal QRA sets detailed in [8], the inherent difficulty in the method of generation, used there, becomes apparent
Maximum of the modulus of kernels in Gauss-Turan quadratures
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2008-06-01
We study the kernels K_{n,s}(z) in the remainder terms R_{n,s}(f) of the Gauss-Turan quadrature formulae for analytic functions on elliptical contours with foci at pm 1 , when the weight omega is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel \\vert K_{n,s}(z)\\vert attains its maximum on the real axis (positive real semi-axis) for each ngeq n_0, n_0Dn_0(rho,s) . It was stated as a conjecture in [Mathematics of Computation 72 (2003), 1855-1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes n in the corresponding Gauss-Turan quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each ngeq n_0, n_0Dn_0(rho,s) . Numerical examples are included. Retrieve articles in all Journals with MSC (1991): [41]41A55, [42]65D30, [43]65D32
Spherical-earth gravity and magnetic anomaly modeling by Gauss-Legendre quadrature integration
NASA Technical Reports Server (NTRS)
Von Frese, R. R. B.; Hinze, W. J.; Braile, L. W.; Luca, A. J.
1981-01-01
Gauss-Legendre quadrature integration is used to calculate the anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical earth. The procedure involves representation of the anomalous source as a distribution of equivalent point gravity poles or point magnetic dipoles. The distribution of equivalent point sources is determined directly from the volume limits of the anomalous body. The variable limits of integration for an arbitrarily shaped body are obtained from interpolations performed on a set of body points which approximate the body's surface envelope. The versatility of the method is shown by its ability to treat physical property variations within the source volume as well as variable magnetic fields over the source and observation surface. Examples are provided which illustrate the capabilities of the technique, including a preliminary modeling of potential field signatures for the Mississippi embayment crustal structure at 450 km.
Generation of fast neturon spectra using an adaptive Gauss-Kronrod Quadrature algorithm
NASA Astrophysics Data System (ADS)
Triplett, Brian Scott
A lattice physics calculation is often the first step in analyzing a nuclear reactor. This calculation condenses regions of the reactor into average parameters (i.e., group constants) that can be used in coarser full-core, time-dependent calculations. This work presents a high-fidelity deterministic method for calculating the neutron energy spectrum in an infinite medium. The spectrum resulting from this calculation can be used to generate accurate group constants. This method includes a numerical algorithm based on Gauss-Kronrod Quadrature to determine the neutron transfer source to a given energy while controlling numerical error. This algorithm was implemented in a pointwise transport solver program called Pointwise Fast Spectrum Generator (PWFSG). PWFSG was benchmarked against the Monte Carlo program MCNP and another pointwise spectrum generation program, CENTRM, for a set of fast reactor infinite medium example cases. PWFSG showed good agreement with MCNP, yielding coefficients of determination above 98% for all example cases. In addition, PWFSG had 6 to 8 times lower flux estimation error than CENTRM in the cases examined. With run-times comparable to CENTRM, PWFSG represents a robust set of methods for generation of fast neutron spectra with increased accuracy without increased computational cost.
Complete gravity field of an ellipsoidal prism by Gauss-Legendre quadrature
NASA Astrophysics Data System (ADS)
Roussel, C.; Verdun, J.; Cali, J.; Masson, F.
2015-12-01
The increasing availability of geophysical models of the Earth's lithosphere and mantle has generated renewed interest in computation of theoretical gravity effects at global and regional scales. At the same time, the increasing availability of gravity gradient anomalies derived from satellite measurements, such as those provided by GOCE satellite, requires mathematical methods that directly model the gravity gradient anomalies in the same reference frame as GOCE gravity gradients. Our main purpose is to interpret these anomalies in terms of source and density distribution. Numerical integration methods for calculating gravity gradient values are generally based on a mass discretization obtained by decomposing the Earth's layers into a finite number of elementary solid bodies. In order to take into account the curvature of the Earth, spherical prisms or `tesseroids' have been established unequivocally as accurate computation tools for determining the gravitational effects of large-scale structures. The question which then arises from, is whether gravity calculation methods using spherical prisms remain valid when factoring in the ellipticity of the Earth. In the paper, we outline a comprehensive method to numerically compute the complete gravity field with the help of the Gauss-Legendre quadrature involving ellipsoidal shaped prisms. The assessment of this new method is conducted by comparison between the gravity gradient values of simple sources obtained by means of numerical and analytical calculations, respectively. A comparison of the gravity gradients obtained from PREM and LITHO1.0 models using spherical- and ellipsoidal-prism-based methods is also presented. Numerical results indicate that the error on gravity gradients, caused by the use of the spherical prism instead of its ellipsoidal counterpart to describe an ellipsoidally shaped Earth, is useful for a joint analysis with those deduced from GOCE satellite measurements. Provided that a suitable scaling
NASA Astrophysics Data System (ADS)
Gorbachev, D. V.; Ivanov, V. I.
2015-08-01
Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles.
Sainath, Kamalesh; Teixeira, Fernando L
2014-05-01
We discuss the application of complex-plane Gauss-Laguerre quadrature (CGLQ) to efficiently evaluate two-dimensional Fourier integrals arising as the solution to electromagnetic fields radiated by elementary dipole antennas embedded within planar-layered media exhibiting arbitrary material parameters. More specifically, we apply CGLQ to the long-standing problem of rapidly and efficiently evaluating the semi-infinite length "tails" of the Fourier integral path while simultaneously and robustly guaranteeing absolute, exponential convergence of the field solution despite diversity in the doubly anisotropic layer parameters, source type (i.e., electric or equivalent magnetic dipole), source orientation, observed field type (magnetic or electric), (nonzero) frequency, and (nonzero) source-observer separation geometry. The proposed algorithm exhibits robustness despite unique challenges arising for the fast evaluation of such two-dimensional integrals. Herein we develop the mathematical treatment to rigorously evaluate the tail integrals using CGLQ, as well as discuss and address the specific issues posed to the CGLQ method when anisotropic, layered media are present. To empirically demonstrate the CGLQ algorithm's computational efficiency, versatility, and accuracy, we perform a convergence analysis along with two case studies related to modeling of electromagnetic resistivity tools employed in geophysical prospection of layered, anisotropic Earth media and validating the ability of isoimpedance substrates to enhance the radiation performance of planar antennas placed in close proximity to metallic ground planes. PMID:25353911
Characterizing curves satisfying the Gauss-Christoffel theorem
NASA Astrophysics Data System (ADS)
Berriochoa, E.; Cachafeiro, A.
2009-12-01
In this paper we obtain the reciprocal of the classical Gauss theorem for quadrature formulas. Indeed we characterize the support of the measures having quadrature formulas with the exactness given in the Gauss theorem.
Positive quadrature formulas III
NASA Astrophysics Data System (ADS)
Peherstorfer, Franz
2008-12-01
First we discuss briefly our former characterization theorem for positive interpolation quadrature formulas (abbreviated qf), provide an equivalent characterization in terms of Jacobi matrices, and give links and applications to other qf, in particular to Gauss-Kronrod quadratures and recent rediscoveries. Then for any polynomial t_n which generates a positive qf, a weight function (depending on n ) is given with respect to which t_n is orthogonal to mathbb{P}_{n-1} . With the help of this result an asymptotic representation of the quadrature weights is derived. In general the asymptotic behaviour is different from that of the Gaussian weights. Only under additional conditions do the quadrature weights satisfy the so-called circle law. Corresponding results are obtained for positive qf of Radau and Lobatto type.
NASA Astrophysics Data System (ADS)
Rexer, Moritz; Hirt, Christian
2015-11-01
In geodesy and geophysics, spherical harmonic techniques are popular for modelling topography and potential fields with ever-increasing spatial resolution. For ultra-high-degree spherical harmonic modelling, i.e. degree 10,000 or more, classical algorithms need to be extended to avoid under- or overflow problems associated with the computation of associated Legendre functions (ALFs). In this work, two quadrature algorithms—the Gauss-Legendre (GL) quadrature and the quadrature following Driscoll/Healy (DH)—and their implementation for the purpose of ultra-high (surface) spherical harmonic analysis of spheroid functions are reviewed and modified for application to ultra-high degree. We extend the implementation of the algorithms in the SHTOOLS software package (v2.8) by (1) the X-number (or Extended Range Arithmetic) method for accurate computation of ALFs and (2) OpenMP directives enabling parallel processing within the analysis. Our modifications are shown to achieve feasible computation times and a very high precision: a degree-21,600 band-limited (=frequency limited) spheroid topographic function may be harmonically analysed with a maximum space-domain error of 3 × 10^{-5} and 5 × 10^{-5} m in 6 and 17 h using 14 CPUs for the GL and for the DH quadrature, respectively. While not being inferior in terms of precision, the GL quadrature outperforms the DH algorithm in terms of computation time. In the second part of the paper, we apply the modified quadrature algorithm to represent for—the first time—gridded topography models for Earth, Moon and Mars as ultra-high-degree series expansions comprising more than 2 billion coefficients. For the Earth's topography, we achieve a resolution of harmonic degree 43,200 (equivalent to 500 m in the space domain), for the Moon of degree 46,080 (equivalent to 120 m) and Mars to degree 23,040 (equivalent to 460 m). For the quality of the representation of the topographic functions in spherical harmonics, we use the
Error Bounds for Quadrature Methods Involving Lower Order Derivatives
ERIC Educational Resources Information Center
Engelbrecht, Johann; Fedotov, Igor; Fedotova, Tanya; Harding, Ansie
2003-01-01
Quadrature methods for approximating the definite integral of a function f(t) over an interval [a,b] are in common use. Examples of such methods are the Newton-Cotes formulas (midpoint, trapezoidal and Simpson methods etc.) and the Gauss-Legendre quadrature rules, to name two types of quadrature. Error bounds for these approximations involve…
Quadrature, Interpolation and Observability
NASA Technical Reports Server (NTRS)
Hodges, Lucille McDaniel
1997-01-01
Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method to certain non-polynomial functions as early as 1884. Conditions that guarantee the existence of quadrature formulas for certain collections of functions were studied by Tchebycheff, and his work was extended by others. Today, a class of functions which satisfies these conditions is called a Tchebycheff System. This thesis contains the definition of a Tchebycheff System, along with the theorems, proofs, and definitions necessary to guarantee the existence of quadrature formulas for such systems. Solutions of discretely observable linear control systems are of particular interest, and observability with respect to a given output function is defined. The output function is written as a linear combination of a collection of orthonormal functions. Orthonormal functions are defined, and their properties are discussed. The technique for evaluating the coefficients in the output function involves evaluating the definite integral of functions which can be shown to form a Tchebycheff system. Therefore, quadrature formulas for these integrals exist, and in many cases are known. The technique given is useful in cases where the method of direct calculation is unstable. The condition number of a matrix is defined and shown to be an indication of the the degree to which perturbations in data affect the accuracy of the solution. In special cases, the number of data points required for direct calculation is the same as the number required by the method presented in this thesis. But the method is shown to require more data points in other cases. A lower bound for the number of data points required is given.
On Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae
NASA Astrophysics Data System (ADS)
Joulak, Hédi; Beckermann, Bernhard
2009-12-01
Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the present note we show the positivity of the corresponding weights; this positivity has been conjectured already by Gautschi. As a consequence, we establish several convergence theorems for these quadrature formulae.
NASA Astrophysics Data System (ADS)
Gautschi, Walter
2009-06-01
The generation of generalized Gauss-Radau and Gauss-Lobatto quadrature formulae by methods developed by us earlier breaks down in the case of Jacobi and Laguerre measures when the order of the quadrature rules becomes very large. The reason for this is underflow resp. overflow of the respective monic orthogonal polynomials. By rescaling of the polynomials, and other corrective measures, the problem can be circumvented, and formulae can be generated of orders as high as 1,000.
Exponential fitting quadrature rule for functional equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Paternoster, B.; Santomauro, G.
2012-09-01
A Gaussian quadrature rule for periodic integrand function is presented. The weights and nodes depend on the frequency of the problem and they are constructed by following the exponential fitting theory. The composite rule based on this formula is derived. The analysis of the error is carried out and it proves that the exponentially fitted Gaussian rule is more accurate than the classical Gauss-Legendre rule when oscillatory functions are treated. Some numerical tests are presented.
Orthogonal rational functions and quadrature on an interval
NASA Astrophysics Data System (ADS)
van Deun, J.; Bultheel, A.
2003-04-01
Rational functions with real poles and poles in the complex lower half-plane, orthogonal on the real line, are well known. Quadrature formulas similar to the Gauss formulas for orthogonal polynomials have been studied. We generalize to the case of arbitrary complex poles and study orthogonality on a finite interval. The zeros of the orthogonal rational functions are shown to satisfy a quadratic eigenvalue problem. In the case of real poles, these zeros are used as nodes in the quadrature formulas.
Uniform positive-weight quadratures for discrete ordinate transport calculations
Carew, J.F.; Zamonsky, G.
1999-02-01
Mechanical quadratures that allow systematic improvement and solution convergence are derived for application of the discrete ordinates method to the Boltzmann transport equation. the quadrature directions are arranged on n latitudinal levels, are uniformly distributed over the unit sphere, and have positive weights. Both a uniform and equal-weight quadrature set UE{sub n} and a uniform and Gauss-weight quadrature set UG{sub n} are derived. These quadratures have the advantage over the standard level-symmetric LQ{sub n} quadrature sets in that the weights are positive for all orders, and the solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased the points approach a uniform continuous distribution on the unit sphere and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased. Numerical calculations were performed to evaluate the application of the UE{sub n} quadrature set. Comparisons of the exact moments and those calculated using the UE{sub n} quadrature set demonstrate that the moment integrals are performed accurately except for distributions that are very sharply peaked along the direction of the polar axis. A series of DORT transport calculations of the >1-Mev neutron flux for a typical reactor core/pressure vessel geometry were also carried out. These calculations employed the UE{sub n} (n = 6, 10, 12, 18, and 24) quadratures and indicate that the UE{sub n} solutions have converged to within {approximately}0.5%. The UE{sub 24} solutions were also found to be more accurate than the calculations performed with the S{sub 16} level-symmetric quadratures.
ERIC Educational Resources Information Center
Rice, Kathryn; Scott, Paul
2005-01-01
This article presents a brief biography of Johann Carl Friedrich Gauss. Gauss was born on April 30, 1777, in the German city of Braunschweig (Brunswick). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze. Neither of Gauss's parents had much education, his father could read and write, but earned his living doing menial jobs such as…
NASA Astrophysics Data System (ADS)
Čársky, Petr
2010-09-01
The UGU term was used as a model of the UGT term, and its evaluation by numerical quadrature was examined systematically with a training set of eight molecules. Minimum numbers of points have been determined for radial Gauss-Legendre and angular Lebedev quadratures that preserve the accuracy needed for practical applications. These quadratures are recommended for efficient calculation of electron scattering by polyatomic molecules.
The development of accurate and efficient methods of numerical quadrature
NASA Technical Reports Server (NTRS)
Feagin, T.
1973-01-01
Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.
NASA Astrophysics Data System (ADS)
Evans, W. A. B.; Torre, A.
2012-11-01
The paper focusses on the advantages of using high-order Gauss-Legendre quadratures for the precise evaluation of integrals with both smooth and rapidly changing integrands. Aspects of their precision are analysed in the light of Gauss' error formula. Some "test examples" are considered and evaluated in multiple precision to ≈ 200 significant decimal digits with David Bailey's multiprecision package to eliminate truncation/rounding errors. The increase of precision on doubling the number of subintervals is analysed, the relevant quadrature attribute being the precision increment. In order to exemplify the advantages that high-order quadrature afford, the technique is then used to evaluate several plots of the Rayleigh-Sommerfeld diffraction integral for axi-symmetric source fields defined on a planar aperture. A comparison of the high-order quadrature method against various FFT-based methods is finally given.
Buchenauer, C. Jerald
1984-01-01
The quadrature phase angle .phi.(t) of a pair of quadrature signals S.sub.1 (t) and S.sub.2 (t) is digitally encoded on a real time basis by a quadrature digitizer for fractional .phi.(t) rotational excursions and by a quadrature up/down counter for full .phi.(t) rotations. The pair of quadrature signals are of the form S.sub.1 (t)=k(t) sin .phi.(t) and S.sub.2 (t)=k(t) cos .phi.(t) where k(t) is a signal common to both. The quadrature digitizer and the quadrature up/down counter may be used together or singularly as desired or required. Optionally, a digital-to-analog converter may follow the outputs of the quadrature digitizer and the quadrature up/down counter to provide an analog signal output of the quadrature phase angle .phi.(t).
Buchenauer, C.J.
1981-09-23
The quadrature phase angle phi (t) of a pair of quadrature signals S/sub 1/(t) and S/sub 2/(t) is digitally encoded on a real time basis by a quadrature digitizer for fractional phi (t) rotational excursions and by a quadrature up/down counter for full phi (t) rotations. The pair of quadrature signals are of the form S/sub 1/(t) = k(t) sin phi (t) and S/sub 2/(t) = k(t) cos phi (t) where k(t) is a signal common to both. The quadrature digitizer and the quadrature up/down counter may be used together or singularly as desired or required. Optionally, a digital-to-analog converter may follow the outputs of the quadrature digitizer and the quadrature up/down counter to provide an analog signal output of the quadrature phase angle phi (t).
Gauss-Green cubature and moment computation over arbitrary geometries
NASA Astrophysics Data System (ADS)
Sommariva, Alvise; Vianello, Marco
2009-09-01
We have implemented in Matlab a Gauss-like cubature formula over arbitrary bivariate domains with a piecewise regular boundary, which is tracked by splines of maximum degree p (spline curvilinear polygons). The formula is exact for polynomials of degree at most 2n-1 using N~cmn2 nodes, 1<=c<=p, m being the total number of points given on the boundary. It does not need any decomposition of the domain, but relies directly on univariate Gauss-Legendre quadrature via Green's integral formula. Several numerical tests are presented, including computation of standard as well as orthogonal moments over a nonstandard planar region.
Quadrature Mixer LO Leakage Suppression Through Quadrature DC Bias
BALDWIN, JESSE G; DUBBERT, DALE F.
2002-05-01
A new concept has been developed which allows direct-to-RF conversion of digitally synthesized waveforms. The concept named Quadrature Error Corrected Digital Waveform Synthesis (QECDWS) employs quadrature amplitude and phase predistortion to the complex waveform to reduce the undesirable quadrature image. Another undesirable product of QECDWS-based RF conversion is the Local Oscillator (LO) leakage through the quadrature upconverter (mixer). A common technique for reducing this LO leakage is to apply a quadrature bias to the mixer I and Q inputs. This report analyzes this technique through theory, lab measurement, and data analysis for a candidate quadrature mixer for Synthetic Aperture Radar (SAR) applications.
Quadrature wavelength scanning interferometry.
Moschetti, Giuseppe; Forbes, Alistair; Leach, Richard K; Jiang, Xiang; O'Connor, Daniel
2016-07-10
A novel method to double the measurement range of wavelength scanning interferometery (WSI) is described. In WSI the measured optical path difference (OPD) is affected by a sign ambiguity, that is, from an interference signal it is not possible to distinguish whether the OPD is positive or negative. The sign ambiguity can be resolved by measuring an interference signal in quadrature. A method to obtain a quadrature interference signal for WSI is described, and a theoretical analysis of the advantages is reported. Simulations of the advantages of the technique and of signal errors due to nonideal quadrature are discussed. The analysis and simulation are supported by experimental measurements to show the improved performances. PMID:27409307
NASA Astrophysics Data System (ADS)
Monien, H.
2010-04-01
Gaussian quadrature is a well-known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums has found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of Gaussian formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a kink singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has a very rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters.
NASA Astrophysics Data System (ADS)
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Discrete Ordinate Quadrature Selection for Reactor-based Eigenvalue Problems
Jarrell, Joshua J; Evans, Thomas M; Davidson, Gregory G
2013-01-01
In this paper we analyze the effect of various quadrature sets on the eigenvalues of several reactor-based problems, including a two-dimensional (2D) fuel pin, a 2D lattice of fuel pins, and a three-dimensional (3D) reactor core problem. While many quadrature sets have been applied to neutral particle discrete ordinate transport calculations, the Level Symmetric (LS) and the Gauss-Chebyshev product (GC) sets are the most widely used in production-level reactor simulations. Other quadrature sets, such as Quadruple Range (QR) sets, have been shown to be more accurate in shielding applications. In this paper, we compare the LS, GC, QR, and the recently developed linear-discontinuous finite element (LDFE) sets, as well as give a brief overview of other proposed quadrature sets. We show that, for a given number of angles, the QR sets are more accurate than the LS and GC in all types of reactor problems analyzed (2D and 3D). We also show that the LDFE sets are more accurate than the LS and GC sets for these problems. We conclude that, for problems where tens to hundreds of quadrature points (directions) per octant are appropriate, QR sets should regularly be used because they have similar integration properties as the LS and GC sets, have no noticeable impact on the speed of convergence of the solution when compared with other quadrature sets, and yield more accurate results. We note that, for very high-order scattering problems, the QR sets exactly integrate fewer angular flux moments over the unit sphere than the GC sets. The effects of those inexact integrations have yet to be analyzed. We also note that the LDFE sets only exactly integrate the zeroth and first angular flux moments. Pin power comparisons and analyses are not included in this paper and are left for future work.
On a quadrature formula of Gori and Micchelli
NASA Astrophysics Data System (ADS)
Yang, Shijun
2005-04-01
Sparked by Bojanov (J. Comput. Appl. Math. 70 (1996) 349), we provide an alternate approach to quadrature formulas based on the zeros of the Chebyshev polynomial of the first kind for any weight function w introduced and studied in Gori and Micchelli (Math. Comp. 65 (1996) 1567), thereby improving on their observations. Upon expansion of the divided differences, we obtain explicit expressions for the corresponding Cotes coefficients in Gauss-Turan quadrature formulas for and I(fTn;w) for a Gori-Micchelli weight function. It is also interesting to mention what has been neglected for about 30 years by the literature is that, as a consequence of expansion of the divided differences in the special case when , the solution of the famous Turan's Problem 26 raised in 1980 was in fact implied by a result of Micchelli and Rivlin (IBM J. Res. Develop. 16 (1972) 372) in 1972. Some concluding comments are made in the final section.
Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature
Brito, K. D.; Sprague, M. A.
2012-10-01
Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for a given model size or total computation time.
Digital quadrature phase detection
Smith, James A.; Johnson, John A.
1992-01-01
A system for detecting the phase of a frequency of phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2.pi. when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2.pi. when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention.
Digital quadrature phase detection
Smith, J.A.; Johnson, J.A.
1992-05-26
A system for detecting the phase of a frequency or phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2[pi] when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2[pi] when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention. 6 figs.
An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures
NASA Astrophysics Data System (ADS)
Calabrò, F.; Corbo Esposito, A.
2009-07-01
This work is devoted to the study of quadrature rules for integration with respect to (w.r.t.) general probability measures with known moments. Automatic calculation of the Clenshaw-Curtis rules is considered and analyzed. It is shown that it is possible to construct these rules in a stable manner for quadrature w.r.t. balanced measures. In order to make a comparison Gauss rules and their stable implementation for integration w.r.t. balanced measures are recalled. Convergence rates are tested in the case of binomial measures.
Optimized quadrature surface coil designs
Kumar, Ananda; Bottomley, Paul A.
2008-01-01
Background Quadrature surface MRI/MRS detectors comprised of circular loop and figure-8 or butterfly-shaped coils offer improved signal-to-noise-ratios (SNR) compared to single surface coils, and reduced power and specific absorption rates (SAR) when used for MRI excitation. While the radius of the optimum loop coil for performing MRI at depth d in a sample is known, the optimum geometry for figure-8 and butterfly coils is not. Materials and methods The geometries of figure-8 and square butterfly detector coils that deliver the optimum SNR are determined numerically by the electromagnetic method of moments. Figure-8 and loop detectors are then combined to create SNR-optimized quadrature detectors whose theoretical and experimental SNR performance are compared with a novel quadrature detector comprised of a strip and a loop, and with two overlapped loops optimized for the same depth at 3 T. The quadrature detection efficiency and local SAR during transmission for the three quadrature configurations are analyzed and compared. Results The SNR-optimized figure-8 detector has loop radius r8 ∼ 0.6d, so r8/r0 ∼ 1.3 in an optimized quadrature detector at 3 T. The optimized butterfly coil has side length ∼ d and crossover angle of ≥ 150° at the center. Conclusions These new design rules for figure-8 and butterfly coils optimize their performance as linear and quadrature detectors. PMID:18057975
Discrete ordinates with new quadrature sets and modified source conditions
Ganguly, K.; Allen, E.J., Victory, H.D. Jr. )
1989-01-01
A major shortcoming of the discrete ordinates method with the Gauss-Legendre quadrature set is that when the number of secondaries per primary c and the order of approximation N are not too large, all the (N + 1)v (the flux being of the form exp({minus}x/v)) lie in ({minus}1,1). It is known, however, that the largest v{sub j} corresponding to the asymptotic flux is greater than unity. The Legendre polynomial used for obtaining the quadrature set is orthogonal with respect to weight unity in the range ({minus}1,1). However, the Case and Zweifel eigenfunctions derived from the exact solution of one-speed transport theory are orthogonal with respect to a complicated weight function w({mu}) and {mu} in the half-range and full-range cases, respectively. In this paper, the authors have used a set of orthogonal polynomials with respect to w ({mu}) to develop quadrature sets to be used in the discrete ordinates calculation.
Fast evaluation of quadrature formulae on the sphere
NASA Astrophysics Data System (ADS)
Keiner, Jens; Potts, Daniel
2008-03-01
Recently, a fast approximate algorithm for the evaluation of expansions in terms of standard mathrm{L}^2left(mathbb{S}^2right) -orthonormal spherical harmonics at arbitrary nodes on the sphere mathbb{S}^2 has been proposed in [S. Kunis and D. Potts. Fast spherical Fourier algorithms. JE Comput. Appl. Math., 161:75-98, 2003]. The aim of this paper is to develop a new fast algorithm for the adjoint problem which can be used to compute expansion coefficients from sampled data by means of quadrature rules. We give a formulation in matrix-vector notation and an explicit factorisation of the spherical Fourier matrix based on the former algorithm. Starting from this, we obtain the corresponding factorisation of the adjoint spherical Fourier matrix and are able to describe the associated algorithm for the adjoint transformation which can be employed to evaluate quadrature rules for arbitrary weights and nodes on the sphere. We provide results of numerical tests showing the stability of the obtained algorithm using as examples classical Gauss-Legendre and Clenshaw-Curtis quadrature rules as well as the HEALPix pixelation scheme and an equidistribution.
Numerical Quadrature and Operator Splitting in Finite Element Methods for Cardiac Electrophysiology
Krishnamoorthi, Shankarjee; Sarkar, Mainak; Klug, William S.
2015-01-01
SUMMARY We examine carefully the numerical accuracy and computational efficiency of alternative formulations of the finite-element solution procedure for the mono-domain equations of cardiac electrophysiology (EP), focusing on the interaction of spatial quadrature implementations with operator splitting, examining both nodal and Gauss quadrature methods, and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of “lumped” approximations of consistent capacitance and mass matrices. Most generally we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state-variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally we illustrate some of the physiological consequences of discretization error in EP simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce non-uniform meshes having a large distribution of element sizes. PMID:23873868
Noncoaxial Bessel-Gauss beams.
Huang, Chaohong; Zheng, Yishu; Li, Hanqing
2016-04-01
We proposed a new family of noncoaxial Gauss-truncated Bessel beams through multiplying conventional symmetrical Bessel beams by a noncoaxial Gauss function. These beams can also be regarded as the exponential-truncated version of Bessel-Gauss beams since they can be transformed into the product of Bessel-Gauss beams and an exponential window function along a certain Cartesian axis. The closed-form solutions of the angular spectra and paraxial propagation of these beams were derived. These beams have asymmetrical intensity distributions and carry the same orbit angular momentum per photon as the corresponding Bessel-Gauss beams. While propagating along the z axis, the mth (m≠0) noncoaxial Bessel-Gauss beams rotate their intensity distributions and the mth-order vortex at the beam center has a transverse shift along the direction perpendicular to the offset axis. Depending on the product of the transverse scalar factor of the Bessel beams and the offset between the Gaussian window function and the center of the Bessel beams, the noncoaxial Bessel-Gauss beams can produce unit vortices with opposite signs in pairs during propagation. PMID:27140757
Harris, R.; Wang, Z.; Liu, Y.
2007-11-19
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.
NASA Astrophysics Data System (ADS)
Harris, Rob; Wang, Z. J.; Liu, Yen
2008-01-01
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.
NASA Astrophysics Data System (ADS)
Ying, Teh Yuan; Yaacob, Nazeeruddin
2013-04-01
In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed. The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six. In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage order.
NASA Astrophysics Data System (ADS)
Ying, Teh Yuan; Yaacob, Nazeeruddin
2013-04-01
In this paper, a new implicit Runge-Kutta method which based on a 7-point Gauss-Kronrod-Lobatto quadrature formula is developed. The resulting implicit method is a 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method, or in brief as GKLM(7,10)-IIIA. GKLM(7,10)-IIIA requires seven function of evaluations at each integration step and it gives accuracy of order ten. In addition, GKLM(7,10)-IIIA has stage order seven and being A-stable. Numerical experiments compare the accuracy between GKLM(7,10)-IIIA and the classical 5-stage tenth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKLM(7,10)-IIIA is more accurate than the 5-stage tenth order Gauss-Legendre method because GKLM(7,10)-IIIA has higher stage order.
Length Scales in Bayesian Automatic Adaptive Quadrature
NASA Astrophysics Data System (ADS)
Adam, Gh.; Adam, S.
2016-02-01
Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1-16 (2012)] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule), mesoscopic (Simpson rule), and macroscopic (quadrature sums of high algebraic degrees of precision). Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived.
Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
1997-01-01
This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.
Quadrature formulas for Fourier coefficients
NASA Astrophysics Data System (ADS)
Bojanov, Borislav; Petrova, Guergana
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives.
A Gaussian quadrature method for total energy analysis in electronic state calculations
NASA Astrophysics Data System (ADS)
Fukushima, Kimichika
This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.
Colon Cancer Risk Assessment - Gauss Program
An executable file (in GAUSS) that projects absolute colon cancer risk (with confidence intervals) according to NCI’s Colorectal Cancer Risk Assessment Tool (CCRAT) algorithm. GAUSS is not needed to run the program.
Error Analysis of Quadrature Rules. Classroom Notes
ERIC Educational Resources Information Center
Glaister, P.
2004-01-01
Approaches to the determination of the error in numerical quadrature rules are discussed and compared. This article considers the problem of the determination of errors in numerical quadrature rules, taking Simpson's rule as the principal example. It suggests an approach based on truncation error analysis of numerical schemes for differential…
Gauss-Bonnet gravitational baryogenesis
NASA Astrophysics Data System (ADS)
Odintsov, S. D.; Oikonomou, V. K.
2016-09-01
In this letter we study some variant forms of gravitational baryogenesis by using higher order terms containing the partial derivative of the Gauss-Bonnet scalar coupled to the baryonic current. This scenario extends the well known theory that uses a similar coupling between the Ricci scalar and the baryonic current. One appealing feature of the scenario we study is that the predicted baryon asymmetry during a radiation domination era is non-zero. We calculate the baryon to entropy ratio for the Gauss-Bonnet term and by using the observational constraints we investigate which are the allowed forms of the R + F (G) gravity controlling the evolution. Also we briefly discuss some alternative higher order terms that can generate a non-zero baryon asymmetry, even in the conformal invariance limit.
Spherical-earth Gravity and Magnetic Anomaly Modeling by Gauss-legendre Quadrature Integration
NASA Technical Reports Server (NTRS)
Vonfrese, R. R. B.; Hinze, W. J.; Braile, L. W.; Luca, A. J. (Principal Investigator)
1981-01-01
The anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical Earth for an arbitrary body represented by an equivalent point source distribution of gravity poles or magnetic dipoles were calculated. The distribution of equivalent point sources was determined directly from the coordinate limits of the source volume. Variable integration limits for an arbitrarily shaped body are derived from interpolation of points which approximate the body's surface envelope. The versatility of the method is enhanced by the ability to treat physical property variations within the source volume and to consider variable magnetic fields over the source and observation surface. A number of examples verify and illustrate the capabilities of the technique, including preliminary modeling of potential field signatures for Mississippi embayment crustal structure at satellite elevations.
Shang, J.S.; Andrienko, D.A.; Huang, P.G.; Surzhikov, S.T.
2014-06-01
An efficient computational capability for nonequilibrium radiation simulation via the ray tracing technique has been accomplished. The radiative rate equation is iteratively coupled with the aerodynamic conservation laws including nonequilibrium chemical and chemical–physical kinetic models. The spectral properties along tracing rays are determined by a space partition algorithm of the nearest neighbor search process, and the numerical accuracy is further enhanced by a local resolution refinement using the Gauss–Lobatto polynomial. The interdisciplinary governing equations are solved by an implicit delta formulation through the diminishing residual approach. The axisymmetric radiating flow fields over the reentry RAM-CII probe have been simulated and verified with flight data and previous solutions by traditional methods. A computational efficiency gain nearly forty times is realized over that of the existing simulation procedures.
Gaussian quadrature formulae for arbitrary positive measures.
Fernandes, Andrew D; Atchley, William R
2006-01-01
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218
A generalized discrepancy and quadrature error bound
NASA Astrophysics Data System (ADS)
Hickernell, F. J.
1998-01-01
An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which depends only on the quadrature rule, is defined as a generalized discrepancy. The generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the L-p-star discrepancy and P-alpha that arises in the study of lattice rules.
Crafting a Gauss Gun Demonstration
NASA Astrophysics Data System (ADS)
Blodgett, Matthew E.; Blodgett, E. D.
2006-12-01
A Gauss Gun launches a ferromagnetic projectile using a pulsed electromagnet. This demonstration provides a nice counterpoint to the popular Thompson's jumping ring demonstration, which launches a nonferromagnetic ring via repulsion of an induced current. The pulsed current must be short enough in duration so that the projectile is not retarded by lingering current in the launch solenoid, but also large enough to provide a suitably impressive velocity. This project involved an iterative design process, as we worked through balancing all the different design criteria. We recommend it as a very nice electronics design project which will produce a very portable and enjoyable demonstration. AAPT sponsor Earl Blodgett.
Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.
Kiselev, Aleksei P; Plachenov, Alexandr B
2016-04-01
The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given. PMID:27140777
Antenna-array, phase quadrature tracking system
NASA Technical Reports Server (NTRS)
Cubley, H. D.
1970-01-01
Phase relationship between input signals appearing on widely-spaced parallel connected antenna elements in array is automatically adjusted in phase quadrature tracking system. Compact and lightweight design permit use in wide variety of airborne communications networks.
Calculates Angular Quadrature Weights and Cosines.
Energy Science and Technology Software Center (ESTSC)
1988-02-18
DSNQUAD calculates the angular quadrature weights and cosines for use in CCC-254/ANISN-ORNL. The subroutines in DSNQUAD were lifted from the XSDRN-PM code, which is supplied with the CCC-475/ SCALIAS-77 package.
Past and Future SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, Steven; Poletto, G.
2006-01-01
With the launch of SOHO, it again became possible to carry out quadrature observations. In comparison with earlier observations, the new capabilities of coronal spectroscopy with UVCS and in situ ionization state and composition with Ulysses/SWICS enabled new types of studies. Results from two studies serve as examples: (i) The acceleration profile of wind from small coronal holes. (ii) A high-coronal reconnecting current sheet as the source of high ionization state Fe in a CME at Ulysses. Generally quadrature observations last only for a few days, when Ulysses is within ca. 5 degrees of the limb. This means luck is required for the phenomenon of interest to lie along the radial direction to Ulysses. However, when Ulysses is at high southern latitude in winter 2007 and high northern latitude in winter 2008, there will be unusually favorable configurations for quadrature observations with SOHO and corresponding bracketing limb observations from STEREO A/B. Specifically, Ulysses will be within 5 degrees of the limb from December 2006 to May 2007 and within 10 degrees of the limb from December 2007 to May 2008. These long-lasting quadratures and bracketing STEREO A/B observations overcome the limitations inherent in the short observation intervals of typical quadratures. Furthermore, ionization and charge state measurements like those on Ulysses will also be made on STEREO and these will be essential for identification of CME ejecta - one of the prime objectives for STEREO.
Quadrature formulae for problems in mechanics
NASA Astrophysics Data System (ADS)
Milovanović, Gradimir V.; Igić, Tomislav; Tončev, Novica
2012-09-01
The fast progress in recent years in symbolic computation and variable-precision arithmetic provide a possibility for generating the recursion coefficients in the three-term recurrence relation for orthogonal polynomials with respect to several nonclassical weight functions, as well as the construction of the corresponding quadrature rules of Gaussian type. Such quadratures are very important in many applications in engineering (fracture mechanics, damage mechanics, etc.), as well as in other computational and applied sciences. The boundary element method (BEM), finite element method (FEM), methods for solving integral equations, etc. very often require the numerical evaluation of one dimensional or multiple integrals with singular or near singular integrands with a high precision. In this paper we give some improvements of quadrature rules of Gaussian type with logarithmic and/or algebraic singularities. A numerical examples is included.
The Tortured History of Gauss's Law
NASA Astrophysics Data System (ADS)
Spencer, Ross
2009-10-01
American physics textbooks contain the following equation, which is called Gauss's law: E .d S = qenclosed ɛ0 It is odd, however, that biographies of Karl Friedrich Gauss (1777-1855) contain no mention of this law. A brief history of this important result will be presented in which it will be shown that what we call Gauss's law today was originally guessed at by Joseph Priestly (1733-1804) after he read a letter from Benjamin Franklin (1706-1790), then was derived, forgotten, and re-derived several times in two different contexts by many of the luminaries of physics in the eighteenth and nineteenth centuries.
Summation Paths in Clenshaw-Curtis Quadrature
NASA Astrophysics Data System (ADS)
Adam, S.; Adam, Gh.
2016-02-01
Two topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion of the integrand is to be done within a mathematical structure consisting of the union of coefficient families ordered into complete binary trees. Second, the scrutiny of the decay rates of the involved even and odd rank Chebyshev expansion coefficients with the increase of their rank labels enables the definition of Bayesian decision paths for the advancement to the numerical output.
TEACHING PHYSICS: Gauss's law - a forgotten tool?
NASA Astrophysics Data System (ADS)
Severn, John
2000-07-01
Gauss's law is a powerful tool that can be used to resolve symmetrical situations involving various fields, where traditional approaches would involve the use of integral calculus. Born out of the dynamics of fluids, its main teaching use has traditionally been largely in the area of electrostatic problems. However, in the area of gravitation its use is not so well known. This article starts by introducing Gauss's law with electrostatics, and then uses the law in the application of some simple gravitational problems.
Runge-Kutta based generalized convolution quadrature
NASA Astrophysics Data System (ADS)
Lopez-Fernandez, Maria; Sauter, Stefan
2016-06-01
We present the Runge-Kutta generalized convolution quadrature (gCQ) with variable time steps for the numerical solution of convolution equations for time and space-time problems. We present the main properties of the method and a convergence result.
NASA Astrophysics Data System (ADS)
Ezz-Eldien, S. S.
2016-07-01
This manuscript presents a new numerical approach to approximate the solution of a class of fractional variational problems. The presented approach is consisting of using the shifted Legendre orthonormal polynomials as basis functions of the operational matrix of fractional derivatives (described in the Caputo sense) and that of fractional integrals (described in the sense of Riemann-Liouville) with the help of the Legendre-Gauss quadrature formula together with the Lagrange multipliers method for converting such fractional variational problems into easier problems that consist of solving an algebraic system in the unknown coefficients. The convergence of the proposed method is analyzed. Finally, in order to demonstrate the accuracy of the present method, some test problems are introduced with their approximate solutions and comparisons with other numerical approaches.
Optically controlled quadrature coupler on silicon substrate
NASA Astrophysics Data System (ADS)
Bhadauria, Avanish; Sharma, Sonia; Sonania, Shikha; Akhtar, Jamil
2016-03-01
In this paper, we have proposed and studied an optically controlled quadrature coupler fabricated on silicon substrate. The optically controlled quadrature coupler can be realized by terminating its coupled or through ports by optically induced load. Simulation and experimental results show that by varying optical intensity, we can control the phase and amplitude of output RF signal and can realize optically controlled reflection type attenuator, reflection type phase-shifter and ultrafast switches. The new kind of proposed device can be useful for ultra-fast signal processing and modulation schemes in high speed communication especially in QPSK modulation. The optical control has several advantages over conventional techniques such as MEMS and other semiconductor switching, which have several inherent disadvantages and limitations like low response time, low power handling capacity, device parasitic and non-linearity.
Comment on "Gauss-Bonnet inflation"
NASA Astrophysics Data System (ADS)
Hikmawan, Getbogi; Soda, Jiro; Suroso, Agus; Zen, Freddy P.
2016-03-01
Recently, an interesting inflationary scenario, named Gauss-Bonnet inflation, was proposed by Kanti et al. [Phys. Rev. D 92, 041302 (2015); Phys. Rev. D 92, 083524 (2015)]. In the model, there is no inflaton potential, but the inflaton couples to the Guass-Bonnet term. In the case of quadratic coupling, they find inflation occurs with a graceful exit. The scenario is attractive because of the natural setup. However, we show there exists a gradient instability in the tensor perturbations in this inflationary model. We further prove the no-go theorem for Gauss-Bonnet inflation without an inflaton potential.
Kerr-Gauss-Bonnet black holes: Exact analytical solution
Alexeyev, S. Popov, N.; Startseva, M.; Barrau, A. Grain, J.
2008-04-15
Gauss-Bonnet gravity provides one of the most promising frameworks for studying curvature corrections to the Einstein action in supersymmetric string theories while avoiding ghosts and keeping second-order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for a long time, the Kerr-Gauss-Bonnet metric was missing. A five dimensional Gauss-Bonnet solution is obtained analytically for spinning black holes, and the related thermodynamical properties are briefly outlined.
Galileo, Gauss, and the Green Monster
ERIC Educational Resources Information Center
Kalman, Dan; Teague, Daniel J.
2013-01-01
Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…
Experimental generation of Hermite-Gauss and Ince-Gauss beams through kinoform phase holograms
NASA Astrophysics Data System (ADS)
Mellado-Villaseñor, Gabriel; Aguirre-Olivas, Dilia; Sánchez-de-la-Llave, David; Arrizón, Victor
2015-08-01
We generate Hermite-Gauss and Ince-Gauss beams by using kinoform phase holograms encoded onto a liquid crystal display. The phase transmittance of this holograms coincide with the phases of such beams. Scale versions of the desired beams appear at the Fourier domain of the KPHs. When an appropriated pupil size is employed, the method synthesizes HG and IG beams with relatively high accuracy and high efficiency. It is noted that experimental and numerical results are agreement with the theory.
Virtual source for a Laguerre-Gauss beam
NASA Astrophysics Data System (ADS)
Seshadri, S. R.
2002-11-01
A virtual source that generates a cylindrically symmetric Laguerre-Gauss wave of radial mode number n is introduced. An expression is derived for this Laguerre-Gauss wave that in the appropriate limit yields the corresponding Laguerre-Gauss beam. From the spectral representation of the Laguerre-Gauss wave, the first three orders of nonparaxial corrections for the paraxial Laguerre-Gauss beam are determined. On the beam axis, the number of orders of nonvanishing nonparaxial corrections is found to be equal to n.
Entanglement temperature with Gauss-Bonnet term
NASA Astrophysics Data System (ADS)
Pal, Shesansu Sekhar; Panda, Sudhakar
2015-09-01
We compute the entanglement temperature using the first law-like of thermodynamics, ΔE =Tent ΔSEE, up to Gauss-Bonnet term in the Jacobson-Myers entropy functional in any arbitrary spacetime dimension. The computation is done when the entangling region is the geometry of a slab. We also show that such a Gauss-Bonnet term, which becomes a total derivative, when the co-dimension two hypersurface is four dimensional, does not contribute to the finite term in the entanglement entropy. We observe that the Weyl-squared term does not contribute to the entanglement entropy. It is important to note that the calculations are performed when the entangling region is very small and the energy is calculated using the normal Hamiltonian.
Positive interpolatory quadrature formulas and para-orthogonal polynomials
NASA Astrophysics Data System (ADS)
Bultheel, Adhemar; Daruis, Leyla; Gonzalez-Vera, Pablo
2005-07-01
We establish a relation between quadrature formulas on the interval [-1,1] that approximate integrals of the form and Szego quadrature formulas on the unit circle that approximate integrals of the form . The functions [mu](x) and [omega]([theta]) are assumed to be weight functions on [-1,1] and [-[pi],[pi
Causal structures in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Izumi, Keisuke
2014-08-01
We analyze causal structures in Gauss-Bonnet gravity. It is known that Gauss-Bonnet gravity potentially has superluminal propagation of gravitons due to its noncanonical kinetic terms. In a theory with superluminal modes, an analysis of causality based on null curves makes no sense, and thus, we need to analyze them in a different way. In this paper, using the method of the characteristics, we analyze the causal structure in Gauss-Bonnet gravity. We have the result that, on a Killing horizon, gravitons can propagate in the null direction tangent to the Killing horizon. Therefore, a Killing horizon can be a causal edge as in the case of general relativity; i.e. a Killing horizon is the "event horizon" in the sense of causality. We also analyze causal structures on nonstationary solutions with (D-2)-dimensional maximal symmetry, including spherically symmetric and flat spaces. If the geometrical null energy condition, RABNANB≥0 for any null vector NA, is satisfied, the radial velocity of gravitons must be less than or equal to that of light. However, if the geometrical null energy condition is violated, gravitons can propagate faster than light. Hence, on an evaporating black hole where the geometrical null energy condition is expected not to hold, classical gravitons can escape from the "black hole" defined with null curves. That is, the causal structures become nontrivial. It may be one of the possible solutions for the information loss paradox of evaporating black holes.
Correlated quadratures of resonance fluorescence and the generalized uncertainty relation
NASA Technical Reports Server (NTRS)
Arnoldus, Henk F.; George, Thomas F.; Gross, Rolf W. F.
1994-01-01
Resonance fluorescence from a two-state atom has been predicted to exhibit quadrature squeezing below the Heisenberg uncertainty limit, provided that the optical parameters (Rabi frequency, detuning, laser linewidth, etc.) are chosen carefully. When the correlation between two quadratures of the radiation field does not vanish, however, the Heisenberg limit for quantum fluctuations might be an unrealistic lower bound. A generalized uncertainty relation, due to Schroedinger, takes into account the possible correlation between the quadrature components of the radiation, and it suggests a modified definition of squeezing. We show that the coherence between the two levels of a laser-driven atom is responsible for the correlation between the quadrature components of the emitted fluorescence, and that the Schrodinger uncertainty limit increases monotonically with the coherence. On the other hand, the fluctuations in the quadrature field diminish with an increasing coherence, and can disappear completely when the coherence reaches 1/2, provided that certain phase relations hold.
Scalar field evolution in Gauss-Bonnet black holes
Abdalla, E.; Konoplya, R.A.; Molina, C.
2005-10-15
It is presented a thorough analysis of scalar perturbations in the background of Gauss-Bonnet, Gauss-Bonnet-de Sitter and Gauss-Bonnet-anti-de Sitter black hole spacetimes. The perturbations are considered both in frequency and time domain. The dependence of the scalar field evolution on the values of the cosmological constant {lambda} and the Gauss-Bonnet coupling {alpha} is investigated. For Gauss-Bonnet and Gauss-Bonnet-de Sitter black holes, at asymptotically late times either power-law or exponential tails dominate, while for Gauss-Bonnet-anti-de Sitter black hole, the quasinormal modes govern the scalar field decay at all times. The power-law tails at asymptotically late times for odd-dimensional Gauss-Bonnet black holes does not depend on {alpha}, even though the black hole metric contains {alpha} as a new parameter. The corrections to quasinormal spectrum due to Gauss-Bonnet coupling is not small and should not be neglected. For the limit of near extremal value of the (positive) cosmological constant and pure de Sitter and anti-de Sitter modes in Gauss-Bonnet gravity we have found analytical expressions.
The May 1997 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Suess, Steven T.; Poletto, G.; Romoli, M.; Neugebauer, M.; Goldstein, B. E.; Simnett, G.
2000-01-01
We present results from the May 1997 SOHO-Ulysses quadrature, near sunspot minimum. Ulysses was at 5.1 AU, 100 north of the solar equator, and off the east limb. It was, by chance, also at the very northern edge of the streamer belt. Nevertheless, SWOOPS detected only slow, relatively smooth wind and there was no direct evidence of fast wind from the northern polar coronal hole or of mixing with fast wind. LASCO images show that the streamer belt at 10 N was narrow and sharp at the beginning and end of the two week observation interval, but broadened in the middle. A corresponding change in density, but not flow speed, occurred at Ulysses. Coronal densities derived from UVCS show that physical parameters in the lower corona are closely related to those in the solar wind, both over quiet intervals and in transient events on the limb. One small transient observed by both LASCO and UVCS is analyzed in detail.
Power flow control using quadrature boosters
NASA Astrophysics Data System (ADS)
Sadanandan, Sandeep N.
A power system that can be controlled within security constraints would be an advantage to power planners and real-time operators. Controlling flows can lessen reliability issues such as thermal limit violations, power stability problems, and/or voltage stability conditions. Control of flows can also mitigate market issues by reducing congestion on some lines and rerouting power to less loaded lines or onto preferable paths. In the traditional control of power flows, phase shifters are often used. More advanced methods include using Flexible AC Transmission System (FACTS) Controllers. Some examples include Thyristor Controlled Series Capacitors, Synchronous Series Static Compensators, and Unified Power Flow Controllers. Quadrature Boosters (QBs) have similar structures to phase-shifters, but allow for higher voltage magnitude during real power flow control. In comparison with other FACTS controllers QBs are not as complex and not as expensive. The present study proposes to use QBs to control power flows on a power system. With the inclusion of QBs, real power flows can be controlled to desired scheduled values. In this thesis, the linearized power flow equations used for power flow analysis were modified for the control problem. This included modifying the Jacobian matrix, the power error vector, and calculating the voltage injected by the quadrature booster for the scheduled real power flow. Two scenarios were examined using the proposed power flow control method. First, the power flow in a line in a 5-bus system was modified with a QB using the method developed in this thesis. Simulation was carried out using Matlab. Second, the method was applied to a 30-bus system and then to a 118-bus system using several QBs. In all the cases, the calculated values of the QB voltages led to desired power flows in the designated line.
Efficient generation of Hermite-Gauss and Ince-Gauss beams through kinoform phase elements.
Aguirre-Olivas, Dilia; Mellado-Villaseñor, Gabriel; Sánchez-de-la-Llave, David; Arrizón, Victor
2015-10-01
We discuss the generation of Hermite-Gauss and Ince-Gauss beams employing phase elements whose transmittances coincide with the phase modulations of such beams. A scaled version of the desired field appears, distorted by marginal optical noise, at the element's Fourier domain. The motivation to perform this study is that, in the context of the proposed approach, the desired beams are generated with the maximum possible efficiency. A disadvantage of the method is the distortion of the desired beams by the influence of several nondesired beam modes generated by the phase elements. We evaluate such distortion employing the root mean square deviation as a figure of merit. PMID:26479622
Does the Gauss-Bonnet term stabilize wormholes?
NASA Astrophysics Data System (ADS)
Kokubu, Takafumi; Maeda, Hideki; Harada, Tomohiro
2015-12-01
The effect of the Gauss-Bonnet term on the existence and dynamical stability of thin-shell wormholes as negative tension branes is studied in the arbitrary-dimensional spherically, planar and hyperbolically symmetric spacetimes. We consider radial perturbations against the shell for the solutions that have the Z2 symmetry and admit the general relativistic limit. It is shown that the Gauss-Bonnet term shrinks the parameter region that admits static wormholes. The effect of the Gauss-Bonnet term on the stability depends on the spacetime symmetry. For planar symmetric wormholes, the Gauss-Bonnet term does not affect their stability. If the coupling constant is positive but small, the Gauss-Bonnet term tends to destabilize spherically symmetric wormholes, while it stabilizes hyperbolically symmetric wormholes. The Gauss-Bonnet term can destabilize hyperbolically symmetric wormholes as a non-perturbative effect, but spherically symmetric wormholes cannot be stable.
Black holes in Gauss-Bonnet gravity's rainbow
NASA Astrophysics Data System (ADS)
Hendi, Seyed Hossein; Faizal, Mir
2015-08-01
In this paper, we will generalize the Gauss-Bonnet gravity to an energy-dependent Gauss-Bonnet theory of gravity, which we shall call the Gauss-Bonnet gravity's rainbow. We will also couple this theory to a Maxwell's theory. We will analyze black hole solutions in this energy-dependent Gauss-Bonnet gravity's rainbow. We will calculate the modifications to the thermodynamics of black holes in the Gauss-Bonnet's gravity's rainbow. We will demonstrate that even though the thermodynamics of the black holes get modified in the Gauss-Bonnet gravity's rainbow, the first law of thermodynamics still holds for this modified thermodynamics. We will also comment on the thermal stability of the black hole solutions in this theory.
Multivariate curve-fitting in GAUSS
Bunck, C.M.; Pendleton, G.W.
1988-01-01
Multivariate curve-fitting techniques for repeated measures have been developed and an interactive program has been written in GAUSS. The program implements not only the one-factor design described in Morrison (1967) but also includes pairwise comparisons of curves and rates, a two-factor design, and other options. Strategies for selecting the appropriate degree for the polynomial are provided. The methods and program are illustrated with data from studies of the effects of environmental contaminants on ducklings, nesting kestrels and quail.
Higgs inflation in Gauss-Bonnet braneworld
NASA Astrophysics Data System (ADS)
Cai, Rong-Gen; Guo, Zong-Kuan; Wang, Shao-Jiang
2015-09-01
The measured masses of the Higgs boson and top quark indicate that the effective potential of the standard model either develops an unstable electroweak vacuum or stands stable all the way up to the Planck scale. In the latter case in which the top quark mass is about 2 σ below its present central value, the Higgs boson can be the inflaton with the help of a large nonminimal coupling to curvature in four dimensions. We propose a scenario in which the Higgs boson can be the inflaton in a five-dimensional Gauss-Bonnet braneworld model to solve both the unitarity and stability problems which usually plague Higgs inflation. We find that in order for Higgs inflation to happen successfully in the Gauss-Bonnet regime, the extra dimension scale must appear roughly in the range between the TeV scale and the instability scale of standard model. At the tree level, our model can give rise to a naturally small nonminimal coupling ξ ˜O (1 ) for the Higgs quartic coupling λ ˜O (0.1 ) if the extra dimension scale lies at the TeV scale. At the loop level, the inflationary predictions at the tree level are preserved. Our model can be confronted with future experiments and observations from both particle physics and cosmology.
Reheating in Gauss-Bonnet-coupled inflation
NASA Astrophysics Data System (ADS)
van de Bruck, Carsten; Longden, Chris; Dimopoulos, Konstantinos
2016-07-01
We investigate the feasibility of models of inflation with a large Gauss-Bonnet coupling at late times, which have been shown to modify and prevent the end of inflation. Despite the potential of Gauss-Bonnet models in predicting favorable power spectra, capable of greatly lowering the tensor-to-scalar ratio compared to now-disfavored models of standard chaotic inflation, it is important to also understand in what context it is possible for postinflationary (p)reheating to proceed and hence recover an acceptable late-time cosmology. We argue that in the previously studied inverse power law coupling case, reheating cannot happen due to a lack of oscillatory solutions for the inflaton, and that neither instant preheating nor gravitational particle production would avoid this problem due to the persistence of the inflaton's energy density, even if it were to partially decay. Hence we proceed to define a minimal generalization of the model which can permit perturbative reheating and study the consequences of this, including heavily modified dynamics during reheating and predictions of the power spectra.
Experimental study of quadrature spring rate at tuned dry gyro
NASA Astrophysics Data System (ADS)
Hayakawa, Yoshiaki; Murayama, Naoshi
A survey result on the mechanism of quadrature spring rate occurring at the tuned dry gyro is given. It is noted that the quadrature spring rate is a damping torque. This damping torque is similar to the spring reaction torque generated by the flexure displacement angles and drives the gyro rotor back to a balanced position. In order to investigate the mechanism of damping occurring at the gyro rotor, the relation between surrounding gas pressure and damping factor under gyro nonoperating was measured. Furthermore, the drag torque acting on the gyro rotor was measured by the back EMF method at different surrounding gas pressure. As a result of these testings, it was found out that the quadrature spring rate was generated by gas movement of the flexure around and drag forces due to bearing loss and windage loss, and the mechanism and magnitude of each damping torque which are contributor to the quadrature spring rate were extracted separately.
Squeezing quadrature rotation in the acoustic band via optomechanics
NASA Astrophysics Data System (ADS)
Guccione, Giovanni; Slatyer, Harry J.; Carvalho, André R. R.; Buchler, Ben C.; Lam, Ping Koy
2016-03-01
We examine the use of optomechanically generated squeezing to obtain a sensitivity enhancement for interferometers in the gravitational-wave band. The intrinsic dispersion characteristics of optomechanical squeezing around the mechanical frequency are able to produce squeezing at different quadratures over the spectrum, a feature required by gravitational-wave interferometers to beat the standard quantum limit over an extended frequency range. Under realistic assumptions we show that the amount of available squeezing and the intrinsic quadrature rotation may provide, compared to similar amounts of fixed-quadrature squeezing, a detection advantage. A significant challenge for this scheme, however, is the amount of excess noise that is generated in the unsqueezed quadrature at frequencies near the mechanical resonance.
Algorithm 699 - A new representation of Patterson's quadrature formulae
NASA Technical Reports Server (NTRS)
Krogh, Fred T.; Van Snyder, W.
1991-01-01
A method is presented to reduce the number of coefficients necessary to represent Patterson's quadrature formulae. It also reduces the amount of storage necessary for storing function values, and produces slightly smaller error in evaluating the formulae.
Optical encryption system using quadrature multiplexing
NASA Astrophysics Data System (ADS)
Islam, Mohammed Nazrul; Alam, Mohammad S.
2006-08-01
Optical security systems have attracted much research interest recently for information security and fraud deterrent applications. A number of encryption techniques have been proposed in the literature, which includes double random-phase encryption, polarization encoding, encryption and verification using a multiplexed minimum average correlation energy phase-encrypted filter. Most of these reports employ a pseudo-random code for each information to be encrypted, where it requires individual storage capacity or transmission channel for further processing of each information. The objective of this paper is to develop an optical encryption system employing quadrature multiplexing to enhance the storage/transmission capacity of the system. Two information signals are encrypted using the same code but employing two orthogonal functions and then they are multiplexed together in the same domain. As the orthogonal functions have zero cross-correlation between them, so the encrypted information are expected to be unaffected by each other. Each encryption and multiplexing process can accommodate two information signals for a single code and a single storage cell or transmission channel. The same process can be performed in multiple steps to increase the multiplexing capability of the system. For decryption purpose, the composite encoded signal is correlated using the appropriate code and the appropriate function. The proposed technique has been found to work excellent in computer simulation with binary as well as gray level images. It has also been verified that the encrypted images remain secure, because no unwanted reproduction is possible without having the appropriate code and function.
Two integrator loop quadrature oscillators: A review
Soliman, Ahmed M.
2012-01-01
A review of the two integrator loop oscillator circuits providing two quadrature sinusoidal output voltages is given. All the circuits considered employ the minimum number of capacitors namely two except one circuit which uses three capacitors. The circuits considered are classified to four different classes. The first class includes floating capacitors and floating resistors and the active building blocks realizing these circuits are the Op Amp or the OTRA. The second class employs grounded capacitors and includes floating resistors and the active building blocks realizing these circuits are the DCVC or the unity gain cells or the CFOA. The third class employs grounded capacitors and grounded resistors and the active building blocks realizing these circuits are the CCII. The fourth class employs grounded capacitors and no resistors and the active building blocks realizing these circuits are the TA. Transformation methods showing the generation of different classes from each other is given in details and this is one of the main objectives of this paper. PMID:25685396
An exponentially fitted quadrature rule over unbounded intervals
NASA Astrophysics Data System (ADS)
Conte, D.; Paternoster, B.; Santomauro, G.
2012-09-01
A new class of quadrature formulae for the computation of integrals over unbounded intervals with oscillating integrand is illustrated. Such formulae are a generalization of the gaussian quadrature formulae by exploiting the Exponential Fitting theory. The coefficients depend on the frequency of oscillation, in order to improve the accuracy of the solution. The construction of the methods with 1, 2 and 3 nodes is described, together with the comparison of the order of accuracy with respect to classical formulae.
Quadrature mixture LO suppression via DSW DAC noise dither
Dubbert, Dale F.; Dudley, Peter A.
2007-08-21
A Quadrature Error Corrected Digital Waveform Synthesizer (QECDWS) employs frequency dependent phase error corrections to, in effect, pre-distort the phase characteristic of the chirp to compensate for the frequency dependent phase nonlinearity of the RF and microwave subsystem. In addition, the QECDWS can employ frequency dependent correction vectors to the quadrature amplitude and phase of the synthesized output. The quadrature corrections cancel the radars' quadrature upconverter (mixer) errors to null the unwanted spectral image. A result is the direct generation of an RF waveform, which has a theoretical chirp bandwidth equal to the QECDWS clock frequency (1 to 1.2 GHz) with the high Spurious Free Dynamic Range (SFDR) necessary for high dynamic range radar systems such as SAR. To correct for the problematic upconverter local oscillator (LO) leakage, precision DC offsets can be applied over the chirped pulse using a pseudo-random noise dither. The present dither technique can effectively produce a quadrature DC bias which has the precision required to adequately suppress the LO leakage. A calibration technique can be employed to calculate both the quadrature correction vectors and the LO-nulling DC offsets using the radar built-in test capability.
Emergent universe supported by chiral cosmological fields in 5D Einstein-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Chervon, S. V.; Maharaj, S. D.; Beesham, Aroonkumar; Kubasov, A. S.
2014-07-01
We propose the application of the chiral cosmological model (CCM) for the Einstein--Gauss--Bonnet (EGB) theory of gravitation with the aim of finding new models of the Emergent Universe (EmU) scenario. We analysed the EmU supported by two chiral cosmological fields for a spatially flat universe, while we have used three chiral fields when we investigated open and closed universes. To prove the validity of the EmU scenario we fixed the scale factor and found the exact solution by decomposition of EGB equations and solving the chiral field dynamics equation. To this end, we suggested the decomposition of the EGB equations in such a way that the first chiral field is responsible for the Einstein part of the model, while the second field, together with kinetic interaction term, is connected with the Gauss--Bonnet part of the theory. We proved that both fields are phantom ones under this decomposition, and that the model has a solution if the kinetic interaction between the fields equals a constant. We have presented the exact solution in terms of cosmic time. This was done for a spatially flat universe. In the case of open and closed universes we introduced the third chiral field (canonical for closed and phantom for open universe) which is responsible for the EGB and curvature parts. The solution of the third field equation is obtained in quadratures. Thus we have proved that the CCM is able to support EmU scenario in EGB gravity for spatially flat, open and closed universes.
NASA Astrophysics Data System (ADS)
Harris, Robert Evan
2008-10-01
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and nonlinear advection equations, and the Euler equations. The new quadrature-free approach is then extended to handle local adaptive hp-refinement (grid and order refinement). Efficient edge-based adaptation utilizing a binary tree search algorithm is employed. Several different adaptation criteria which focus computational effort near high gradient regions are presented. Both h- and p-refinements are presented in a general framework where it is possible to perform either or both on any grid cell at any time. Several well-known inviscid flow test cases, subjected to various levels of adaptation, are utilized to demonstrate the effectiveness of the method. An analysis of the accuracy and stability properties of the spectral volume (SV) method is then presented. The current work seeks to address the issue of stability, as well as polynomial quality, in the design of SV partitions. A new approach is presented, which efficiently locates stable partitions by means of constrained minimization. Once stable partitions are located, a
Electromagnetic modified Bessel-Gauss beams and waves.
Seshadri, S R
2008-01-01
The transverse magnetic (TM) modified Bessel-Gauss beams and their full-wave generalizations are treated. Attention is paid to the spreading properties on propagation of the null in the radiation intensity pattern for the azimuthal mode numbers m=0 and 1. The rate of spreading of the null in the propagation direction is significantly less for the TM modified Bessel-Gauss waves than those for the corresponding TM Bessel-Gauss waves. The total power transported by the waves is determined and compared with that of the corresponding paraxial beam to estimate the quality of the paraxial beam approximation of the wave. The dependence of the quality of the paraxial beam approximation on the azimuthal mode number, the beam shape parameter, and the ratio of the beam waist to the wavelength has a regular pattern for the TM Bessel-Gauss wave and not for the TM modified Bessel-Gauss wave. PMID:18157205
Gaussian quadrature inference for continuous-variable quantum key distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, L.; Imre, S.
2016-05-01
We propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We demonstrate the results through the adaptive multicarrier quadrature division (AMQD) scheme. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of GQI. We prove the secret key rate formulas for a multiple access multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) scheme. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario.
The Fall 2000 and Fall 2001 SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.
2000-01-01
SOHO-Ulysses quadrature occurs when the SOHO-Sun-Ulysses included angle is 90 degrees. It is only at such times that the same plasma leaving the Sun in the direction of Ulysses can first be remotely analyzed with SOHO instruments and then later be sampled in situ by Ulysses instruments. The quadratures in December 2000 and 2001 are of special significance because Ulysses will be near the south and north heliographic poles, respectively, and the solar cycle will be near sunspot maximum. Quadrature geometry is sometimes confusing and observations are influenced by solar rotation. The Fall 2000 and 2001 quadratures are more complex than usual because Ulysses is not in a true polar orbit and the orbital speed of Ulysses about the Sun is becoming comparable to the speed of SOHO about the Sun. In 2000 Ulysses will always be slightly behind the pole but will appear to hang over the pole for over two months because it is moving around the Sun in the same direction as SOHO. In 20001, Ulysses will be slightly in front of the pole so that its footpoint will be directly observable. Detailed plots will be shown of the relative positions of SOHO and Ulysses will their relative positions. In neither case is true quadrature actually achieved, but this works to the observers advantage in 2001.
The Fall 2000 and Fall 2001 SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.; Rose, M. Franklin (Technical Monitor)
2001-01-01
SOHO-Ulysses quadrature occurs when the SOHO-Sun-Ulysses included angle is 90 degrees. It is only at such times that the same plasma leaving the Sun in the direction of Ulysses can first be remotely analyzed with SOHO instruments and then later be sampled in situ by Ulysses instruments. The quadratures in December 2000 and 2001 are of special significance because Ulysses will be near the south and north heliographic poles, respectively, and the solar cycle will be near sunspot maximum. Quadrature geometry is sometimes confusing and observations are influenced by solar rotation. The Fall 2000 and 2001 quadratures are more complex than usual because Ulysses is not in a true polar orbit and the orbital speed of Ulysses about the Sun is becoming comparable to the speed of SOHO about the Sun. In 2000 Ulysses will always be slightly behind the pole but will appear to hang over the pole for over two months because it is moving around the Sun in the same direction as SOHO. In 2001 Ulysses will be slightly in front of the pole so that its footpoint will be directly observable. Detailed plots will be shown of the relative positions of SOHO and Ulysses will their relative positions. In neither case is true quadrature actually achieved, but this works to the observers advantage in 2001.
Radiating black hole solutions in Einstein-Gauss-Bonnet gravity
Dominguez, Alfredo E.; Gallo, Emanuel
2006-03-15
In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as the Gauss-Bonnet versions of the Bonnor-Vaidya (de Sitter/anti-de Sitter) solution, a global monopole, and the Husain black holes. We also present a more general version of this theorem in which less restrictive conditions on the energy-momentum tensor are imposed. As an application of this theorem, we present the exact solution describing a black hole radiating a charged null fluid in a Born-Infeld nonlinear electrodynamics.
Error estimates for Gaussian quadratures of analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2009-12-01
For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points ±1 and the sum of semi-axes [varrho]>1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.
An Algorithm to Evaluate Imbalances of Quadrature Mixers
NASA Astrophysics Data System (ADS)
Asami, Koji; Arai, Michiaki
It is essential, as bandwidths of wireless communications get wider, to evaluate the imbalances among quadrature mixer ports, in terms of carrier phase offset, IQ gain imbalance, and IQ skew. Because it is time consuming to separate skew, gain imbalance and carrier phase offset evaluation during test is often performed using a composite value, without separation of the imbalance factors. This paper describes an algorithm for enabling separation among quadrature mixer gain imbalance, carrier phase offset, and skew. Since the test time is reduced by the proposed method, it can be applied during high volume production testing.
Strong gravitational lensing with Gauss-Bonnet correction
Sadeghi, J.; Vaez, H. E-mail: h.vaez@umz.ac.ir
2014-06-01
In this paper we investigate the strong gravitational lensing in a five dimensional background with Gauss-Bonnet gravity, so that in 4-dimensions the Gauss-Bonnet correction disappears. By considering the logarithmic term for deflection angle, we obtain the deflection angle α-circumflex and corresponding parameters ā and b-bar . Finally, we estimate some properties of relativistic images such as θ{sub ∞}, s and r{sub m}.
Accelerating Airy-Gauss-Kummer localized wave packets
NASA Astrophysics Data System (ADS)
Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi; Huang, Tingwen
2014-01-01
A general approach to generating three-dimensional nondiffracting spatiotemporal solutions of the linear Schrödinger equation with an Airy-beam time-dependence is reported. A class of accelerating optical pulses with the structure of Airy-Gauss-Kummer vortex beams is obtained. Our results demonstrate that the optical field contributions to the Airy-Gauss-Kummer accelerating optical wave packets of the cylindrical symmetry can be characterized by the radial and angular mode numbers.
Applying Quadrature Rules with Multiple Nodes to Solving Integral Equations
Hashemiparast, S. M.; Avazpour, L.
2008-09-01
There are many procedures for the numerical solution of Fredholm integral equations. The main idea in these procedures is accuracy of the solution. In this paper, we use Gaussian quadrature with multiple nodes to improve the solution of these integral equations. The application of this method is illustrated via some examples, the related tables are given at the end.
Wave-Based Inversion & Imaging for the Optical Quadrature Microscope
Lehman, S K
2005-10-27
The Center for Subsurface Sensing & Imaging System's (CenSSIS) Optical Quadrature Microscope (OQM) is a narrow band visible light microscope capable of measuring both amplitude and phase of a scattered field. We develop a diffraction tomography, that is, wave-based, scattered field inversion and imaging algorithm, for reconstructing the refractive index of the scattering object.
Gaussian rational quadrature formulas for ill-scaled integrands
NASA Astrophysics Data System (ADS)
Illán González, J. R.
2009-12-01
A flexible treatment of Gaussian quadrature formulas based on rational functions is given to evaluate the integral , when f is meromorphic in a neighborhood V of the interval I and W(x) is an ill-scaled weight function. Some numerical tests illustrate the power of this approach in comparison with Gautschi's method.
Archimedes Quadrature of the Parabola: A Mechanical View
ERIC Educational Resources Information Center
Oster, Thomas J.
2006-01-01
In his famous quadrature of the parabola, Archimedes found the area of the region bounded by a parabola and a chord. His method was to fill the region with infinitely many triangles each of whose area he could calculate. In his solution, he stated, without proof, three preliminary propositions about parabolas that were known in his time, but are…
Trapezoidal rule quadrature algorithms for MIMD distributed memory computers
Lyness, J.N.; Plowman, S.E.
1994-08-01
An approach to multi-dimensional quadrature, designed to exploit parallel architectures, is described. This involves transforming the integral in such a way that an accurate result is given by the trapezoidal rule; and by evaluating the resulting sum in a manner which may be efficiently implemented on parallel architectures. This approach is to be implemented in the Liverpool NAG transputer library.
From Lobatto Quadrature to the Euler Constant "e"
ERIC Educational Resources Information Center
Khattri, Sanjay Kumar
2010-01-01
Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…
NUT-charged black holes in Gauss-Bonnet gravity
Dehghani, M.H.; Mann, R.B.
2005-12-15
We investigate the existence of Taub-NUT (Newman-Unti-Tamburino) and Taub-bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in d dimensions. We find that for all nonextremal NUT solutions of Einstein gravity having no curvature singularity at r=N, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter {alpha} goes to zero. Furthermore there are no NUT solutions in Gauss-Bonnet gravity that yield nonextremal NUT solutions to Einstein gravity having a curvature singularity at r=N in the limit {alpha}{yields}0. Indeed, we have nonextreme NUT solutions in 2+2k dimensions with nontrivial fibration only when the 2k-dimensional base space is chosen to be CP{sup 2k}. We also find that the Gauss-Bonnet gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a two-dimensional factor space of positive curvature. Indeed, when the base space has at most one positively curved two-dimensional space as one of its factor spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though there a curvature singularity exists at r=N. We also find that one can have bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces of zero or positive constant curvature. The only case for which one does not have bolt solutions is in the absence of a cosmological term with zero curvature base space.
The AGS Ggamma Meter and Calibrating the Gauss Clock
Ahrens, Leif
2014-03-31
During AGS Polarized Proton acceleration periods, one output from the AGS Ggamma Meter, namely the energy (or Ggamma) calculated from the magnetic field in the AGS main magnets and the beam radius- both measured in particular instant, is used to figure out the times in the AGS magnet acceleration cycle when the beam passes through a particular set of depolarizing resonances. The resonance set occur whenever a particle’s Ggamma (energy*(G/m) becomes nearly equal to n*Qx (i.e. any integer multiplied by the horizontal betatron tune). This deliverable is why the machinery is referred to as the ''Ggamma Meter'' rather than the AGS energy meter. The Ggamma Meter takes as inputs a set of measurements of frequency (F(t)), radius (r(t)), and gauss clock counts (GCC(t)). The other energy (GgammaBr) assumes the field when the gauss clock starts counting is known. The change in field to time t is given by the measured accumulated gauss clock counts multiplied by the gauss clock calibration (gauss/GCC). In order to deal with experimental data, this calibration factor gets an added ad hoc complication, namely a correction dependent on the rate of change the counting rate. The Ggamma meter takes GCC(t) and together with the past history for this cycle calculates B(t).
Black strings in Gauss-Bonnet theory are unstable
NASA Astrophysics Data System (ADS)
Giacomini, Alex; Oliva, Julio; Vera, Aldo
2015-05-01
We report the existence of unstable s-wave modes for black strings in Gauss-Bonnet theory (which is quadratic in the curvature) in seven dimensions. This theory admits analytic uniform black strings that are, in the transverse section, black holes of the same Gauss-Bonnet theory in six dimensions. All the components of the perturbation can be written in terms of a single component and its derivatives. For this, we find a master equation that admits bounded solutions provided the characteristic time of the exponential growth of the perturbation is related to the wave number along the extra direction, as in general relativity. It is known that these configurations suffer from a thermal instability; therefore, the results presented here provide evidence for the Gubser-Mitra conjecture in the context of Gauss-Bonnet theory. Because of the nontriviality of the curvature of the background, all of the components of the metric perturbation appear in the linearized equations. Similar to spherical black holes, the black strings should be obtained as the short-distance limit r ≪α1 /2 of the black-string solution of Einstein-Gauss-Bonnet theory (which is not known analytically), where α is the Gauss-Bonnet coupling.
Framed 4-graphs: Euler tours, Gauss circuits and rotating circuits
Il'yutko, Denis P
2011-09-30
We consider connected finite 4-valent graphs with the structure of opposite edges at each vertex (framed 4-graphs). For any of such graphs there exist Euler tours, in travelling along which at each vertex we turn from an edge to a nonopposite one (rotating circuits); and at the same time, it is not true that for any such graph there exists an Euler tour passing from an edge to the opposite one at each vertex (a Gauss circuit). The main result of the work is an explicit formula connecting the adjacency matrices of the Gauss circuit and an arbitrary Euler tour. This formula immediately gives us a criterion for the existence of a Gauss circuit on a given framed 4-graph. It turns out that the results are also valid for all symmetric matrices (not just for matrices realisable by a chord diagram). Bibliography: 24 titles.
Braneworld dynamics in Einstein-Gauss-Bonnet gravity
Maeda, Hideki; Sahni, Varun; Shtanov, Yuri
2007-11-15
We discuss the cosmological evolution of a braneworld in five-dimensional Gauss-Bonnet gravity. Our discussion allows the fifth (bulk) dimension to be spacelike as well as timelike. The resulting equations of motion have the form of a cubic equation in the (H{sup 2},({rho}+{sigma}){sup 2}) plane, where {sigma} is the brane tension and {rho} is the matter density. This allows us to conduct a comprehensive pictorial analysis of cosmological evolution for the Gauss-Bonnet brane. The many interesting properties of this braneworld include the possibility of accelerated expansion at late times. For a finite region in parameter space the accelerated expansion can be phantomlike so that w<-1. At late times, this branch approaches de Sitter space (w=-1) and avoids the big-rip singularities usually present in phantom models. For a timelike extra dimension the Gauss-Bonnet brane can bounce and avoid the initial singularity.
Interacting Ricci dark energy in scalar Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Chattopadhyay, Surajit; Pasqua, Antonio; Aly, Ayman A.
2014-02-01
This paper reports a study on the cosmological application of interacting Ricci Dark Energy (RDE) density in the scalar Gauss-Bonnet framework. The interacting holographic RDE model has been employed to obtain the equation of state (EoS) in a spatially flat universe. The main results of this paper are that the reconstructed potential of scalar Gauss-Bonnet gravity for the interacting RDE model decays with the evolution of the universe. However, it is an increasing function of the scalar field . Both the strong and weak energy conditions are violated. A phantom-like behavior of the EoS parameter has been obtained. The effective EoS parameter stays below -1 but tends to -1 with the evolution of the universe. However, it cannot cross the phantom boundary. Finally, the interacting RDE model in Gauss-Bonnet gravity gives accelerated expansion of the universe.
N+1 formalism in Einstein-Gauss-Bonnet gravity
Torii, Takashi; Shinkai, Hisa-aki
2008-10-15
Towards the investigation of the full dynamics in a higher-dimensional and/or a stringy gravitational model, we present the basic equations of the Einstein-Gauss-Bonnet gravity theory. We show the (N+1)-dimensional version of the Arnowitt-Deser-Misner decomposition including Gauss-Bonnet terms, which shall be the standard approach to treat the space-time as a Cauchy problem. Because of the quasilinear property of the Gauss-Bonnet gravity, we find that the evolution equations can be in a treatable form in numerics. We also show the conformally transformed constraint equations for constructing the initial data. We discuss how the constraints can be simplified by tuning the powers of conformal factors. Our equations can be used both for timelike and spacelike foliations.
Framed 4-graphs: Euler tours, Gauss circuits and rotating circuits
NASA Astrophysics Data System (ADS)
Il'yutko, Denis P.
2011-09-01
We consider connected finite 4-valent graphs with the structure of opposite edges at each vertex (framed 4-graphs). For any of such graphs there exist Euler tours, in travelling along which at each vertex we turn from an edge to a nonopposite one (rotating circuits); and at the same time, it is not true that for any such graph there exists an Euler tour passing from an edge to the opposite one at each vertex (a Gauss circuit). The main result of the work is an explicit formula connecting the adjacency matrices of the Gauss circuit and an arbitrary Euler tour. This formula immediately gives us a criterion for the existence of a Gauss circuit on a given framed 4-graph. It turns out that the results are also valid for all symmetric matrices (not just for matrices realisable by a chord diagram). Bibliography: 24 titles.
Accurate Computation of Gaussian Quadrature for Tension Powers
NASA Astrophysics Data System (ADS)
Singer, Saša
2007-09-01
We consider Gaussian quadrature formulæ which exactly integrate a system of tension powers 1,x,x2,…,xn-3, sinh(px), cosh(px), on a given interval [a,b], where n⩾4 is an even integer and p>0 is a given tension parameter. In some applications it is essential that p can be changed dynamically, and we need an efficient "on-demand" algorithm that calculates the nodes and weights of Gaussian quadrature formulas for many different values of p, which are not known in advance. It is an interesting numerical challenge to achieve the required full machine precision accuracy in such an algorithm, for all possible values of p. By exploiting various analytic and numerical techniques, we show that this can be done efficiently for all reasonably low values of n that are of any practical importance.
Quadrature formulae for classes of functions of low smoothness
Nursultanov, E D; Tleukhanova, N T
2003-10-31
For Sobolev and Korobov spaces of functions of several variables a quadrature formula with explicitly defined coefficients and nodes is constructed. This formula is precise for trigonometric polynomials with harmonics from the corresponding step hyperbolic cross. The error of the quadrature formula in the classes W{sup {alpha}}{sub p}[0,1]{sup n}, E{sup {alpha}}[0,1]{sup n} is o((ln M){sup {beta}}/M{sup {alpha}}), where M is the number of nodes and {beta} is a parameter depending on the class. The problem of the approximate calculation of multiple integrals for functions in W{sup {alpha}}{sub p}[0,1]{sup n} is considered in the case when this class does not lie in the space of continuous functions, that is, for {alpha}{<=}1/p.
Extraction of quadrature phase information from multiple pulse NMR signals
NASA Technical Reports Server (NTRS)
Rhim, W.-K.; Burum, D. P.; Vaughan, R. W.
1976-01-01
A multiple pulse sequence (8-pulse sequence) used for high-resolution solid state NMR is analyzed with regard to the information available from each of the four wide sampling windows. It is demonstrated that full quadrature phase information can be obtained using only a single phase detector and that, for the commonly encountered situation where the spectral width is much less than the folding frequency, the signals from the various windows can be combined easily using standard complex Fourier transform software. An improvement in the signal-to-noise ratio equal to the square root of 3 is obtained over either standard single or quadrature phase detection schemes. Procedures for correcting spectral distortions are presented.
Efficient quadrature multichannel processor algorithms for MCD applications
NASA Astrophysics Data System (ADS)
Corden, I. R.; Carrasco, R. A.
1992-06-01
The forthcoming third generation of satellites incorporating multichannel demodulator (MCD) processors, and the needs apparent within aviation systems, induce the requirement for efficient band processing algorithms with specific regard to the quadrature processing arrangement. This paper presents a coherent z-domain formulation of the pertinent digital transmultiplexer algorithms for the on-board processing (OBP) scenario, with a view to establishig a set of desirable algorithmic properties suitable for the preferred complex oriented quadrature processing algorithms. Stemming from the principles set forth, an ensemble of new algorithms based upon mixes of Hilbert transforming and real transform algorithms is presented, wherein the established concepts relating to the telephone network transmultiplexer algorithms are able to be exploited in certain cases. Further, the computational load of one of the methods is lower than that of a known prominent OBP related technique. The computational necessities of the various algorithms are laid down for comparative purposes in addition to the mathematical descriptions.
Buchdahl's inequality in five dimensional Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Wright, Matthew
2016-07-01
The Buchdahl limit for static spherically symmetric isotropic stars is generalised to the case of five dimensional Gauss-Bonnet gravity. Our result depends on the sign of the Gauss-Bonnet coupling constant α . When α >0, we find, unlike in general relativity, that the bound is dependent on the stellar structure, in particular the central energy density and we find that stable stellar structures can exist arbitrarily close to the black hole horizon. Thus stable stars can exist with extra mass in this theory compared to five dimensional general relativity. For α <0 it is found that the Buchdahl bound is more restrictive than the general relativistic case.
Best quadrature formula on Sobolev class with Chebyshev weight
NASA Astrophysics Data System (ADS)
Xie, Congcong
2008-05-01
Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KWr[-1,1] with Chebyshev weight. The given function information means that the values of a function f[set membership, variant]KWr[-1,1] and its derivatives up to r-1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples.
Solar Wind Characteristics from SOHO-Sun-Ulysses Quadrature Observations
NASA Technical Reports Server (NTRS)
Poletto, Giannina; Suess, Steve T.; Six, N. Frank (Technical Monitor)
2002-01-01
Over the past few years, we have been running SOHO (Solar and Heliospheric Observatory)-Sun-Ulysses quadrature campaigns, aimed at comparing the plasma properties at coronal altitudes with plasma properties at interplanetary distances. Coronal plasma has been observed by SOHO experiments: mainly, we used LASCO (Large Angle and Spectrometric Coronagraph Experiment) data to understand the overall coronal configuration at the time of quadratures and analyzed SUMER (Solar Ultraviolet Measurements of Emitted Radiation), CDS (Coronal Diagnostic Spectrometer) and UVCS (Ultraviolet Coronagraph Spectrometer) data to derive its physical characteristics. At interplanetary distances, SWICS (Solar Wind Ion Composition Spectrometer) and SWOOPS (Solar Wind Observation over the Poles of the Sun) aboard Ulysses provided us with interplanetary plasma data. Here we report on results from some of the campaigns. We notice that, depending on the geometry of the quadrature, i.e. on whether the radial to Ulysses traverses the corona at high or low latitudes, we are able to study different kinds of solar wind. In particular, a comparison between low-latitude and high-latitude wind, allowed us to provide evidence for differences in the acceleration of polar, fast plasma and equatorial, slow plasma: the latter occurring at higher levels and through a more extended region than fast wind. These properties are shared by both the proton and heavy ions outflows. Quadrature observations may provide useful information also on coronal vs. in situ elemental composition. To this end, we analyzed spectra taken in the corona, at altitudes ranging between approx. 1.02 and 2.2 solar radii, and derived the abundances of a number of ions, including oxygen and iron. Values of the O/Fe ratio, at coronal levels, have been compared with measurements of this ratio made by SWICS at interplanetary distances. Our results are compared with previous findings and predictions from modeling efforts.
An Application of the Quadrature-Free Discontinuous Galerkin Method
NASA Technical Reports Server (NTRS)
Lockard, David P.; Atkins, Harold L.
2000-01-01
The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.
Statistical Quadrature Evolution for Continuous-Variable Quantum Key Distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, Laszlo; Imre, Sandor
2016-05-01
We propose a statistical quadrature evolution (SQE) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The SQE framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. We define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of our method. We prove the secret key rate formulas for a multiple access multicarrier CVQKD. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario. This work was partially supported by the GOP-1.1.1-11-2012-0092 project sponsored by the EU and European Structural Fund, by the Hungarian Scientific Research Fund - OTKA K-112125, and by the COST Action MP1006.
Testing the Empirical Shock Arrival Model Using Quadrature Observations
NASA Technical Reports Server (NTRS)
Gopalswamy, N.; Makela, P.; Xie, H.; Yashiro, S.
2013-01-01
The empirical shock arrival (ESA) model was developed based on quadrature data from Helios (in situ) and P-78 (remote sensing) to predict the Sun-Earth travel time of coronal mass ejections (CMEs). The ESA model requires earthward CME speed as input, which is not directly measurable from coronagraphs along the Sun-Earth line. The Solar Terrestrial Relations Observatory (STEREO) and the Solar and Heliospheric Observatory (SOHO) were in quadrature during 20102012, so the speeds of Earth-directed CMEs were observed with minimal projection effects. We identified a set of 20 full halo CMEs in the field of view of SOHO that were also observed in quadrature by STEREO. We used the earthward speed from STEREO measurements as input to the ESA model and compared the resulting travel times with the observed ones from L1 monitors. We find that the model predicts the CME travel time within about 7.3 h, which is similar to the predictions by the ENLIL model. We also find that CME-CME and CME-coronal hole interaction can lead to large deviations from model predictions.
Hou, Chieh; Ateshian, Gerard A
2016-01-01
Fibrous biological tissues may be modeled using a continuous fiber distribution (CFD) to capture tension-compression nonlinearity, anisotropic fiber distributions, and load-induced anisotropy. The CFD framework requires spherical integration of weighted individual fiber responses, with fibers contributing to the stress response only when they are in tension. The common method for performing this integration employs the discretization of the unit sphere into a polyhedron with nearly uniform triangular faces (finite element integration or FEI scheme). Although FEI has proven to be more accurate and efficient than integration using spherical coordinates, it presents three major drawbacks: First, the number of elements on the unit sphere needed to achieve satisfactory accuracy becomes a significant computational cost in a finite element (FE) analysis. Second, fibers may not be in tension in some regions on the unit sphere, where the integration becomes a waste. Third, if tensed fiber bundles span a small region compared to the area of the elements on the sphere, a significant discretization error arises. This study presents an integration scheme specialized to the CFD framework, which significantly mitigates the first drawback of the FEI scheme, while eliminating the second and third completely. Here, integration is performed only over the regions of the unit sphere where fibers are in tension. Gauss-Kronrod quadrature is used across latitudes and the trapezoidal scheme across longitudes. Over a wide range of strain states, fiber material properties, and fiber angular distributions, results demonstrate that this new scheme always outperforms FEI, sometimes by orders of magnitude in the number of computational steps and relative accuracy of the stress calculation. PMID:26291492
Advanced quadratures and periodic boundary conditions in parallel 3D S{sub n} transport
Manalo, K.; Yi, C.; Huang, M.; Sjoden, G.
2013-07-01
Significant updates in numerical quadratures have warranted investigation with 3D Sn discrete ordinates transport. We show new applications of quadrature departing from level symmetric (S{sub 2}o). investigating 3 recently developed quadratures: Even-Odd (EO), Linear-Discontinuous Finite Element - Surface Area (LDFE-SA), and the non-symmetric Icosahedral Quadrature (IC). We discuss implementation changes to 3D Sn codes (applied to Hybrid MOC-Sn TITAN and 3D parallel PENTRAN) that can be performed to accommodate Icosahedral Quadrature, as this quadrature is not 90-degree rotation invariant. In particular, as demonstrated using PENTRAN, the properties of Icosahedral Quadrature are suitable for trivial application using periodic BCs versus that of reflective BCs. In addition to implementing periodic BCs for 3D Sn PENTRAN, we implemented a technique termed 'angular re-sweep' which properly conditions periodic BCs for outer eigenvalue iterative loop convergence. As demonstrated by two simple transport problems (3-group fixed source and 3-group reflected/periodic eigenvalue pin cell), we remark that all of the quadratures we investigated are generally superior to level symmetric quadrature, with Icosahedral Quadrature performing the most efficiently for problems tested. (authors)
An Exodus II specification for handling gauss points.
Thompson, David C.; Jortner, Jeffrey N.; Pebay, Philippe Pierre
2007-11-01
This report specifies the way in which Gauss points shall be named and ordered when storing them in an EXODUS II file so that they may be properly interpreted by visualization tools. This naming convention covers hexahedra and tetrahedra. Future revisions of this document will cover quadrilaterals, triangles, and shell elements.
Accelerated expansion of the Universe in Gauss-Bonnet gravity
Dehghani, M.H.
2004-09-15
We show that in Gauss-Bonnet gravity with negative Gauss-Bonnet coefficient and without a cosmological constant, one can explain the acceleration of the expanding Universe. We first introduce a solution of the Gauss-Bonnet gravity with negative Gauss-Bonnet coefficient and no cosmological constant term in an empty (n+1)-dimensional bulk. This solution can generate a de Sitter spacetime with curvature n(n+1)/{l_brace}(n-2)(n-3) vertical bar {alpha} vertical bar {r_brace}. We show that an (n-1)-dimensional brane embedded in this bulk can have an expanding feature with acceleration. We also considered a four-dimensional brane world in a five-dimensional empty space with zero cosmological constant and obtain the modified Friedmann equations. The solution of these modified equations in matter-dominated era presents an expanding Universe with negative deceleration and positive jerk which is consistent with the recent cosmological data. We also find that for this solution, the 'n' th derivative of the scale factor with respect to time can be expressed only in terms of Hubble and deceleration parameters.
Holographic vector superconductor in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Lu, Jun-Wang; Wu, Ya-Bo; Cai, Tuo; Liu, Hai-Min; Ren, Yin-Shuan; Liu, Mo-Lin
2016-02-01
In the probe limit, we numerically study the holographic p-wave superconductor phase transitions in the higher curvature theory. Concretely, we study the influences of Gauss-Bonnet parameter α on the Maxwell complex vector model (MCV) in the five-dimensional Gauss-Bonnet-AdS black hole and soliton backgrounds, respectively. In the two backgrounds, the improving Gauss-Bonnet parameter α and dimension of the vector operator Δ inhibit the vector condensate. In the black hole, the condensate quickly saturates a stable value at lower temperature. Moreover, both the stable value of condensate and the ratio ωg /Tc increase with α. In the soliton, the location of the second pole of the imaginary part increases with α, which implies that the energy of the quasiparticle excitation increases with the improving higher curvature correction. In addition, the influences of the Gauss-Bonnet correction on the MCV model are similar to the ones on the SU(2) p-wave model, which confirms that the MCV model is a generalization of the SU(2) Yang-Mills model even without the applied magnetic field to some extent.
Understanding Gauss's Law Using Spreadsheets
ERIC Educational Resources Information Center
Baird, William H.
2013-01-01
Some of the results from the electrostatics portion of introductory physics are particularly difficult for students to understand and/or believe. For students who have yet to take vector calculus, Gauss's law is far from obvious and may seem more difficult than Coulomb's. When these same students are told that the minimum potential…
Quadrature rules with multiple nodes for evaluating integrals with strong singularities
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.
2006-05-01
We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.
Chen, Hua-Pin
2014-01-01
The electronically tunable quadrature oscillator using a single multiple-output current controlled current differencing transconductance amplifier (MO-CCCDTA) and grounded passive components is presented. The proposed configuration uses a single MO-CCCDTA, two grounded capacitors and one grounded resistor. Two high-output impedance quadrature current signals and two quadrature voltage signals with 90° phase difference. The oscillation condition and oscillation frequency of the proposed quadrature oscillator are independently controllable. The use of only grounded passive components makes the proposed circuit ideal for integrated circuit implementation. PMID:25121124
Noise-cancelling quadrature magnetic position, speed and direction sensor
Preston, Mark A.; King, Robert D.
1996-01-01
An array of three magnetic sensors in a single package is employed with a single bias magnet for sensing shaft position, speed and direction of a motor in a high magnetic noise environment. Two of the three magnetic sensors are situated in an anti-phase relationship (i.e., 180.degree. out-of-phase) with respect to the relationship between the other of the two sensors and magnetically salient target, and the third magnetic sensor is situated between the anti-phase sensors. The result is quadrature sensing with noise immunity for accurate relative position, speed and direction measurements.
Parametric generation of quadrature squeezing of mirrors in cavity optomechanics
Liao, Jie-Qiao; Law, C. K.
2011-03-15
We propose a method to generate quadrature-squeezed states of a moving mirror in a Fabry-Perot cavity. This is achieved by exploiting the fact that when the cavity is driven by an external field with a large detuning, the moving mirror behaves as a parametric oscillator. We show that parametric resonance can be reached approximately by modulating the driving field amplitude at a frequency matching the frequency shift of the mirror. The parametric resonance leads to an efficient generation of squeezing, which is limited by the thermal noise of the environment.
Experimental demonstration of microring quadrature phase-shift keying modulators.
Dong, Po; Xie, Chongjin; Chen, Long; Fontaine, Nicolas K; Chen, Young-kai
2012-04-01
Advanced optical modulation formats are a key technology to increase the capacity of optical communication networks. Mach-Zehnder modulators are typically used to generate various modulation formats. Here, we report the first experimental demonstration of quadrature phase-shift keying (QPSK) modulation using compact microring modulators. Generation of 20 Gb/s QPSK signals is demonstrated with 30 μm radius silicon ring modulators with drive voltages of ~6 V. These compact QPSK modulators may be used in miniature optical transponders for high-capacity optical data links. PMID:22466187
The Weyl-Cartan Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Haghani, Zahra; Khosravi, Nima; Shahidi, Shahab
2015-11-01
In this paper, we consider the generalized Gauss-Bonnet action in four-dimensional Weyl-Cartan spacetime. In this spacetime, the presence of a torsion tensor and Weyl vector implies that the generalized Gauss-Bonnet action will not be a total derivative in four-dimensional spacetime. It will be shown that the higher than two time derivatives can be removed from the action by choosing a suitable set of parameters. In the special case where only the trace part of the torsion remains, the model reduces to general relativity plus two vector fields, one of which is massless and the other is massive. We will then obtain the healthy region of the five-dimensional parameter space of the theory in some special cases.
Dark energy from Gauss-Bonnet and nonminimal couplings
NASA Astrophysics Data System (ADS)
Granda, L. N.; Jimenez, D. F.
2014-12-01
We consider a scalar-tensor model of dark energy with Gauss-Bonnet and nonminimal couplings. Exact cosmological solutions were found in the absence of potential that give equations of state of dark energy consistent with current observational constraints, but with different asymptotic behaviors depending on the couplings of the model. A detailed reconstruction procedure is given for the scalar potential and the Gauss-Bonnet coupling for any given cosmological scenario. In particular we consider conditions for the existence of a variety of cosmological solutions with accelerated expansion, including quintessence, phantom, de Sitter, and Little Rip. For the case of quintessence and phantom we have found a scalar potential of the Albrecht-Skordis type, where the potential is an exponential with a polynomial factor.
Laguerre-Gauss beams versus Bessel beams showdown: peer comparison.
Mendoza-Hernández, Job; Arroyo-Carrasco, Maximino Luis; Iturbe-Castillo, Marcelo David; Chávez-Cerda, Sabino
2015-08-15
We present for the first time a comparison under similar circumstances between Laguerre-Gauss beams (LGBs) and Bessel beams (BB), and show that the former can be a better option for many applications in which BBs are currently used. By solving the Laguerre-Gauss differential equation in the asymptotic limit of a large radial index, we find the parameters to perform a peer comparison, showing that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do. We also demonstrate that LGBs, which have the property of self-healing, are more robust in the sense that they can propagate further than BBs under similar initial conditions. PMID:26274648
Flat Gauss illumination for the step-and-scan lithographic system
NASA Astrophysics Data System (ADS)
Chen, Ming; Wang, Ying; Zeng, Aijun; Zhu, Jing; Yang, Baoxi; Huang, Huijie
2016-08-01
To meet the uniform dose exposure in optical lithography, it is desirable to get uniform illumination in the scanning direction on wafer for the step-and-scan lithographic system. We present a flat Gauss illumination for the step-and-scan lithographic system in this paper. Through flat Gauss illumination in scanning direction, pulse quantization effect could be reduced effectively. Correspondingly, the uniformity of the reticle and wafer is improved. Compared with the trapezoid illumination, flat Gauss illumination could keep the slit edge fixed, and pulse quantization effect will not be enhanced. Moreover flat Gauss illumination could be obtained directly without defocusing and blocking, which results in high energy efficiency and high throughput of the lithography. A design strategy for flat Gauss illumination is also proposed which offers high uniformity illumination, fixed slope and integral energy of flat Gauss illumination in different coherence factors. The strategy describes a light uniform device which contains first microlens array, second microlens array, one-dimensional Gauss diffuser and a Fourier lens. The device produces flat Gauss illumination directly at the scanning slit. The design and simulation results show that the uniformity of flat Gauss illumination in two directions satisfy the requirements of lithographic illumination system and the slope. In addition, slit edge of flat Gauss illumination does not change.
Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM.
Sorokina, Mariia; Sygletos, Stylianos; Ellis, Andrew; Turitsyn, Sergei
2015-07-01
We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats). PMID:26125381
A Family of Exponential Fitting Direct Quadrature Methods for Volterra Integral Equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Ferro, M.; Ixaru, L. Gr.; Paternoster, B.
2010-09-01
A new class of direct quadrature methods for the solution of Volterra Integral Equations with periodic solution is illustrated. Such methods are based on an exponential fitting gaussian quadrature formula, whose coefficients depend on the problem parameters, in order to better reproduce the behavior the analytical solution. The construction of the methods is described, together with the analysis of the order of accuracy.
General n-dimensional quadrature transform and its application to interferogram demodulation.
Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis
2003-05-01
Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward. PMID:12747439
The Nature of the Nodes, Weights and Degree of Precision in Gaussian Quadrature Rules
ERIC Educational Resources Information Center
Prentice, J. S. C.
2011-01-01
We present a comprehensive proof of the theorem that relates the weights and nodes of a Gaussian quadrature rule to its degree of precision. This level of detail is often absent in modern texts on numerical analysis. We show that the degree of precision is maximal, and that the approximation error in Gaussian quadrature is minimal, in a…
Quadrature phase interferometer for high resolution force spectroscopy.
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A; Bellon, Ludovic
2013-09-01
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5×10(-15) m/√Hz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm. PMID:24089852
Double-Referential Holography and Spatial Quadrature Amplitude Modulation
NASA Astrophysics Data System (ADS)
Zukeran, Keisuke; Okamoto, Atsushi; Takabayashi, Masanori; Shibukawa, Atsushi; Sato, Kunihiro; Tomita, Akihisa
2013-09-01
We proposed a double-referential holography (DRH) that allows phase-detection without external additional beams. In the DRH, phantom beams, prepared in the same optical path as signal beams and preliminary multiplexed in a recording medium along with the signal, are used to produce interference fringes on an imager for converting a phase into an intensity distribution. The DRH enables stable and high-accuracy phase detection independent of the fluctuations and vibrations of the optical system owing to medium shift and temperature variation. Besides, the collinear arrangement of the signal and phantom beams leads to the compactness of the optical data storage system. We conducted an experiment using binary phase modulation signals for verifying the DRH operation. In addition, 38-level spatial quadrature amplitude modulation signals were successfully reproduced with the DRH by numerical simulation. Furthermore, we verified that the distributed phase-shifting method moderates the dynamic range consumption for the exposure of phantom beams.
Quadrature phase interferometer for high resolution force spectroscopy
NASA Astrophysics Data System (ADS)
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A.; Bellon, Ludovic
2013-09-01
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5 × 10^{-15} m/sqrtHz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.
Quadrature phase interferometer for high resolution force spectroscopy
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A.; Bellon, Ludovic
2013-09-15
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5×10{sup −15} m/√(Hz)), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.
Weighted discrete least-squares polynomial approximation using randomized quadratures
NASA Astrophysics Data System (ADS)
Zhou, Tao; Narayan, Akil; Xiu, Dongbin
2015-10-01
We discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation. The problem stems from uncertainty quantification (UQ), where the independent variables of the functions are random variables with specified probability measure. We propose to construct the least squares approximation on points randomly and uniformly sampled from tensor product Gaussian quadrature points. We analyze the stability properties of this method and prove that the method is asymptotically stable, provided that the number of points scales linearly (up to a logarithmic factor) with the cardinality of the polynomial space. Specific results in both bounded and unbounded domains are obtained, along with a convergence result for Chebyshev measure. Numerical examples are provided to verify the theoretical results.
Terahertz single-shot quadrature phase-shifting interferometry.
Földesy, Péter
2012-10-01
A single-shot quadrature phase-shifting interferometry architecture is presented that is applicable to antenna coupled detector technologies. The method is based on orthogonally polarized object and reference beams and on linear and circular polarization sensitive antennas in space-division multiplexing. The technique can be adapted to two-, three-, and four-step and Gabor holography recordings. It is also demonstrated that the space-division multiplexing does not necessarily cause sparse sampling. A sub-THz detector array is presented containing multiple on-chip antennas and FET plasma wave detectors implemented in a 90 nm complementary metal-oxide semiconductor technology. As an example, two-step phase-shifting reconstruction results are given at 360 GHz. PMID:23027273
Self-similar propagation of Hermite-Gauss water-wave pulses.
Fu, Shenhe; Tsur, Yuval; Zhou, Jianying; Shemer, Lev; Arie, Ady
2016-01-01
We demonstrate both theoretically and experimentally propagation dynamics of surface gravity water-wave pulses, having Hermite-Gauss envelopes. We show that these waves propagate self-similarly along an 18-m wave tank, preserving their general Hermite-Gauss envelopes in both the linear and the nonlinear regimes. The measured surface elevation wave groups enable observing the envelope phase evolution of both nonchirped and linearly frequency chirped Hermite-Gauss pulses, hence allowing us to measure Gouy phase shifts of high-order Hermite-Gauss pulses for the first time. Finally, when increasing pulse amplitude, nonlinearity becomes essential and the second harmonic of Hermite-Gauss waves was observed. We further show that these generated second harmonic bound waves still exhibit self-similar Hermite-Gauss shapes along the tank. PMID:26871174
Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature
NASA Technical Reports Server (NTRS)
Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)
2000-01-01
This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.
Quadrature squeezed photons from a two-level system.
Schulte, Carsten H H; Hansom, Jack; Jones, Alex E; Matthiesen, Clemens; Le Gall, Claire; Atatüre, Mete
2015-09-10
Resonance fluorescence arises from the interaction of an optical field with a two-level system, and has played a fundamental role in the development of quantum optics and its applications. Despite its conceptual simplicity, it entails a wide range of intriguing phenomena, such as the Mollow-triplet emission spectrum, photon antibunching and coherent photon emission. One fundamental aspect of resonance fluorescence--squeezing in the form of reduced quantum fluctuations in the single photon stream from an atom in free space--was predicted more than 30 years ago. However, the requirement to operate in the weak excitation regime, together with the combination of modest oscillator strength of atoms and low collection efficiencies, has continued to necessitate stringent experimental conditions for the observation of squeezing with atoms. Attempts to circumvent these issues had to sacrifice antibunching, owing to either stimulated forward scattering from atomic ensembles or multi-photon transitions inside optical cavities. Here, we use an artificial atom with a large optical dipole enabling 100-fold improvement of the photon detection rate over the natural atom counterpart and reach the necessary conditions for the observation of quadrature squeezing in single resonance-fluorescence photons. By implementing phase-dependent homodyne intensity-correlation detection, we demonstrate that the electric field quadrature variance of resonance fluorescence is three per cent below the fundamental limit set by vacuum fluctuations, while the photon statistics remain antibunched. The presence of squeezing and antibunching simultaneously is a fully non-classical outcome of the wave-particle duality of photons. PMID:26322581
Nonzonal Expressions of GAUSS-KRÜGER Projection in Polar Regions
NASA Astrophysics Data System (ADS)
Li, Zhongmei; Bian, Shaofeng; Liu, Qiang; Li, Houpu; Chen, Cheng; Hu, Yanfeng
2016-06-01
With conformal colatitude introduced, based on the mathematical relationship between exponential and logarithmic functions by complex numbers, strict equation of complex conformal colatitude is derived, and then theoretically strict nonzonal expressions of Gauss projection in polar regions are carried out. By means of the computer algebra system, correctness of these expressions is verified, and sketches of Gauss-krüger projection without bandwidth restriction in polar regions are charted. In the Arctic or Antarctic region, graticule of nonzonal Gauss projection complies with people's reading habit and reflects real ground-object distribution. Achievements in this paper could perfect mathematical basis of Gauss projection and provide reference frame for polar surveying and photogrammetry.
Fractional Hamiltonian monodromy from a Gauss-Manin monodromy
Sugny, D.; Jauslin, H. R.; Mardesic, P.; Pelletier, M.; Jebrane, A.
2008-04-15
Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskii, and Zhilinskii, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); and Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m:-n resonant systems.
Extension of Gauss' method for the solution of Kepler's equation
NASA Technical Reports Server (NTRS)
Battin, R. H.; Fill, T. J.
1978-01-01
Gauss' method for solving Kepler's equation is extended to arbitrary epochs and orbital eccentricities. Although originally developed for near parabolic orbits in the vicinity of pericenter, a generalization of the method leads to a highly efficient algorithm which compares favorably to other methods in current use. A key virtue of the technique is that convergence is obtained by a method of successive substitutions with an initial approximation that is independent of the orbital parameters. The equations of the algorithm are universal, i.e., independent of the nature of the orbit whether elliptic, hyperbolic, parabolic or rectilinear.
Gauss's law test of gravity at short range
NASA Technical Reports Server (NTRS)
Moody, M. V.; Paik, H. J.
1993-01-01
A null test of the gravitational inverse-square law can be performed by testing Gauss's law for the field. We have constructed a three-axis superconducting gravity gradiometer and carried out such a test. A lead pendulum weighing 1500 kg was used to produce a time-varying field. This experiment places a new (2-sigma) limit of alpha = (0.9 + or - 4.6) x 10 exp -4 at lambda of 1.5 m, where alpha and lambda are parameters for the generalized potential phi = -(GM/r)(l + alpha e exp -r/lambda).
Gauss-Bonnet Brane World Gravity with a Scalar Field
Davis, Stephen C.
2004-11-17
The effective four-dimensional, linearised gravity of a brane world model with one extra dimension and a single brane is analysed. The model includes higher order curvature terms (such as the Gauss-Bonnet term) and a conformally coupled scalar field. Large and small distance gravitational laws are derived. In contrast to the corresponding Einstein gravity models, it is possible to obtain solutions with localised gravity which are compatible with observations. Solutions with non-standard large distance Newtonian potentials are also described.
NASA Astrophysics Data System (ADS)
Knizhnerman, Leonid
2010-01-01
Stability of passing from Gaussian quadrature data to the Lanczos recurrence coefficients is considered. Special attention is paid to estimates explicitly expressed in terms of quadrature data and not having weights in denominators. It has been shown that the recent approach, exploiting integral representation of Hankel determinants, implies quantitative improvement of D. Laurie's constructive estimate. It has also been demonstrated that a particular implementation on the Hankel determinant approach gives an estimate being unimprovable up to a coefficient; the corresponding example involves quadrature data with a small but not too small weight. It follows that polynomial increase of a general case upper bound in terms of the dimension is unavoidable.
Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation
NASA Technical Reports Server (NTRS)
Mcreynolds, S. R.
1975-01-01
A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.
NASA Technical Reports Server (NTRS)
Desmarais, R. N.
1975-01-01
Computer programs for computing Gaussian quadrature abscissas and weights are described. For the classical case the programs use Laguerre iteration to compute abscissas as zeros of orthogonal polynomials. The polynomials are evaluated from known recursion coefficients. The nonclassical case is handled similarly except that the recursion coefficients are computed by numerical integration. A sample problem, with input and output, is presented to illustrate the use of the programs. It computes the quadrature abscissas and weights associated with the weight function over the interval (0,1) for quadrature orders from 16 to 96 in increments of 8.
NASA Astrophysics Data System (ADS)
Bauman, Brian J.; Xiao, Hong
2010-08-01
Forbes introduced the usage of Gaussian quadratures in optical design for circular pupils and fields, and for a specific visible wavelength band. In this paper, Gaussian quadrature methods of selecting rays in ray-tracing are derived for noncircular pupil shapes, such as obscured and vignetted apertures. In addition, these methods are generalized for square fields, and for integrating performance over arbitrary wavelength bands. Integration over wavelength is aided by the use of a novel chromatic coordinate. These quadratures achieve low calculations with fewer rays (by orders of magnitude) than uniform sampling schemes.
Energy conditions in modified Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
García, Nadiezhda Montelongo; Harko, Tiberiu; Lobo, Francisco S. N.; Mimoso, José P.
2011-05-01
In considering alternative higher-order gravity theories, one is liable to be motivated in pursuing models consistent and inspired by several candidates of a fundamental theory of quantum gravity. Indeed, motivations from string/M theory predict that scalar field couplings with the Gauss-Bonnet invariant, G, are important in the appearance of nonsingular early time cosmologies. In this work, we discuss the viability of an interesting alternative gravitational theory, namely, modified Gauss-Bonnet gravity or f(G) gravity. We consider specific realistic forms of f(G) analyzed in the literature that account for the late-time cosmic acceleration and that have been found to cure the finite-time future singularities present in the dark energy models. We present the general inequalities imposed by the energy conditions and use the recent estimated values of the Hubble, deceleration, jerk and snap parameters to examine the viability of the above-mentioned forms of f(G) imposed by the weak energy condition.
Gauss-Newton method for DEM co-registration
NASA Astrophysics Data System (ADS)
Wang, Kunlun; Zhang, Tonggang
2015-12-01
Digital elevation model (DEM) co-registration is one of the hottest research problems, and it is the critical technology for multi-temporal DEM analysis, which has wide potential application in many fields, such as geological hazards. Currently, the least-squares principle is used in most DEM co-registration methods, in which the matching parameters are obtained by iteration; the surface co-registration is then accomplished. To improve the iterative convergence rate, a Gauss-Newton method for DEM co-registration (G-N) is proposed in this paper. A gradient formula based on a gridded discrete surface is derived in theory, and then the difficulty of applying the Gauss-Newton method to DEM matching is solved. With the G-N algorithm, the surfaces approach each other along the maximal gradient direction, and therefore the iterative convergence and the performance efficiency of the new method can be enhanced greatly. According to experimental results based on the simulated datasets, the average convergence rates of rotation and translation parameters of the G-N algorithm are increased by 40 and 15% compared to those of the ICP algorithm, respectively. The performance efficiency of the G-N algorithm is 74.9% better.
Controllable light capsules employing modified Bessel-Gauss beams
NASA Astrophysics Data System (ADS)
Gong, Lei; Liu, Weiwei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei
2016-07-01
We report, in theory and experiment, on a novel class of controlled light capsules with nearly perfect darkness, directly employing intrinsic properties of modified Bessel-Gauss beams. These beams are able to naturally create three-dimensional bottle-shaped region during propagation as long as the parameters are properly chosen. Remarkably, the optical bottle can be controlled to demonstrate various geometries through tuning the beam parameters, thereby leading to an adjustable light capsule. We provide a detailed insight into the theoretical origin and characteristics of the light capsule derived from modified Bessel-Gauss beams. Moreover, a binary digital micromirror device (DMD) based scheme is first employed to shape the bottle beams by precise amplitude and phase manipulation. Further, we demonstrate their ability for optical trapping of core-shell magnetic microparticles, which play a particular role in biomedical research, with holographic optical tweezers. Therefore, our observations provide a new route for generating and controlling bottle beams and will widen the potentials for micromanipulation of absorbing particles, aerosols or even individual atoms.
Gauss-Bonnet modified gravity models with bouncing behavior
NASA Astrophysics Data System (ADS)
Escofet, Anna; Elizalde, Emilio
2016-06-01
The following issue is addressed: How the addition of a Gauss-Bonnet term (generically coming from most fundamental theories, as string and M theories), to a viable model, can change the specific properties, and even the physical nature, of the corresponding cosmological solutions? Specifically, brand new original dark energy models are obtained in this way with quite interesting properties, which exhibit, in a unified fashion, the three distinguished possible cosmological phases corresponding to phantom matter, quintessence and ordinary matter, respectively. A model, in which the equation of state (EoS) parameter, w, is a function of time, is seen to lead either to a singularity of the Big Rip kind or to a bouncing solution which evolves into a de Sitter universe with w = ‑1. Moreover, new Gauss-Bonnet modified gravity models with bouncing behavior in the early stages of the universe evolution are obtained and tested for the validity and stability of the corresponding solutions. They allow for a remarkably natural, unified description of a bouncing behavior at early times and accelerated expansion at present.
Controllable light capsules employing modified Bessel-Gauss beams
Gong, Lei; Liu, Weiwei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei
2016-01-01
We report, in theory and experiment, on a novel class of controlled light capsules with nearly perfect darkness, directly employing intrinsic properties of modified Bessel-Gauss beams. These beams are able to naturally create three-dimensional bottle-shaped region during propagation as long as the parameters are properly chosen. Remarkably, the optical bottle can be controlled to demonstrate various geometries through tuning the beam parameters, thereby leading to an adjustable light capsule. We provide a detailed insight into the theoretical origin and characteristics of the light capsule derived from modified Bessel-Gauss beams. Moreover, a binary digital micromirror device (DMD) based scheme is first employed to shape the bottle beams by precise amplitude and phase manipulation. Further, we demonstrate their ability for optical trapping of core-shell magnetic microparticles, which play a particular role in biomedical research, with holographic optical tweezers. Therefore, our observations provide a new route for generating and controlling bottle beams and will widen the potentials for micromanipulation of absorbing particles, aerosols or even individual atoms. PMID:27388558
Energy conditions in modified Gauss-Bonnet gravity
Garcia, Nadiezhda Montelongo; Harko, Tiberiu; Lobo, Francisco S. N.; Mimoso, Jose P.
2011-05-15
In considering alternative higher-order gravity theories, one is liable to be motivated in pursuing models consistent and inspired by several candidates of a fundamental theory of quantum gravity. Indeed, motivations from string/M theory predict that scalar field couplings with the Gauss-Bonnet invariant, G, are important in the appearance of nonsingular early time cosmologies. In this work, we discuss the viability of an interesting alternative gravitational theory, namely, modified Gauss-Bonnet gravity or f(G) gravity. We consider specific realistic forms of f(G) analyzed in the literature that account for the late-time cosmic acceleration and that have been found to cure the finite-time future singularities present in the dark energy models. We present the general inequalities imposed by the energy conditions and use the recent estimated values of the Hubble, deceleration, jerk and snap parameters to examine the viability of the above-mentioned forms of f(G) imposed by the weak energy condition.
Gauss-Bonnet black holes with nonconstant curvature horizons
Maeda, Hideki
2010-06-15
We investigate static and dynamical n({>=}6)-dimensional black holes in Einstein-Gauss-Bonnet gravity of which horizons have the isometries of an (n-2)-dimensional Einstein space with a condition on its Weyl tensor originally given by Dotti and Gleiser. Defining a generalized Misner-Sharp quasilocal mass that satisfies the unified first law, we show that most of the properties of the quasilocal mass and the trapping horizon are shared with the case with horizons of constant curvature. It is shown that the Dotti-Gleiser solution is the unique vacuum solution if the warp factor on the (n-2)-dimensional Einstein space is nonconstant. The quasilocal mass becomes constant for the Dotti-Gleiser black hole and satisfies the first law of the black-hole thermodynamics with its Wald entropy. In the non-negative curvature case with positive Gauss-Bonnet constant and zero cosmological constant, it is shown that the Dotti-Gleiser black hole is thermodynamically unstable. Even if it becomes locally stable for the nonzero cosmological constant, it cannot be globally stable for the positive cosmological constant.
Controllable light capsules employing modified Bessel-Gauss beams.
Gong, Lei; Liu, Weiwei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei
2016-01-01
We report, in theory and experiment, on a novel class of controlled light capsules with nearly perfect darkness, directly employing intrinsic properties of modified Bessel-Gauss beams. These beams are able to naturally create three-dimensional bottle-shaped region during propagation as long as the parameters are properly chosen. Remarkably, the optical bottle can be controlled to demonstrate various geometries through tuning the beam parameters, thereby leading to an adjustable light capsule. We provide a detailed insight into the theoretical origin and characteristics of the light capsule derived from modified Bessel-Gauss beams. Moreover, a binary digital micromirror device (DMD) based scheme is first employed to shape the bottle beams by precise amplitude and phase manipulation. Further, we demonstrate their ability for optical trapping of core-shell magnetic microparticles, which play a particular role in biomedical research, with holographic optical tweezers. Therefore, our observations provide a new route for generating and controlling bottle beams and will widen the potentials for micromanipulation of absorbing particles, aerosols or even individual atoms. PMID:27388558
Crossing of the phantom divide using tachyon-Gauss-Bonnet gravity
Sadeghi, J.; Banijamali, A.; Milani, F.; Setare, M. R.
2009-06-15
In this paper we consider two models. First, we study tachyon-Gauss-Bonnet gravity and obtain the condition of the equation of state crossing -1. Second, we discuss the modified Gauss-Bonnet gravity with the tachyon field and show the condition of {omega} crossing -1. Also, we plot figures for {omega} numerically in special potential and coupling function.
Cui, Junning; He, Zhangqiang; Jiu, Yuanwei; Tan, Jiubin; Sun, Tao
2016-09-01
The demand for minimal cyclic nonlinearity error in laser interferometry is increasing as a result of advanced scientific research projects. Research shows that the quadrature phase error is the main effect that introduces cyclic nonlinearity error, and polarization-mixing cross talk during beam splitting is the main error source that causes the quadrature phase error. In this paper, a new homodyne quadrature laser interferometer configuration based on nonpolarization beam splitting and balanced interference between two circularly polarized laser beams is proposed. Theoretical modeling indicates that the polarization-mixing cross talk is elaborately avoided through nonpolarizing and Wollaston beam splitting, with a minimum number of quadrature phase error sources involved. Experimental results show that the cyclic nonlinearity error of the interferometer is up to 0.6 nm (peak-to-valley value) without any correction and can be further suppressed to 0.2 nm with a simple gain and offset correction method. PMID:27607285
Electronically Tunable Differential Integrator: Linear Voltage Controlled Quadrature Oscillator
Nandi, Rabindranath; Pattanayak, Sandhya; Das, Sagarika
2015-01-01
A new electronically tunable differential integrator (ETDI) and its extension to voltage controlled quadrature oscillator (VCQO) design with linear tuning law are proposed; the active building block is a composite current feedback amplifier with recent multiplication mode current conveyor (MMCC) element. Recently utilization of two different kinds of active devices to form a composite building block is being considered since it yields a superior functional element suitable for improved quality circuit design. The integrator time constant (τ) and the oscillation frequency (ωo) are tunable by the control voltage (V) of the MMCC block. Analysis indicates negligible phase error (θe) for the integrator and low active ωo-sensitivity relative to the device parasitic capacitances. Satisfactory experimental verifications on electronic tunability of some wave shaping applications by the integrator and a double-integrator feedback loop (DIFL) based sinusoid oscillator with linear fo variation range of 60 KHz~1.8 MHz at low THD of 2.1% are verified by both simulation and hardware tests. PMID:27347537
Modulator-free quadrature amplitude modulation signal synthesis
Liu, Zhixin; Kakande, Joseph; Kelly, Brian; O’Carroll, John; Phelan, Richard; Richardson, David J.; Slavík, Radan
2014-01-01
The ability to generate high-speed on–off-keyed telecommunication signals by directly modulating a semiconductor laser’s drive current was one of the most exciting prospective applications of the nascent field of laser technology throughout the 1960s. Three decades of progress led to the commercialization of 2.5 Gbit s−1-per-channel submarine fibre optic systems that drove the growth of the internet as a global phenomenon. However, the detrimental frequency chirp associated with direct modulation forced industry to use external electro-optic modulators to deliver the next generation of on–off-keyed 10 Gbit s−1 systems and is absolutely prohibitive for today’s (>)100 Gbit s−1 coherent systems, which use complex modulation formats (for example, quadrature amplitude modulation). Here we use optical injection locking of directly modulated semiconductor lasers to generate complex modulation format signals showing distinct advantages over current and other currently researched solutions. PMID:25523757
Quantitative phase imaging using grating-based quadrature phase interferometer
NASA Astrophysics Data System (ADS)
Wu, Jigang; Yaqoob, Zahid; Heng, Xin; Cui, Xiquan; Yang, Changhuei
2007-02-01
In this paper, we report the use of holographic gratings, which act as the free-space equivalent of the 3x3 fiber-optic coupler, to perform full field phase imaging. By recording two harmonically-related gratings in the same holographic plate, we are able to obtain nontrivial phase shift between different output ports of the gratings-based Mach-Zehnder interferometer. The phase difference can be adjusted by changing the relative phase of the recording beams when recording the hologram. We have built a Mach-Zehnder interferometer using harmonically-related holographic gratings with 600 and 1200 lines/mm spacing. Two CCD cameras at the output ports of the gratings-based Mach-Zehnder interferometer are used to record the full-field quadrature interferograms, which are subsequently processed to reconstruct the phase image. The imaging system has ~12X magnification with ~420μmx315μm field-of-view. To demonstrate the capability of our system, we have successfully performed phase imaging of a pure phase object and a paramecium caudatum.
Information entropy of Gegenbauer polynomials and Gaussian quadrature
NASA Astrophysics Data System (ADS)
Sánchez-Ruiz, Jorge
2003-05-01
In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.
Modeling of optical quadrature microscopy for imaging mouse embryos
NASA Astrophysics Data System (ADS)
Warger, William C., II; DiMarzio, Charles A.
2008-02-01
Optical quadrature microscopy (OQM) has been shown to provide the optical path difference through a mouse embryo, and has led to a novel method to count the total number of cells further into development than current non-toxic imaging techniques used in the clinic. The cell counting method has the potential to provide an additional quantitative viability marker for blastocyst transfer during in vitro fertilization. OQM uses a 633 nm laser within a modified Mach-Zehnder interferometer configuration to measure the amplitude and phase of the signal beam that travels through the embryo. Four cameras preceded by multiple beamsplitters record the four interferograms that are used within a reconstruction algorithm to produce an image of the complex electric field amplitude. Here we present a model for the electric field through the primary optical components in the imaging configuration and the reconstruction algorithm to calculate the signal to noise ratio when imaging mouse embryos. The model includes magnitude and phase errors in the individual reference and sample paths, fixed pattern noise, and noise within the laser and detectors. This analysis provides the foundation for determining the imaging limitations of OQM and the basis to optimize the cell counting method in order to introduce additional quantitative viability markers.
Modulator-free quadrature amplitude modulation signal synthesis
NASA Astrophysics Data System (ADS)
Liu, Zhixin; Kakande, Joseph; Kelly, Brian; O'Carroll, John; Phelan, Richard; Richardson, David J.; Slavík, Radan
2014-12-01
The ability to generate high-speed on-off-keyed telecommunication signals by directly modulating a semiconductor laser’s drive current was one of the most exciting prospective applications of the nascent field of laser technology throughout the 1960s. Three decades of progress led to the commercialization of 2.5 Gbit s-1-per-channel submarine fibre optic systems that drove the growth of the internet as a global phenomenon. However, the detrimental frequency chirp associated with direct modulation forced industry to use external electro-optic modulators to deliver the next generation of on-off-keyed 10 Gbit s-1 systems and is absolutely prohibitive for today’s (>)100 Gbit s-1 coherent systems, which use complex modulation formats (for example, quadrature amplitude modulation). Here we use optical injection locking of directly modulated semiconductor lasers to generate complex modulation format signals showing distinct advantages over current and other currently researched solutions.
Electronically Tunable Differential Integrator: Linear Voltage Controlled Quadrature Oscillator.
Nandi, Rabindranath; Pattanayak, Sandhya; Venkateswaran, Palaniandavar; Das, Sagarika
2015-01-01
A new electronically tunable differential integrator (ETDI) and its extension to voltage controlled quadrature oscillator (VCQO) design with linear tuning law are proposed; the active building block is a composite current feedback amplifier with recent multiplication mode current conveyor (MMCC) element. Recently utilization of two different kinds of active devices to form a composite building block is being considered since it yields a superior functional element suitable for improved quality circuit design. The integrator time constant (τ) and the oscillation frequency (ω o ) are tunable by the control voltage (V) of the MMCC block. Analysis indicates negligible phase error (θ e ) for the integrator and low active ω o -sensitivity relative to the device parasitic capacitances. Satisfactory experimental verifications on electronic tunability of some wave shaping applications by the integrator and a double-integrator feedback loop (DIFL) based sinusoid oscillator with linear f o variation range of 60 KHz~1.8 MHz at low THD of 2.1% are verified by both simulation and hardware tests. PMID:27347537
Radiation transport modeling using extended quadrature method of moments
NASA Astrophysics Data System (ADS)
Vikas, V.; Hauck, C. D.; Wang, Z. J.; Fox, R. O.
2013-08-01
The radiative transfer equation describes the propagation of radiation through a material medium. While it provides a highly accurate description of the radiation field, the large phase space on which the equation is defined makes it numerically challenging. As a consequence, significant effort has gone into the development of accurate approximation methods. Recently, an extended quadrature method of moments (EQMOM) has been developed to solve univariate population balance equations, which also have a large phase space and thus face similar computational challenges. The distinct advantage of the EQMOM approach over other moment methods is that it generates moment equations that are consistent with a positive phase space density and has a moment inversion algorithm that is fast and efficient. The goal of the current paper is to present the EQMOM method in the context of radiation transport, to discuss advantages and disadvantages, and to demonstrate its performance on a set of standard one-dimensional benchmark problems that encompass optically thin, thick, and transition regimes. Special attention is given in the implementation to the issue of realizability—that is, consistency with a positive phase space density. Numerical results in one dimension are promising and lay the foundation for extending the same framework to multiple dimensions.
Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods
Cao, Huiliang; Li, Hongsheng; Kou, Zhiwei; Shi, Yunbo; Tang, Jun; Ma, Zongmin; Shen, Chong; Liu, Jun
2016-01-01
This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses’ quadrature errors are different, and the quadrature correction system should be arranged independently. The process leading to quadrature error is proposed, and the Charge Injecting Correction (CIC), Quadrature Force Correction (QFC) and Coupling Stiffness Correction (CSC) methods are introduced. The correction objects of these three methods are the quadrature error signal, force and the coupling stiffness, respectively. The three methods are investigated through control theory analysis, model simulation and circuit experiments, and the results support the theoretical analysis. The bias stability results based on CIC, QFC and CSC are 48 °/h, 9.9 °/h and 3.7 °/h, respectively, and this value is 38 °/h before quadrature error correction. The CSC method is proved to be the better method for quadrature correction, and it improves the Angle Random Walking (ARW) value, increasing it from 0.66 °/√h to 0.21 °/√h. The CSC system general test results show that it works well across the full temperature range, and the bias stabilities of the six groups’ output data are 3.8 °/h, 3.6 °/h, 3.4 °/h, 3.1 °/h, 3.0 °/h and 4.2 °/h, respectively, which proves the system has excellent repeatability. PMID:26751455
A fast method of numerical quadrature for p-version finite element matrices
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1993-01-01
A new technique of numerical quadrature especially suited for p-version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.
The relationship of Carl Friedrich Gauss with his Hungarian scientist friends
NASA Astrophysics Data System (ADS)
Vargha, Magda
Gauss had been in close contact with four Hungarian astronomers: Farkas Bolyai, Franz Xaver von Zach, János Pasquich and Pál Tittel. All these friendships were different from each other, if only because of the various ages and social standings in which these Hungarians lived. Gauss had always shown great interest in the latter. With the exception of Pasquich, all three friendships had started out as close, and in the end Gauss had repaid poorly what he received. His correspondence with Pasquich was quite different. Towards the end of his contact with Pasquich, Gauss had lifted himself above his usual indifference. With the help of his German astronomer friends, Gauss did everything he could to vindicate Pasquich, who had been accused in front of the whole astronomical community of publishing invented observations.
Volcano clustering determination: Bivariate Gauss vs. Fisher kernels
NASA Astrophysics Data System (ADS)
Cañón-Tapia, Edgardo
2013-05-01
Underlying many studies of volcano clustering is the implicit assumption that vent distribution can be studied by using kernels originally devised for distribution in plane surfaces. Nevertheless, an important change in topology in the volcanic context is related to the distortion that is introduced when attempting to represent features found on the surface of a sphere that are being projected into a plane. This work explores the extent to which different topologies of the kernel used to study the spatial distribution of vents can introduce significant changes in the obtained density functions. To this end, a planar (Gauss) and a spherical (Fisher) kernels are mutually compared. The role of the smoothing factor in these two kernels is also explored with some detail. The results indicate that the topology of the kernel is not extremely influential, and that either type of kernel can be used to characterize a plane or a spherical distribution with exactly the same detail (provided that a suitable smoothing factor is selected in each case). It is also shown that there is a limitation on the resolution of the Fisher kernel relative to the typical separation between data that can be accurately described, because data sets with separations lower than 500 km are considered as a single cluster using this method. In contrast, the Gauss kernel can provide adequate resolutions for vent distributions at a wider range of separations. In addition, this study also shows that the numerical value of the smoothing factor (or bandwidth) of both the Gauss and Fisher kernels has no unique nor direct relationship with the relevant separation among data. In order to establish the relevant distance, it is necessary to take into consideration the value of the respective smoothing factor together with a level of statistical significance at which the contributions to the probability density function will be analyzed. Based on such reference level, it is possible to create a hierarchy of
Directional dual-tree complex wavelet packet transforms for processing quadrature signals.
Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin
2016-03-01
Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals. PMID:25388779
Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds
NASA Astrophysics Data System (ADS)
Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung
2016-06-01
We describe a Lie Algebra on the moduli space of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions {{F}g^alg, g ≥ 1}, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.
Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds
NASA Astrophysics Data System (ADS)
Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung
2016-05-01
We describe a Lie Algebra on the moduli space of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions {{F}g^alg, g ≥ 1} , which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.
Fractional Hamiltonian monodromy from a Gauss-Manin monodromy
NASA Astrophysics Data System (ADS)
Sugny, D.; Mardešić, P.; Pelletier, M.; Jebrane, A.; Jauslin, H. R.
2008-04-01
Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskií, and Zhilinskií, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); Nekhoroshev, Sadovskií, and Zhilinskií, Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m :-n resonant systems.
Near infrared reflectance analysis by Gauss-Jordan linear algebra
NASA Astrophysics Data System (ADS)
Honigs, D. E.; Freelin, J. M.; Hieftje, G. M.
1983-02-01
Near-infrared reflectance analysis (NIRA) is an analytical technique that uses the near-infrared diffuse reflectance of a sample at several discrete wavelengths to predict the concentration of one or more of the chemical species in that sample. However, because near-infrared bands from solid samples are both abundant and broad, the reflectance at a given wavelength usually contains contributions from several sample components, requiring extensive calculations on overlapped bands. In the present study, these calculations have been performed using an approach similar to that employed in multi-component spectrophotometry, but with Gauss-Jordan linear algebra serving as the computational vehicle. Using this approach, correlations for percent protein in wheat flour and percent benzene in hydrocarbons have been obtained and are evaluated. The advantages of a linear-algebra approach over the common one employing stepwise regression are explored.
Extended Gaussian quadratures for functions with an end-point singularity of logarithmic type
NASA Astrophysics Data System (ADS)
Pachucki, K.; Puchalski, M.; Yerokhin, V. A.
2014-11-01
The extended Gaussian quadrature rules are shown to be an efficient tool for numerical integration of wide class of functions with singularities of logarithmic type. The quadratures are exact for the functions pol1n-1(x)+lnx pol2n-1(x), where pol1n-1(x) and pol2n-1(x) are two arbitrary polynomials of degree n-1 and n is the order of the quadrature formula. We present an implementation of numerical algorithm that calculates the nodes and the weights of the quadrature formulas, provide a Fortran code for numerical integration, and test the performance of different kinds of Gaussian quadratures for functions with logarithmic singularities. Catalogue identifier: AETP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2535 No. of bytes in distributed program, including test data, etc.: 39 963 Distribution format: tar.gz Programming language: Mathematica, Fortran. Computer: PCs or higher performance computers. Operating system: Linux, Windows, MacOS. RAM: Kilobytes. Classification: 4.11. Nature of problem: Quadrature formulas for numerical integration, effective for a wide class of functions with end-point singularities of logarithmic type. Solution method: The method of solution is based on the algorithm developed in Ref. [1] with some modifications. Running time: Milliseconds to minutes. J. Ma, V. Rokhlin, S. Wandzura, Generalized Gaussian quadrature rules for systems of arbitrary functions, Soc. Indust. Appl. Math. J. Numer. Anal. 33 (3) (1996) 971-996.
Valuing option on the maximum of two assets using improving modified Gauss-Seidel method
NASA Astrophysics Data System (ADS)
Koh, Wei Sin; Muthuvalu, Mohana Sundaram; Aruchunan, Elayaraja; Sulaiman, Jumat
2014-07-01
This paper presents the numerical solution for the option on the maximum of two assets using Improving Modified Gauss-Seidel (IMGS) iterative method. Actually, this option can be governed by two-dimensional Black-Scholes partial differential equation (PDE). The Crank-Nicolson scheme is applied to discretize the Black-Scholes PDE in order to derive a linear system. Then, the IMGS iterative method is formulated to solve the linear system. Numerical experiments involving Gauss-Seidel (GS) and Modified Gauss-Seidel (MGS) iterative methods are implemented as control methods to test the computational efficiency of the IMGS iterative method.
Quasispherical gravitational collapse in 5D Einstein-Gauss-Bonnet gravity
Ghosh, Sushant G.; Jhingan, S.
2010-07-15
We obtain a general five-dimensional quasispherical collapsing solutions of irrotational dust in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. These solutions are a generalization, to Einstein-Gauss-Bonnet gravity, of the five-dimensional quasispherical Szkeres like collapsing solutions in general relativity. It is found that the collapse proceeds in the same way as in the analogous spherical collapse, i.e., there exists regular initial data such that the collapse proceed to form naked singularities violating cosmic censorship conjecture. The effect of Gauss-Bonnet quadratic curvature terms on the formation and locations of the apparent horizon is deduced.
Holographic superconductors in Gauss-Bonnet gravity with Born-Infeld electrodynamics
Jing Jiliang; Wang Liancheng; Pan Qiyuan; Chen Songbai
2011-03-15
We investigate the holographic superconductors in Gauss-Bonnet gravity with Born-Infeld electrodynamics. We find that the Gauss-Bonnet constant, the model parameters, and the Born-Infeld coupling parameter will affect the formation of the scalar hair, the transition point of the phase transition from the second order to the first order, and the relation connecting the gap frequency in conductivity with the critical temperature. The combination of Gauss-Bonnet gravity and the Born-Infeld electrodynamics provides richer physics in the phase transition and the condensation of the scalar hair.
NASA Astrophysics Data System (ADS)
Kulikov, G. Yu.
2015-06-01
A technique for constructing nested implicit Runge-Kutta methods in the class of mono-implicit formulas of this type is studied. These formulas are highly efficient in practice, since the dimension of the original system of differential equations is preserved, which is not possible in the case of implicit multistage Runge-Kutta formulas of the general from. On the other hand, nested implicit Runge-Kutta methods inherit all major properties of general formulas of this form, such as A-stability, symmetry, and symplecticity in a certain sense. Moreover, they can have sufficiently high stage and classical orders and, without requiring high extra costs, can ensure dense output of integration results of the same accuracy as the order of the underlying method. Thus, nested methods are efficient when applied to the numerical integration of differential equations of various sorts, including stiff and nonstiff problems, Hamiltonian systems, and invertible equations. In this paper, previously proposed nested methods based on the Gauss quadrature formulas are generalized to Lobatto-type methods. Additionally, a unified technique for constructing all such methods is proposed. Its performance is demonstrated as applied to embedded examples of nested implicit formulas of various orders. All the methods constructed are supplied with tools for local error estimation and automatic variable-stepsize mesh generation based on an optimal stepsize selection. These numerical methods are verified by solving test problems with known solutions. Additionally, a comparative analysis of these methods with Matlab built-in solvers is presented.
Design and Application of Quadrature Compensation Patterns in Bulk Silicon Micro-Gyroscopes
Ni, Yunfang; Li, Hongsheng; Huang, Libin
2014-01-01
This paper focuses on the detailed design issues of a peculiar quadrature reduction method named system stiffness matrix diagonalization, whose key technology is the design and application of quadrature compensation patterns. For bulk silicon micro-gyroscopes, a complete design and application case was presented. The compensation principle was described first. In the mechanical design, four types of basic structure units were presented to obtain the basic compensation function. A novel layout design was proposed to eliminate the additional disturbing static forces and torques. Parameter optimization was carried out to maximize the available compensation capability in a limited layout area. Two types of voltage loading methods were presented. Their influences on the sense mode dynamics were analyzed. The proposed design was applied on a dual-mass silicon micro-gyroscope developed in our laboratory. The theoretical compensation capability of a quadrature equivalent angular rate no more than 412 °/s was designed. In experiments, an actual quadrature equivalent angular rate of 357 °/s was compensated successfully. The actual compensation voltages were a little larger than the theoretical ones. The correctness of the design and the theoretical analyses was verified. They can be commonly used in planar linear vibratory silicon micro-gyroscopes for quadrature compensation purpose. PMID:25356646
Schuyler, Adam D; Maciejewski, Mark W; Stern, Alan S; Hoch, Jeffrey C
2015-01-01
Nonuniform sampling (NUS) in multidimensional NMR permits the exploration of higher dimensional experiments and longer evolution times than the Nyquist Theorem practically allows for uniformly sampled experiments. However, the spectra of NUS data include sampling-induced artifacts and may be subject to distortions imposed by sparse data reconstruction techniques, issues not encountered with the discrete Fourier transform (DFT) applied to uniformly sampled data. The characterization of these NUS-induced artifacts allows for more informed sample schedule design and improved spectral quality. The DFT–Convolution Theorem, via the point-spread function (PSF) for a given sampling scheme, provides a useful framework for exploring the nature of NUS sampling artifacts. In this work, we analyze the PSFs for a set of specially constructed NUS schemes to quantify the interplay between randomization and dimensionality for reducing artifacts relative to uniformly undersampled controls. In particular, we find a synergistic relationship between the indirect time dimensions and the “quadrature phase dimension” (i.e. the hypercomplex components collected for quadrature detection). The quadrature phase dimension provides additional degrees of freedom that enable partial-component NUS (collecting a subset of quadrature components) to further reduce sampling-induced aliases relative to traditional full-component NUS (collecting all quadrature components). The efficacy of artifact reduction is exponentially related to the dimensionality of the sample space. Our results quantify the utility of partial-component NUS as an additional means for introducing decoherence into sampling schemes and reducing sampling artifacts in high dimensional experiments. PMID:25899289
Axial quasinormal modes of Einstein-Gauss-Bonnet-dilaton neutron stars
NASA Astrophysics Data System (ADS)
Blázquez-Salcedo, Jose Luis; González-Romero, Luis Manuel; Kunz, Jutta; Mojica, Sindy; Navarro-Lérida, Francisco
2016-01-01
We investigate axial quasinormal modes of realistic neutron stars in Einstein-Gauss-Bonnet-dilaton gravity. We consider eight realistic equations of state containing nuclear, hyperonic, and hybrid matter. We focus on the fundamental curvature mode and compare the results with those of pure Einstein theory. We observe that the frequency of the modes is increased by the presence of the Gauss-Bonnet-dilaton, while the impact on the damping time is typically smaller. Interestingly, we obtain that universal relations valid in pure Einstein theory still hold for Einstein-Gauss-Bonnet-dilaton gravity, and we propose a method to use these phenomenological relations to constrain the value of the Gauss-Bonnet coupling.
Intra-cavity generation of a superposition of Bessel-Gauss beams
NASA Astrophysics Data System (ADS)
Wong-Campos, Jaime D.; Hernandez-Aranda, Raul I.
2012-10-01
The generation of intra-cavity superpositions of Bessel-Gauss beams in an axicon resonator is studied numerically by means of a genetic algorithm. The coherent superposition of low order modes is induced by introducing crossed wires within the simulated cavity. Two different strategies are shown to be equivalent for the generation of the same superposition of two Bessel-Gauss beams with opposite azimuthal orders. In the first strategy the angle between a pair of cross-wires is varied for mode selection, the second consists on introducing a number of crosswires at equally spaced angles in which the number of wires corresponds exactly to the order of the superposed modes. Our results suggest a direct method for generating experimentally a coherent mode superposition of Bessel-Gauss beams using an axicon-based Bessel-Gauss resonator. These beams are relevant in areas such as optical trapping and micromanipulatio
Higgs inflation with a Gauss-Bonnet term in the Jordan frame
NASA Astrophysics Data System (ADS)
van de Bruck, Carsten; Longden, Chris
2016-03-01
We consider an extension of Higgs inflation in which the Higgs field is coupled to the Gauss-Bonnet term. Working solely in the Jordan frame, we first recover the standard predictions of field inflation without a Gauss-Bonnet term. We then calculate the power spectra for scalar and tensor perturbations in the presence of a coupling to a Gauss-Bonnet term. We show that generically the predictions of Higgs inflation are robust and the contributions to the power spectra coming from the Gauss-Bonnet term are negligible. We find, however, that the end of inflation can be strongly modified and that we hence expect the details of (p)reheating to be significantly altered, leading to some concerns over the feasibility of the model which require further investigation.
Holographic Schwinger effect in a confining background with Gauss-Bonnet corrections
NASA Astrophysics Data System (ADS)
Zhang, Shao-Jun; Abdalla, E.
2016-05-01
We study the effect of higher-derivative terms on holographic Schwinger effect by introducing the Gauss-Bonnet term in the gravity sector. Anti-de Sitter soliton background is considered which is dual to confining phase of the boundary field theory. By calculating the potential between the produced pair, we find that larger Gauss-Bonnet factor λ makes the pair lighter. We apply numerical method to calculate the production rate for various cases. The results show that the Gauss-Bonnet term enhances the production rate. The critical behaviors near the two critical values of the electric field are also investigated, and it is found that the two critical indexes are not affected by the Gauss-Bonnet term and thus suggests a possible universality.
Parallel full-waveform inversion in the frequency domain by the Gauss-Newton method
NASA Astrophysics Data System (ADS)
Zhang, Wensheng; Zhuang, Yuan
2016-06-01
In this paper, we investigate the full-waveform inversion in the frequency domain. We first test the inversion ability of three numerical optimization methods, i.e., the steepest-descent method, the Newton-CG method and the Gauss- Newton method, for a simple model. The results show that the Gauss-Newton method performs well and efficiently. Then numerical computations for a benchmark model named Marmousi model by the Gauss-Newton method are implemented. Parallel algorithm based on message passing interface (MPI) is applied as the inversion is a typical large-scale computational problem. Numerical computations show that the Gauss-Newton method has good ability to reconstruct the complex model.
Řeháček, Jaroslav; Teo, Yong Siah; Hradil, Zdeněk; Wallentowitz, Sascha
2015-01-01
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterodyne detection can often lead to the latter giving more accurate estimates. This observation is also partly a manifestation of a fundamental relationship between the respective data uncertainties for the two schemes. In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection. PMID:26195198
Quadrature rules for finite element approximations of 1D nonlocal problems
NASA Astrophysics Data System (ADS)
Zhang, Xiaoping; Gunzburger, Max; Ju, Lili
2016-04-01
It is well known that calculations of the entries of the stiffness matrix in the finite element approximations of nonlocal diffusion and mechanics models are often very time-consuming due to the double integration process over the domain and the singularities of the nonlocal kernel functions. In this paper, we propose some effective and accurate quadrature rules for computing these double integrals for one-dimensional nonlocal problems; in particular, for problems with highly singular kernels, the corresponding inner integrals can be first evaluated exactly in our method, and the outer one then will be approximated by some popular quadrature rules. With these quadrature rules, the assembly of the stiffness matrix in the finite element method for the nonlocal problems becomes similar to that for the classical partial differential equations and is thus quite efficient.
On the Computation of High Order Rys Quadrature Weights and Nodes
NASA Technical Reports Server (NTRS)
Schwenke, David W.
2014-01-01
Since its introduction in 1976, the Rys Quadrature method has proven a very attractive method for evaluating electron repulsion integrals for calculations using Gaussian type orbitals. Since then, there have been considerable refinements of the method, but at it's core, Gaussian weights and nodes are used to exactly evaluate using a numerical approach to the transform integral. One of the powers of the Rys Quadrature method is the relative ease in evaluating integrals involving functions of high angular momentum. In this work we report on the complete resolution of these numerical difficulties, and we have easily computed accurate quadrature weights and nodes up to order 101. All calculations were carried out using 128-bit precision.
Phase measurement device using inphase and quadrature components for phase estimation
NASA Technical Reports Server (NTRS)
Halverson, Peter G. (Inventor); Ware, Brent (Inventor); Shaddock, Daniel A. (Inventor); Spero, Robert E. (Inventor)
2009-01-01
A phasemeter for estimating the phase of a signal. For multi-tone signals, multiple phase estimates may be provided. An embodiment includes components operating in the digital domain, where a sampled input signal is multiplied by cosine and sine terms to provide estimates of the inphase and quadrature components. The quadrature component provides an error signal that is provided to a feedback loop, the feedback loop providing a model phase that tends to track the phase of a tone in the input signal. The cosine and sine terms are generated from the model phase. The inphase and quadrature components are used to form a residual phase, which is added to the model phase to provide an estimate of the phase of the input signal. Other embodiments are described and claimed.
Low-Latitude Solar Wind During the Fall 1998 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Poletto, G.; Suess, S. T.; Biesecker, D. A.; Esser, R.; Gloeckler, G.; Ko, Y.-K.; Zurbuchen, T. H.
2002-01-01
Solar and Heliospheric Observatory (SOH0)-Ulysses quadratures occur when the SOHO-Sun-Ulysses-included angle is 90 deg. These offer the opportunity to directly compare properties of plasma parcels, observed by SOHO [Dorningo et al.] in the low corona, with properties of the same parcels measured, in due time, in situ, by Ulysses [ Wenzel et al]. We refer the reader to Suess et al. for an extended discussion of SOHO-Ulysses quadrature geometry. Here it suffices to recall that there are two quadratures per year, as SOHO makes its one-year revolution around the Sun. This, because SOHO is at the L1 Lagrangian point, in essentially the same place as the Earth, while Ulysses is in a near-polar -5-year solar orbit with a perihelion of 1.34 AU and aphelion of 5.4 AU.
On the equivalence of Gaussian elimination and Gauss-Jordan reduction in solving linear equations
NASA Technical Reports Server (NTRS)
Tsao, Nai-Kuan
1989-01-01
A novel general approach to round-off error analysis using the error complexity concepts is described. This is applied to the analysis of the Gaussian Elimination and Gauss-Jordan scheme for solving linear equations. The results show that the two algorithms are equivalent in terms of our error complexity measures. Thus the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.
NASA Astrophysics Data System (ADS)
Christoforou, Cleopatra; Slemrod, Marshall
2015-12-01
In this paper, the method of compensated compactness is applied to the problem of isometric immersion of a two-dimensional Riemannian manifold with negative Gauss curvature into three-dimensional Euclidean space. Previous applications of the method to this problem have required decay of order t -4 in the Gauss curvature. Here, we show that the decay of Hong (Commun Anal Geom 1:487-514, 1993) t -2- δ/2 where δ ∈ (0, 4) suffices.
Thermodynamics of Gauss-Bonnet-dilaton Lifshitz black branes
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Dehghani, M. H.; Sheykhi, A.
2015-09-01
We explore an effective supergravity action in the presence of a massless gauge field which contains a Gauss-Bonnet term as well as a dilaton field. We construct a new class of black brane solutions of this theory with a Lifshitz asymptotic by fixing the parameters of the model such that the asymptotic Lifshitz behavior can be supported. Then we construct the well-defined finite action through the use of the counterterm method. We also obtain two independent constants along the radial coordinate by combining the equations of motion. Calculations of these two constants at infinity through the use of the large-r behavior of the metric functions show that our solution respects the no-hair theorem. Furthermore, we combine these two constants in order to get a constant C which is proportional to the energy of the black brane. We calculate this constant at the horizon in terms of the temperature and entropy and at large-r in terms of the geometrical mass. By calculating the value of the energy density through the use of the counterterm method, we obtain the relation between the energy density, the temperature, and the entropy. This relation is the generalization of the well-known Smarr formula for AdS black holes. Finally, we study the thermal stability of our black brane solution and show that it is stable under thermal perturbations.
Vainshtein mechanism in Gauss-Bonnet gravity and Galileon aether
NASA Astrophysics Data System (ADS)
Gannouji, Radouane; Sami, M.
2012-01-01
We derive field equations of Gauss-Bonnet gravity in four dimensions after dimensional reduction of the action and demonstrate that in this scenario the Vainshtein mechanism operates in the flat spherically symmetric background. We show that inside this Vainshtein sphere the fifth force is negligibly small compared to the gravitational force. We also investigate the stability of the spherically symmetric solution, and clarify the vocabulary used in the literature about the hyperbolicity of the equation and the ghost-Laplacian stability conditions. We find superluminal behavior of the perturbation of the field in the radial direction. However, because of the presence of the nonlinear terms, the structure of the space-time is modified and as a result the field does not propagate in the Minkowski metric but rather in an “aether” composed of the scalar field π(r). We thereby demonstrate that the superluminal behavior does not create time paradoxes thanks to the absence of causal closed curves. We also derive the stability conditions for a Friedmann universe in context with scalar and tensor perturbations and we study the cosmology of the model.
Black Hole Thermodynamic Products in Einstein Gauss Bonnet Gravity
NASA Astrophysics Data System (ADS)
Biswas, Ritabrata
2016-07-01
By now, there are many hints from string theory that collective excitations of solitonic objects can be described by effective low energy theories. The entropy of general rotating black holes in five dimensions may be interpreted as an indication that, it derives from two independent microscopic contributions and each of these may be attributed to a gas of strings. In the present work, we consider a charged black hole in five dimensional Einstein Gauss Bonnet gravity. In spite of presenting the thermodynamic quantities' product as summation/ subtraction of two independent integers, our motive is to check whether the product of the same quantity for event horizon and Cauchy horizon is free of mass, i.e., global, or not. We derive the thermodynamic products of characteristic parameters to mark which are global. We further interpret the stability of the black holes by computing the specific heat for both horizons. Stable and unstable phases of horizons are pointed out. The phase transitions with respect to the charge in nature of specific heat are also observed. All these calculation might be helpful to understand the microscopic nature of such black holes.
Charged black hole solutions in Gauss-Bonnet-massive gravity
NASA Astrophysics Data System (ADS)
Hendi, S. H.; Panahiyan, S.; Panah, B. Eslam
2016-01-01
Motivated by high interest in the close relation between string theory and black hole solutions, in this paper, we take into account the Einstein-Gauss-Bonnet Lagrangian in the context of massive gravity. We examine the possibility of black hole in this regard, and discuss the types of horizons. Next, we calculate conserved and thermodynamic quantities and check the validity of the first law of thermodynamics. In addition, we investigate the stability of these black holes in context of canonical ensemble. We show that number, type and place of phase transition points may be significantly affected by different parameters. Next, by considering cosmological constant as thermodynamical pressure, we will extend phase space and calculate critical values. Then, we construct thermodynamical spacetime by considering mass as thermodynamical potential. We study geometrical thermodynamics of these black holes in context of heat capacity and extended phase space. We show that studying heat capacity, geometrical thermodynamics and critical behavior in extended phase space lead to consistent results. Finally, we will employ a new method for obtaining critical values and show that the results of this method are consistent with those of other methods.
Laguerre-Gauss basis functions in observer models
NASA Astrophysics Data System (ADS)
Burgess, Arthur E.
2003-05-01
Observer models based on linear classifiers with basis functions (channels) are useful for evaluation of detection performance with medical images. They allow spatial domain calculations with a covariance matrix of tractable size. The term "channelized Fisher-Hotelling observer" will be used here. It is also called the "channelized Hotelling observer" model. There are an infinite number of basis function (channel ) sets that could be employed. Examples of channel sets that have been used include: difference of Gaussian (DOG) filters, difference of Mesa (DOM) filters and Laguerre-Gauss (LG) basis functions. Another option, sums of LG functions (LGS), will also be presented here. This set has the advantage of having no DC response. The effect of the number of images used to estimate model observer performance will be described, for both filtered 1/f3 noise and GE digital mammogram backgrounds. Finite sample image sets introduce both bias and variance to the estimate. The results presented here agree with previous work on linear classifiers. The LGS basis set gives a small but statistically significant reduction in bias. However, this may not be of much practical benefit. Finally, the effect of varying the number of basis functions included in the set will be addressed. It was found that four LG bases or three LGS bases are adequate.
Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David
2013-05-21
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes. PMID:23697409
NASA Astrophysics Data System (ADS)
Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David
2013-05-01
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.
Efficient modelling of gravity effects due to topographic masses using the Gauss-FFT method
NASA Astrophysics Data System (ADS)
Wu, Leyuan
2016-04-01
We present efficient Fourier-domain algorithms for modelling gravity effects due to topographic masses. The well-known Parker's formula originally based on the standard fast Fourier transform (FFT) algorithm is modified by applying the Gauss-FFT method instead. Numerical precision of the forward and inverse Fourier transforms embedded in Parker's formula and its extended forms are significantly improved by the Gauss-FFT method. The topographic model is composed of two major aspects, the geometry and the density. Versatile geometric representations, including the mass line model, the mass prism model, the polyhedron model and smoother topographic models interpolated from discrete data sets using high-order splines or pre-defined by analytical functions, in combination with density distributions that vary both laterally and vertically in rather arbitrary ways following exponential or general polynomial functions, now can be treated in a consistent framework by applying the Gauss-FFT method. The method presented has been numerically checked by space-domain analytical and hybrid analytical/numerical solutions already established in the literature. Synthetic and real model tests show that both the Gauss-FFT method and the standard FFT method run much faster than space-domain solutions, with the Gauss-FFT method being superior in numerical accuracy. When truncation errors are negligible, the Gauss-FFT method can provide forward results almost identical to space-domain analytical or semi-numerical solutions in much less time.
Rapidly rotating neutron stars in dilatonic Einstein-Gauss-Bonnet theory
NASA Astrophysics Data System (ADS)
Kleihaus, Burkhard; Kunz, Jutta; Mojica, Sindy; Zagermann, Marco
2016-03-01
We construct sequences of rapidly rotating neutron stars in dilatonic Einstein-Gauss-Bonnet theory, employing two equations of state for the nuclear matter. We analyze the dependence of the physical properties of these neutron stars on the Gauss-Bonnet coupling strength. For a given equation of state we determine the physically relevant domain of rapidly rotating neutron stars, which is delimited by the set of neutron stars rotating at the Kepler limit, the set of neutron stars along the secular instability line, and the set of static neutron stars. As compared to Einstein gravity, the presence of the Gauss-Bonnet term decreases this domain, leading to lower values for the maximum mass as well as to smaller central densities. The quadrupole moment is decreased by the Gauss-Bonnet term for rapidly rotating neutron stars, while it is increased for slowly rotating neutron stars. The universal relation between the quadrupole moment and the moment of inertia found in general relativity appears to extend to dilatonic Einstein-Gauss-Bonnet theory with very little dependence on the coupling strength of the Gauss-Bonnet term. The neutron stars carry a small dilaton charge.
Cao, Yuan; Chan, Erwin H W; Wang, Xudong; Feng, Xinhuan; Guan, Bai-ou
2015-10-15
A photonic microwave quadrature filter is presented. It has a very simple structure, very low phase imbalance, and high signal-to-noise ratio performance. Experimental results are presented that demonstrate a photonic microwave quadrature filter with a 3 dB operating frequency range of 10.5-26.5 GHz, an amplitude and phase imbalance of less than ±0.3 dB and ±0.15°, and a signal-to-noise ratio of more than 121 dB in a 1 Hz noise bandwidth. PMID:26469589
Microwave photonic quadrature filter based on an all-optical programmable Hilbert transformer.
Huang, Thomas X H; Yi, Xiaoke; Minasian, Robert A
2011-11-15
A microwave photonic quadrature filter, new to our knowledge, based on an all-optical Hilbert transformer is presented. It is based on mapping of a Hilbert transform transfer function between the optical and electrical domains, using a programmable Fourier-domain optical processor and high-speed photodiodes. The technique enables the realization of an extremely wide operating bandwidth, tunable programmable bandwidth, and a highly precise amplitude and phase response. Experimental results demonstrate a microwave quadrature filter from 10 to 20 GHz, which achieves an amplitude imbalance of less than ±0.23 dB and a phase imbalance of less than ±0.5°. PMID:22089590
Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity
NASA Astrophysics Data System (ADS)
Bultheel, Adhemar; Daruis, Leyla; González-Vera, Pablo
2009-09-01
In this paper we investigate the Szego-Radau and Szego-Lobatto quadrature formulas on the unit circle. These are (n+m)-point formulas for which m nodes are fixed in advance, with m=1 and m=2 respectively, and which have a maximal domain of validity in the space of Laurent polynomials. This means that the free parameters (free nodes and positive weights) are chosen such that the quadrature formula is exact for all powers zj, -p<=j<=p, with p=p(n,m) as large as possible.
NASA Astrophysics Data System (ADS)
Amin, Najam Muhammad; Zhigong, Wang; Zhiqun, Li
2015-05-01
A down-conversion in-phase/quadrature (I/Q) mixer employing a folded-type topology, integrated with a passive differential quadrature all-pass filter (D-QAF), in order to realize the final down-conversion stage of a 60 GHz receiver architecture is presented in this work. Instead of employing conventional quadrature generation techniques such as a polyphase filter or a frequency divider for the local oscillator (LO) of the mixer, a passive D-QAF structure is employed. Fabricated in a 65 nm CMOS process, the mixer exhibits a voltage gain of 7-8 dB in an intermediate frequency (IF) band ranging from 10 MHz-1.75 GHz. A fixed LO frequency of 12 GHz is used to down-convert a radio frequency (RF) band of 10.25-13.75 GHz. The mixer displays a third order input referred intercept point (IIP3) ranging from -8.75 to -7.37 dBm for a fixed IF frequency of 10 MHz and a minimum single-sideband noise figure (SSB-NF) of 11.3 dB. The mixer draws a current of 6 mA from a 1.2 V supply voltage dissipating a power of 7.2 mW. Project supported by the National High Technology Research and Development Program of China (No. 2011AA010200).
Oder, J.M.
1997-12-01
Several new quadrature sets for use in the discrete ordinates method of solving the Boltzmann neutral particle transport equation are derived. These symmetric quadratures extend the traditional symmetric quadratures by allowing ordinates perpendicular to one or two of the coordinate axes. Comparable accuracy with fewer required ordinates is obtained. Quadratures up to seventh order are presented. The validity and efficiency of the quadratures is then tested and compared with the Sn level symmetric quadratures relative to a Monte Carlo benchmark solution. The criteria for comparison include current through the surface, scalar flux at the surface, volume average scalar flux, and time required for convergence. Appreciable computational cost was saved when used in an unstructured tetrahedral cell code using highly accurate characteristic methods. However, no appreciable savings in computation time was found using the new quadratures compared with traditional Sn methods on a regular Cartesian mesh using the standard diamond difference method. These quadratures are recommended for use in three-dimensional calculations on an unstructured mesh.
Dark matter relic density in Gauss-Bonnet braneworld cosmology
NASA Astrophysics Data System (ADS)
Meehan, Michael T.; Whittingham, Ian B.
2014-12-01
The relic density of symmetric and asymmetric dark matter in a Gauss-Bonnet (GB) modified Randall-Sundrum (RS) type II braneworld cosmology is investigated. The existing study of symmetric dark matter in a GB braneworld (Okada and Okada, 2009) found that the expansion rate was reduced compared to that in standard General Relativity (GR), thereby delaying particle freeze-out and resulting in relic abundances which are suppressed by up to Script O(10-2). This is in direct contrast to the behaviour observed in RS braneworlds where the expansion rate is enhanced and the final relic abundance boosted. However, this finding that relic abundances are suppressed in a GB braneworld is based upon a highly contrived situation in which the GB era evolves directly into a standard GR era, rather than passing through a RS era as is the general situation. This collapse of the RS era requires equating the mass scale mα of the GB modification and the mass scale mσ of the brane tension. However, if the GB contribution is to be considered as the lowest order correction from string theory to the RS action, we would expect mα > mσ. We investigate the effect upon the relic abundance of choosing more realistic values for the ratio Script Rm ≡ mα/mσ and find that the relic abundance can be either enhanced or suppressed by more than two orders of magnitude. However, suppression only occurs for a small range of parameter choices and, overwhelmingly, the predominant situation is that of enhancement as we recover the usual Randall-Sundrum type behaviour in the limit Script Rm gg 1. We use the latest observational bound ΩDMh2 = 0.1187 ± 0.0017 to constrain the various model parameters and briefly discuss the implications for direct/indirect dark matter detection experiments as well as dark matter particle models.
Serbes, G; Aydin, N
2011-01-01
Dual-tree complex wavelet transform (DTCWT), which is a shift invariant transform with limited redundancy, is an improved version of discrete wavelet transform. Complex quadrature signals are dual channel signals obtained from the systems employing quadrature demodulation. An example of such signals is quadrature Doppler signal obtained from blood flow analysis systems. Prior to processing Doppler signals using the DTCWT, directional flow signals must be obtained and then two separate DTCWT applied, increasing the computational complexity. In this study, in order to decrease computational complexity, a symmetrical modified DTCWT algorithm is proposed (SMDTCWT). A comparison between the new transform and the symmetrical phasing-filter technique is presented. Additionally denoising performance of SMDTCWT is compared with the DWT and the DTCWT using simulated signals. The results show that the proposed method gives the same output as the symmetrical phasing-filter method, the computational complexity for processing quadrature signals using DTCWT is greatly reduced and finally the SMDTCWT based denoising outperforms conventional DWT with same computational complexity. PMID:22255416
NASA Astrophysics Data System (ADS)
Warger, William C., II; Newmark, Judith A.; Zhao, Bing; Warner, Carol M.; DiMarzio, Charles A.
2006-02-01
Present imaging techniques used in in vitro fertilization (IVF) clinics are unable to produce accurate cell counts in developing embryos past the eight-cell stage. We have developed a method that has produced accurate cell counts in live mouse embryos ranging from 13-25 cells by combining Differential Interference Contrast (DIC) and Optical Quadrature Microscopy. Optical Quadrature Microscopy is an interferometric imaging modality that measures the amplitude and phase of the signal beam that travels through the embryo. The phase is transformed into an image of optical path length difference, which is used to determine the maximum optical path length deviation of a single cell. DIC microscopy gives distinct cell boundaries for cells within the focal plane when other cells do not lie in the path to the objective. Fitting an ellipse to the boundary of a single cell in the DIC image and combining it with the maximum optical path length deviation of a single cell creates an ellipsoidal model cell of optical path length deviation. Subtracting the model cell from the Optical Quadrature image will either show the optical path length deviation of the culture medium or reveal another cell underneath. Once all the boundaries are used in the DIC image, the subtracted Optical Quadrature image is analyzed to determine the cell boundaries of the remaining cells. The final cell count is produced when no more cells can be subtracted. We have produced exact cell counts on 5 samples, which have been validated by Epi-Fluorescence images of Hoechst stained nuclei.
A Simple Approximation for the Symbol Error Rate of Triangular Quadrature Amplitude Modulation
NASA Astrophysics Data System (ADS)
Duy, Tran Trung; Kong, Hyung Yun
In this paper, we consider the error performance of the regular triangular quadrature amplitude modulation (TQAM). In particular, using an accurate exponential bound of the complementary error function, we derive a simple approximation for the average symbol error rate (SER) of TQAM over Additive White Gaussian Noise (AWGN) and fading channels. The accuracy of our approach is verified by some simulation results.
NUMERICAL APPROXIMATION OF SEMI-INTEGRALS AND SEMIDERIVATIVES BY PRODUCT QUADRATURE RULES
This paper is concerned with the numerical calculation of the semi-integral and semiderivative of a function f, whose values f (xj) are known on a discrete set of abscissas 0 = x(1) < x(2) < ... < x(n). A family of product quadrature rules is developed to approximate the semi-int...
A multivariate quadrature based moment method for LES based modeling of supersonic combustion
NASA Astrophysics Data System (ADS)
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2012-07-01
The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.
Saturation dependence of the quadrature conductivity of oil-bearing sands
NASA Astrophysics Data System (ADS)
Schmutz, M.; Blondel, A.; Revil, A.
2012-02-01
We have investigated the complex conductivity of oil-bearing sands with six distinct oil types including sunflower oil, silicone oil, gum rosin, paraffin, engine oil, and an industrial oil of complex composition. In all these experiments, the oil was the non-wetting phase. The in-phase (real) conductivity follows a power law relationship with the saturation (also known as the second Archie's law) but with a saturation exponent n raging from 1.1 to 3.1. In most experiments, the quadrature conductivity follows also a power law relationship with the water saturation but with a power law exponent p can be either positive or negative. For some samples, the quadrature conductivity first increases with saturation and then decreases indicating that two processes compete in controlling the quadrature conductivity. One is related to the insulating nature of the oil phase and a second could be associated with the surface area of the oil / water interface. The quadrature conductivity seems to be influenced not only by the value of the saturation exponent n (according to the Vinegar and Waxman model, p = n - 1), but also by the surface area between the oil phase and the water phase especially for very water-repellent oil having a fractal oil-water interface.
P-T phase diagram of a holographic s+p model from Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Nie, Zhang-Yu; Zeng, Hui
2015-10-01
In this paper, we study the holographic s+p model in 5-dimensional bulk gravity with the Gauss-Bonnet term. We work in the probe limit and give the Δ-T phase diagrams at three different values of the Gauss-Bonnet coefficient to show the effect of the Gauss-Bonnet term. We also construct the P-T phase diagrams for the holographic system using two different definitions of the pressure and compare the results.
Dark matter relic density in Gauss-Bonnet braneworld cosmology
Meehan, Michael T.; Whittingham, Ian B. E-mail: Ian.Whittingham@jcu.edu.au
2014-12-01
The relic density of symmetric and asymmetric dark matter in a Gauss-Bonnet (GB) modified Randall-Sundrum (RS) type II braneworld cosmology is investigated. The existing study of symmetric dark matter in a GB braneworld (Okada and Okada, 2009) found that the expansion rate was reduced compared to that in standard General Relativity (GR), thereby delaying particle freeze-out and resulting in relic abundances which are suppressed by up to O(10{sup −2}). This is in direct contrast to the behaviour observed in RS braneworlds where the expansion rate is enhanced and the final relic abundance boosted. However, this finding that relic abundances are suppressed in a GB braneworld is based upon a highly contrived situation in which the GB era evolves directly into a standard GR era, rather than passing through a RS era as is the general situation. This collapse of the RS era requires equating the mass scale m{sub α} of the GB modification and the mass scale m{sub σ} of the brane tension. However, if the GB contribution is to be considered as the lowest order correction from string theory to the RS action, we would expect m{sub α} > m{sub σ}. We investigate the effect upon the relic abundance of choosing more realistic values for the ratio R{sub m} ≡ m{sub α}/m{sub σ} and find that the relic abundance can be either enhanced or suppressed by more than two orders of magnitude. However, suppression only occurs for a small range of parameter choices and, overwhelmingly, the predominant situation is that of enhancement as we recover the usual Randall-Sundrum type behaviour in the limit R{sub m} >> 1. We use the latest observational bound Ω{sub DM}h{sup 2} = 0.1187 ± 0.0017 to constrain the various model parameters and briefly discuss the implications for direct/indirect dark matter detection experiments as well as dark matter particle models.
Pang, Yong; Yu, Baiying; Vigneron, Daniel B.
2014-01-01
Quadrature coils are often desired in MR applications because they can improve MR sensitivity and also reduce excitation power. In this work, we propose, for the first time, a quadrature array design strategy for parallel transmission at 298 MHz using single-feed circularly polarized (CP) patch antenna technique. Each array element is a nearly square ring microstrip antenna and is fed at a point on the diagonal of the antenna to generate quadrature magnetic fields. Compared with conventional quadrature coils, the single-feed structure is much simple and compact, making the quadrature coil array design practical. Numerical simulations demonstrate that the decoupling between elements is better than –35 dB for all the elements and the RF fields are homogeneous with deep penetration and quadrature behavior in the area of interest. Bloch equation simulation is also performed to simulate the excitation procedure by using an 8-element quadrature planar patch array to demonstrate its feasibility in parallel transmission at the ultrahigh field of 7 Tesla. PMID:24649430
Pang, Yong; Yu, Baiying; Vigneron, Daniel B; Zhang, Xiaoliang
2014-02-01
Quadrature coils are often desired in MR applications because they can improve MR sensitivity and also reduce excitation power. In this work, we propose, for the first time, a quadrature array design strategy for parallel transmission at 298 MHz using single-feed circularly polarized (CP) patch antenna technique. Each array element is a nearly square ring microstrip antenna and is fed at a point on the diagonal of the antenna to generate quadrature magnetic fields. Compared with conventional quadrature coils, the single-feed structure is much simple and compact, making the quadrature coil array design practical. Numerical simulations demonstrate that the decoupling between elements is better than -35 dB for all the elements and the RF fields are homogeneous with deep penetration and quadrature behavior in the area of interest. Bloch equation simulation is also performed to simulate the excitation procedure by using an 8-element quadrature planar patch array to demonstrate its feasibility in parallel transmission at the ultrahigh field of 7 Tesla. PMID:24649430
Our best juniors still struggle with Gauss's Law: Characterizing their difficulties
NASA Astrophysics Data System (ADS)
Pepper, Rachel E.; Chasteen, Stephanie V.; Pollock, Steven J.; Perkins, Katherine K.
2010-10-01
We discuss student conceptual difficulties with Gauss's law observed in an upper-division Electricity and Magnetism (E&M) course. Difficulties at this level have been described in previous work; we present further quantitative and qualitative evidence that upper-division students still struggle with Gauss's law. This evidence is drawn from analysis of upper-division E&M conceptual post-tests, traditional exams, and formal student interviews. Examples of student difficulties include difficulty with the inverse nature of the problem, difficulty articulating complete symmetry arguments, and trouble recognizing that in situations without sufficient symmetry it is impossible (rather than "difficult") to calculate the electric field using Gauss's law. One possible explanation for some of these conceptual difficulties is that even students at the upper level may struggle to connect mathematical expressions to physical meanings.
Magnetic-field effects on p-wave phase transition in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Wu, Ya-Bo; Lu, Jun-Wang; Jin, Yong-Yi; Lu, Jian-Bo; Zhang, Xue; Wu, Si-Yu; Wang, Cui
2014-07-01
In the probe limit, we study the holographic p-wave phase transition in the Gauss-Bonnet gravity via numerical and analytical methods. Concretely, we study the influences of the external magnetic field on the Maxwell complex vector model in the five-dimensional Gauss-Bonnet-AdS black hole and soliton backgrounds, respectively. For the two backgrounds, the results show that the magnetic field enhances the superconductor phase transition in the case of the lowest Landau level, while the increasing Gauss-Bonnet parameter always hinders the vector condensate. Moreover, the Maxwell complex vector model is a generalization of the SU(2) Yang-Mills model all the time. In addition, the analytical results backup the numerical results. Furthermore, this model might provide a holographic realization for the QCD vacuum instability.
Gauss-bonnet black holes and possibilities for their experimental search
Alexeyev, S. O. Rannu, K. A.
2012-03-15
Corollaries of gravity models with second-order curvature corrections in the form of a Gauss-Bonnet term and possibilities (or impossibilities) for their experimental search or observations are discussed. The full version of the four-dimensional Schwarzschild-Gauss-Bonnet black hole solution and the constraint on the possible minimal black hole mass following from this model are considered. Using our solution as a model for the final stages of Hawking evaporation of black holes with a low initial mass (up to 10{sup 15} g) whose lifetime is comparable to that of our Universe, we have revealed differences in the patterns of evaporation: we have obtained high values of the emitted energy and showed the impossibility of an experimental search for primordial black holes by their evaporation products. Scenarios for the evaporation of Gauss-Bonnet black holes in multidimensional gravity models and possibilities for their experimental search are also discussed.
NASA Technical Reports Server (NTRS)
Sidi, A.; Israeli, M.
1986-01-01
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.