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.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).
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).
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, 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.
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.
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.
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.
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
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.
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.
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.
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.
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…
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…
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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)
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.
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.
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…
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.
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
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
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.
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.
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.
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.
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…
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
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.
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.
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
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
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.
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.
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)
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.
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.
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
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.
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.
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.
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
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; 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.
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.
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
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.
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
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
2016-05-01
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.
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.
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.
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.
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.
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.
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
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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...
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; 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
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
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.
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.
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.
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.
A fast Gauss-Newton optimizer for estimating human body orientation.
Lee, Jung Keun; Park, Edward J
2008-01-01
This paper presents a quaternion-based Gauss-Newton optimizer for tracking human body orientation using inertial/magnetic sensors. Since a computationally efficient and robust algorithm for estimating orientation is critical for low-cost and real-time ambulatory purposes, the optimizer is formulated using a virtual rotation concept in order to decrease the computing time. In addition, to guard against the effects of fast body motions and temporary ferromagnetic disturbances, a situational measurement vector selection procedure is adopted in conjunction with the Gauss-Newton optimizer. PMID:19163001
An Alternative Realization of Gauss-Newton for Frequency-Domain Acoustic Waveform Inversion
NASA Astrophysics Data System (ADS)
Liu, Y.; Yang, J.; Chi, B.; Dong, L.
2014-12-01
Since FWI was studied under the least-square misfit optimization proposed by Tarantola (1984) in time domain, it has been greatly improved by many researchers. Pratt (1998) developed FWI in frequency domain using a Gauss-Newton optimization. In recent years, FWI has been widely studied under the framework of adjoint-state methods, as summarized by Plessix (2006). Preconditioning and high order gradients are important for FWI. Many researches have focused on the Newton optimization, in which the calculation of inverse Hessian is the key problem. Pseudo Hessian such as the diagonal Hessian was firstly used to approximate inverse Hessian (Choi & Shin, 2007). Then Gauss-Newton or l-BFGS method was widely studied to iteratively calculate the inverse approximate Hessian Haor full Hessian (Sheen et al., 2006). Full Hessian is the base of the exact Newton optimization. Fichtner and Trampert (2011) presented an extension of the adjoint-state method to directly compute the full Hessian; Métivier et al. (2012) proposed a general second-order adjoint-state formula for Hessian-vector product to tackle Gauss-Newton and exact Newton. Liu et al. (2014) proposed a matrix-decomposition FWI (MDFWI) based on Born kernel. They used the Born Fréchet kernel to explicitly calculate the gradient of the objective function through matrix decomposition, no full Fréchet kernel being stored in memory beforehand. However, they didn't give a method to calculate the Gauss-Newton. In this paper, We propose a method based on Born Fréchet kernel to calculate the Gauss-Newton for acoustic full waveform inversion (FWI). The Gauss-Newton is iteratively constructed without needing to store the huge approximate Hessian (Ha) or Fréchet kernel beforehand, and the inverse of Ha is not need to be calculated either. This procedure can be efficiently accomplished through matrix decomposition. More resolved result and faster convergence are obtained when this Gauss-Newton is applied in FWI based on the Born
NASA Astrophysics Data System (ADS)
Glassmeier, K.-H.; Tsurutani, B. T.
2014-02-01
This is a translation of the Allgemeine Theorie des Erdmagnetismus published by Carl Friedrich Gauss in 1839 in the Resultate aus den Beobachtungen des Magnetischen Vereins im Jahre 1838. The current translation is based on an earlier translation by Elizabeth Juliana Sabine published in 1841. This earlier translation has been revised, corrected, and extended. Numerous biographical comments on the scientists named in the original text have been added as well as further information on the observational material used by Carl Friedrich Gauss. An attempt is made to provide a readable text to a wider scientific community, a text laying the foundation of today's understanding of planetary magnetic fields.
Correspondence between entropy-corrected holographic and Gauss-Bonnet dark-energy models
NASA Astrophysics Data System (ADS)
Setare, M. R.; Jamil, Mubasher
2010-11-01
In the present work we investigate the cosmological implications of the entropy-corrected holographic dark-energy (ECHDE) density in the Gauss-Bonnet framework. This is motivated from the loop quantum gravity corrections to the entropy-area law. Assuming the two cosmological scenarios are valid simultaneously, we show that there is a correspondence between the ECHDE scenario in flat universe and the phantom dark-energy model in the framework of the Gauss-Bonnet theory with a potential. This correspondence leads consistently to an accelerating universe.
Re-creating Gauss's method for non-electrical absolute measurements of magnetic fields and moments
NASA Astrophysics Data System (ADS)
Van Baak, D. A.
2013-10-01
In 1832, Gauss made the first absolute measurements of magnetic fields and of magnetic moments in experiments that are straightforward and instructive to replicate. We show, using rare-earth permanent magnets and a variation of Gauss's technique, that the horizontal component of the ambient geomagnetic field, as well as the size of the magnetic moments of such magnets, can be found. The method shows the connection between the SI and cgs emu unit systems for these quantities and permits an absolute realization of the Ampere with considerable precision.
Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave.
Lin, Jiao; Dellinger, Jean; Genevet, Patrice; Cluzel, Benoit; de Fornel, Frederique; Capasso, Federico
2012-08-31
A new surface wave is introduced, the cosine-Gauss beam, which does not diffract while it propagates in a straight line and tightly bound to the metallic surface for distances up to 80 μm. The generation of this highly localized wave is shown to be straightforward and highly controllable, with varying degrees of transverse confinement and directionality, by fabricating a plasmon launcher consisting of intersecting metallic gratings. Cosine-Gauss beams have potential for applications in plasmonics, notably for efficient coupling to nanophotonic devices, opening up new design possibilities for next-generation optical interconnects. PMID:23002838
Generation and self-healing of a radially polarized Bessel-Gauss beam
NASA Astrophysics Data System (ADS)
Wu, Gaofeng; Wang, Fei; Cai, Yangjian
2014-04-01
We report experimental generation of a radially polarized Bessel-Gauss (RPBG) beam of order 1 with the help of a spatial light modulator, a spiral phase plate, and a radial polarization converter. Furthermore, we carry out a comparative study of the self-healing properties of a RPBG beam and a linearly polarized Bessel-Gauss (LPBG) beam which are blocked by a sector-shaped opaque obstacle both experimentally and numerically. Our results clearly show that the self-healing ability of a RPBG beam indeed is superior to that of a LPBG beam, and some physical interpretations are given. Our results will be useful for particle trapping and microscopy.
NASA Astrophysics Data System (ADS)
Gabriel, C.; Aiello, A.; Berg-Johansen, S.; Marquardt, Ch.; Leuchs, G.
2012-07-01
Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [C. Gabriel et al., Phys. Rev. Lett. 106, 060502 (2011)]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, -1.2 dB ± 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations are, depending on the measurement scheme.
A PWM quadrature-booster phase shifter for ac power transmission
Lopes, L.A.C.; Joos, G.; Ooi, B.T.
1997-01-01
The conventional structures used for phase shifters employ quadrature voltage injection controlled by means of on-load tap changers that require considerable maintenance. Line-commutated thyristor structures have been proposed to replace tap changers, but problems related to filter requirements or the number of switches have limited their utilization. This paper proposes a pulse width modulation (PWM) quadrature-booster phase shifter based on a force-commutated ac controller. It offers features such as fast dynamic response, continuous variation of the phase angle with low harmonic injection, and it requires a simple power structure and can be controlled by adjusting the duty cycle of the switches. The operating principles of the proposed phase shifter are analyzed and their feasibility is demonstrated through digital simulation and experimental implementation.
Solution of stochastic media transport problems using a numerical quadrature-based method
Pautz, S. D.; Franke, B. C.; Prinja, A. K.; Olson, A. J.
2013-07-01
We present a new conceptual framework for analyzing transport problems in random media. We decompose such problems into stratified subproblems according to the number of material pseudo-interfaces within realizations. For a given subproblem we assign pseudo-interface locations in each realization according to product quadrature rules, which allows us to deterministically generate a fixed number of realizations. Quadrature integration of the solutions of these realizations thus approximately solves each subproblem; the weighted superposition of solutions of the subproblems approximately solves the general stochastic media transport problem. We revisit some benchmark problems to determine the accuracy and efficiency of this approach in comparison to randomly generated realizations. We find that this method is very accurate and fast when the number of pseudo-interfaces in a problem is generally low, but that these advantages quickly degrade as the number of pseudo-interfaces increases. (authors)
NASA Astrophysics Data System (ADS)
Pierré, J.-E.; Passieux, J.-C.; Périé, J.-N.; Bugarin, F.; Robert, L.
2016-02-01
Like subset-based methods, the very first finite element versions of digital image correlation were closely related to the regular structure of images, as they were based on regular quadrilateral elements corresponding to an integer number of pixels. The use of unstructured meshes, to exploit the full potential of FE-DIC in structural mechanics, is now widespread. Most of the time, the formulation, the quadrature and the definition of the region of interest still rely on the pixels grid. In this paper, a formulation in the physical coordinate system and not in the image frame is proposed for 2D digital image correlation. In addition to a more precise definition of the region of interest, it allows the use of a more accurate quadrature rule. It is also shown that lens distortions can be successfully taken into account directly with such a formalism.
Adams, M.L. ); Wareing, T.A. )
1993-01-01
We study diffusion-synthetic acceleration (DSA) for within-group scattering iterations in discrete ordinates calculations. We consider analytic (not spatially discretized) equations in Cartesian coordinates with linearly anisotropic scattering. We place no restrictions on the discrete ordinates quadrature set. We assume an infinite homogeneous medium. Our main results are as follows: 1. DSA is unstable in two dimensions (2D) and three dimensions (3D), given forward-peaked scattering. It can be stabilized by taking extra transport sweeps each iteration. 2. Standard DSA is unstable, given any quadrature set that does not correctly integrate linear functions of angle. 3. Relative to one dimension (ID), DSA's performance is degraded in 2D and 3D.
NASA Astrophysics Data System (ADS)
Zhen, Shenglai; Chen, Bo; Yuan, Liang; Li, Min; Liang, Jing; Yu, Benli
2010-03-01
In-phase and quadrature-phase (I/Q) signals often need to be formed in the laser interferometric vibration measurement technique. To avoid the disadvantages of traditional I/Q signals forming methods such as effect of piezoelectric ceramic (PZT) for generating high frequency carrier, or optical configuration with complicated structure, a novel interferometric vibration measurement sensor with quadrature detection is proposed. The sensor utilizes simple optical configuration which contains 1/8 wave plate to generate two I/Q signals, then the signals were processed by arctangent algorithm which is compiled by Labview software through data acquisition card. Theoretical analysis and experimental Lissajous figures synthesis prove the phase orthogonality of the two signals. The experimental results indicate that the system can measure the vibration displacement accurately.
An accurate quadrature technique for the contact boundary in 3D finite element computations
NASA Astrophysics Data System (ADS)
Duong, Thang X.; Sauer, Roger A.
2015-01-01
This paper presents a new numerical integration technique for 3D contact finite element implementations, focusing on a remedy for the inaccurate integration due to discontinuities at the boundary of contact surfaces. The method is based on the adaptive refinement of the integration domain along the boundary of the contact surface, and is accordingly denoted RBQ for refined boundary quadrature. It can be used for common element types of any order, e.g. Lagrange, NURBS, or T-Spline elements. In terms of both computational speed and accuracy, RBQ exhibits great advantages over a naive increase of the number of quadrature points. Also, the RBQ method is shown to remain accurate for large deformations. Furthermore, since the sharp boundary of the contact surface is determined, it can be used for various purposes like the accurate post-processing of the contact pressure. Several examples are presented to illustrate the new technique.
Quadrature algorithms to the luminosity distance with a time-dependent dark energy model
Yue, Nan-Nan; Liu, De-Zi; Pei, Xiao-Xing; Zhang, Tong-Jie; Yang, Zhi-Liang; Zhu, Fang-Fang E-mail: bingzi@mail.bnu.edu.cn E-mail: fiona-90@live.cn E-mail: zlyang@bnu.edu.cn
2011-11-01
In our previous work [1], we have proposed two methods for computing the luminosity distance d{sub L}{sup Λ} in ΛCDM model. In this paper, two effective quadrature algorithms, known as Romberg Integration and composite Gaussian Quadrature, are presented to calculate the luminosity distance d{sub L}{sup CPL} in the Chevallier-Polarski-Linder parametrization(CPL) model. By comparing both the efficiency and accuracy of the two algorithms, we find that the second is more promising. Moreover, we develop another strategy adapted for approximating d{sub L}{sup Λ} in flat ΛCDM universe. To some extent, our methods can make contributions to the recent numerical stimulation for the investigation of dark energy cosmology.
New Adaptive Method for IQ Imbalance Compensation of Quadrature Modulators in Predistortion Systems
NASA Astrophysics Data System (ADS)
Zareian, Hassan; Vakili, Vahid Tabataba
2009-12-01
Imperfections in quadrature modulators (QMs), such as inphase and quadrature (IQ) imbalance, can severely impact the performance of power amplifier (PA) linearization systems, in particular in adaptive digital predistorters (PDs). In this paper, we first analyze the effect of IQ imbalance on the performance of a memory orthogonal polynomials predistorter (MOP PD), and then we propose a new adaptive algorithm to estimate and compensate the unknown IQ imbalance in QM. Unlike previous compensation techniques, the proposed method was capable of online IQ imbalance compensation with faster convergence, and no special calibration or training signals were needed. The effectiveness of the proposed IQ imbalance compensator was validated by simulations. The results clearly show the performance of the MOP PD to be enhanced significantly by adding the proposed IQ imbalance compensator.
Analysis of V-cycle multigrid algorithms for forms defined by numerical quadrature
Bramble, J.H. . Dept. of Mathematics); Goldstein, C.I.; Pasciak, J.E. . Applied Mathematics Dept.)
1994-05-01
The authors describe and analyze certain V-cycle multigrid algorithms with forms defined by numerical quadrature applied to the approximation of symmetric second-order elliptic boundary value problems. This approach can be used for the efficient solution of finite element systems resulting from numerical quadrature as well as systems arising from finite difference discretizations. The results are based on a regularity free theory and hence apply to meshes with local grid refinement as well as the quasi-uniform case. It is shown that uniform (independent of the number of levels) convergence rates often hold for appropriately defined V-cycle algorithms with as few as one smoothing per grid. These results hold even on applications without full elliptic regularity, e.g., a domain in R[sup 2] with a crack.
Quadrature conductivity: A quantitative indicator of bacterial abundance in porous media
Chi Zhang; Andre Revil; Yoshiko Fujita; Junko Munakata-Marr; George Redden
2014-09-01
ABSTRACT The abundance and growth stages of bacteria in subsurface porous media affect the concentrations and distributions of charged species within the solid-solution interfaces. Therefore, spectral induced polarization (SIP) measurements can be used to monitor changes in bacterial biomass and growth stage. Our goal was to gain a better understanding of the SIP response of bacteria present in a porous material. Bacterial cell surfaces possess an electric double layer and therefore become polarized in an electric field. We performed SIP measurements over the frequency range of 0.1–1 kHz on cell suspensions alone and cell suspensions mixed with sand at four pore water conductivities. We used Zymomonas mobilis at four different cell densities (in- cluding the background). The quadrature conductivity spectra exhibited two peaks, one around 0.05–0.10 Hz and the other around 1–10 Hz. Because SIP measurements on bacterial suspensions are typically made at frequencies greater than 1 Hz, these peaks have not been previously reported. In the bac-terial suspensions in growth medium, the quadrature conduc-tivity at peak I was linearly proportional to the density of the bacteria. For the case of the suspensions mixed with sands, we observed that peak II presented a smaller increase in the quadrature conductivity with the cell density. A comparison of the experiments with and without sand grains illustrated the effect of the porous medium on the overall quadrature con- ductivity response (decrease in the amplitude and shift of the peaks to the lower frequencies). Our results indicate that for a given porous medium, time-lapse SIP has potential for mon- itoring changes in bacterial abundance within porous media.
Schrenk, Bernhard; Dris, Stefanos; Bakopoulos, Paraskevas; Lazarou, Ioannis; Voigt, Karsten; Zimmermann, Lars; Avramopoulos, Hercules
2012-08-01
Optical quadrature amplitude modulation (QAM) is experimentally demonstrated with a low-complexity modulator based on a semiconductor optical amplifier and electroabsorption modulator. Flexible amplitude/phase format transmission is achieved. The applicability of octary QAM for coherent optical access networks with sustainable 3 Gb/s per-user bandwidth is investigated for a long reach of 100 km, and its compatibility with a potentially high split is verified. PMID:22859139
Hayward, Thomas J; Oba, Roger M
2013-07-01
Numerical methods are presented for approximating the probability density functions (pdf's) of acoustic fields and receiver-array responses induced by a given joint pdf of a set of acoustic environmental parameters. An approximation to the characteristic function of the random acoustic field (the inverse Fourier transform of the field pdf) is first obtained either by construction of the empirical characteristic function (ECF) from a random sample of the acoustic parameters, or by application of generalized Gaussian quadrature to approximate the integral defining the characteristic function. The Fourier transform is then applied to obtain an approximation of the pdf by a continuous function of the field variables. Application of both the ECF and generalized Gaussian quadrature is demonstrated in an example of a shallow-water ocean waveguide with two-dimensional uncertainty of sound speed and attenuation coefficient in the ocean bottom. Both approximations lead to a smoother estimate of the field pdf than that provided by a histogram, with generalized Gaussian quadrature providing a smoother estimate at the tails of the pdf. Potential applications to acoustic system performance quantification and to nonparametric acoustic signal processing are discussed. PMID:23862782
The Gauss and Ampere Laws: Different Laws but Similar Difficulties for Student Learning
ERIC Educational Resources Information Center
Guisasola, Jenaro; Almudi, Jose M.; Salinas, Julia; Zuza, Kristina; Ceberio, Mikel
2008-01-01
This study aims to analyse university students' reasoning regarding two laws of electromagnetism: Gauss's law and Ampere's law. It has been supposed that the problems seen in understanding and applying both laws do not spring from students' misconceptions. Students habitually use reasoning known in the literature as 'common sense' methodology that…
Horizons of radiating black holes in Einstein-Gauss-Bonnet gravity
Ghosh, S. G.; Deshkar, D. W.
2008-02-15
A Vaidya-based model of a radiating black hole is studied in a 5-dimensional Einstein gravity with Gauss-Bonnet contribution of quadratic curvature terms. The structure and locations of the apparent and event horizons of the radiating black hole are determined.
Schimpf, Damian N; Putnam, William P; Grogan, Michael D W; Ramachandran, Siddharth; Kärtner, Franz X
2013-07-29
We derive solutions for radially polarized Bessel-Gauss beams in free-space by superimposing decentered Gaussian beams with differing polarization states. We numerically show that the analytical result is applicable even for large semi-aperture angles, and we experimentally confirm the analytical expression by employing a fiber-based mode-converter. PMID:23938719
An Alternative Method to Gauss-Jordan Elimination: Minimizing Fraction Arithmetic
ERIC Educational Resources Information Center
Smith, Luke; Powell, Joan
2011-01-01
When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…
NASA Astrophysics Data System (ADS)
Kamel, Osman M.; Ammar, M. K.
2006-12-01
Firstly we derive Gauss' perturbation equation for parabolic motion using Murray-Dermott and Kovalevsky procedures. Secondly, we easily deduce the variations of the orbital elements for the parabolic trajectories due to a small impulse at any point along the path and at the vertex of the parabola.
On the geometry of the Gauss map of conformal foliations by lines
NASA Astrophysics Data System (ADS)
Burel, Jean-Marie; Gudmundsson, Sigmundur
2004-01-01
Let {cal F} be an oriented conformal foliation of connected, totally geodesic and 1-dimensional leaves in mathbb{R}(n+1) . We prove that if n≥ 3 then the Gauss map phi{:} U {->} S(n) of {cal F} is a non-constant n-harmonic morphism if and only if it is a radial projection.
Tolman-Oppenheimer-Volkoff equations in modified Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Momeni, D.; Myrzakulov, R.
2015-11-01
Based on a stringy inspired Gauss-Bonnet (GB) modification of classical gravity, we constructed a model for neutron stars. We derived the modified forms of Tolman-Oppenheimer-Volkoff (TOV) equations for a generic function of f(G) gravity. The hydrostatic equations remained unchanged but the dynamical equations for metric functions are modified due to the effects of GB term.
NASA Astrophysics Data System (ADS)
Xu, Luopeng; Dan, Youquan; Wang, Qingyuan
2015-10-01
The continuous wavelet transform (CWT) introduces an expandable spatial and frequency window which can overcome the inferiority of localization characteristic in Fourier transform and windowed Fourier transform. The CWT method is widely applied in the non-stationary signal analysis field including optical 3D shape reconstruction with remarkable performance. In optical 3D surface measurement, the performance of CWT for optical fringe pattern phase reconstruction usually depends on the choice of wavelet function. A large kind of wavelet functions of CWT, such as Mexican Hat wavelet, Morlet wavelet, DOG wavelet, Gabor wavelet and so on, can be generated from Gauss wavelet function. However, so far, application of the Gauss wavelet transform (GWT) method (i.e. CWT with Gauss wavelet function) in optical profilometry is few reported. In this paper, the method using GWT for optical fringe pattern phase reconstruction is presented first and the comparisons between real and complex GWT methods are discussed in detail. The examples of numerical simulations are also given and analyzed. The results show that both the real GWT method along with a Hilbert transform and the complex GWT method can realize three-dimensional surface reconstruction; and the performance of reconstruction generally depends on the frequency domain appearance of Gauss wavelet functions. For the case of optical fringe pattern of large phase variation with position, the performance of real GWT is better than that of complex one due to complex Gauss series wavelets existing frequency sidelobes. Finally, the experiments are carried out and the experimental results agree well with our theoretical analysis.
Wu, S.H.; Wu, C.Y.; Hsu, P.
1996-12-31
This work considers radiative heat transfer in a three-dimensional, rectangular, scattering medium exposed to diffuse radiation. Applying the quadrature method with singularity subtraction to the exact integral equations in terms of the moments of intensity can generate highly accurate solutions, and so the method is adopted in this work. The example solutions provided are for radiative equilibrium in homogeneous absorbing-emitting media, and for radiative transfer in nonhomogeneous absorbing-scattering (isotropic and linearly anisotropic) media with non-reflecting surfaces. To validate the solutions, the present results are compared with the solutions obtained by the YIX method and other methods.
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
NASA Technical Reports Server (NTRS)
Campbell, Joel
2008-01-01
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
Mathews, K.A.; Brennan, C.R.
1995-12-31
The exponential characteristic method is one of a family of nonlinear spatial quadratures which are positive and at least second order accurate. The authors initially developed the method in slab geometry, where it gave accurate results for deep penetration problems using coarse meshes. Characteristic methods are restricted to Cartesian geometries, so they next tested it with rectangular cells, where it was again a strong performer. Here the authors extend the method to unstructured grids of arbitrarily shaped and oriented triangles and report on its performance.
Optimization of quadrature signal processing for laser interferometers for demanding applications
NASA Astrophysics Data System (ADS)
PodŻorny, Tomasz; Budzyń, Grzegorz; Tkaczyk, Jakub
2016-06-01
Presented paper performs an analysis of quadrature signal processing algorithms for high demanding laser interferometry applications. Careful signal processing is required to minimize nonlinearities which come from optical path and components' imperfections, and reduce overall instrumental error. Paper focuses on algebraic fits, because implementation for real time systems was a main requirement. The most demanding applications are stationary measurements where the position slightly fluctuates in the range below one fringe period. Therefore, analysis was performed for samples that were spread along a few milliradians of a full circle.
Nodal systems with maximal domain of exactness for Gaussian quadrature formulas
NASA Astrophysics Data System (ADS)
Berriochoa, E.; Cachafeiro, A.
2008-03-01
The aim of this work is to study quadrature formulas for measures on the complex plane. The novelty of our contribution is to consider the exactness on subspaces of polynomials on the variables z and . Using this approach we characterize, in a unified way, the classical nodal systems for measures on the real line and the nodal systems for measures on the unit circle, which are based on para-orthogonal polynomials. We also characterize the nodal systems on the unit circle, which are not based on para-orthogonal polynomials (only for the case of nodal systems with 1 or 2 points).
Extremal states for photon number and quadratures as gauges for nonclassicality
NASA Astrophysics Data System (ADS)
Hradil, Z.; Řeháček, J.; de la Hoz, P.; Leuchs, G.; Sánchez-Soto, L. L.
2015-04-01
Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertainty relation, as well as a couple of weaker inequalities obtained by relaxing some restrictions of the problem. We also find the intelligent states saturating that relation and complete their characterization by considering extra constraints on the second-order moments of the variables involved. Using these moments, we construct performance measures tailored to diagnose photon-added and Schrödinger-cat-like states, among others.
On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands
NASA Astrophysics Data System (ADS)
Cruz-Barroso, Ruymán; González-Vera, Pablo; Njåstad, Olav
2007-04-01
In this paper, quadrature formulas with an arbitrary number of nodes and exactly integrating trigonometric polynomials up to degree as high as possible are constructed in order to approximate 2?-periodic weighted integralsE For this purpose, certain bi-orthogonal systems of trigonometric functions are introduced and their most relevant properties studied. Some illustrative numerical examples are also given. The paper completes the results previously given by Szeg? in Magy Tud Akad Mat Kut Intez K?zl 8:255?273, 1963 and by some of the authors in Annales Mathematicae et Informaticae 32:5?44, 2005.
Automatic IQ Imbalance Compensation Technique for Quadrature Modulator by Single-Tone Testing
NASA Astrophysics Data System (ADS)
Kim, Minseok; Konishi, Yohei; Takada, Jun-Ichi; Gao, Boxin
This letter proposes an automatic IQ imbalance compensation technique for quadrature modulators by means of spectrum measurement of RF signal using a spectrum analyzer. The analyzer feeds back only magnitude information of the frequency spectrum of the signal. To realize IQ imbalance compensation, the conventional method of steepest descent is modified; the descent direction is empirically determined and a variable step-size is introduced for accelerating convergence. The experimental results for a four-channel transmitter operating at 11GHz are presented for verification.
Vibration analysis of shear deformable circular arches by the differential quadrature method
NASA Astrophysics Data System (ADS)
Kang, K.; Bert, C. W.; Striz, A. G.
1995-06-01
The differential quadrature method is applied in the computation of the eigenvalues of the equations of motion governing in-plane and out-of-plane vibration of circular arches, based on the Bresse-Timoshenko beam theory in which both rotatory inertia and shear deformation are taken into account. Fundamental frequencies are calculated for arches of rectangular and circular cross sections under clamped-clamped end conditions and the results are compared with numerical solutions by another method. The present method gives good accuracy with only a limited number of grid points.
NASA Astrophysics Data System (ADS)
Rousseau, Guy; Gay, David; Piché, Michel
2006-09-01
A recent analysis [G. Rousseau, D. Gay and M. Piché, One-dimensional description of cylindrically symmetric laser beams: application to Bessel-type nondiffracting beams, J. Opt. Soc. Am. A, 22 (2005) 1274] has shown that any cylindrically symmetric laser beam can be synthesized from a single wave called a constituent wave. This representation allows the introduction of one-dimensional Cartesian root-mean-square (rms) parameters to describe the conical structure of cylindrically symmetric laser beams. In this paper, we compare the rms characterization of Bessel-Gauss beams in polar coordinates with that of their respective constituent waves in Cartesian coordinates. Numerical results reveal an asymptotic correspondence between polar and Cartesian rms parameters of Bessel-Gauss beams propagating in a nondiffracting regime. Such a correspondence eliminates misleading interpretations about the propagation factor and the Rayleigh range of nondiffracting Bessel-type beams characterized in terms of polar rms parameters.
Conformal mass in Einstein-Gauss-Bonnet AdS gravity
NASA Astrophysics Data System (ADS)
Jatkar, Dileep P.; Kofinas, Georgios; Miskovic, Olivera; Olea, Rodrigo
2015-05-01
In this paper, we show that the physical information given by conserved charges for asymptotically AdS spacetimes in Einstein-Gauss-Bonnet AdS gravity is encoded in the electric part of the Weyl tensor. This result generalizes the conformal mass definition by Ashtekar-Magnon-Das (AMD) to a gravity theory with a Gauss-Bonnet term. This proof makes use of the Noether charges obtained from an action renormalized by the addition of counterterms which depend on the extrinsic curvature (Kounterterms). If the asymptotic fall-off behavior of the Weyl tensor is same as the one considered in the AMD method, then the Kounterterm charges and the AMD charges agree in any dimension.
Excitation of high orbital angular momentum Rydberg states with Laguerre-Gauss beams
NASA Astrophysics Data System (ADS)
Rodrigues, J. D.; Marcassa, L. G.; Mendonça, J. T.
2016-04-01
We consider the excitation of Rydberg states through photons carrying an intrinsic orbital angular momentum degree of freedom. Laguerre-Gauss modes, with a helical wave-front structure, correspond to such a set of laser beams, which carry {{\\ell }}0 units of orbital angular momentum in their propagation direction, with ℓ 0 the winding number. We demonstrate that, in a proper geometry setting, this orbital angular momentum can be transferred to the internal degrees of freedom of the atoms, thus violating the standard dipole selection rules. Higher orbital angular momentum states become accessible through a single photon excitation process. We investigate how the spacial structure of the Laguerre-Gauss beam affects the radial coupling strength, assuming the simplest case of hydrogen-like wavefunctions. Finally we discuss a generalization of the angular momentum coupling, in order to include the effects of the fine and hyperfine splitting, in the context of the Wigner-Eckart theorem.
Magnetic fields greater than 10 to the 20th power gauss. [in astrophysical systems
NASA Technical Reports Server (NTRS)
Lerche, I.; Schramm, D. N.
1977-01-01
Zaumen (1976) found that spontaneous pair production in a uniform magnetic field should be a feasible process for field strengths at least of the order of 10 to the 20th power gauss. This note points out that a magnetic field of this order of magnitude is most unlikely to occur in realistic astrophysical situations because of the large dynamical and quantum-mechanical effects such a field would produce. It is suggested that Zaumen's calculation would probably have little bearing on the suspected evolution of astrophysical systems since other processes (either dynamical or quantum-mechanical) apparently limit the field strength before such high magnetic fields would be reached. An upper limit of about 10 to the 16th power gauss is obtained by considering the isotropy of the 3-K blackbody radiation, the formation of collapsed objects in very high magnetic fields, and magnetic bremsstrahlung processes in quantum electrodynamics.
Gauss-Seidel Accelerated: Implementing Flow Solvers on Field Programmable Gate Arrays
Chassin, David P.; Armstrong, Peter R.; Chavarría-Miranda, Daniel; Guttromson, Ross T.
2006-06-01
Non-linear steady-state power flow solvers have typically relied on the Newton-Raphson method to efficiently compute solutions on today's computer systems. Field Programmable Gate Array (FPGA) devices, which have recently been integrated into high-performance computers by major computer system vendors, offer an opportunity to significantly increase the performance of power flow solvers. However, only some algorithms are suitable for an FPGA implementation. The Gauss-Seidel method of solving the AC power flow problem is an excellent example of such an opportunity. In this paper we discuss algorithmic design considerations, optimization, implementation, and performance results of the implementation of the Gauss-Seidel method running on a Silicon Graphics Inc. Altix-350 computer equipped with a Xilinx Virtex II 6000 FPGA.
Area functional relation for 5D-Gauss-Bonnet-AdS black hole
NASA Astrophysics Data System (ADS)
Pradhan, Parthapratim
2016-08-01
We present area (or entropy) functional relation for multi-horizons five dimensional (5D) Einstein-Maxwell-Gauss-Bonnet-AdS black hole. It has been observed by exact and explicit calculation that some complicated function of two or three horizons area is mass-independent whereas the entropy product relation is not mass-independent. We also study the local thermodynamic stability of this black hole. The phase transition occurs at certain condition. Smarr mass formula and first law of thermodynamics have been derived. This mass-independent relation suggests they could turn out to be an universal quantity and further helps us to understanding the nature of black hole entropy (both interior and exterior) at the microscopic level. In the "Appendix", we have derived the thermodynamic products for 5D Einstein-Maxwell-Gauss-Bonnet black hole with vanishing cosmological constant.
Stability of anti-de sitter space in Einstein-Gauss-Bonnet gravity.
Deppe, Nils; Kolly, Allison; Frey, Andrew; Kunstatter, Gabor
2015-02-20
Recently it has been argued that in Einstein gravity anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass-energy content of the spacetime is too small, thereby restoring the stability of anti-de Sitter spacetime in this context. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude. PMID:25763946
Extremal dyonic black holes in D=4 Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Chen, Chiang-Mei; Gal'Tsov, Dmitri V.; Orlov, Dmitry G.
2008-11-01
We investigate extremal dyon black holes in the Einstein-Maxwell-dilaton theory with higher curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. In the same theory without the Gauss-Bonnet term the extremal dyon solutions exist only for discrete values of the dilaton coupling constant a. We show that the Gauss-Bonnet term acts as a dyon hair tonic enlarging the allowed values of a to continuous domains in the plane (a,qm) where qm is the magnetic charge. In the limit of the vanishing curvature coupling (a large magnetic charge) the dyon solutions obtained tend to the Reissner-Nordström solution but not to the extremal dyons of the Einstein-Maxwell-dilaton theory. Both solutions have the same dependence of the horizon radius in terms of charges. The entropy of new dyonic black holes interpolates between the Bekenstein-Hawking value in the limit of the large magnetic charge (equivalent to the vanishing Gauss-Bonnet coupling) and twice this value for the vanishing magnetic charge. Although an expression for the entropy can be obtained analytically using purely local near-horizon solutions, its interpretation as the black hole entropy is legitimate only once the global black hole solution is known to exist, and we obtain numerically the corresponding conditions on the parameters. Thus, a purely local analysis is insufficient to fully understand the entropy of the curvature-corrected black holes. We also find dyon solutions which are not asymptotically flat, but approach the linear dilaton background at infinity. They describe magnetic black holes on the electric linear dilaton background.
Taub-NUT/bolt black holes in Gauss-Bonnet-Maxwell gravity
Dehghani, M.H.; Hendi, S. H.
2006-04-15
We present a class of higher-dimensional solutions to Gauss-Bonnet-Maxwell equations in 2k+2 dimensions with a U(1) fibration over a 2k-dimensional base space B. These solutions depend on two extra parameters, other than the mass and the Newman-Unti-Tamburino charge, which are the electric charge q and the electric potential at infinity V. We find that the form of metric is sensitive to geometry of the base space, while the form of electromagnetic field is independent of B. We investigate the existence of Taub-Newman-Unti-Tamburino/bolt solutions and find that in addition to the two conditions of uncharged Newman-Unti-Tamburino solutions, there exist two other conditions. These two extra conditions come from the regularity of vector potential at r=N and the fact that the horizon at r=N should be the outer horizon of the black hole. We find that for all nonextremal Newman-Unti-Tamburino solutions of Einstein gravity having no curvature singularity at r=N, there exist Newman-Unti-Tamburino solutions in Gauss-Bonnet-Maxwell gravity. Indeed, we have nonextreme Newman-Unti-Tamburino solutions in 2+2k dimensions only when the 2k-dimensional base space is chosen to be CP{sup 2k}. We also find that the Gauss-Bonnet-Maxwell gravity has extremal Newman-Unti-Tamburino solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature, even though there a curvature singularity exists at r=N. We also find that one can have bolt solutions in Gauss-Bonnet-Maxwell gravity with any base space. The only case for which one does not have black hole solutions is in the absence of a cosmological term with zero curvature base space.
Experimental generation of Mathieu-Gauss beams with a phase-only spatial light modulator.
Hernández-Hernández, R J; Terborg, R A; Ricardez-Vargas, I; Volke-Sepúlveda, K
2010-12-20
We present a novel method for the efficient generation of even, odd, and helical Mathieu-Gauss beams of arbitrary order and ellipticity by means of a phase-only spatial light modulator (SLM). Our method consists of displaying the phase of the desired beam in the SLM; the reconstructed field is obtained on-axis following a spatial filtering process with an annular aperture. The propagation invariance and topological properties of the generated beams are investigated numerically and experimentally. PMID:21173824
Extremal dyonic black holes in D=4 Gauss-Bonnet gravity
Chen, C.-M.; Gal'tsov, Dmitri V.; Orlov, Dmitry G.
2008-11-15
We investigate extremal dyon black holes in the Einstein-Maxwell-dilaton theory with higher curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. In the same theory without the Gauss-Bonnet term the extremal dyon solutions exist only for discrete values of the dilaton coupling constant a. We show that the Gauss-Bonnet term acts as a dyon hair tonic enlarging the allowed values of a to continuous domains in the plane (a,q{sub m}) where q{sub m} is the magnetic charge. In the limit of the vanishing curvature coupling (a large magnetic charge) the dyon solutions obtained tend to the Reissner-Nordstroem solution but not to the extremal dyons of the Einstein-Maxwell-dilaton theory. Both solutions have the same dependence of the horizon radius in terms of charges. The entropy of new dyonic black holes interpolates between the Bekenstein-Hawking value in the limit of the large magnetic charge (equivalent to the vanishing Gauss-Bonnet coupling) and twice this value for the vanishing magnetic charge. Although an expression for the entropy can be obtained analytically using purely local near-horizon solutions, its interpretation as the black hole entropy is legitimate only once the global black hole solution is known to exist, and we obtain numerically the corresponding conditions on the parameters. Thus, a purely local analysis is insufficient to fully understand the entropy of the curvature-corrected black holes. We also find dyon solutions which are not asymptotically flat, but approach the linear dilaton background at infinity. They describe magnetic black holes on the electric linear dilaton background.
NASA Technical Reports Server (NTRS)
Chapman, G.; Kirk, D.
1974-01-01
The parameter identification scheme being used is a differential correction least squares procedure (Gauss-Newton method). The position, orientation, and derivatives of these quantities with respect to the parameters of interest (i.e., sensitivity coefficients) are determined by digital integration of the equations of motion and the parametric differential equations. The application of this technique to three vastly different sets of data is used to illustrate the versatility of the method and to indicate some of the problems that still remain.
Geophex Airborne Unmanned Survey System (GAUSS). Topical report, October 1993--September 1996
1998-12-31
This document is a Final Technical Report that describes the results of the Geophex Airborne Unmanned Survey System (GAUSS) research project. The objectives were to construct a geophysical data acquisition system that uses a remotely operated unmanned aerial vehicle (UAV) and to evaluate its effectiveness for characterization of hazardous environmental sites. The GAUSS is a data acquisition system that mitigates the potential risk to personnel during geophysical characterization of hazardous or radioactive sites. The fundamental basis of the GAUSS is as follows: (1) an unmanned survey vehicle carries geophysical sensors into a hazardous location, (2) the pilot remains outside the hazardous site and operates the vehicle using radio control, (3) geophysical measurements and their spatial locations are processed by an automated data-acquisition system which displays data on an off-site monitor in real-time, and (4) the pilot uses the display to direct the survey vehicle for complete site coverage. The objective of our Phase I research was to develop a data acquisition and processing (DAP) subsystem and geophysical sensors suitable for UAV deployment. We integrated these two subsystems to produce an automated, hand-held geophysical surveying system. The objective of the Phase II effort was to modify the subsystems and integrate them into an airborne prototype. The completed GAUSS DAP system consists of a UAV platform, a laser tracking and ranging subsystem, a telemetry subsystem, light-weight geophysical sensors, a base-station computer (BC), and custom-written survey control software (SCS). We have utilized off-the-shelf commercial products, where possible, to reduce cost and design time.
Propagation Dynamics of Nonspreading Cosine-Gauss Water-Wave Pulses.
Fu, Shenhe; Tsur, Yuval; Zhou, Jianying; Shemer, Lev; Arie, Ady
2015-12-18
Linear gravity water waves are highly dispersive; therefore, the spreading of initially short wave trains characterizes water surface waves, and is a universal property of a dispersive medium. Only if there is sufficient nonlinearity does this envelope admit solitary solutions which do not spread and remain in fixed forms. Here, in contrast to the nonlinear localized wave packets, we present both theoretically and experimentally a new type of linearly nondispersive water wave, having a cosine-Gauss envelope, as well as its higher-order Hermite cosine-Gauss variations. We show that these waves preserve their width despite the inherent dispersion while propagating in an 18-m wave tank, accompanied by a slowly varying carrier-envelope phase. These wave packets exhibit self-healing; i.e., they are restored after bypassing an obstacle. We further demonstrate that these nondispersive waves are robust to weakly nonlinear perturbations. In the strong nonlinear regime, symmetry breaking of these waves is observed, but their cosine-Gauss shapes are still approximately preserved during propagation. PMID:26722925
Wake Numerical Simulation Based on the Park-Gauss Model and Considering Atmospheric Stability
NASA Astrophysics Data System (ADS)
Yang, Xiangsheng; Zhao, Ning; Tian, Linlin; Zhu, Jun
2016-06-01
In this paper, a new Park-Gauss model based on the assumption of the Park model and the Eddy-viscosity model is investigated to conduct the wake numerical simulation for solving a single wind turbine problem. The initial wake radius has been modified to improve the model’s numerical accuracy. Then the impact of the atmospheric stability based on the Park-Gauss model has been studied in the wake region. By the comparisons and the analyses of the test results, it turns out that the new Park-Gauss model could achieve better effects of the wind velocity simulation in the wake region. The wind velocity in the wake region recovers quickly under the unstable atmospheric condition provided the wind velocity is closest to the test result, and recovers slowly under stable atmospheric condition in case of the wind velocity is lower than the test result. Meanwhile, the wind velocity recovery falls in between the unstable and stable neutral atmospheric conditions.
Asymptotically (anti)-de Sitter solutions in Gauss-Bonnet gravity without a cosmological constant
Dehghani, M.H.
2004-09-15
In this paper I show that one can have asymptotically de Sitter, anti-de Sitter (AdS), and flat solutions in Gauss-Bonnet gravity without a cosmological constant term in field equations. First, I introduce static solutions whose three surfaces at fixed r and t have constant positive (k=1), negative (k=-1), or zero (k=0) curvature. I show that for k={+-}1 one can have asymptotically de Sitter, AdS, and flat spacetimes, while for the case of k=0, one has only asymptotically AdS solutions. Some of these solutions present naked singularities, while some others are black hole or topological black hole solutions. I also find that the geometrical mass of these five-dimensional spacetimes is m+2{alpha}|k|, which is different from the geometrical mass m of the solutions of Einstein gravity. This feature occurs only for the five-dimensional solutions, and is not repeated for the solutions of Gauss-Bonnet gravity in higher dimensions. Second, I add angular momentum to the static solutions with k=0, and introduce the asymptotically AdS charged rotating solutions of Gauss-Bonnet gravity. Finally, I introduce a class of solutions which yields an asymptotically AdS spacetime with a longitudinal magnetic field, which presents a naked singularity, and generalize it to the case of magnetic rotating solutions with two rotation parameters.
Propagation Dynamics of Nonspreading Cosine-Gauss Water-Wave Pulses
NASA Astrophysics Data System (ADS)
Fu, Shenhe; Tsur, Yuval; Zhou, Jianying; Shemer, Lev; Arie, Ady
2015-12-01
Linear gravity water waves are highly dispersive; therefore, the spreading of initially short wave trains characterizes water surface waves, and is a universal property of a dispersive medium. Only if there is sufficient nonlinearity does this envelope admit solitary solutions which do not spread and remain in fixed forms. Here, in contrast to the nonlinear localized wave packets, we present both theoretically and experimentally a new type of linearly nondispersive water wave, having a cosine-Gauss envelope, as well as its higher-order Hermite cosine-Gauss variations. We show that these waves preserve their width despite the inherent dispersion while propagating in an 18-m wave tank, accompanied by a slowly varying carrier-envelope phase. These wave packets exhibit self-healing; i.e., they are restored after bypassing an obstacle. We further demonstrate that these nondispersive waves are robust to weakly nonlinear perturbations. In the strong nonlinear regime, symmetry breaking of these waves is observed, but their cosine-Gauss shapes are still approximately preserved during propagation.
State space orderings for Gauss-Seidel in Markov chains revisited
Dayar, T.
1996-12-31
Symmetric state space orderings of a Markov chain may be used to reduce the magnitude of the subdominant eigenvalue of the (Gauss-Seidel) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the Gauss-Seidel splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semi-convergent. On the other hand, there are semi-convergent symmetric state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. An algorithm that orders the states of a Markov chain so as to increase the likelihood of satisfying Property-R is presented. The computational complexity of the ordering algorithm is less than that of a single Gauss-Seidel iteration (for sparse matrices). In doing all this, the aim is to gain an insight for faster converging orderings. Results from a variety of applications improve the confidence in the algorithm.
From entropy-maximization to equality-maximization: Gauss, Laplace, Pareto, and Subbotin
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2014-12-01
The entropy-maximization paradigm of statistical physics is well known to generate the omnipresent Gauss law. In this paper we establish an analogous socioeconomic model which maximizes social equality, rather than physical disorder, in the context of the distributions of income and wealth in human societies. We show that-on a logarithmic scale-the Laplace law is the socioeconomic equality-maximizing counterpart of the physical entropy-maximizing Gauss law, and that this law manifests an optimized balance between two opposing forces: (i) the rich and powerful, striving to amass ever more wealth, and thus to increase social inequality; and (ii) the masses, struggling to form more egalitarian societies, and thus to increase social equality. Our results lead from log-Gauss statistics to log-Laplace statistics, yield Paretian power-law tails of income and wealth distributions, and show how the emergence of a middle-class depends on the underlying levels of socioeconomic inequality and variability. Also, in the context of asset-prices with Laplace-distributed returns, our results imply that financial markets generate an optimized balance between risk and predictability.
Application of Quadrature Methods for Re-Weighting in Lattice QCD
Abdou Abdel-Rehim, William Detmold, Kostas Orginos
2011-12-01
Re-weighting is a useful tool that has been employed in Lattice QCD in different contexts including, tuning the strange quark mass, approaching the light quark mass regime, and simulating electromagnetic fields on top of QCD gauge configurations. In case of re-weighting the sea quark mass, the re-weighting factor is given by the ratio of the determinants of two Dirac operators D{sub a} and D{sub b}. A popular approach for computing this ratio is to use a pseudofermion representation of the determinant of the composite operator {Omega} = D{sub a}(D{sub b}{sup {dagger}}D{sub b}){sup -1} D{sub a}{sup {dagger}}. Here, we study using quadrature methods together with noise vectors to compute the ratio of determinants. We show that, with quadrature methods each determinant can be computed separately using the operators {Omega}{sub a} = D{sub a}{sup {dagger}}D{sub a} and {Omega}{sub b} = D{sub b}{sup {dagger}} D{sub b}. We also discuss using bootstrap re-sampling to remove the bias from the determinant estimator.
First CFOA-based explicit-current-output quadrature sinusoidal oscillators using grounded capacitors
NASA Astrophysics Data System (ADS)
Lahiri, Abhirup; Jaikla, Winai; Siripruchyanun, Montree
2013-02-01
To date, no current-feedback operational amplifier (CFOA)-based sinusoidal oscillator has been reported which provides all the following features simultaneously: (i) current-mode quadrature sinusoidal oscillator providing two explicit-current-outputs (ECOs) from high output impedance terminals, (ii) employing no more than three CFOA ICs and six passive components, which include two grounded capacitors, (iii) offers independent tuning of the condition of oscillation (CO) via a resistor and (iv) provides tunability of the ratio of amplitudes of the generated quadrature ECOs via a separate resistor. To the best of authors' knowledge, this article reports first CFOA-based QOs in current-mode (i.e. providing two ECO signals). Experimental results using AD844 CFOA ICs from Analog Devices have been included to verify the workability of the proposed oscillator circuits. An example automatic gain control (AGC) loop to regulate the oscillation amplitude and control the THD has also been used and verified using SPICE simulations using the AD844 macro-model.
Shilyagin, P A; Gelikonov, G V; Gelikonov, V M; Moiseev, A A; Terpelov, D A
2014-07-31
We have thoroughly investigated the method of simultaneous reception of spectral components with the achromatised quadrature phase shift between two portions of a reference wave, designed for the effective suppression of the 'mirror' artefact in the resulting image obtained by means of spectral domain optical coherence tomography (SD OCT). We have developed and experimentally tested a phase-shifting element consisting of a beam divider, which splits the reference optical beam into the two beams, and of delay lines being individual for each beam, which create a mutual phase difference of π/2 in the double pass of the reference beam. The phase shift achromatism over a wide spectral range is achieved by using in the delay lines the individual elements with different dispersion characteristics. The ranges of admissible adjustment parameters of the achromatised delay line are estimated for exact and inexact conformity of the geometric characteristics of its components to those calculated. A possibility of simultaneous recording of the close-to-quadrature spectral components with a single linear photodetector element is experimentally confirmed. The suppression of the artefact mirror peak in the OCT-signal by an additional 9 dB relative to the level of its suppression is experimentally achieved when the air delay line is used. Two-dimensional images of the surface positioned at an angle to the axis of the probe beam are obtained with the correction of the 'mirror' artefact while maintaining the dynamic range of the image. (laser biophotonics)
Selcuk, N.; Kayakol, N.
1996-11-01
Effects of order of approximation (S{sub 2} and S{sub 4}), angular quadrature (S{sub n} and S{sub n}{prime}) and spatial differencing (diamond and variable-weight) schemes, on the predictive accuracy of discrete ordinates method were investigated by predicting the distributions of radiative flux density and source term of a rectangular enclosure problem and comparing the results with exact solutions produced previously. The enclosure problem is based on data reported earlier on a large-scale experimental furnace with steep temperature gradients. It is a black-walled enclosure containing an absorbing-emitting medium of constant properties. Comparisons show that better agreement is obtained in radiative energy source terms than in flux densities and that the order of approximation plays a more significant role than angular quadrature and spatial differencing schemes in the accuracy of predicted radiative flux densities and radiative energy source terms. Only slight improvements are obtained when S{sub n} and variable-weight differencing schemes are employed.
Mathews, K.; Sjoden, G.; Minor, B. )
1994-09-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in slab geometry is derived and compared with current methods. It is similar to the linear characteristic (or, in slab geometry, the linear nodal) quadrature but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx), whose parameters are root-solved to match the known (from the previous iteration) average and first moment of the source over the cell. Like the linear adaptive method, the exponential characteristic method is positive and nonlinear but more accurate and more readily extended to other cell shapes. The nonlinearity has not interfered with convergence. The authors introduce the exponential moment functions,'' a generalization of the functions used by Walters in the linear nodal method, and use them to avoid numerical ill-conditioning. The method exhibits O([Delta]x[sup 4]) truncation error on fine enough meshes; the error is insensitive to mesh size for coarse meshes. In a shielding problem, it is accurate to 10% using 16-mfp-thick cells; conventional methods err by 8 to 15 orders of magnitude. The exponential characteristic method is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems.
Methods to Prescribe Particle Motion to Minimize Quadrature Error in Meshfree Methods
NASA Astrophysics Data System (ADS)
Templeton, Jeremy; Erickson, Lindsay; Morris, Karla; Poliakoff, David
2015-11-01
Meshfree methods are an attractive approach for simulating material systems undergoing large-scale deformation, such as spray break up, free surface flows, and droplets. Particles, which can be easily moved, are used as nodes and/or quadrature points rather than a relying on a fixed mesh. Most methods move particles according to the local fluid velocity that allows for the convection terms in the Navier-Stokes equations to be easily accounted for. However, this is a trade-off against numerical accuracy as the flow can often move particles to configurations with high quadrature error, and artificial compressibility is often required to prevent particles from forming undesirable regions of high and low concentrations. In this work, we consider the other side of the trade-off: moving particles based on reducing numerical error. Methods derived from molecular dynamics show that particles can be moved to minimize a surrogate for the solution error, resulting in substantially more accurate simulations at a fixed cost. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
A dual-band quadrature VCO with gain proportional to oscillation frequency
NASA Astrophysics Data System (ADS)
Wenrui, Zhu; Haigang, Yang; Tongqiang, Gao; Hui, Zhang
2013-08-01
This paper presents a novel dual-band quadrature voltage controlled oscillator (VCO) with the gain proportional to the oscillation frequency. Frequency synthesizers with this VCO can reduce the bandwidth fluctuation over all the frequency ranges without compensation or calibration. Besides the original switched capacitor array, an extra switched varactor array is adopted for the implementation of the proposed VCO. The tuning technique of changing the values of the capacitor and varactor at the same ratio is also derived. For verification purposes, a 2.5 G/3.5 G dual-band quadrature VCO is fabricated in a 0.13 μm CMOS process for WiMAX applications. Measurement results show that the VCO gain is closely proportional to the oscillation frequency with ±16% variation over the entire frequency range. The phase noise is -138.15 dBc/Hz at 10 MHz from the 2.5 GHz carrier and -137.44 dBc/Hz at 10 MHz from the 3.5 GHz carrier.
A multivariate quadrature based approach for LES based supersonic combustion modeling
NASA Astrophysics Data System (ADS)
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2010-11-01
The direct quadrature method of moments (DQMOM) was developed to solve high-dimensional probability density function (PDF) equations that arise in the description of turbulent combustion. This method is particularly useful in shock-containing supersonic internal flows such as those encountered in scramjet engines. In the DQMOM approach, the PDF is described in terms of a finite number of weighted delta functions whose weights and locations in composition space are obtained by solving specific transport equations. Since this approach is fully Eulerian in nature, it is advantageous compared to conventional Lagrangian methods used for solving the PDF transport equation. However, implementation of this formulation in the context of the large eddy simulation (LES) methodology leads to large numerical errors. For instance, the high-resolution numerical schemes used in LES lead to non-realizable and diffusive evolution of the DQMOM equations. Here, we propose a novel semi-discrete quadrature method of moments (SeQMOM) that overcomes this problem. A decoupling procedure is used to extend this method to multivariate PDF descriptions. The numerical implementation in LES as well as validation exercises will be presented.
Low-Latitude Solar Wind During the Fall 1998 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Poletto, G.; Suess, Steven T.; Biesecker, D.; Esser, R.; Gloeckler, G.; Zurbuchen, T.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
The Fall 1998 SOlar-Heliospheric Observatory (SOHO) - Ulysses quadrature occurred when Ulysses was at 5.2 AU, 17.4 deg South of the equator, and off the West line of the Sun. SOHO coronal observations, at heliocentric distances of a few solar radii, showed that the line through the solar center and Ulysses crossed, over the first days of observations, a dark, weakly emitting area and through the northern edge of a streamer complex during the second half of the quadrature campaign. Ulysses in situ observations showed this transition to correspond to a decrease from higher speed wind typical of coronal hole flow to low speed wind. Physical parameters (density, temperature, flow speed) of the low latitude coronal plasma sampled over the campaign are determined using constraints from what is the same plasma measured later in situ and simulating the intensities of the Hydrogen Lyman-alpha and OVI 1032 and 1037 Angstrom lines, measured by the Ultra Violet Coronagraph Spectrometer (UVCS) on SOHO. The densities, temperatures and outflow speed are compared with the same characteristic flow parameters for high-latitude fast wind streams and typical slow solar wind.
A quadrature based method of moments for nonlinear Fokker-Planck equations
NASA Astrophysics Data System (ADS)
Otten, Dustin L.; Vedula, Prakash
2011-09-01
Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.
Suppressing the mechanical quadrature error of a quartz double-H gyroscope through laser trimming
NASA Astrophysics Data System (ADS)
Zhao, Ke; Feng, Li-Hui; Wang, Qian-Qian; Liu, Ming-Zhi; Wang, Ben-Guo; Cui, Fang; Sun, Yu-Nan
2013-11-01
In this paper, we introduce a z-axis quartz gyroscope using a double-H tuning fork, which has a high sensitivity. However, it also causes a large mechanical quadrature error. The laser trimming method is used to suppress this error at quartz level. The trimming law is obtained through the finite element method (FEM). A femtosecond laser processing system is used to trim the gold balancing masses on the beams, and experimental results are basically consistent with the simulated ones. The mechanical quadrature error is suppressed by 96%, from 26.3° s-1 to 1.1° s-1. Nonlinearity changes from 1.48% to 0.30%, angular random walk (ARW) is reduced from 2.19° h-1/2 to 1.42° h-1/2, and bias instability is improved by a factor of 7.7, from 197.6° h-1 to 25.4° h-1.
Patsourakos, Spiros; Vourlidas, Angelos E-mail: vourlidas@nrl.navy.mil
2009-08-01
The nature of coronal mass ejection (CME)-associated low corona propagating disturbances, 'extreme ultraviolet (EUV) waves', has been controversial since their discovery by EIT on SOHO. The low-cadence, single-viewpoint EUV images and the lack of simultaneous inner corona white-light observations have hindered the resolution of the debate on whether they are true waves or just projections of the expanding CME. The operation of the twin EUV imagers and inner corona coronagraphs aboard STEREO has improved the situation dramatically. During early 2009, the STEREO Ahead (STA) and Behind (STB) spacecrafts observed the Sun in quadrature having a {approx}90 deg. angular separation. An EUV wave and CME erupted from active region 11012, on February 13, when the region was exactly at the limb for STA and hence at disk center for STB. The STEREO observations capture the development of a CME and its accompanying EUV wave not only with high cadence but also in quadrature. The resulting unprecedented data set allowed us to separate the CME structures from the EUV wave signatures and to determine without doubt the true nature of the wave. It is a fast-mode MHD wave after all.
Performance of a Coded Non-Square Quadrature Amplitude Modulation Scheme over Fading Channels
NASA Astrophysics Data System (ADS)
Li, L.; Divsalar, D.; Dolinar, S.
2004-02-01
It is shown that a non-square (NS) 2^(2n+1)-ary quadrature amplitude modulation (QAM) can be decomposed into a single-parity-check (SPC) block encoder and a memoryless modulator with independent in-phase (I) and quadrature (Q) symbol mapping. When NS-2^(2n+1)-QAM is concatenated with a forward-error-correcting (FEC) code, iterative demodulation and decoding of the FEC code and the inherent SPC code of NS-2^(2n+1)-QAM exploits the modulation's inherent memory and its independent I- and Q-channel mapping and demapping. The capacity and the bit-/symbol-error-rate (BER/SER) performance of coded and uncoded NS-2^(2n+1)-QAM systems are given for both additive white Gaussian noise (AWGN) channels and Rayleigh fading channels and are compared to those of other conventional 2^(2n+1)-ary systems. Simulation results show that, with iterative demodulation and decoding, coded NS-8QAM outperforms three conventional 8-ary systems by at least 0.65 dB on AWGN channels and by at least 0.57 dB on Rayleigh fading channels at BER = 10^(-5), when the FEC code is a concatenation of (15,11) Hamming codes with rate-1 accumulator codes, while coded NS-32QAM outperforms standard 32QAM by about 0.45 dB on AWGN channels and by about 0.27 dB on Rayleigh fading channels.
NASA Astrophysics Data System (ADS)
Pavluchenko, Sergey A.
2016-07-01
In this paper we perform a systematic study of vacuum spatially flat anisotropic [(3 +D )+1 ]-dimensional Einstein-Gauss-Bonnet cosmological models. We consider models that topologically are the product of two flat isotropic submanifolds with different scale factors. One of these submanifolds is three dimensional and represents our 3D space and the other is D dimensional and represents extra dimensions. We consider no Ansatz on the scale factors, which makes our results quite general. With both Einstein-Hilbert and Gauss-Bonnet contributions in play and with the symmetry involved, the cases with D =1 , D =2 , D =3 , and D ≥4 have different dynamics due to the different structures of the equations of motion. We analytically analyze equations of motion in all cases and describe all possible regimes. It appears that the only regimes with nonsingular future asymptotes are the Kasner regime in general relativity and exponential regimes. As of the past asymptotes, for a smooth transition only the Kasner regime in Gauss-Bonnet is an option. With this at hand, we are down to only two viable regimes: the "pure" Kasner regime [transition from a high-energy (Gauss-Bonnet) to a low-energy (general relativity) Kasner regime] and a transition from a high-energy Kasner regime to an anisotropic exponential solution. It appears that these regimes take place for different signs of the Gauss-Bonnet coupling α : the "pure" Kasner regime occurs for α >0 at low D and α <0 for high D ; the anisotropic exponential regime is reached only for α >0 . So if we restrain ourselves with α >0 solutions (which would be the case, say, if we identify α with inverse string tension in heterotic string theory), the only late-time regimes are Kasner for D =1 , 2 and anisotropic exponential for D ≥2 . Also, low-energy Kasner regimes [a (t )∝tp] have expansion rates for (3 +1 )-dimensional subspace ("our Universe") ranging from p =0.5 (D =1 ) to p =1 /√{3 }≈0.577 (D →∞ ), which
NASA Astrophysics Data System (ADS)
Hasegawa, Takemitsu; Hibino, Susumu; Hosoda, Yohsuke; Ninomiya, Ichizo
2007-08-01
An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162?170, 1980) of adaptive type based on the Newton?Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207?217, 1991; ACM Trans. Math. Softw. 17:218?232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner?s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229?259. Academic, Orlando, FL, 1971).
NASA Astrophysics Data System (ADS)
Ogawa, Hisashi; Ohdan, Hideaki; Miyata, Kazunori; Taguchi, Masahiro; Makino, Kenzo; Yonezawa, Hidehiro; Yoshikawa, Jun-ichi; Furusawa, Akira
2016-06-01
Real-time controls based on quantum measurements are powerful tools for various quantum protocols. However, their experimental realization has been limited by mode mismatch between the temporal mode of quadrature measurement and that heralded by photon detection. Here, we demonstrate real-time quadrature measurement of a single-photon wave packet induced by photon detection by utilizing continuous temporal-mode matching between homodyne detection and an exponentially rising temporal mode. Single photons in exponentially rising modes are also expected to be useful resources for interactions with other quantum systems.
Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals
Quine, Richard W.; Rinard, George A.; Eaton, Sandra S.; Eaton, Gareth R.
2014-01-01
The use of multiple synchronized outputs from an AWG provides the opportunity to perform EPR experiments differently than by conventional EPR. We report a method for reconstructing the quadrature EPR spectrum from periodic signals that are generated with sinusoidal magnetic field modulation such as continuous wave (CW), multiharmonic, or rapid scan experiments. The signal is down-converted to an intermediate frequency (IF) that is less than the field scan or field modulation frequency and then digitized in a single channel. This method permits use of a high-pass analog filter before digitization to remove the strong non-EPR signal at the IF, that might otherwise overwhelm the digitizer. The IF is the difference between two synchronized X-band outputs from a Tektronix AWG 70002A arbitrary waveform generator (AWG), one of which is for excitation and the other is the reference for down-conversion. To permit signal averaging, timing was selected to give an exact integer number of full cycles for each frequency. In the experiments reported here the IF was 5 kHz and the scan frequency was 40 kHz. To produce sinusoidal rapid scans with a scan frequency eight times IF, a third synchronized output generated a square wave that was converted to a sine wave. The timing of the data acquisition with a Bruker SpecJet II was synchronized by an external clock signal from the AWG. The baseband quadrature signal in the frequency domain was reconstructed. This approach has the advantages that (i) the non-EPR response at the carrier frequency is eliminated, (ii) both real and imaginary EPR signals are reconstructed from a single physical channel to produce an ideal quadrature signal, and (iii) signal bandwidth does not increase relative to baseband detection. Spectra were obtained by deconvolution of the reconstructed signals for solid BDPA (1,3-bisdiphenylene-2-phenylallyl) in air, 0.2 mM trityl OX63 in water, 15N perdeuterated tempone, and a nitroxide with a 0.5 G partially
Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals.
Tseitlin, Mark; Yu, Zhelin; Quine, Richard W; Rinard, George A; Eaton, Sandra S; Eaton, Gareth R
2014-10-30
The use of multiple synchronized outputs from an arbitrary waveform generator (AWG) provides the opportunity to perform EPR experiments differently than by conventional EPR. We report a method for reconstructing the quadrature EPR spectrum from periodic signals that are generated with sinusoidal magnetic field modulation such as continuous wave (CW), multiharmonic, or rapid scan experiments. The signal is down-converted to an intermediate frequency (IF) that is less than the field scan or field modulation frequency and then digitized in a single channel. This method permits use of a high-pass analog filter before digitization to remove the strong non-EPR signal at the IF, that might otherwise overwhelm the digitizer. The IF is the difference between two synchronized X-band outputs from a Tektronix AWG 70002A, one of which is for excitation and the other is the reference for down-conversion. To permit signal averaging, timing was selected to give an exact integer number of full cycles for each frequency. In the experiments reported here the IF was 5kHz and the scan frequency was 40kHz. To produce sinusoidal rapid scans with a scan frequency eight times IF, a third synchronized output generated a square wave that was converted to a sine wave. The timing of the data acquisition with a Bruker SpecJet II was synchronized by an external clock signal from the AWG. The baseband quadrature signal in the frequency domain was reconstructed. This approach has the advantages that (i) the non-EPR response at the carrier frequency is eliminated, (ii) both real and imaginary EPR signals are reconstructed from a single physical channel to produce an ideal quadrature signal, and (iii) signal bandwidth does not increase relative to baseband detection. Spectra were obtained by deconvolution of the reconstructed signals for solid BDPA (1,3-bisdiphenylene-2-phenylallyl) in air, 0.2mM trityl OX63 in water, (15)N perdeuterated tempone, and a nitroxide with a 0.5G partially-resolved proton
Fast wavelength-scanning interferometry technique with derivative detection of quadrature signals
NASA Astrophysics Data System (ADS)
Číp, O.; Mikel, B.; Lazar, J.
2006-04-01
We present a laser interferometer where a narrow-line width tuneable VCSEL laser (Vertical-Cavity Surface-Emitting Laser) working at 760 nm is used. For the detection of an absolute distance, we have used a fast wavelength-scanning interferometry technique. In the first part of the work we introduce the absolute laser interferometer as a demonstrator for research of a digital detection of quadrature signals (X-cos and Y-sin). This interferometer uses polarized beams and magnitude division of interference fringes. The wavelength of VCSEL laser is swept with the mode-hop free tuning range more than 1.2 nm, by means of the amplitude modulation of the injection current. At the same time, the operating temperature of the VCSEL is stabilized with a fast digital temperature controller. We control the wavelength value and whole tuning process of the laser with the frequency lock to selected modes of an external Fabry-Perot etalon. Except the frequency lock, the Fabry-Perot mode spectrum identifies wavelength-tuning interval of VCSEL during each sweep. A digital signal processor (DSP) is heart of the control and detection system. It samples intensity signal from Fabry- Perot etalon and X-Y quadrature signals from the detection unit of the interferometer. After 1 nm sweep of the VCSEL wavelength, we obtain a number of passed interference fringes and the number of passed Fabry-Perot resonance modes, at the same time. On basis of these measured quantities we are able to calculate the instantaneous value of the optical path length difference between the measuring and reference arm of the demonstrational interferometer. The other part of the work is oriented to research and experimental testing of the digital detection of quadrature signals (X-cos and Y-sin) processed only on basis of one intensity signal (X-axis) that is produced by a simple photo-detector. On basis of traditional inversion function arctan(Y/X) we are able to determine instantaneous phase between interference
Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals
NASA Astrophysics Data System (ADS)
Tseitlin, Mark; Yu, Zhelin; Quine, Richard W.; Rinard, George A.; Eaton, Sandra S.; Eaton, Gareth R.
2014-12-01
The use of multiple synchronized outputs from an arbitrary waveform generator (AWG) provides the opportunity to perform EPR experiments differently than by conventional EPR. We report a method for reconstructing the quadrature EPR spectrum from periodic signals that are generated with sinusoidal magnetic field modulation such as continuous wave (CW), multiharmonic, or rapid scan experiments. The signal is down-converted to an intermediate frequency (IF) that is less than the field scan or field modulation frequency and then digitized in a single channel. This method permits use of a high-pass analog filter before digitization to remove the strong non-EPR signal at the IF, that might otherwise overwhelm the digitizer. The IF is the difference between two synchronized X-band outputs from a Tektronix AWG 70002A, one of which is for excitation and the other is the reference for down-conversion. To permit signal averaging, timing was selected to give an exact integer number of full cycles for each frequency. In the experiments reported here the IF was 5 kHz and the scan frequency was 40 kHz. To produce sinusoidal rapid scans with a scan frequency eight times IF, a third synchronized output generated a square wave that was converted to a sine wave. The timing of the data acquisition with a Bruker SpecJet II was synchronized by an external clock signal from the AWG. The baseband quadrature signal in the frequency domain was reconstructed. This approach has the advantages that (i) the non-EPR response at the carrier frequency is eliminated, (ii) both real and imaginary EPR signals are reconstructed from a single physical channel to produce an ideal quadrature signal, and (iii) signal bandwidth does not increase relative to baseband detection. Spectra were obtained by deconvolution of the reconstructed signals for solid BDPA (1,3-bisdiphenylene-2-phenylallyl) in air, 0.2 mM trityl OX63 in water, 15N perdeuterated tempone, and a nitroxide with a 0.5 G partially
Fürstenau, N; Schmidt, M; Bock, W J; Urbanczyk, W
1998-02-01
We describe the combination of a polarimetric pressure sensor with a two-wavelength passive quadrature demodulation system allowing for dynamic pressure sensing in the 10-MPa range with unambiguous fringe counting. Furthermore, continuous phase measurement with the arctan method applied to the quadrature interference signals after automatic offset subtraction is demonstrated for the first time, to our knowledge. A single low-coherent superluminescent diode is used as a light source, and a polarizing beam splitter in combination with two adjustable interference filters of slightly different central wavelengths serves for the creation of the quadrature signals. Results of initial experiments with 60-ms pressure relaxation-time constants with the fringe-counting technique demonstrate the performance that was predicted theoretically. The measured pressure sensitivity exhibits excellent agreement with the previous research of Bock and Urbanczyk [IEEE Trans. Instrum. Meas. 44, 694-697 (1995)] using a polarimetric readout. The fringe-contrast variation and the measurement range obtained experimentally show the fiber dispersion to influence dephasing (deviation from quadrature) and visibility decrease significantly with increasing pressure. PMID:18268638
Sorgenfrei, B L; Edelstein, W A
1996-07-01
Using separate preamplifiers for the two outputs of a quadrature receive coil (and then combining the preamplifier outputs in a quadrature hybrid) provides a better signal-to-noise ratio (SNR) than is obtained by directly combining the quadrature outputs in a hybrid followed by a single preamplifier. The advantage of the two-preamplifier configuration increases when the body coil impedance changes and is no longer matched to 50 ohms. Using 0.4 dB noise figure preamplifiers, theory predicts 1.53, 0.42, 0, 0.42, and 1.53 dB SNR advantage of the two-preamplifier configuration over the one-preamplifier arrangement at body coil impedances of 12.5, 25, 50, 100, and 200 ohms, respectively. Experimental hot/cold resistor noise figure measurements indicate 2.86, 0.65, 0.36, 0.83, and 1.40 dB noise figure advantage for the two preamplifier configuration relative to the one-preamplifier configuration at those impedances. Empirical gains larger than theoretically calculated are attributable to insertion losses of various circuit elements, such as the quadrature hybrid, for the one-preamplifier configuration. PMID:8795028
NASA Astrophysics Data System (ADS)
Shizgal, Bernie D.
2016-08-01
Nonclassical quadratures based on a new set of half-range polynomials, Tn(x) , orthogonal with respect to w(x) =e - x - b /√{ x } for x ∈ [ 0 , ∞) are employed in the efficient calculation of the nuclear fusion reaction rate coefficients from cross section data. The parameter b = B /√{kB T } in the weight function is temperature dependent and B is the Gamow factor. The polynomials Tn(x) satisfy a three term recurrence relation defined by two sets of recurrence coefficients, αn and βn. These recurrence coefficients define in turn the tridiagonal Jacobi matrix whose eigenvalues are the quadrature points and the weights are calculated from the first components of the eigenfunctions. For nonresonant nuclear reactions for which the astrophysical function can be expressed as a lower order polynomial in the relative energy, the convergence of the thermal average of the reactive cross section with this nonclassical quadrature is extremely rapid requiring in many cases 2-4 quadrature points. The results are compared with other libraries of nuclear reaction rate coefficient data reported in the literature.
Khaleghi, Salman; Chitgarha, Mohammad Reza; Yilmaz, Omer F; Tur, Moshe; Haney, Michael W; Langrock, Carsten; Fejer, Martin M; Willner, Alan E
2013-05-15
We experimentally demonstrate a reconfigurable optical converter/encoder for quadrature amplitude modulated (QAM) signals. The system utilizes nonlinear wavelength multicasting, conversion-dispersion delays, and simultaneous nonlinear multiplexing and sampling. We show baud rate tunability (31 and 20 Gbaud) and reconfigurable conversions from lower-order QAM signals to higher-order QAM signals (e.g., 64-QAM). PMID:23938882
Stochastic path integral approach to continuous quadrature measurement of a single fluorescing qubit
NASA Astrophysics Data System (ADS)
Jordan, Andrew N.; Chantasri, Areeya; Huard, Benjamin
I will present a theory of continuous quantum measurement for a superconducting qubit undergoing fluorescent energy relaxation. The fluorescence of the qubit is detected via a phase-preserving heterodyne measurement, giving the cavity mode quadrature signals as two continuous qubit readout results. By using the stochastic path integral approach to the measurement physics, we obtain the most likely fluorescence paths between chosen boundary conditions on the state, and compute approximate correlation functions between all stochastic variables via diagrammatic perturbation theory. Of particular interest are most-likely paths describing increasing energy during the florescence. Comparison to Monte Carlo numerical simulation and experiment will be discussed. This work was supported by US Army Research Office Grants No. W911NF-09-0-01417 and No. W911NF-15-1-0496, by NSF Grant DMR-1506081, by John Templeton Foundation Grant ID 58558, and by the DPSTT Project Thailand.
Real-space quadrature: A convenient, efficient representation for multipole expansions
NASA Astrophysics Data System (ADS)
Rogers, David M.
2015-02-01
Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem—completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson's operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation.
NASA Technical Reports Server (NTRS)
Dobson, Chris C.; Jones, Jonathan E.; Chavers, Greg
2003-01-01
A polychromatic microwave quadrature interferometer has been characterized using several laboratory plasmas. Reflections between the transmitter and the receiver have been observed, and the effects of including reflection terms in the data reduction equation have been examined. An error analysis which includes the reflections, modulation of the scene beam amplitude by the plasma, and simultaneous measurements at two frequencies has been applied to the empirical database, and the results are summarized. For reflection amplitudes around 1096, the reflection terms were found to reduce the calculated error bars for electron density measurements by about a factor of 2. The impact of amplitude modulation is also quantified. In the complete analysis, the mean error bar for high- density measurements is 7.596, and the mean phase shift error for low-density measurements is 1.2". .
Stress fields around two pores in an elastic body: exact quadrature domain solutions
Crowdy, Darren
2015-01-01
Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky–Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores. PMID:26339198
Kienreich, I. W.; Temmer, M.; Veronig, A. M. E-mail: mat@igam.uni-graz.a
2009-10-01
We present the first observations of a global coronal wave ('EIT wave') from the two STEREO satellites in quadrature. The wave's initiation site was at the disk center in STEREO-B and precisely on the limb in STEREO-A. These unprecedented observations from the STEREO Extreme Ultraviolet Imaging (EUVI) instruments enable us to gain insight into the wave's kinematics, initiation, and three-dimensional structure. The wave propagates globally over the whole solar hemisphere visible to STEREO-B with a constant velocity of {approx}263 +- 16 km s{sup -1}. From the two STEREO observations, we derive a height of the wave in the range of {approx}80-100 Mm. Comparison of the wave kinematics with the early phase of the erupting coronal mass ejection (CME) structure indicates that the wave is initiated by the CME lateral expansion, and then propagates freely with a velocity close to the fast magnetosonic speed in the quiet solar corona.
All-atomic generation and noise-quadrature filtering of squeezed vacuum in hot Rb vapor
NASA Astrophysics Data System (ADS)
Horrom, Travis; Romanov, Gleb; Novikova, Irina; Mikhailov, Eugeniy E.
2013-01-01
With our all-atomic squeezing and filtering setup, we demonstrate control over the noise amplitudes and manipulation of the frequency-dependent squeezing angle of a squeezed vacuum quantum state by passing it through an atomic medium with electromagnetically induced transparency (EIT). We generate low sideband frequency squeezed vacuum using the polarization self-rotation effect in a hot Rb vapor cell, and direct it through a second atomic vapor subject to EIT conditions. We use the frequency-dependent absorption of the EIT window to demonstrate an example of squeeze amplitude attenuation and squeeze angle rotation of the quantum noise quadratures of the squeezed probe. These studies have implications for quantum memory and storage as well as gravitational wave interferometric detectors.
Minor, B.; Mathews, K.
1995-07-01
The exponential characteristic (EC) spatial quadrature for discrete ordinates neutral particle transport previously introduced in slab geometry is extended here to x-y geometry with rectangular cells. The method is derived and compared with current methods. It is similar to the linear characteristic (LC) quadrature (a linear-linear moments method) but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx + cy), whose parameters are rootsolved to match the known (from the previous iteration) spatial average and first moments of the source over the cell. Similarly, EC assumes exponential distributions of flux along cell edges through which particles enter the cell, with parameters chosen to match the average and first moments of flux, as passed from the adjacent, upstream cells (or as determined by boundary conditions). Like the linear adaptive (LA) method, EC is positive and nonlinear. It is more accurate than LA and does not require subdivision of cells. The nonlinearity has not interfered with convergence. The exponential moment functions, which were introduced with the slab geometry method, are extended to arbitrary dimensions (numbers of arguments) and used to avoid numerical ill conditioning. As in slab geometry, the method approaches O({Delta}x{sup 4}) global truncation error on fine-enough meshes, while the error is insensitive to mesh size for coarse meshes. Performance of the method is compared with that of the step characteristic, LC, linear nodal, step adaptive, and LA schemes. The EC method is a strong performer with scattering ratios ranging from 0 to 0.9 (the range tested), particularly so for lower scattering ratios. As in slab geometry, EC is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems.
Analytical and numerical study of Gauss-Bonnet holographic superconductors with Power-Maxwell field
NASA Astrophysics Data System (ADS)
Sheykhi, Ahmad; Salahi, Hamid Reza; Montakhab, Afshin
2016-04-01
We provide an analytical as well as a numerical study of the holographic s-wave superconductors in Gauss-Bonnet gravity with Power-Maxwell electrodynamics. We limit our study to the case where scalar and gauge fields do not have an effect on the background metric. We use a variational method, based on Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. Interestingly enough, we observe that unlike Born-Infeld-like nonlinear electrodynamics which decrease the critical temperature compared to the linear Maxwell field, the Power-Maxwell electrodynamics is able to increase the critical temperature of the holographic superconductors in the sublinear regime. We find that requiring the finite value for the gauge field on the asymptotic boundary r → ∞, restricts the power parameter, q, of the Power-Maxwell field to be in the range 1 /2 < q < ( d - 1) /2. Our study indicates that it is quite possible to make condensation easier as q decreases in its allowed range. We also find that for all values of q, the condensation can be affected by the Gauss-Bonnet coefficient α. However, the presence of the Gauss-Bonnet term makes the transition slightly harder. Finally, we obtain an analytic expression for the order parameter and thus obtain the associated critical exponent near the phase transition. We find that the critical exponent has its universal value of β = 1 /2 regardless of the parameters q, α as well as dimension d, consistent with mean-field values obtained in previous studies.
Parallelization of Lower-Upper Symmetric Gauss-Seidel Method for Chemically Reacting Flow
NASA Technical Reports Server (NTRS)
Yoon, Seokkwan; Jost, Gabriele; Chang, Sherry
2005-01-01
Development of technologies for exploration of the solar system has revived an interest in computational simulation of chemically reacting flows since planetary probe vehicles exhibit non-equilibrium phenomena during the atmospheric entry of a planet or a moon as well as the reentry to the Earth. Stability in combustion is essential for new propulsion systems. Numerical solution of real-gas flows often increases computational work by an order-of-magnitude compared to perfect gas flow partly because of the increased complexity of equations to solve. Recently, as part of Project Columbia, NASA has integrated a cluster of interconnected SGI Altix systems to provide a ten-fold increase in current supercomputing capacity that includes an SGI Origin system. Both the new and existing machines are based on cache coherent non-uniform memory access architecture. Lower-Upper Symmetric Gauss-Seidel (LU-SGS) relaxation method has been implemented into both perfect and real gas flow codes including Real-Gas Aerodynamic Simulator (RGAS). However, the vectorized RGAS code runs inefficiently on cache-based shared-memory machines such as SGI system. Parallelization of a Gauss-Seidel method is nontrivial due to its sequential nature. The LU-SGS method has been vectorized on an oblique plane in INS3D-LU code that has been one of the base codes for NAS Parallel benchmarks. The oblique plane has been called a hyperplane by computer scientists. It is straightforward to parallelize a Gauss-Seidel method by partitioning the hyperplanes once they are formed. Another way of parallelization is to schedule processors like a pipeline using software. Both hyperplane and pipeline methods have been implemented using openMP directives. The present paper reports the performance of the parallelized RGAS code on SGI Origin and Altix systems.
Five-dimensional black strings in Einstein-Gauss-Bonnet gravity
Kobayashi, Tsutomu; Tanaka, Takahiro
2005-04-15
We consider black-string-type solutions in five-dimensional Einstein-Gauss-Bonnet gravity. Numerically constructed solutions under static, axially symmetric and translationally invariant metric ansatz are presented. The solutions are specified by two asymptotic charges: mass of a black string and a scalar charge associated with the radion part of the metric. Regular black string solutions are found if and only if the two charges satisfy a fine-tuned relation, and otherwise the spacetime develops a singular event horizon or a naked singularity. We can also generate bubble solutions from the black strings by using a double Wick rotation.
Observational limits on Gauss-Bonnet and Randall-Sundrum gravities
Alexeyev, S. O. Rannu, K. A.; Dyadina, P. I.; Latosh, B. N.; Turyshev, S. G.
2015-06-15
We discuss the possibilities of experimental search for the new physics predicted by the Gauss-Bonnet and the Randall-Sundrum theories of gravity. The effective four-dimensional spherically symmetrical solutions of these theories are analyzed. We consider these solutions in the weak-field limit and in the process of the primordial black hole evaporation. We show that the predictions of the discussed models are the same as of general relativity. Hence, current experiments are not applicable for such search, and therefore different methods of observation and higher accuracy are required.
Black hole initial data in Gauss-Bonnet gravity: Momentarily static case
Yoshino, Hirotaka
2011-05-15
We study the method for generating the initial data of black hole systems in Gauss-Bonnet gravity. The initial data are assumed to be momentarily static and conformally flat. Although the equation for the conformal factor is highly nonlinear, it is successfully solved by numerical relaxation for one-black-hole and two-black-hole systems. The common apparent horizon is studied in the two-black-hole initial data, and the result suggests that the Penrose inequalities are satisfied in this system. This is the first step for simulating black hole collisions in higher-curvature theories.
Some exact solutions with torsion in 5D Einstein-Gauss-Bonnet gravity
Canfora, F.; Giacomini, A.; Willison, S.
2007-08-15
Exact solutions with torsion in Einstein-Gauss-Bonnet gravity are derived. These solutions have a cross product structure of two constant curvature manifolds. The equations of motion give a relation for the coupling constants of the theory in order to have solutions with nontrivial torsion. This relation is not the Chern-Simons combination. One of the solutions has an AdS{sub 2}xS{sup 3} structure and is so the purely gravitational analogue of the Bertotti-Robinson space-time where the torsion can be seen as the dual of the covariantly constant electromagnetic field.
The role of Lagrange multiplier in Gauss-Bonnet dark energy
NASA Astrophysics Data System (ADS)
Makarenko, Andrey N.
2016-04-01
We review accelerating cosmology in Gauss-Bonnet gravity with Lagrange multiplier constraint studied in [S. Capozziello, A. N. Makarenko and S. D. Odintsov, Phys. Rev. D 87 (2013) 084037, arXiv: 1302.0093 [gr-qc], S. Capozziello, M. Francaviglia and A. N. Makarenko, Astrophys. Space Sci. 349 (2014) 603-609, arXiv: 1304.5440 [gr-qc]. Several examples of dark energy universes are presented. We can get new dark energy solutions (with additional scalar) as well as certain limits to earlier found accelerating solutions.
Small-displacement measurements using high-order Hermite-Gauss modes
Sun, Hengxin; Liu, Kui; Liu, Zunlong; Guo, Pengliang; Zhang, Junxiang; Gao, Jiangrui
2014-03-24
We present a scheme for small-displacement measurements using high-order Hermite-Gauss modes and balanced homodyne detection. We demonstrate its use with experimental results of displacement measurements using fundamental transverse mode TEM{sub 00} and first order transverse mode TEM{sub 10} as signal modes. The results show a factor of 1.41 improvement in measurement precision with the TEM{sub 10} mode compared with that with the TEM{sub 00} mode. This scheme has potential applications in precision metrology, atomic force microscopy, and optical imaging.
Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation
NASA Astrophysics Data System (ADS)
Bu, Yanyan; Lublinsky, Michael; Sharon, Amir
2015-06-01
Relativistic hydrodynamics dual to Einstein-Gauss-Bonnet gravity in asymptotic AdS5 space is under study. To linear order in the amplitude of the fluid velocity and temperature, we derive the fluid's stress-energy tensor via an all-order resummation of the derivative terms. Each order is accompanied by new transport coefficients, which all together could be compactly absorbed into two functions of momenta, referred to as viscosity functions. Via inverse Fourier transform, these viscosities appear as memory functions in the constitutive relation between components of the stress-energy tensor.
A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes
NASA Technical Reports Server (NTRS)
Carpenter, Russell; Lee, Taesul
2008-01-01
Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.
GPU-accelerated Modeling and Element-free Reverse-time Migration with Gauss Points Partition
NASA Astrophysics Data System (ADS)
Zhen, Z.; Jia, X.
2014-12-01
Element-free method (EFM) has been applied to seismic modeling and migration. Compared with finite element method (FEM) and finite difference method (FDM), it is much cheaper and more flexible because only the information of the nodes and the boundary of the study area are required in computation. In the EFM, the number of Gauss points should be consistent with the number of model nodes; otherwise the accuracy of the intermediate coefficient matrices would be harmed. Thus when we increase the nodes of velocity model in order to obtain higher resolution, we find that the size of the computer's memory will be a bottleneck. The original EFM can deal with at most 81×81 nodes in the case of 2G memory, as tested by Jia and Hu (2006). In order to solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP), and utilize the GPUs to improve the computation efficiency. Considering the characteristics of the Gaussian points, the GPP method doesn't influence the propagation of seismic wave in the velocity model. To overcome the time-consuming computation of the stiffness matrix (K) and the mass matrix (M), we also use the GPUs in our computation program. We employ the compressed sparse row (CSR) format to compress the intermediate sparse matrices and try to simplify the operations by solving the linear equations with the CULA Sparse's Conjugate Gradient (CG) solver instead of the linear sparse solver 'PARDISO'. It is observed that our strategy can significantly reduce the computational time of K and Mcompared with the algorithm based on CPU. The model tested is Marmousi model. The length of the model is 7425m and the depth is 2990m. We discretize the model with 595x298 nodes, 300x300 Gauss cells and 3x3 Gauss points in each cell. In contrast to the computational time of the conventional EFM, the GPUs-GPP approach can substantially improve the efficiency. The speedup ratio of time consumption of computing K, M is 120 and the
Kink-antikink, trapping bags and five-dimensional Gauss-Bonnet gravity
Giovannini, Massimo
2006-10-15
Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension, allows classes of solutions where two scalar fields combine either in a kink-antikink system or in a trapping-bag configuration. While the kink-antikink system can be interpreted as a pair of gravitating domain walls with opposite topological charges, the trapping-bag solution consists of a domain wall supplemented by a nontopological defect. In both classes of solutions, for large absolute values of the bulk coordinate (i.e. far from the core of the defects), the geometry is given by five-dimensional anti-de Sitter space.
Gauss' law and nonlinear plane waves for Yang-Mills theory
NASA Astrophysics Data System (ADS)
Tsapalis, A.; Politis, E. P.; Maintas, X. N.; Diakonos, F. K.
2016-04-01
We investigate nonlinear plane-wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the SU(3) theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary nonzero mass and are exact extrema of the nonlinear YM action. Among them, a unique harmonic plane wave with a nontrivial pattern in phase, spin, and color is identified. Similar solutions are present in the SU(4) case, while they are absent from the SU(2) theory.
Winnerl, S; Zimmermann, B; Peter, F; Schneider, H; Helm, M
2009-02-01
We report on emission and detection of pulsed terahertz radiation of radial and azimuthal polarization by microstructured photoconductive antennas. To this end the electrode geometry of the emitter is inverse to the desired THz field pattern and a second periodic structure prevents destructive interference effects. Beam profiles of freely propagating THz waves are studied for divergent and refocused beams. They can be well described as the lowest order Bessel-Gauss modes with a divergence comparable to linearly polarized Gaussian beams. Additionally, mode sensitive detection is demonstrated for radially polarized radiation. PMID:19188986
Black holes with scalar hair in Einstein-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Brihaye, Y.; Ducobu, L.
2016-05-01
The Einstein-Gauss-Bonnet gravity in five dimensions is extended by scalar fields and the corresponding equations are reduced to a system of nonlinear differential equations. A large family of regular solutions of these equations is shown to exist. Generically, these solutions are spinning black holes with scalar hairs. They can be characterized (but not uniquely) by an horizon and an angular velocity on this horizon. Taking particular limits, the black holes approach boson star or become extremal, in any case the limiting configurations remain hairy.
5D radiating black holes in Einstein-Yang-Mills-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Ghosh, S. G.
2011-10-01
We derive nonstatic spherically symmetric solutions of a null fluid, in five dimension (5D), to Einstein-Yang-Mills (EYM) equations with the coupling of Gauss-Bonnet (GB) combination of quadratic curvature terms, namely, 5D EYMGB radiating black hole solution. It is shown that, in the limit, we can recover known radiating black hole solutions. The spherically symmetric known 5D static black hole solutions are also retrieved. The effect of the GB term and Yang-Mills (YM) gauge charge on the structure and location of horizons, of the 5D radiating black hole, is also discussed.
NASA Astrophysics Data System (ADS)
Bendinelli, O.; Parmeggiani, G.; Piccioni, A.; Zavatti, F.
1987-10-01
Modification of the Newton-Gauss linearization method in the Tikhonov regularization sense is described. Its ability to give reliable estimates of a large number of parameters is shown by application to the PSF determination from CCD frames. Extension of the Van Altena and Auer star-image model using a weighted sum of two Gaussians, and explicitly taking its integration on the pixel into account, enables the authors to determine the PSF up to about 10 mag below the central value with an error fit in the range 0.01 - 0.03 mag arcsec-2.
Uniqueness of the Gauss-Bonnet-Chern formula (after Gilkey-Park-Sekigawa)
NASA Astrophysics Data System (ADS)
Navarro, Alberto; Navarro, José
2016-03-01
On an oriented Riemannian manifold, the Gauss-Bonnet-Chern formula establishes that the Pfaffian of the metric represents, in de Rham cohomology, the Euler class of the tangent bundle. Hence, if the underlying manifold is compact, the integral of the Pfaffian is a topological invariant; namely, the Euler characteristic of the manifold. In this paper we refine a classical result, originally due to Gilkey, that characterizes this formula as the only (non-trivial) integral of a differential invariant that is independent of the underlying metric. To this end, we use some computations regarding dimensional identities of the curvature due to Gilkey-Park-Sekigawa (Gilkey, 2012; Navarro and Navarro, 2014).
Phantom-like behavior of a DGP-inspired Scalar-Gauss-Bonnet gravity
Nozari, Kourosh; Azizi, Tahereh; Setare, M.R. E-mail: t.azizi@umz.ac.ir
2009-10-01
We study the phantom-like behavior of a DGP-inspired braneworld scenario where curvature correction on the brane is taken into account. We include a possible modification of the induced gravity on the brane by incorporating higher order curvature terms of Gauss-Bonnet type. We investigate the cosmological implications of the model and we show that the normal branch of the scenario self-accelerates in this modified scenario without introducing any dark energy component. Also, a phantom-like behavior can be realized in this model without introducing any phantom field that suffers from serious difficulties such as violation of the null energy condition.
Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity
Hu Yapeng; Sun Peng; Zhang Jianhui
2011-06-15
Using the AdS/CFT correspondence, we study the hydrodynamics with conserved current from the dual Maxwell-Gauss-Bonnet gravity. After constructing the perturbative solution to the first order based on the boosted black brane solution in the bulk Maxwell-Gauss-Bonnet gravity, we extract the stress tensor and conserved current of the dual conformal fluid on its boundary, and also find the effect of the Gauss-Bonnet term on the dual conformal fluid. Our results show that the Gauss-Bonnet term can affect the parameters such as the shear viscosity {eta}, entropy density s, thermal conductivity {kappa} and electrical conductivity {sigma}. However, it does not affect the so-called Wiedemann-Franz law which relates {kappa} to {sigma}, while it affects the ratio {eta}/s. In addition, another interesting result is that {eta}/s can also be affected by the bulk Maxwell field in our case, which is consistent with some previous results predicted through the Kubo formula. Moreover, the anomalous magnetic and vortical effects by adding the Chern-Simons term are also considered in our case in the Maxwell-Gauss-Bonnet gravity.
NASA Astrophysics Data System (ADS)
Wang, Dong; Tsui, Kwok-Leung; Zhou, Qiang
2016-05-01
Rolling element bearings are commonly used in machines to provide support for rotating shafts. Bearing failures may cause unexpected machine breakdowns and increase economic cost. To prevent machine breakdowns and reduce unnecessary economic loss, bearing faults should be detected as early as possible. Because wavelet transform can be used to highlight impulses caused by localized bearing faults, wavelet transform has been widely investigated and proven to be one of the most effective and efficient methods for bearing fault diagnosis. In this paper, a new Gauss-Hermite integration based Bayesian inference method is proposed to estimate the posterior distribution of wavelet parameters. The innovations of this paper are illustrated as follows. Firstly, a non-linear state space model of wavelet parameters is constructed to describe the relationship between wavelet parameters and hypothetical measurements. Secondly, the joint posterior probability density function of wavelet parameters and hypothetical measurements is assumed to follow a joint Gaussian distribution so as to generate Gaussian perturbations for the state space model. Thirdly, Gauss-Hermite integration is introduced to analytically predict and update moments of the joint Gaussian distribution, from which optimal wavelet parameters are derived. At last, an optimal wavelet filtering is conducted to extract bearing fault features and thus identify localized bearing faults. Two instances are investigated to illustrate how the proposed method works. Two comparisons with the fast kurtogram are used to demonstrate that the proposed method can achieve better visual inspection performances than the fast kurtogram.
Early-time cosmological solutions in Einstein-scalar-Gauss-Bonnet theory
NASA Astrophysics Data System (ADS)
Kanti, Panagiota; Gannouji, Radouane; Dadhich, Naresh
2015-10-01
In this work, we consider a generalized gravitational theory that contains the Einstein term, a scalar field, and the quadratic Gauss-Bonnet (GB) term. We focus on the early-universe dynamics, and demonstrate that a simple choice of the coupling function between the scalar field and the Gauss-Bonnet term and a simplifying assumption regarding the role of the Ricci scalar can lead to new, analytical, elegant solutions with interesting characteristics. We first argue, and demonstrate in the context of two different models, that the presence of the Ricci scalar in the theory at early times (when the curvature is strong) does not affect the actual cosmological solutions. By considering therefore a pure scalar-GB theory with a quadratic coupling function we derive a plethora of interesting, analytic solutions: for a negative coupling parameter, we obtain inflationary, de Sitter-type solutions or expanding solutions with a de Sitter phase in their past and a natural exit mechanism at later times; for a positive coupling function, we find instead singularity-free solutions with no big bang singularity. We show that the aforementioned solutions arise only for this particular choice of coupling function, a result that may hint at some fundamental role that this coupling function may hold in the context of an ultimate theory.
Static and symmetric wormholes respecting energy conditions in Einstein-Gauss-Bonnet gravity
Maeda, Hideki; Nozawa, Masato
2008-07-15
Properties of n({>=}5)-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant {lambda}. We assume that the spacetime has symmetries corresponding to the isometries of an (n-2)-dimensional maximally symmetric space with the sectional curvature k={+-}1, 0. It is also assumed that the metric is at least C{sup 2} and the (n-2)-dimensional maximally symmetric subspace is compact. Depending on the existence or absence of the general relativistic limit {alpha}{yields}0, solutions are classified into general relativistic (GR) and non-GR branches, respectively, where {alpha} is the Gauss-Bonnet coupling constant. We show that a wormhole throat respecting the dominant energy condition coincides with a branch surface in the GR branch, otherwise the null energy condition is violated there. In the non-GR branch, it is shown that there is no wormhole solution for k{alpha}{>=}0. For the matter field with zero tangential pressure, it is also shown in the non-GR branch with k{alpha}<0 and {lambda}{<=}0 that the dominant energy condition holds at the wormhole throat if the radius of the throat satisfies some inequality. In the vacuum case, a fine-tuning of the coupling constants is shown to be necessary and the radius of a wormhole throat is fixed. Explicit wormhole solutions respecting the energy conditions in the whole spacetime are obtained in the vacuum and dust cases with k=-1 and {alpha}>0.
Thermodynamics of rotating solutions in Gauss-Bonnet-Maxwell gravity and the counterterm method
Dehghani, M. H.; Bordbar, G. H.; Shamirzaie, M.
2006-09-15
By a suitable transformation, we present the (n+1)-dimensional charged rotating solutions of Gauss-Bonnet gravity with a complete set of allowed rotation parameters which are real in the whole spacetime. We show that these charged rotating solutions present black hole solutions with two inner and outer event horizons, extreme black holes, or naked singularities provided the parameters of the solutions are chosen suitable. Using the surface terms that make the action well defined for Gauss-Bonnet gravity and the counterterm method for eliminating the divergences in action, we compute finite action of the solutions. We compute the conserved and thermodynamical quantities through the use of free energy and the counterterm method, and find that the two methods give the same results. We also find that these quantities satisfy the first law of thermodynamics. Finally, we perform a stability analysis by computing the heat capacity and the determinant of Hessian matrix of mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for black objects with zero curvature horizon.
Einstein-Gauss-Bonnet traversable wormholes satisfying the weak energy condition
NASA Astrophysics Data System (ADS)
Mehdizadeh, Mohammad Reza; Zangeneh, Mahdi Kord; Lobo, Francisco S. N.
2015-04-01
In this paper, we explore higher-dimensional asymptotically flat wormhole geometries in the framework of Gauss-Bonnet (GB) gravity and investigate the effects of the GB term, by considering a specific radial-dependent redshift function and by imposing a particular equation of state. This work is motivated by previous assumptions that wormhole solutions were not possible for the k =1 and α <0 case, where k is the sectional curvature of an (n -2 )-dimensional maximally symmetric space, and α is the Gauss-Bonnet coupling constant. However, we emphasize that this discussion is purely based on a nontrivial assumption that is only valid at the wormhole throat, and cannot be extended to the entire radial-coordinate range. In this work, we provide a counterexample to this claim, and find for the first time specific solutions that satisfy the weak energy condition throughout the entire spacetime, for k =1 and α <0 . In addition to this, we also present other wormhole solutions which alleviate the violation of the weak energy condition in the vicinity of the wormhole throat.
Accelerating the Gauss-Seidel Power Flow Solver on a High Performance Reconfigurable Computer
Byun, Jong-Ho; Ravindran, Arun; Mukherjee, Arindam; Joshi, Bharat; Chassin, David P.
2009-09-01
The computationally intensive power flow problem determines the voltage magnitude and phase angle at each bus in a power system for hundreds of thousands of buses under balanced three-phase steady-state conditions. We report an FPGA acceleration of the Gauss-Seidel based power flow solver employed in the transmission module of the GridLAB-D power distribution simulator and analysis tool. The prototype hardware is implemented on an SGI Altix-RASC system equipped with a Xilinx Virtex II 6000 FPGA. Due to capacity limitations of the FPGA, only the bus voltage calculations of the power network are implemented on hardware while the branch current calculations are implemented in software. For a 200,000 bus system, the bus voltage calculation on the FPGA achieves a 48x speed-up with PQ buses and a 62 times for PV over an equivalent sequential software implementation. The average overall speed up of the FPGA-CPU implementation with 100 iterations of the Gauss-Seidel power solver is 2.6x over a software implementation, with the branch calculations on the CPU accounting for 85% of the total execution time. The FPGA-CPU implementation also shows linear scaling with increase in the size of the input power network.
Generalized Misner-Sharp quasilocal mass in Einstein-Gauss-Bonnet gravity
Maeda, Hideki; Nozawa, Masato
2008-03-15
We investigate properties of a quasilocal mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an (n-2)-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant. We assume that the Gauss-Bonnet coupling constant is non-negative. The quasilocal mass was recently defined by one of the authors as a counterpart of the Misner-Sharp quasilocal mass in general relativity. The quasilocal mass is found to be a quasilocal conserved charge associated with a locally conserved current constructed from the generalized Kodama vector and exhibits the unified first law corresponding to the energy-balance law. In the asymptotically flat case, it converges to the Arnowitt-Deser-Misner mass at spacelike infinity, while it converges to the Deser-Tekin and Padilla mass at infinity in the case of asymptotically anti-de Sitter. Under the dominant energy condition, we show the monotonicity of the quasilocal mass for any k, while the positivity on an untrapped hypersurface with a regular center is shown for k=1 and for k=0 with an additional condition, where k={+-}1, 0 is the constant sectional curvature of each spatial section of equipotential surfaces. Under a special relation between coupling constants, positivity of the quasilocal mass is shown for any k without assumptions above. We also classify all the vacuum solutions by utilizing the generalized Kodama vector. Lastly, several conjectures on further generalization of the quasilocal mass in Lovelock gravity are proposed.
Orbital angular momentum density of a general Lorentz–Gauss vortex beam
NASA Astrophysics Data System (ADS)
Zhou, Guoquan; Ji, Zhiyue; Ru, Guoyun
2016-07-01
Based on the vectorial Rayleigh–Sommerfeld integral formulae, the analytical expression of a general Lorentz–Gauss vortex beam with an arbitrary topological charge is derived in free space. By using the analytical expressions of the electromagnetic field beyond the paraxial approximation, the orbital angular momentum density of a general Lorentz–Gauss vortex beam can be calculated. The effects of the linearly polarized angle and the topological charge on the three components of the orbital angular momentum density are investigated in the reference plane. The two transversal components of the orbital angular momentum are composed of two lobes with the same areas and opposite signs. The longitudinal component of the orbital angular momentum density is composed of four lobes with the same areas. The sign of the orbital angular momentum density in a pair of lobes is positive, and that of the orbital angular momentum density in the other pair of lobes is negative. Moreover, the negative magnitude of the orbital angular momentum density is larger than the positive magnitude of the orbital angular momentum density. The linearly polarized angle affects not only the shape and the location of the lobes, but also the magnitude of the three components of the orbital angular momentum density. With increasing the topological charge, the distribution of the orbital angular momentum density expands, the magnitude of the orbital angular momentum density increases, and the shape of the lobe also slightly changes.
Topological black holes for Einstein-Gauss-Bonnet gravity with a nonminimal scalar field
NASA Astrophysics Data System (ADS)
Gaete, Moisés Bravo; Hassaïne, Mokhtar
2013-11-01
We consider the Einstein-Gauss-Bonnet gravity with a negative cosmological constant together with a source given by a scalar field nonminimally coupled in arbitrary dimension D. For a certain election of the cosmological and Gauss-Bonnet coupling constants, we derive two classes of AdS black hole solutions whose horizon is planar. The first family of black holes obtained for a particular value of the nonminimal coupling parameter only depends on a constant M, and the scalar field vanishes as M=0. The second class of solutions corresponds to a two-parametric (with constants M and A) black hole stealth configuration, which is a nontrivial scalar field with a black hole metric such that both sides (gravity and matter parts) of the Einstein equations vanish. In this case, in the vanishing M, the solution reduces to a stealth scalar field on the pure AdS metric. We note that the existence of these two classes of solutions is indicative of the particular choice of the coupling constants, and they cannot be promoted to spherical or hyperboloid black hole solutions in a standard fashion. In the last part, we add to the original action some exact (D-1) forms coupled to the scalar field. The direct benefit of introducing such extra fields is to obtain black hole solutions with a planar horizon for an arbitrary value of the nonminimal coupling parameter.
Mazharimousavi, S. Habib; Halilsoy, M.; Amirabi, Z.
2010-05-15
Recently in [Phys. Rev. D 76, 087502 (2007) and Phys. Rev. D 77, 089903 (2008)] a thin-shell wormhole has been introduced in five-dimensional Einstein-Maxwell-Gauss-Bonnet gravity which was supported by normal matter. We wish to consider this solution and investigate its stability. Our analysis shows that for the Gauss-Bonnet parameter {alpha}<0, stability regions form for a narrow band of finely tuned mass and charge. For the case {alpha}>0, we iterate once more that no stable, normal matter thin-shell wormhole exists.
Quasinormal modes and a new instability of Einstein-Gauss-Bonnet black holes in the de Sitter world
NASA Astrophysics Data System (ADS)
Cuyubamba, M. A.; Konoplya, R. A.; Zhidenko, A.
2016-05-01
Analysis of time-domain profiles for gravitational perturbations shows that Gauss-Bonnet black holes in a de Sitter world possess a new kind of dynamical instability which does not take place for asymptotically flat Einstein-Gauss-Bonnet black holes. The new instability is in the gravitational perturbations of the scalar type and is due to the nonvanishing cosmological constant. Analysis of the quasinormal spectrum in the stability sector shows that although the scalar type of gravitational perturbations alone does not obey Hod's conjectural bound, connecting the damping rate and the Hawking temperature, the vector and tensor types (and thereby the gravitational spectrum as a whole) do obey it.
Mardahl, P.; Verboncoeur, J.; Birdsall, C.K.
1995-12-31
Non-charge conserving current collection algorithms for relativistic PIC plasma simulations can cause errors in Gauss` law. These errors arise from violations of the continuity equation. Two techniques for removing these errors are examined and compared, the Marder correction, a method which corrects electric fields locally and primarily affects short wavelengths, and a divergence correction, which uses a Poisson solve to correct the electric fields so that Gauss` law is enforced. The effect of each method on the spectrum of the error (short wavelengths vs. long) are examined. Computational efficiency and accuracy of the two techniques is compared.
NASA Astrophysics Data System (ADS)
Guo, Xiong-Ying; Zhang, Li-Chun; Zhao, Ren
2014-06-01
We employ the simple analytic method and the variational method of the Strum-Liouville (S-L) eigenvalue problem to analytically study the holographic superconductor phase transition in Gauss-Bonnet gravity with Born-Infeld (BI) electrodynamics in the probe limit, respectively. We find that the scalar hair formation at low temperatures is indeed affected by the Gauss-Bonnet as well as the BI coupling parameters, but also by the scalar field mass and the spacetime dimensional. Our analytic result has been found in agreement with the numerical results.
NASA Technical Reports Server (NTRS)
Clark, William A. (Inventor); Juneau, Thor N. (Inventor); Lemkin, Mark A. (Inventor); Roessig, Allen W. (Inventor)
2001-01-01
A microfabricated vibratory rate gyroscope to measure rotation includes two proof-masses mounted in a suspension system anchored to a substrate. The suspension has two principal modes of compliance, one of which is driven into oscillation. The driven oscillation combined with rotation of the substrate about an axis perpendicular to the substrate results in Coriolis acceleration along the other mode of compliance, the sense-mode. The sense-mode is designed to respond to Coriolis accelerationwhile suppressing the response to translational acceleration. This is accomplished using one or more rigid levers connecting the two proof-masses. The lever allows the proof-masses to move in opposite directions in response to Coriolis acceleration. The invention includes a means for canceling errors, termed quadrature error, due to imperfections in implementation of the sensor. Quadrature-error cancellation utilizes electrostatic forces to cancel out undesired sense-axis motion in phase with drive-mode position.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Rashidi, Mohammad Mehdi
2016-04-01
In this paper, we propose a modified cubic B-spline differential quadrature method (MCB-DQM) to solve three-dimensional (3D) coupled viscous Burger equation with appropriate initial and boundary conditions. In this method, modified cubic B-spline is treated as a basis function in the differential quadrature method (DQM) to compute the weighting coefficients. In this way, the Burger equation is reduced into a system of ordinary differential equations. An optimal strong stability-preserving Runge-Kutta (SSP-RK) method is employed to solve the resulting system of ordinary differential equations. In order to illustrate the accuracy and efficiency of the proposed method, a numerical problem is considered. From the numerical experiment, it is found that the computed result is in good agreement with the exact solution. Stability analysis of the method is also carried out using the matrix stability analysis method and found to be unconditionally stable.
NASA Technical Reports Server (NTRS)
Caves, C. M.; Schumaker, B. L.
1985-01-01
A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Kumar, Jai
2014-11-01
In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.
2007-01-01
During quadrature, plasma seen on the limb of the Sun, along the radi al direction to Ulysses, by SOHO or STEREO can be sampled in situ as lt later passes Ulysses. A figure shows a coronagraph image, the rad ial towards Ulysses at 58 deg. S. and the SOHO/UVCS slit positions d uring one set of observations. A CME subsequently occurred and passed Ulysses (at 3/4 AU) 15 days later.
NASA Astrophysics Data System (ADS)
El-Orany, Faisal A. A.
2006-12-01
For the multiphoton intensity-dependent Jaynes Cummings model (JCM) described by a two-level atom interacting with a radiation field, we prove that there is a relationship between the atomic inversion and the quadrature squeezing. We give the required condition to obtain best information from this relation. Also we show that this relation is only sensitive to large values of the detuning parameter. Furthermore, we discuss briefly such relation for the off-resonance standard JCM.
NASA Astrophysics Data System (ADS)
Warger, William C., II; Newmark, Judith A.; Chang, ChihChing; Brooks, Dana H.; Warner, Carol M.; DiMarzio, Charles A.
2005-03-01
The Multifunctional Staring Mode Microscope was developed to permit three modes of imaging for cell counting in mouse embryos: Optical Quadrature, Differential Interference Contrast (DIC), and Fluorescence Imaging. The Optical Quadrature Microscope, consisting of a modified Mach-Zender Interferometer, uses a 632.8 nm laser to measure the amplitude and phase of the signal beam that travels through the embryo. Four cameras, preceded by multiple beamsplitters, are used to read the four interferograms, which are then combined to produce an image of the complex electric field amplitude. The phase of the complex amplitude is then unwrapped using a 2-D phase unwrap algorithm and images of optical path length are produced. To combine the additional modes of DIC and Fluorescence Imaging with the Optical Quadrature Microscope, a 632.8 nm narrow bandpass beamsplitter was placed at the output of the microscope. This allows the laser light to continue through the Mach-Zender while all other wavelengths are reflected at 90 degrees to another camera. This was effective in combining the three modes as the fluorescence wavelength for the Hoechst stain is well below the bandpass window of the beamsplitter. Both live and fixed samples have been successfully imaged in all three modes. Accuracy in cell counting was achieved by using the DIC image for detecting cell boundaries and the Optical Quadrature image for phase mapping to determine where cells overlap. The final results were verified by Hoechst fluorescence imaging to count the individual nuclei. Algorithms are currently being refined so larger cell counts can be done more efficiently.
A Homodyne Quadrature Laser Interferometer for Micro-Asperity Deformation Analysis
PogaČnik, Aljaž; Požar, Tomaž; Kalin, Mitjan; Možina, Janez
2013-01-01
We report on the successful realization of a contactless, non-perturbing, displacement-measuring system for characterizing the surface roughness of polymer materials used in tribological applications. A single, time-dependent, scalar value, dubbed the collective micro-asperity deformation, is extracted from the normal-displacement measurements of normally loaded polymer samples. The displacement measurements with a sub-nanometer resolution are obtained with a homodyne quadrature laser interferometer. The measured collective micro-asperity deformation is critical for a determination of the real contact area and thus for the realistic contact conditions in tribological applications. The designed measuring system senses both the bulk creep as well as the micro-asperity creep occurring at the roughness peaks. The final results of our experimental measurements are three time-dependent values of the collective micro-asperity deformation for the three selected surface roughnesses. These values can be directly compared to theoretical deformation curves, which can be derived using existing real-contact-area models. PMID:23296328
Recursive, in-place algorithm for the hexagonal orthogonal oriented quadrature image pyramid
NASA Technical Reports Server (NTRS)
Watson, Andrew B.
1989-01-01
Pyramid image transforms have proven useful in image coding and pattern recognition. The hexagonal orthogonal oriented quadrature image pyramid (HOP), transforms an image into a set of orthogonal, oriented, odd and even bandpass subimages. It operates on a hexagonal input lattice and employs seven kernels, each of which occupies a neighborhood consisting of a point and a hexagon of six nearest neighbors. The kernels consist of one lowpass and six bandpass kernels that are orthogonal, self-similar, and localized in space, spatial frequency, orientation, and phase. The kernels are first applied to the image samples to create the first level of the pyramid, then to the lowpass coefficients to create the next level. The resulting pyramid is a compact, efficient image code. Here, a recursive, in-place algorithm for computation of the HOP transform is described. The transform may be regarded as a depth-first traversal of a tree structure. It is shown that the algorithm requires a number of operations that is on the order of the number of pixels.
Accurate phase measurements for thick spherical objects using optical quadrature microscopy
NASA Astrophysics Data System (ADS)
Warger, William C., II; DiMarzio, Charles A.
2009-02-01
In vitro fertilization (IVF) procedures have resulted in the birth of over three million babies since 1978. Yet the live birth rate in the United States was only 34% in 2005, with 32% of the successful pregnancies resulting in multiple births. These multiple pregnancies were directly attributed to the transfer of multiple embryos to increase the probability that a single, healthy embryo was included. Current viability markers used for IVF, such as the cell number, symmetry, size, and fragmentation, are analyzed qualitatively with differential interference contrast (DIC) microscopy. However, this method is not ideal for quantitative measures beyond the 8-cell stage of development because the cells overlap and obstruct the view within and below the cluster of cells. We have developed the phase-subtraction cell-counting method that uses the combination of DIC and optical quadrature microscopy (OQM) to count the number of cells accurately in live mouse embryos beyond the 8-cell stage. We have also created a preliminary analysis to measure the cell symmetry, size, and fragmentation quantitatively by analyzing the relative dry mass from the OQM image in conjunction with the phase-subtraction count. In this paper, we will discuss the characterization of OQM with respect to measuring the phase accurately for spherical samples that are much larger than the depth of field. Once fully characterized and verified with human embryos, this methodology could provide the means for a more accurate method to score embryo viability.
Genovese, Luigi; Deutsch, Thierry
2015-12-21
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in density functional theory (DFT) is given by the external potential or the pseudo-potential describing the interaction between ions and electrons. The accuracy of the collocation method used is therefore very important for the reliability of subsequent treatments like self-consistent field solutions of the electronic structure problems. By construction, the collocation method introduces numerical artifacts typical of real-space treatments, like the so-called egg-box error, which may spoil the numerical stability of the description when the real-space grid is too coarse. As the external potential is an input of the problem, even a highly precise computational treatment cannot cope this inconvenience. We present in this paper a new quadrature scheme that is able to exactly preserve the moments of a given analytic function even for large grid spacings, while reconciling with the traditional collocation method when the grid spacing is small enough. In the context of real-space electronic structure calculations, we show that this method improves considerably the stability of the results for large grid spacings, opening up the path towards reliable low-accuracy DFT calculations with a reduced number of degrees of freedom. PMID:26372293
Real-space quadrature: A convenient, efficient representation for multipole expansions
Rogers, David M.
2015-02-21
Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem—completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson’s operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation.
Algorithm for the Time-Propagation of the Radial Diffusion Equation Based on a Gaussian Quadrature
Gillespie, Dirk
2015-01-01
The numerical integration of the time-dependent spherically-symmetric radial diffusion equation from a point source is considered. The flux through the source can vary in time, possibly stochastically based on the concentration produced by the source itself. Fick’s one-dimensional diffusion equation is integrated over a time interval by considering a source term and a propagation term. The source term adds new particles during the time interval, while the propagation term diffuses the concentration profile of the previous time step. The integral in the propagation term is evaluated numerically using a combination of a new diffusion-specific Gaussian quadrature and interpolation on a diffusion-specific grid. This attempts to balance accuracy with the least number of points for both integration and interpolation. The theory can also be extended to include a simple reaction-diffusion equation in the limit of high buffer concentrations. The method is unconditionally stable. In fact, not only does it converge for any time step Δt, the method offers one advantage over other methods because Δt can be arbitrarily large; it is solely defined by the timescale on which the flux source turns on and off. PMID:26208111
Real-space quadrature: a convenient, efficient representation for multipole expansions.
Rogers, David M
2015-02-21
Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem-completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson's operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation. PMID:25701996
Digital services using quadrature amplitude modulation (QAM) over CATV analog DWDM system
NASA Astrophysics Data System (ADS)
Yeh, JengRong; Selker, Mark D.; Trail, J.; Piehler, David; Levi, Israel
2000-04-01
Dense Wavelength Division Multiplexing (DWDM) has recently gained great popularity as it provides a cost effective way to increase the transmission capacity of the existing fiber cable plant. For a long time, Dense WDM was exclusively used for baseband digital applications, predominantly in terrestrial long haul networks and in some cases in metropolitan and enterprise networks. Recently, the performance of DWDM components and frequency-stabilized lasers has substantially improved while the costs have down significantly. This makes a variety of new optical network architectures economically viable. The first commercial 8- wavelength DWDM system designed for Hybrid Fiber Coax networks was reported in 1998. This type of DWDM system utilizes Sub-Carrier Multiplexing (SCM) of Quadrature Amplitude Modulated (QAM) signals to transport IP data digital video broadcast and Video on Demand on ITU grid lightwave carriers. The ability of DWDM to provide scalable transmission capacity in the optical layer with SCM granularity is now considered by many to be the most promising technology for future transport and distribution of broadband multimedia services.
Direct Quadrature Method of Moments for LES-based Modeling of Supersonic Combustion
NASA Astrophysics Data System (ADS)
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2009-11-01
The LES/transported probability density function (PDF) model has been successfully used for predictive modeling of turbulent combustion in low-speed flows. The PDF approach evolves the joint-distribution of the gas-phase thermochemical composition and is ideally suited for supersonic flows, where conserved-scalar approaches are not valid due to the compressible nature of the flow. In low-speed flows, the high-dimensionality of the PDF transport equation is handled through the use of Monte-Carlo based stochastic methods. However, the presence of shocks and large density and pressure gradients pose significant challenges in the use of these stochastic methods for high-speed flows. In this work, we propose a direct quadrature method of moments (DQMOM) approach, which is a fully Eulerian method for solving the PDF transport equation. Here, the subfilter PDF is discretized in terms of a finite number of delta functions, each characterized by a weight and an abscissa. Eulerian transport equations for these quantities are similar in structure to scalar transport equations and can be solved using finite-volume/finite difference approaches. Here, the accuracy of the DQMOM approach and the numerical implementation of this method using shock-capturing schemes are discussed.
NASA Astrophysics Data System (ADS)
Jamaly, Seyed Mohammad; Hasan Saidi, Mohammad; Ghafourian, Akbar
2007-11-01
In this study, due to the weaknesses of the models with Lagrangian approaches, an attempt has been made to model the spray flow with Eulerian approach. In this regard, the quadrature-based moment closure model for the spray equation, the so-called DQMOM, is applied. This method overcomes the shortcoming of other Eulerian methods while it is in good agreement with the Lagrangian methods. After that, the model has been developed to be able to deal with the evaporating droplets. Moreover, the feasibility of applying non-linear external forces, such as drag forces, and evaporation laws for the droplets are considered and implemented. The required order for the equations in this method has been studied thoroughly as well. Finally, the solution procedure for accurate computations of multi dimension problems is presented. In general, the proposed modified DQMOM method can consider and solve all kinds of spray flows with any desirable dimension for the problem. Here, assuming one-way coupling situation with the gas-phase in an axial engine, the spray phase equations are solved by the proposed method to account for evaporating droplets. Results are compared with the methods with Lagrangian approach and the computational costs and accuracies of the methods are compared as well.
Quadrature Method of Moments for the Simulation of Turbulent Reacting Flows
NASA Astrophysics Data System (ADS)
Raman, Venkatramanan; Pitsch, Heinz; Fox, Rodney
2003-11-01
Computational schemes for turbulent reacting flow systems typically solve the species transport equations using a grid-based Eulerian technique. Such schemes inherently do not contain information about the sub-grid scalar PDF required for the computation of the non-linear reaction source terms and sub-grid scalar dissipation. Though a transport equation for the scalar PDF can be formulated, the high-dimensional equation has to be solved using a computationally expensive particle-based Lagrangian scheme. To overcome this difficulty, the Direct Quadrature Method of Moments (DQMOM) is used to approximate the joint composition PDF by a set of delta functions. The delta-functions are characterized by their location and size, both of which are obtained by solving Eulerian transport equations. Using a N-peak description, N species-moments can be forced to be accurate. The Direct QMOM model is extended to LES schemes and comparisons are made with transported-PDF simulations for both reacting and non-reacting mixing layer setup. Re-formulation of the DQMOM equation leads to conditional multi-environment method that can be used for describing combustion systems that exhibit extinction.
Bottom-series coupled quadrature VCO using the inductive gate voltage boosting technique
NASA Astrophysics Data System (ADS)
Jang, Sheng-Lyang; Chou, Li-Te
2013-09-01
This article presents a new low-voltage bottom-series coupled quadrature voltage-controlled oscillator (QVCO), which consists of two n-core cross-coupled VCOs with the bottom-series coupling transistors. The low-voltage operation is obtained via an inductive gate voltage boosting technique. The proposed CMOS QVCO has been implemented with the TSMC 0.18 µm CMOS technology and the die area is 0.897 × 0.767 mm2. At the supply voltage of 0.7 V, the total power consumption is 1.5 mW. The free-running frequency of the QVCO is tuneable from 3.77 to 4.12 GHz as the tuning voltage is varied from 0.0 to 0.7 V. The measured phase noise at 1 MHz frequency offset is -123.35 dBc/Hz at the oscillation frequency of 4.12 GHz and the figure of merit of the proposed QVCO is -193.5 dBc/Hz.
Low Voltage Low Power Quadrature LC Oscillator Based on Back-gate Superharmonic Capacitive Coupling
NASA Astrophysics Data System (ADS)
Ma, Minglin; Li, Zhijun
2013-09-01
This work introduces a new low voltage low power superharmonic capacitive coupling quadrature LC oscillator (QLCO) made by coupling two identical cross-connected LC oscillators without tail transistor. In each of the core oscillators, the back-gate nodes of the cross-coupled NMOS pair and PMOS pair, acting as common mode nodes, have been connected directly. Then the core oscillators are coupled together via capacitive coupling of the PMOS common mode node in one of the core oscillators to the NMOS common mode node in the other core oscillator, and vice versa. Only capacitors are used for coupling of the two core oscillators and therefore no extra noise sources are imposed on the circuit. Operation of the proposed QLCO was investigated with simulation using a commercial 0.18 µm RF CMOS technology: it shows a power dissipation of 5.2 mW from a 0.6 V supply voltage. Since the proposed core oscillator has Complementary NMOS and PMOS cross coupled pairs, and capacitive coupling method will not introduce extra phase noise, so this circuit can operate with a low phase noise as low as -126.8 dBc/Hz at 1 MHz offset from center oscillation frequency of 2.4 GHz, as confirmed with simulation.
Hu, Wei; Zhao, Zhangyan; Wang, Yunfeng; Zhang, Haiying; Lin, Fujiang
2014-03-01
The designed sensor enables accurate reconstruction of chest-wall movement caused by cardiopulmonary activities, and the algorithm enables estimation of respiration, heartbeat rate, and some indicators of heart rate variability (HRV). In particular, quadrature receiver and arctangent demodulation with calibration are introduced for high linearity representation of chest displacement; 24-bit ADCs with oversampling are adopted for radar baseband acquisition to achieve a high signal resolution; continuous-wavelet filter and ensemble empirical mode decomposition (EEMD) based algorithm are applied for cardio/pulmonary signal recovery and separation so that accurate beat-to-beat interval can be acquired in time domain for HRV analysis. In addition, the wireless sensor is realized and integrated on a printed circuit board compactly. The developed sensor system is successfully tested on both simulated target and human subjects. In simulated target experiments, the baseband signal-to-noise ratio (SNR) is 73.27 dB, high enough for heartbeat detection. The demodulated signal has 0.35% mean squared error, indicating high demodulation linearity. In human subject experiments, the relative error of extracted beat-to-beat intervals ranges from 2.53% to 4.83% compared with electrocardiography (ECG) R-R peak intervals. The sensor provides an accurate analysis for heart rate with the accuracy of 100% for p = 2% and higher than 97% for p = 1%. PMID:24235293
Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?
NASA Astrophysics Data System (ADS)
Benincasa, Dionigi M. T.
2011-07-01
We investigate the relation between the two dimensional Causal Set action, Script S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.
Thick braneworlds and the Gibbons-Kallosh-Linde no-go theorem in the Gauss-Bonnet framework
NASA Astrophysics Data System (ADS)
Dias, M.; Hoff da Silva, J. M.; da Rocha, Roldão
2015-04-01
The sum rules related to thick braneworlds are constructed in order to encompass Gauss-Bonnet terms. The generation of thick branes is hence proposed in a periodic extra dimension scenario, which circumvents the Gibbons-Kallosh-Linde no-go theorem in this context.
Quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map in pseudo-Euclidean 4-space
NASA Astrophysics Data System (ADS)
Milousheva, Velichka; Turgay, Nurettin Cenk
2016-08-01
A Lorentz surface in the four-dimensional pseudo-Euclidean space with neutral metric is called quasi-minimal if its mean curvature vector is lightlike at each point. In the present paper we obtain the complete classification of quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map.
NASA Astrophysics Data System (ADS)
Nozari, Kourosh; Rashidi, Narges
2016-06-01
We study a nonminimal derivative inflationary model in the presence of the Gauss-Bonnet term. To have a complete treatment of the model, we consider a general form of the nonminimal derivative function and also the Gauss-Bonnet coupling term. By following the Arnowitt-Deser-Misner formalism, expanding the action up to the third order in the perturbations and using the correlation functions, we study the perturbation and its non-Gaussian feature in details. We also study the consistency relation that gets modified in the presence of the Gauss-Bonnet term in the action. We compare the results of our consideration in confrontation with Planck2015 observational data and find some constraints on the model's parameters. Our treatment shows that this model in some ranges of the parameters is consistent with the observational data. Also, in some ranges of model's parameters, the model predicts blue-tilted power spectrum. Finally, we show that nonminimal derivative model in the presence of the Gauss-Bonnet term has capability to have large non-Gaussianity.
On the Fourier - Gauss transforms of some q-exponential and q-trigonometric functions
NASA Astrophysics Data System (ADS)
Atakishiyev, N. M.
1996-11-01
We examine the properties of q-exponential and q-trigonometric functions, recently introduced and discussed in the literature. It is shown that they are related to Jackson's q-analogues of the exponential and trigonometric functions by classical Fourier - Gauss transformations.
NASA Technical Reports Server (NTRS)
Cao, Chang-Qi
1996-01-01
The amplitude and transverse quadrature component squeezing of coherent light in high Q cavity by injection of atoms of two-photon transition are studied. The Golubev-Sokolov master equation and generating function approach are utilized to derive the exact variances of photon number and of transverse quadrature component as function of t. The correlation functions and power spectrums of photon number noise and of output photon current noise are also investigated.
Topological black holes in pure Gauss-Bonnet gravity and phase transitions
NASA Astrophysics Data System (ADS)
Aránguiz, Ligeia; Kuang, Xiao-Mei; Miskovic, Olivera
2016-03-01
We study charged, static, topological black holes in pure Gauss-Bonnet gravity in asymptotically AdS space. As in general relativity, the theory possesses a unique nondegenerate AdS vacuum. It also admits charged black hole solutions which asymptotically behave as the Reissner-Nordström AdS black hole. We discuss black hole thermodynamics of these black holes. Then we study phase transitions in a dual quantum field theory in four dimensions, with the Stückelberg scalar field as an order parameter. We find in the probe limit that the black hole can develop hair below some critical temperature, which suggests a phase transition. Depending on the scalar coupling constants, the phase transition can be first or second order. Analysis of the free energy reveals that, comparing the two solutions, the hairy state is energetically favorable, thus a phase transition will occur in a dual field theory.
Slowly-Rotating Black Hole Solution in Einstein-Dilaton-Gauss-Bonnet Gravity
NASA Astrophysics Data System (ADS)
Ayzenberg, Dimitry; Yunes, Nicolas
2015-04-01
We present a stationary and axisymmetric black hole solution in Einstein-Dilaton-Gauss-Bonnet gravity to quadratic order in the ratio of the spin angular momentum to the black hole mass squared. This solution introduces new corrections to previously found nonspinning and linear-in-spin solutions. The location of the event horizon and the ergosphere are modified, as well as the quadrupole moment. The new solution is of Petrov type I, although lower order in spin solutions are of Petrov type D. There are no closed timelike curves or spacetime regions that violate causality outside of the event horizon in the new solution. We calculate the modifications to the binding energy, Kepler's third law, and properties of the innermost stable circular orbit. These modifications are important for determining how the electromagnetic properties of accretion disks around supermassive black holes are changed from those expected in general relativity.
Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem
Cognola, Guido; Zerbini, Sergio; Elizalde, Emilio; Nojiri, Shin'ichi; Odintsov, Sergei D.
2006-04-15
Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, f(G), is added to the general relativity action. We show that a theory of this kind is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence, or phantom cosmic acceleration, with a possibility for the transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with the solar system constraints. Specific properties of f(G) gravity in a de Sitter (dS) universe, such as dS and SdS solutions, their entropy, and its explicit one-loop quantization are studied. The issue of a possible solution of the hierarchy problem in modified gravities is also addressed.
The role of Gauss curvature in a membrane phase separation problem
NASA Astrophysics Data System (ADS)
Gillmor, Susan; Lee, Jieun; Ren, Xiaofeng
2011-12-01
Consider a two-phase lipid vesicle. Below the transition temperature, the phases separate into non-connecting domains that coarsen into larger areas. The free energy of phase properties determines the length of the boundaries separating the regions. The two phases correspond to different lipid compositions, and in cells, this fluctuation in composition is a dynamic process vital to its function. We prove that a small patch of the minority lipids forms at a point of the membrane where the Gauss curvature attains a maximum. This patch has a round shape approximately and its boundary has a constant geodesic curvature. The proof consists of three steps. The construction of a family of good approximate solutions, an improvement of the approximate solutions so that their geodesic curvature is a constant modulo translation, and the identification of an exact solution from the family of the improved approximate solutions. Our theoretical results are supported by vesicle experiments.
Quantum dynamics of electronic transitions with Gauss-Hermite wave packets.
Borrelli, Raffaele; Peluso, Andrea
2016-03-21
A new methodology based on the superposition of time-dependent Gauss-Hermite wave packets is developed to describe the wave function of a system in which several interacting electronic states are coupled to a bath of harmonic oscillators. The equations of motion for the wave function parameters are obtained by employing the Dirac-Frenkel time-dependent variational principle. The methodology is applied to study the quantum dynamical behaviour of model systems with two interacting electronic states characterized by a relatively large reorganization energy and a range of energy biases. The favourable scaling properties make it a promising tool for the study of the dynamics of chemico-physical processes in molecular systems. PMID:27004857
Four-wave mixing in quantum wells using femtosecond pulses with Laguerre-Gauss modes
NASA Astrophysics Data System (ADS)
Persuy, Déborah; Ziegler, Marc; Crégut, Olivier; Kheng, Kuntheak; Gallart, Mathieu; Hönerlage, Bernd; Gilliot, Pierre
2015-09-01
We demonstrate theoretically and experimentally that four-wave mixing processes obey phase-matching conditions that determine not only the conservation of the photon energy and k-momentum but also the orbital angular momentum of light. We report on time-resolved four-wave mixing experiments performed on a CdTe/CdZnTe quantum well in both noncollinear and collinear configurations with Laguerre-Gauss beams. They demonstrate that the polarization wave which is induced in the material keeps memory of the excitation pulse orbital momentum. We show that in the collinear configuration, the large angular acceptance opens up new horizons for improving the spatial resolution in time-resolved experiments.
Physical meaning of the radial index of Laguerre-Gauss beams
NASA Astrophysics Data System (ADS)
Plick, William N.; Krenn, Mario
2015-12-01
The Laguerre-Gauss modes are a class of fundamental and well-studied optical fields. These stable shape-invariant photons, exhibiting circular-cylindrical symmetry, are familiar from laser optics, micromechanical manipulation, quantum optics, communication, and foundational studies in both classical optics and quantum physics. They are characterized, chiefly, by two mode numbers: the azimuthal index indicating the orbital angular momentum of the beam, which itself has spawned a burgeoning and vibrant subfield, and the radial index, which up until recently has largely been ignored. In this paper we develop a differential operator formalism for dealing with the radial modes in both the position and momentum representations and, more importantly, give the meaning of this quantum number in terms of a well-defined physical parameter: the intrinsic hyperbolic momentum charge.
Black hole solutions in string theory with Gauss-Bonnet curvature correction
Maeda, Kei-ichi; Ohta, Nobuyoshi; Sasagawa, Yukinori
2009-11-15
We present the black hole solutions and analyze their properties in the superstring effective field theory with the Gauss-Bonnet curvature correction terms. We find qualitative differences in our results from those obtained in the truncated model in the Einstein frame. The main difference in our model from the truncated one is that the existence of a turning point in the mass-area curve, the mass-entropy curve, and the mass-temperature curve in five and higher dimensions, where we expect a change of stability. We also find a mass gap in our model, where there is no black hole solution. In five dimensions, there exists a maximum black hole temperature and the temperature vanishes at the minimum mass, which is not found in the truncated model.
NASA Astrophysics Data System (ADS)
Hendi, S. H.; Panahiyan, S.
2014-12-01
Motivated by the string corrections on the gravity and electrodynamics sides, we consider a quadratic Maxwell invariant term as a correction of the Maxwell Lagrangian to obtain exact solutions of higher dimensional topological black holes in Gauss-Bonnet gravity. We first investigate the asymptotically flat solutions and obtain conserved and thermodynamic quantities which satisfy the first law of thermodynamics. We also analyze thermodynamic stability of the solutions by calculating the heat capacity and the Hessian matrix. Then, we focus on horizon-flat solutions with an anti-de Sitter (AdS) asymptote and produce a rotating spacetime with a suitable transformation. In addition, we calculate the conserved and thermodynamic quantities for asymptotically AdS black branes which satisfy the first law of thermodynamics. Finally, we perform thermodynamic instability criterion to investigate the effects of nonlinear electrodynamics in canonical and grand canonical ensembles.
Higher-Order Laguerre-Gauss Mode Generation and Interferometry for Gravitational Wave Detectors
NASA Astrophysics Data System (ADS)
Granata, M.; Buy, C.; Ward, R.; Barsuglia, M.
2010-12-01
We report on the first experimental demonstration of higher-order Laguerre-Gauss (LGpℓ) mode generation and interferometry using a method scalable to the requirements of gravitational wave (GW) detection. GW detectors which use higher-order LGpℓ modes will be less susceptible to mirror thermal noise, which is expected to limit the sensitivity of all currently planned terrestrial detectors. We used a diffractive optic and a mode-cleaner cavity to convert a fundamental LG00 Gaussian beam into an LG33 mode with a purity of 98%. The ratio between the power of the LG00 mode of our laser and the power of the LG33 transmitted by the cavity was 36%. By measuring the transmission of our setup using the LG00, we inferred that the conversion efficiency specific to the LG33 mode was 49%. We illuminated a Michelson interferometer with the LG33 beam and achieved a visibility of 97%.
A Gauss-Newton approach to joint image registration and intensity correction.
Ebrahimi, Mehran; Lausch, Anthony; Martel, Anne L
2013-12-01
We develop a new efficient numerical methodology for automated simultaneous registration and intensity correction of images. The approach separates the intensity correction term from the images being registered in a regularized expression. Our formulation is consistent with the existing non-parametric image registration techniques, however, an extra additive intensity correction term is carried throughout. An objective functional is formed for which the corresponding Hessian and Jacobian is computed and employed in a multi-level Gauss-Newton minimization approach. In this paper, our experiments are based on elastic regularization on the transformation and total variation on the intensity correction. Validations on dynamic contrast enhanced MR abdominal images for both real and simulated data verified the efficacy of the model. The pursued approach is flexible in which we can exploit various forms of regularization on the transformation and the intensity correction. PMID:24075154
Critical behavior of charged black holes in Gauss-Bonnet gravity's rainbow
NASA Astrophysics Data System (ADS)
Hendi, Seyed Hossein; Panahiyan, Shahram; Eslam Panah, Behzad; Faizal, Mir; Momennia, Mehrab
2016-07-01
Following an earlier study regarding Gauss-Bonnet-Maxwell black holes in the presence of gravity's rainbow [S. H. Hendi and M. Faizal, Phys. Rev. D 92, 044027 (2015)], in this paper, we consider all constants as energy dependent ones. The geometrical and thermodynamical properties of this generalization is studied and the validation of the first law of thermodynamics is examined. Next, through the use of proportionality between the cosmological constant and the thermodynamical pressure, van der Waals-like behavior of these black holes in extended phase space is investigated. An interesting critical behavior for sets of rainbow functions in this case is reported. Also, the critical behavior of uncharged and charged solutions is analyzed and it is shown that the generalization to a charged case puts an energy dependent restriction on values of different parameters.
Geophex Airborne Unmanned Survey System (GAUSS). Topical report, October 1993--March 1995
1995-03-01
The objectives of the project are to construct a geophysical sensor system based on a remotely operated model helicopter (ROH) and to evaluate the efficacy of the system for characterization of hazardous environmental sites. Geophex Airborne Unmanned Survey System (GAUSS) is a geophysical survey system that uses a ROH as the survey vehicle. We have selected the ROH because of its advantages over fixed wing and ground based vehicles. Lower air speed and superior maneuverability of the ROH make it better suited for geophysical surveys than a fixed wing model aircraft. The ROH can fly close to the ground, allowing detection of weak or subtle anomalies. Unlike ground based vehicles, the ROH can traverse difficult terrain while providing a stable sensor platform. ROH does not touch the ground during the course of a survey and is capable of functioning over water and surf zones. The ROH has been successfully used in the motion picture industry and by geology companies for payload bearing applications. The only constraint to use of the airborne system is that the ROH must remain visible to the pilot. Obstructed areas within a site can be characterized by relocating the base station to alternate positions. GAUSS consists of a ROH with radio controller, a data acquisition and processing (DAP) system, and lightweight digital sensor systems. The objective of our Phase I research was to develop a DAP and sensors suitable for ROH operation. We have constructed these subsystems and integrated them to produce an automated, hand-held geophysical surveying system, referred to as the ``pre-prototype``. We have performed test surveys with the pre-prototype to determine the functionality of the and DAP and sensor subsystems and their suitability for airborne application. The objective of the Phase II effort will be to modify the existing subsystems and integrate them into an airborne prototype. Efficacy of the prototype for geophysical survey of hazardous sites will then be determined.
[A Hyperspectral Imagery Anomaly Detection Algorithm Based on Gauss-Markov Model].
Gao, Kun; Liu, Ying; Wang, Li-jing; Zhu, Zhen-yu; Cheng, Hao-bo
2015-10-01
With the development of spectral imaging technology, hyperspectral anomaly detection is getting more and more widely used in remote sensing imagery processing. The traditional RX anomaly detection algorithm neglects spatial correlation of images. Besides, it does not validly reduce the data dimension, which costs too much processing time and shows low validity on hyperspectral data. The hyperspectral images follow Gauss-Markov Random Field (GMRF) in space and spectral dimensions. The inverse matrix of covariance matrix is able to be directly calculated by building the Gauss-Markov parameters, which avoids the huge calculation of hyperspectral data. This paper proposes an improved RX anomaly detection algorithm based on three-dimensional GMRF. The hyperspectral imagery data is simulated with GMRF model, and the GMRF parameters are estimated with the Approximated Maximum Likelihood method. The detection operator is constructed with GMRF estimation parameters. The detecting pixel is considered as the centre in a local optimization window, which calls GMRF detecting window. The abnormal degree is calculated with mean vector and covariance inverse matrix, and the mean vector and covariance inverse matrix are calculated within the window. The image is detected pixel by pixel with the moving of GMRF window. The traditional RX detection algorithm, the regional hypothesis detection algorithm based on GMRF and the algorithm proposed in this paper are simulated with AVIRIS hyperspectral data. Simulation results show that the proposed anomaly detection method is able to improve the detection efficiency and reduce false alarm rate. We get the operation time statistics of the three algorithms in the same computer environment. The results show that the proposed algorithm improves the operation time by 45.2%, which shows good computing efficiency. PMID:26904830
Thermodynamics of Taub-NUT/bolt-AdS black holes in Einstein-Gauss-Bonnet gravity
Khodam-Mohammadi, A.; Monshizadeh, M.
2009-02-15
We give a review of the existence of Taub-NUT/bolt solutions in Einstein Gauss-Bonnet gravity with the parameter {alpha} in six dimensions. Although the spacetime with base space S{sup 2}xS{sup 2} has a curvature singularity at r=N, which does not admit NUT solutions, we may proceed with the same computations as in the CP{sup 2} case. The investigation of thermodynamics of NUT/bolt solutions in six dimensions is carried out. We compute the finite action, mass, entropy, and temperature of the black hole. Then the validity of the first law of thermodynamics is demonstrated. It is shown that in NUT solutions all thermodynamic quantities for both base spaces are related to each other by substituting {alpha}{sup CP{sup k}}=[(k+1)/k]{alpha}{sup S{sup 2}}{sup xS{sup 2}}{sup x...S{sub k}{sup 2}}. So, no further information is given by investigating NUT solutions in the S{sup 2}xS{sup 2} case. This relation is not true for bolt solutions. A generalization of the thermodynamics of black holes to arbitrary even dimensions is made using a new method based on the Gibbs-Duhem relation and Gibbs free energy for NUT solutions. According to this method, the finite action in Einstein Gauss-Bonnet is obtained by considering the generalized finite action in Einstein gravity with an additional term as a function of {alpha}. Stability analysis is done by investigating the heat capacity and entropy in the allowed range of {alpha}, {lambda}, and N. For NUT solutions in d dimensions, there exists a stable phase at a narrow range of {alpha}. In six-dimensional bolt solutions, the metric is completely stable for B=S{sup 2}xS{sup 2} and is completely unstable for the B=CP{sup 2} case.
Durbin, Timothy J.
1983-01-01
The Gauss optimization technique can be used to identify the parameters of a model of a groundwater system for which the parameter identification problem is formulated as a least squares comparison between the response of the prototype and the response of the model. Unavoidable uncertainty in the true stress on the prototype and in the true response of the prototype to that stress will introduce errors into the parameter identification problem. A method for evaluating errors in the predictions of future water levels due to errors in recharge estimates was demonstrated. The method involves a Monte Carlo simulation of the parameter identification problem and of the prediction problem. The steps in the method are: (1) to prescribe the distribution of the recharge estimates; (2) to use this distribution to generate random sets of recharge estimates; (3) to use the Gauss optimization technique to identify the corresponding set of parameter estimates for each set of recharge estimates; (4) to make the corresponding set of hydraulic head predictions for each set of parameter estimates; and (5) to examine the distribution of hydraulic head predictions and to draw appropriate conclusions. Similarly, the method can be used independently or simultaneously to estimate the effect on hydraulic head predictions of errors in the measured water levels that are used in the parameter identification problem. The fit of the model to the data that are used to identify parameters is not a good indicator of these errors. A Monte Carlo simulation of the parameter identification problem can be used, however, to evaluate the effects on water level predictions of errors in the recharge (and pumpage) data used in the parameter identification problem. (Lantz-PTT)
The 2011 February 15 Coronal Mass Ejection: Reconciling SOHO and STEREO Observations in Quadrature
NASA Technical Reports Server (NTRS)
Gopalswamy, Natchimuthuk
2011-01-01
The Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO observed a fast halo coronal mass ejection on 2011 February 15. The STEREO spacecraft were in quadrature with SOHO (STEREO-A ahead of Earth by 87 degrees and STEREO-B 94 degrees behind Earth), enabling CME measurement using the three spacecraft. The sky-plane speed measured by SOHO/LASCO is closely related to the expansion speed of the CME, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images measured the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (V(sub exp) ) and radial speed (V(sub rad)) derived previously from geometrical considerations (Gopalswamy et al. 2009): = V(sub rad) = 1/2 (1 + cot w) V(sub exp), where w is the half width of the CME. We can also measure the Earthward speed of the CME directly from the STEREO measurements. The travel time to Earth predicted from the Earthward speed using the Empirical Shock Arrival model is approximately 12 hours shorter than the actual travel time obtained from in situ measurements at Ll. The primary reason for this discrepancy seems to be the interaction with the two preceding CMEs that slowed down the CME in question. The CME interaction is also confirmed from the radio enhancement observed by Wind/WAVES and STEREO WAVES experiments.
A quadrature demodulation method based on tracking the ultrasound echo frequency.
Feng, Naizhang; Zhang, Jianqiu; Wang, Weiqi
2006-12-22
The ultrasound echo attenuation depends on frequency, propagating depth and tissue characteristics. Thus, the attenuation dependent on frequency results in a larger attenuation of high frequencies than lower when the wave propagates through the tissue. As a result, the central frequency of the echo generates the increasing downshift with the increasing of depth. In the traditional I/Q demodulation method, it is assumed that the central frequency of the echo is the same as the transmitting frequency and unchanged all time. The assumption directly causes that the acquired I/Q signals are not perfect baseband ones but biased due to the echo attenuation. In addition, the unreasonable assumption will keep the echo from getting better signal-to-noise ratio. A quadrature demodulation method based on tracking the ultrasound echo frequency is proposed in this paper. The method consists of the traditional I/Q demodulator, the frequency tracking module, the phase compensation module and the dynamic filtering module. The outputs of I/Q demodulator are biased. Autocorrelation technique is utilized in the frequency tracking unit to estimate the frequency bias according to the outputs of I/Q demodulator. The estimated bias feeds to the phase compensation unit which can eliminate the frequency bias by simple trigonometric function transform. The compensated signals feed to the dynamic filter and are further processed. The bandwidth of the dynamic filter decreases with the increasing of the depth, which makes the echo acquire better SNR in different depth. The efficiency of the proposed method is testified by both simulations and experiments. PMID:16860363
Niebauer, T M; Constantino, A; Billson, R; Hankla, A; Nelson, P G
2015-06-20
A corner-cube retroreflector has the property that the optical path length for a reflected laser beam is insensitive to rotations about a mathematical point called its optical center (OC). This property is exploited in ballistic absolute gravity meters in which a proof mass containing a corner-cube retroreflector is dropped in a vacuum, and its position is accurately determined with a laser interferometer. In order to avoid vertical position errors when the proof mass rotates during free fall, it is important to collocate its center of mass (COM) with the OC of the retroreflector. This is commonly done using a mechanical scale-based balancing procedure, which has limited accuracy due to the difficulty in finding the exact position of the COM and the OC. This paper describes a novel way to achieve the collocation by incorporating the proof mass into a pendulum and using a quadrature interferometer to interrogate its apparent translation in its twist mode. The mismatch between the COM and OC generates a signal in a quiet part of the spectrum where no mechanical resonance exists. This allows us to tune the position of the COM relative to the OC to an accuracy of about 1 μm in all three axes. This provides a way to directly demonstrate that a rotation of the proof mass by several degrees causes an apparent translation in the direction of the laser beam of less than 1 nm. This technique allows an order of magnitude improvement over traditional methods of balancing. PMID:26193025
NASA Technical Reports Server (NTRS)
Sidi, Avram; Pennline, James A.
1999-01-01
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
NASA Technical Reports Server (NTRS)
Sidi, Avram; Pennline, James A.
1999-01-01
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
SOHO-Ulysses Coordinated Studies During the Two Extended Quadratures and the Alignment of 2007-2008
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.
2007-01-01
During SOHO-Sun-Ulysses quadratures the geometry of the configuration makes it possible to sample "in situ" the plasma parcels that are remotely observed in the corona. Although the quadrature position occurs at a well defined instant in time, we typically take data while Ulysses is within +/- 5 degrees of the limb, with the understanding that plasma sampled by Ulysses over this time interval can all be traced to its source in the corona. The relative positions of SOHO and Ulysses in winter 2007 (19 Dec 2006-28 May 2007) are unusual: the SOHO-Sun-Ulysses included angle is always between 85 and 95 degrees - the quadrature lasts for 5 months! This provides an opportunity for extended observations of specific observing objectives. In addition, in summer 2007, Ulysses (at 1.34 AU) is in near-radial alignment with Earth/ACE/Wind and SOHO, allowing us to analyze radial gradients and propagation in the solar wind and inner heliosphere. Our own quadrature campaigns rely heavily on LASCO and UVCS coronal observations: LASCO giving the overall context above 2 solar radii while the UVCS spectrograph acquired data from - 1.5 to, typically, 4-5 solar radii. In the past, coronal parameters have been derived from data acquired by these two experiments and compared with "in situ" data of Ulysses' SWOOPS and SWICS. Data from other experiments like EIT, CDS, SUMER, Sac Peak Fe XIV maps, magnetic field maps from the Wilcox solar magnetograph, MLSO, from MDI, and from the Ulysses magnetograph experiment have been, and will be, used to complement LASCO/UVCS/SWOOPS and SWICS data. We anticipate that observations by ACE/WIND/STEREO/Hinode and other missions will be relevant as well. During the IHY campaigns, Ulysses will be 52-80 degrees south in winter 2007, near sunspot minimum. Hence, our own scientific objective will be to sample high speed wind or regions of transition between slow and fast wind. This might be a very interesting situation - not met in previous quadratures - allowing
Peng, Sun; Jin, Guo; Tingfeng, Wang
2013-07-01
Based on the generalized Huygens-Fresnel diffraction integral (Collins' formula), the propagation equation of Hermite-Gauss beams through a complex optical system with a limiting aperture is derived. The elements of the optical system may be all those characterized by an ABCD ray-transfer matrix, as well as any kind of apertures represented by complex transmittance functions. To obtain the analytical expression, we expand the aperture transmittance function into a finite sum of complex Gaussian functions. Thus the limiting aperture is expressed as a superposition of a series of Gaussian-shaped limiting apertures. The advantage of this treatment is that we can treat almost all kinds of apertures in theory. As application, we define the width of the beam and the focal plane using an encircled-energy criterion and calculate the intensity distribution of Hermite-Gauss beams at the actual focus of an aperture lens. PMID:24323153
Universal slow fall-off to the unique AdS infinity in Einstein-Gauss-Bonnet gravity
Maeda, Hideki
2008-08-15
In this paper, the following two propositions are proven under the dominant energy condition for the matter field in the higher-dimensional spherically symmetric spacetime in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant {lambda}. First, for {lambda}{<=}0 and {alpha}{>=}0 without a fine-tuning to give a unique anti-de Sitter (AdS) vacuum, where {alpha} is the Gauss-Bonnet coupling constant, vanishing generalized Misner-Sharp mass is equivalent to the maximally symmetric spacetime. Under the fine-tuning, it is equivalent to the vacuum class I spacetime. Second, under the fine-tuning with {alpha}>0, the asymptotically AdS spacetime in the higher-dimensional Henneaux-Teitelboim sense is only a special class of the vacuum class I spacetime. This means the universal slow fall-off to the unique AdS infinity in the presence of physically reasonable matter.
Quasi-Periodic Long-Term Quadrature Light Variability in Early Type Interacting Binary Systems
NASA Astrophysics Data System (ADS)
Peters, Geraldine Joan
2015-08-01
Four years of Kepler observations have revealed a class of Algol-type binaries in which the relative brightness of the quadrature light varies from > 1 to <1 on a time scale of about 100-400 days. The behavior pattern is quasi-periodic. We call these systems L/T (leading hemisphere/ trailing hemisphere) variables. Although L/T inequality in eclipsing binaries has been noted from ground-based photometry by several observers since the early 1950s, the regular or quasi-regular switching between maxima is new. Twenty L/T systems have so far been found in the Kepler database and at least three classes of L/T behavior have been identified. In this presentation I will give an update on the L/T phenomenon gleaned from the Kepler and K2 databases. The Kepler and K2 light curves are being analyzed with the 2015 version of the Wilson-Devinney (WD) program that includes major improvements in modeling star spots (i.e. spot motions due to drift and stellar rotation and spot growth and decay). The prototype L/T variable is WX Draconis (A8V + K0IV, P=1.80 d) which shows L/ T light variations of 2-3%. The primary is a delta Scuti star with a dominant pulsation period of 41 m. Preliminary analysis of the WX Dra data suggests that the L/T variability can be fit with either an accretion hot spot on the primary (T = 2.3 Tphot) that jumps in longitude or a magnetic cool spotted region on the secondary. If the latter model is correct the dark region must occupy at least 20% of the surface of the facing hemisphere of the secondary if it is completely black, or a larger area if not completely black. In both hot and cool spot scenarios magnetic fields must play a role in the activity. Support from NASA grants NNX11AC78G and NNX12AE44G and USC’s Women in Science and Engineering (WiSE) program is greatly appreciated.
Large eddy simulations of coal jet flame ignition using the direct quadrature method of moments
NASA Astrophysics Data System (ADS)
Pedel, Julien
The Direct Quadrature Method of Moments (DQMOM) was implemented in the Large Eddy Simulation (LES) tool ARCHES to model coal particles. LES coupled with DQMOM was first applied to nonreacting particle-laden turbulent jets. Simulation results were compared to experimental data and accurately modeled a wide range of particle behaviors, such as particle jet waviness, spreading, break up, particle clustering and segregation, in different configurations. Simulations also accurately predicted the mean axial velocity along the centerline for both the gas phase and the solid phase, thus demonstrating the validity of the approach to model particles in turbulent flows. LES was then applied to the prediction of pulverized coal flame ignition. The stability of an oxy-coal flame as a function of changing primary gas composition (CO2 and O2) was first investigated. Flame stability was measured using optical measurements of the flame standoff distance in a 40 kW pilot facility. Large Eddy Simulations (LES) of the facility provided valuable insight into the experimentally observed data and the importance of factors such as heterogeneous reactions, radiation or wall temperature. The effects of three parameters on the flame stand-off distance were studied and simulation predictions were compared to experimental data using the data collaboration method. An additional validation study of the ARCHES LES tool was then performed on an air-fired pulverized coal jet flame ignited by a preheated gas flow. The simulation results were compared qualitatively and quantitatively to experimental observations for different inlet stoichiometric ratios. LES simulations were able to capture the various combustion regimes observed during flame ignition and to accurately model the flame stand-off distance sensitivity to the stoichiometric ratio. Gas temperature and coal burnout predictions were also examined and showed good agreement with experimental data. Overall, this research shows that high
Subluminal group velocity and dispersion of Laguerre Gauss beams in free space
Bareza, Nestor D.; Hermosa, Nathaniel
2016-01-01
That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein’s postulate in special relativity. This has been a basic assumption in light’s various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light’s group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam’s divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space. PMID:27231195
A convergence rates result for an iteratively regularized Gauss-Newton-Halley method in Banach space
NASA Astrophysics Data System (ADS)
Kaltenbacher, B.
2015-01-01
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification problems for differential equation models. On the other hand the use of general (non-Hilbert) Banach spaces has recently found much interest due to its usefulness in many applications. This motivates us to extend the second order method from Kaltenbacher (2014 Numer. Math. at press), (see also Hettlich and Rundell 2000 SIAM J. Numer. Anal. 37 587620) to a Banach space setting and analyze its convergence. We here show rates results for a particular source condition and different exponents in the formulation of Tikhonov regularization in each step. This includes a complementary result on the (first order) iteratively regularized Gauss-Newton method in case of a one-homogeneous data misfit term, which corresponds to exact penalization. The results clearly show the possible advantages of using second order information, which get most pronounced in this exact penalization case. Numerical simulations for an inverse source problem for a nonlinear elliptic PDE illustrate the theoretical findings.
A Gauss-Seidel Iteration Scheme for Reference-Free 3-D Histological Image Reconstruction
Daum, Volker; Steidl, Stefan; Maier, Andreas; Köstler, Harald; Hornegger, Joachim
2015-01-01
Three-dimensional (3-D) reconstruction of histological slice sequences offers great benefits in the investigation of different morphologies. It features very high-resolution which is still unmatched by in-vivo 3-D imaging modalities, and tissue staining further enhances visibility and contrast. One important step during reconstruction is the reversal of slice deformations introduced during histological slice preparation, a process also called image unwarping. Most methods use an external reference, or rely on conservative stopping criteria during the unwarping optimization to prevent straightening of naturally curved morphology. Our approach shows that the problem of unwarping is based on the superposition of low-frequency anatomy and high-frequency errors. We present an iterative scheme that transfers the ideas of the Gauss-Seidel method to image stacks to separate the anatomy from the deformation. In particular, the scheme is universally applicable without restriction to a specific unwarping method, and uses no external reference. The deformation artifacts are effectively reduced in the resulting histology volumes, while the natural curvature of the anatomy is preserved. The validity of our method is shown on synthetic data, simulated histology data using a CT data set and real histology data. In the case of the simulated histology where the ground truth was known, the mean Target Registration Error (TRE) between the unwarped and original volume could be reduced to less than 1 pixel on average after 6 iterations of our proposed method. PMID:25312918
Constraints on modified Gauss-Bonnet gravity during big bang nucleosynthesis
NASA Astrophysics Data System (ADS)
Kusakabe, Motohiko; Koh, Seoktae; Kim, K. S.; Cheoun, Myung-Ki
2016-02-01
Modified gravity is considered to be one of the possible explanations of the accelerated expansions of the present and the early universe. We study the effects of modified gravity on big bang nucleosynthesis (BBN). If the effects of modified gravity are significant during the BBN epoch, they should be observed as changes of primordial light element abundances. We assume a f (G ) term with the Gauss-Bonnet term G , during the BBN epoch. A power-law relation of d f /d G ∝tp where t is the cosmic time was assumed for the function f (G ) as an example case. We solve time evolutions of physical variables during BBN in the f (G ) gravity model numerically, and we analyzed the calculated results. It is found that a proper solution for the cosmic expansion rate can be lost in some parameter region. In addition, we show that calculated results of primordial light element abundances can be significantly different from observational data. Especially, observational limits on the primordial D abundance leads to the strongest constraint on the f (G ) gravity. We then derive constraints on parameters of the f (G ) gravity taking into account the existence of the solution of expansion rate and final light element abundances.
Auxiliary functions for molecular integrals with Slater-type orbitals. II. Gauss transform methods
NASA Astrophysics Data System (ADS)
Ema, I.; López, R.; Fernández, J. J.; Ramírez, G.; Rico, J. F.
The Gauss transform of Slater-type orbitals is used to express several types of molecular integrals involving these functions in terms of simple auxiliary functions. After reviewing this transform and the way it can be combined with the shift operator technique, a master formula for overlap integrals is derived and used to obtain multipolar moments associated to fragments of two-center distributions and overlaps of derivatives of Slater functions. Moreover, it is proved that integrals involving two-center distributions and irregular harmonics placed at arbitrary points (which determine the electrostatic potential, field and field gradient, as well as higher order derivatives of the potential) can be expressed in terms of auxiliary functions of the same type as those appearing in the overlap. The recurrence relations and series expansions of these functions are thoroughly studied, and algorithms for their calculation are presented. The usefulness and efficiency of this procedure are tested by developing two independent codes: one for the derivatives of the overlap integrals with respect to the centers of the functions, and another for derivatives of the potential (electrostatic field, field gradient, and so forth) at arbitrary points.0
Subluminal group velocity and dispersion of Laguerre Gauss beams in free space.
Bareza, Nestor D; Hermosa, Nathaniel
2016-01-01
That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein's postulate in special relativity. This has been a basic assumption in light's various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light's group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam's divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space. PMID:27231195
Subluminal group velocity and dispersion of Laguerre Gauss beams in free space
NASA Astrophysics Data System (ADS)
Bareza, Nestor D.; Hermosa, Nathaniel
2016-05-01
That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein’s postulate in special relativity. This has been a basic assumption in light’s various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light’s group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam’s divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space.
Late cosmic acceleration in a vector-Gauss-Bonnet gravity model
NASA Astrophysics Data System (ADS)
Oliveros, A.; Solis, Enzo L.; Acero, Mario A.
2016-12-01
In this work, we study a general vector-tensor model of dark energy (DE) with a Gauss-Bonnet term coupled to a vector field and without explicit potential terms. Considering a spatially flat Friedmann-Robertson-Walker (FRW) type universe and a vector field without spatial components, the cosmological evolution is analyzed from the field equations of this model considering two sets of parameters. In this context, we have shown that it is possible to obtain an accelerated expansion phase of the universe since the equation state parameter w satisfies the restriction - 1 < w < -1/3 (for suitable values of model parameters). Further, analytical expressions for the Hubble parameter H, equation state parameter w and the invariant scalar ϕ are obtained. We also find that the square of the speed of sound is negative for all values of redshift, therefore, the model presented here shows a sign of instability under small perturbations. We finally perform an analysis using H(z) observational data and we find that for the free parameter ξ in the interval (-23.9,-3.46) × 10-5, at 99.73% C.L. (and fixing η = -1 and ω = 1/4), the model has a good fit to the data.
Stability of Gauss-Bonnet black holes in anti-de Sitter space-time against scalar field condensation
Brihaye, Yves; Hartmann, Betti
2011-10-15
We study the stability of static, hyperbolic Gauss-Bonnet black holes in (4+1)-dimensional anti-de Sitter (AdS) space-time against the formation of scalar hair. Close to extremality the black holes possess a near-horizon topology of AdS{sub 2}xH{sup 3} such that within a certain range of the scalar field mass one would expect that they become unstable to the condensation of an uncharged scalar field. We confirm this numerically and observe that there exists a family of hairy black hole solutions labeled by the number of nodes of the scalar field function. We construct explicit examples of solutions with a scalar field that possesses zero nodes, one node, and two nodes, respectively, and show that the solutions with nodes persist in the limit of Einstein gravity, i.e. for vanishing Gauss-Bonnet coupling. We observe that the interval of the mass for which scalar field condensation appears decreases with increasing Gauss-Bonnet coupling and/or with increasing node number.
NASA Astrophysics Data System (ADS)
Chang, Chun; Huang, Benxiong; Xu, Zhengguang; Li, Bin
2015-12-01
A partial-response-pulse-shaped 16-ary quadrature amplitude modulation (16QAM) format called quadrature duoquaternary (QDQ) modulation, which can achieve higher spectral efficiency than Nyquist-pulse-shaped 16QAM and realize super-Nyquist wavelength-division-multiplexing (WDM) transmission, is proposed. The dual-polarized QDQ (DP-QDQ) modulation principle and coherent reception based on digital signal processing (DSP) are presented. The performance of the DP-QDQ scheme is investigated in 32-GBaud super-Nyquist-WDM systems by simulation. The simulation results show that DP-QDQ has only a 1.3 dB optical-signal-to-noise-ratio (OSNR) penalty for the 28-GHz-spaced 5-channel super-Nyquist-WDM case relative to the single-channel case. Compared with Nyquist-pulse-shaped 16QAM, DP-QDQ not only has a higher spectral efficiency, but also a lower sensitivity to sampling time error and a better dispersion tolerance. The 28-GHz-spaced 5-channel super-Nyquist-WDM DP-QDQ system can successfully implement 1520-km transmission at the forward-error-correction (FEC) bit-error-rate (BER) requirements.
Sjoden, G.E.
1992-03-01
A new discrete ordinates spatial quadrature scheme is presented for solving neutral particle transport problems. This new scheme, called the exponential characteristic method, is developed here in slab geometry with isotropic scattering. This method uses a characteristic integration of the Boltzmann transport equation with an exponential function as the assumed from of the source distribution, continuous across each spatial cell. The exponential source function is constructed to globally conserve zeroth and first spatial source moments and is non-negative. Characteristic integration ensures non-negative fluxes and flux moments. Numerical testing indicates that convergence of the exponential characteristic scheme is fourth order in the limit of vanishingly thin cells. Highly accurate solutions to optically thick problems can result using this scheme with very coarse meshes. Comparing accuracy and computational cost with existing spatial quadrature schemes (diamond difference, linear discontinuous, linear characteristic, linear adaptive, etc.), the exponential characteristic scheme typically performed best. This scheme is expected to be expandable to two dimensions in a straight forward manner. Due to the high accuracies achievable using coarse meshes, this scheme may allow researchers to obtain solutions to transport problems once thought too large or too difficult to be adequately solved conventional computer systems.
NASA Astrophysics Data System (ADS)
Kiani, Maryam; Pourtakdoust, Seid H.
2014-12-01
A novel algorithm is presented in this study for estimation of spacecraft's attitudes and angular rates from vector observations. In this regard, a new cubature-quadrature particle filter (CQPF) is initially developed that uses the Square-Root Cubature-Quadrature Kalman Filter (SR-CQKF) to generate the importance proposal distribution. The developed CQPF scheme avoids the basic limitation of particle filter (PF) with regards to counting the new measurements. Subsequently, CQPF is enhanced to adjust the sample size at every time step utilizing the idea of confidence intervals, thus improving the efficiency and accuracy of the newly proposed adaptive CQPF (ACQPF). In addition, application of the q-method for filter initialization has intensified the computation burden as well. The current study also applies ACQPF to the problem of attitude estimation of a low Earth orbit (LEO) satellite. For this purpose, the undertaken satellite is equipped with a three-axis magnetometer (TAM) as well as a sun sensor pack that provide noisy geomagnetic field data and Sun direction measurements, respectively. The results and performance of the proposed filter are investigated and compared with those of the extended Kalman filter (EKF) and the standard particle filter (PF) utilizing a Monte Carlo simulation. The comparison demonstrates the viability and the accuracy of the proposed nonlinear estimator.
Yue, Yang; Zhang, Bo; Wang, Qiang; Lofland, Rob; O'Neil, Jason; Anderson, Jon
2016-03-21
Dual-polarization quadrature amplitude modulation (DP-QAM) is one of the feasible paths towards 100-Gb/s, 400-Gb/s and 1-Tb/s optical fiber communications systems. For DP-QAM transmitter, the time mismatch between the in-phase and quadrature (IQ) or x-polarized and y-polarized (XY) tributary channels is known as the IQ or XY skew. Large uncompensated IQ or XY skew can significantly degrade the optical fiber communications system performance. Sometimes, time-interleaved return-to-zero (RZ) DP signal is preferred with lower nonlinear polarization scattering induced penalty. In this work, detection and alignment of DP-QAM transmitter IQ and XY skews using reconfigurable interference is experimentally demonstrated. For IQ skew detection, a total dynamic range of 26.4 dB is achieved with ~1-dB power change for 0.5-ps skew from well alignment. For XY skew detection, it shows 23.2-dB dynamic range, and ~1.5-dB power change is achieved for 1-ps XY skew. Fast detection algorithm for arbitrary skew is also proposed and experimentally verified. The scheme is compatible with different modulation formats, flexible data sequences, and variable waveforms. PMID:27136859
Li, Ye; Yu, Baiying; Pang, Yong; Vigneron, Daniel B; Zhang, Xiaoliang
2013-01-01
The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR) in magnetic resonance (MR) imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM) technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM) and the differential mode (DM) of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays. PMID:24265823
Li, Ye; Yu, Baiying; Pang, Yong; Vigneron, Daniel B.; Zhang, Xiaoliang
2013-01-01
The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR) in magnetic resonance (MR) imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM) technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM) and the differential mode (DM) of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays. PMID:24265823
Application of a quadrature-based moments method to the modeling of volcanic plumes
NASA Astrophysics Data System (ADS)
de'Michieli Vitturi, Mattia; Barsotti, Sara; Neri, Augusto
2014-05-01
(namely the moments) are then derived and their transport equations formulated. For this work we extended, by adopting the method of moments, the Eulerian steady-state volcanic plume model presented in Barsotti et al. (2008). Differently from the original works where pyroclastic particles were partitioned in a finite number of classes with different size and properties, the new model is able to consider a continuous size distribution function of pyroclasts, f(D), representing the particles (for unit volume) with diameter between D and D+dD. Accordingly, transport equations for the moments of the ash particles size distribution are derived and the equations of the plume are expressed in terms of the moments. Here we present the new multiphase model formulation based on the implementation of the quadrature method of moments together with its advantages and drawbacks with respect to previous approaches. Results of a sensitivity analysis of the model with respect to the parameters of the continuous distribution describing the grain sizes at the vent (lognormal or beta distributions) are also shown and discussed. Barsotti, S., Neri, A., and Scire, J.: The VOL-CALPUFF model for atmospheric ash dispersal: 1. Approach and physical formulation, Journal of Geophysical Research, 113, 2008.
Gauss-Bonnet assisted braneworld inflation in light of BICEP2 and Planck data
NASA Astrophysics Data System (ADS)
Neupane, Ishwaree P.
2014-12-01
Motivated by the idea that quantum gravity corrections usually suppress the power of the scalar primordial spectrum (E-mode) more than the power of the tensor primordial spectrum (B-mode), in this paper we construct a concrete gravitational theory in five-dimensions for which V (ϕ )∝ϕn -type inflation (n ≥1 ) generates an appropriate tensor-to-scalar ratio that may be compatible with the BICEP2 and Planck data together. The true nature of gravity is five-dimensional and described by the action S =∫d5x √{|g | }M3(-6 λ M2+R +α M-2R2) where M is the five-dimensional Planck mass and R2=R2-4 Ra bRa b+Ra b c dRa b c d is the Gauss-Bonnet (GB) term. The five-dimensional "bulk" spacetime is anti-de Sitter (λ <0 ) for which inflation ends naturally. The effects of R2 term on the magnitudes of scalar and tensor fluctuations and spectral indices are shown to be important at the energy scale of inflation. For GB-assisted m2ϕ2-inflation, inflationary constraints from BICEP2 and Planck, such as, ns≃0.9603 (±0.0073 ), r =0.16 (+0.06 -0.05 ) and V*1 /4≳1.5 ×1 016 GeV are all satisfied for (-λ α )≃(3 -300 )×1 0-5.
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Carbone, Ludovico; Fulda, Paul; Bond, Charlotte; Brueckner, Frank; Brown, Daniel; Wang, Mengyao; Lodhia, Deepali; Palmer, Rebecca; Freise, Andreas
2013-01-01
Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light. We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry. PMID:23962813
Generalized second law of thermodynamics on the apparent horizon in modified Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Abdolmaleki, A.; Najafi, T.
2016-01-01
Modified gravity (MG) and generalized second law (GSL) of thermodynamics are interesting topics in the modern cosmology. In this regard, we investigate the GSL of gravitational thermodynamics in the framework of modified Gauss-Bonnet (GB) gravity or f(G)-gravity. We consider a spatially FRW universe filled with the pressureless matter and radiation enclosed by the dynamical apparent horizon with the Hawking temperature. For two viable f(G) models, we first numerically solve the set of differential equations governing the dynamics of f(G)-gravity. Then, we obtain the evolutions of the Hubble parameter, the GB curvature invariant term, the density and equation of state (EoS) parameters as well as the deceleration parameter. In addition, we check the energy conditions for both models and finally examine the validity of the GSL. For the selected f(G) models, we conclude that both models have a stable de Sitter attractor. The EoS parameters behave quite similar to those of the ΛCDM model in the radiation/matter dominated epochs, then they enter the phantom region before reaching the de Sitter attractor with ω = -1. The deceleration parameter starts from the radiation/matter dominated eras, then transits from a cosmic deceleration to acceleration and finally approaches a de Sitter regime at late times, as expected. Furthermore, the GSL is respected for both models during the standard radiation/matter dominated epochs. Thereafter when the universe becomes accelerating, the GSL is violated in some ranges of scale factor. At late times, the evolution of the GSL predicts an adiabatic behavior for the accelerated expansion of the universe.
NASA Technical Reports Server (NTRS)
Suess, Steven; Corti, G.; Poletto, G.; Sterling, A.; Moore, R.
2006-01-01
At the time of the spring 2003 Ulysses-SOHO-Sun quadrature, Ulysses was off the East limb of the Sun at 14.5 degrees north latitude and 4.91 AU. LASCO/C2 images show small transient events that originated from near the limb on May 25, 26 and 27 in the north-east quadrant, along with a large Coronal Mass Ejection (CME) that originated from an active region near disk center on May 26. Ulysses data bear clear signatures of the large CME, specifically including an enhanced abundance of highly ionized Fe. SOHO/UVCS spectra at 1.75 solar radii, near the radial direction to Ulysses, give no evidence of emission from high temperature lines, even for the large CME: instead, for the small events, occasional transient high emission in cool lines was observed, such as the CIII 977 Angstrom line usually absent at coronal levels. Each of these events lasted ca. 1 hour or less and never affected lines from ions forming above ca. 106K. Compact eruptions in Helium 304 Angstrom EIT images, related to the small UVCS transients, were observed at the limb of the Sun over the same period. At least one of these surge events produced a narrow CME observed in LASCO/C2. Most probably all these events are compact magnetic explosions (surges/jets, from around a small island of included polarity) which ejected cool material from lower levels. Ulysses data have been analyzed to find evidence of the cool, narrow CME events, but none or little was found. This puzzling scenario, where events seen by UVCS have no in situ counterparts and vice versa, can be partially explained once the region where the large CME originated is recognized as being at the center of the solar disk so that the CME material was actually much further from the Sun than the 1.7 Rsun height of the UVCS slit off the limb. Conversely, the narrow events may simply have missed Ulysses or been too brief for reliable signatures in composition and ionization state. A basic feature demonstrated by these observations is that large
NASA Astrophysics Data System (ADS)
de Basabe, Jonás D.
2011-08-01
Zhou & Greenhalgh have recently presented an application of the Gaussian quadrature grid to seismic modelling in which the authors propose a meshing scheme that partitions the domain independently of the discontinuities in the media parameters. This comment aims to clarify the implications that this strategy has on the accuracy.
NASA Astrophysics Data System (ADS)
Mao, Youxin; Flueraru, Costel; Chang, Shoude; Popescu, Dan P.; Sowa, Michael G.
2011-05-01
A performance analysis of signal to noise ratio for an optical coherence tomography system with quadrature detection and a semiconductor optical amplifier in the sample arm is discussed. The results are compared and discussed in relation to a conventional OCT system (without optical amplification). An increase of the signal to noise ratio up to 14 dB at a depth of 0.5 mm is obtained compared to the system without the optical amplifier. Overall, an improvement was demonstrated for signal coming from deeper regions within the samples. Arterial plaque from a myocardial infarction-prone Watanabe heritable hyperlipidemic (WHHLMI) rabbit is visualized and characterized using this system. Improvement of signal to noise ratio increases the penetration depth possible for OCT images, from 1 mm to 2 mm within the vessel wall of an artery. Preliminary results show that vulnerable plaque with fibrous cap, macrophage accumulations and calcification in the arterial tissue are measurable with this OCT system.
Minor, B.M.
1993-09-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport with rectangular cells is developed. Numerical problems arising in the derivation required the development of exponential moment functions. These functions are used to remove indeterminant forms which can cause catastrophic cancellations. The EC method is positive and nonlinear. It conserves particles and satisfies first moment balance. Comparisons of the EC method's performance to other methods in optically thin and thick spatial cells were performed. For optically thin cells, the EC method was shown to converge to the correct answer, with third order truncation error in the thin cell limit. In deep penetration problems, the EC method attained its highest computational efficiencies compared to the other methods. For all the deep penetration problems examined, the number of spatial cells required by the EC method to attain a desired accuracy was less than the other methods.... Mathematics functions, Nuclear radiation, Nuclear engineering, Radiation attenuation, Radiation shielding, Transport theory, Radiation transport.
NASA Technical Reports Server (NTRS)
Watson, J. S.; Mistretta, G. D.; Bonavito, N. L.
1975-01-01
A quadrature algorithm is presented which employs analytical expressions for the variations of satellite orbital elements caused by air drag. The Hamiltonian is formally preserved and the Jacobi constants of the motion are advanced with time through the variational equations. The atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabulated data at all altitudes and simultaneously reduces the variational equations to definite integrals with closed form evaluations, whose limits are in terms of the eccentric anomaly. Results are given for two intense air drag satellites and indicate that the satellite ephemerides produced by this method in conjunction with the Vinti program are of very high accuracy.
NASA Astrophysics Data System (ADS)
Ghasemi, Seiyed E.; Hatami, M.; Hatami, J.; Sahebi, S. A. R.; Ganji, D. D.
2016-02-01
In this paper, flow analysis for a non-Newtonian third grade blood in coronary and femoral arteries is simulated numerically. Blood is considered as the third grade non-Newtonian fluid under periodic body acceleration motion and pulsatile pressure gradient. Differential Quadrature Method (DQM) and Crank Nicholson Method (CNM) are used to solve the Partial Differential Equation (PDE) governing equation by which a good agreement between them was observed in the results. The influences of some physical parameters such as amplitude, lead angle and body acceleration frequency on non-dimensional velocity and profiles are considered. For instance, the results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, ϕ, make higher velocity profiles in the center line of both arteries.
Quadrature Rotating-Frame Gradient Fields for Ultra-Low FieldNuclear Magnetic Resonance and Imaging
Bouchard, Louis-Serge
2005-12-30
Magnetic resonance imaging (MRI) in very low fields isfundamentally limited by untruncated concomitant gradients which causesevere distortions in image acquisition and volume selection if thegradient fields are strong compared to the static field. In this paper,it is shown that gradient fields oscillating in quadrature can be usedfor spatial encoding in low fields and provide substantial improvementsover conventional encoding methods using static gradients. In particular,cases where the gradient field is comparable to or higher than theexternal field, Gmax/B0>1, are examined. It is shown thatundistorted slice selection and image encoding is possible because ofsmaller geometric phase errors introduced during cyclic motions of theHamiltonian. In the low field limit (Gmax/B_0 ->infinity) sliceselection is achieved with a combination of soft pulse segments and acoherent train of hard pulses to average out concomitant fields over thefast scale of the rf Hamiltonian.
NASA Astrophysics Data System (ADS)
Greenhalgh, Stewart; Zhou, Bing; Maurer, Hansruedi
2010-05-01
We have developed a modified version of the spectral element method (SEM), called the Gaussian Quadrature Grid (GQG) approach, for frequency domain 3D seismic modelling in arbitrary heterogeneous, anisotropic media. The model may incorporate an arbitrary free-surface topography and irregular subsurface interfaces. Unlike the SEM ,it does not require a powerful mesh generator such as the Delauney Triangular or TetGen. Rather, the GQG approach replaces the element mesh with Gaussian quadrature abscissae to directly sample the physical properties of the model parameters and compute the weighted residual or variational integral. This renders the model discretisation simple and easily matched to the model topography, as well as direct control of the model paramterisation for subsequent inversion. In addition, it offers high accuracy in numerical modelling provided that an appropriate density of the Gaussian quadrature abscissae is employed. The second innovation of the GQG is the incorporation of a new implementation of perfectly matched layers to suppress artificial reflections from the domain margins. We employ PML model parameters (specified complex valued density and elastic moduli) rather than explicitly solving the governing wave equation with a complex co-ordinate system as in conventional approaches. Such an implementation is simple, general, effective and easily extendable to any class of anisotropy and other numerical modelling methods. The accuracy of the GQG approach is controlled by the number of Gaussian quadrature points per minimum wavelength, the so-called sampling density. The optimal sampling density should be the one which enables high definition of geological characteristics and high precision of the variational integral evaluation and spatial differentiation. Our experiments show that satisfactory results can be obtained using sampling densities of 5 points per minimum wavelength. Efficiency of the GQG approach mainly depends on the linear
NASA Technical Reports Server (NTRS)
Smith, A. C.; Yang, H.
1989-01-01
The quadrature phase detection technique was used to simultaneously monitor the phase and amplitude of a toneburst signal normally reflected from an adhesively bonded steel-to-rubber interface. The measured phase was found to show a positive shift for all bonded samples with respect to the disbonded state - the phase shift being larger for samples with weaker bonds, as manifested by smaller values of applied tensile loads at failure. A model calculation, which incorporates the concept of interfacial strength into the usual problem of wave propagation in multilayered media, was used to deduce a bond-quality parameter from an experimentally measured phase shift. This bond-quality parameter was found to be correlated with the tensile strength of the adhesive bonds at failure loads.
NASA Astrophysics Data System (ADS)
Fakir, Md. Moslemuddin; Khatun, Sabira; Jusoh, Abdul Wahab; Ramli, Mohammad Fadzli; Muhamad, Wan Zuki Azman Wan
2015-05-01
Finite Element Method (FEM) and Differential Quadrature Method (DQM) are two very important numerical solution techniques to solve engineering and physical science problems. Usually elements are sub-divided uniformly in FEM (conventional FEM, CFEM) to obtain temperature distribution behavior in a fin with extra computational complexity to obtain a fair solution with required accuracy. In this paper an algorithm to enhance the FEM (named EFEM) is presented by considering non-uniform sub-elements and applied successfully to investigate one dimensional heat distribution phenomenon in an insulated-tip thin rectangular fin. The obtained results are compared with CFEM, efficient DQM (EDQM, with non-uniform mesh generation) and exact solution. EFEM results exhibits more accuracy than CFEM and EDQM and agree very well with exact solution showing its potentiality.
Tze, Chia-Hsiung . Dept. of Physics)
1989-01-01
By way of the Gauss-Bonnet-Chern theorem, we present a higher dimensional extension of Polyakov's regularization of Wilson loops of point solitons. Spacetime paths of extended objects become hyper-ribbons with self-linking, twisting and writhing numbers. specifically we discuss the exotic spin and statistical phase entanglements of geometric n-membrane solitons of D-dimensional KP{sub 1} {sigma}-models with an added Hopf-Chern-Simons term where (n, D, K) = (0, 3, C), (2, 7, H), (6, 15, {Omega}). They are uniquely linked to the complex and quaternion and octonion division algebras. 22 refs.
NASA Astrophysics Data System (ADS)
Sahabandu, C.; Suranyi, P.; Vaz, C.; Wijewardhana, L. C.
2006-02-01
We investigate the thermodynamics of static black objects such as black holes, black strings and their generalizations to D dimensions (“black branes”) in a gravitational theory containing the four-dimensional Gauss-Bonnet term in the action, with D-4 dimensions compactified torus. The entropies of black holes and black branes are compared to obtain information on the stability of these objects and to find their phase diagrams. We demonstrate the existence of a critical mass, which depends on the scale of the compactified dimensions, below which the black hole entropy dominates over the entropy of the black membrane.
NASA Astrophysics Data System (ADS)
Xu, Si-Liu; Belić, Milivoj R.
2014-11-01
We investigate the existence of spatiotemporal necklace vortex solitons or light bullets in the complex Ginzburg-Landau equation with the modulated Kummer-Gauss (KG) external lattice potential and the spiraling phase of vorticities S=0,1 , and 2. We find localized vortex necklaces in a three-dimensional nonlinear medium, trapped by the KG external potential with different orders of vorticity. Stable and quasi-stable solitons form from input pulses with embedded vorticity. The stability is established by calculating growth rates of the perturbed eigenmodes. We establish that spatiotemporal necklace solitons may coexist in a large domain of the parameter space.
NASA Astrophysics Data System (ADS)
Fox, R. O.; Laurent, F.; Massot, M.
2008-03-01
The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v,u;x,t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. [F. Laurent, M. Massot, P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, J. Comput. Phys. 194 (2004) 505-543]. The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox [D.L. Marchisio, R.O. Fox, Solution of population balance equations using the direct quadrature method of moments, J. Aerosol Sci. 36 (2005) 43-73] to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to focus on the difficulties associated with treating size-dependent coalescence and to avoid numerical uncertainty issues associated with two-way coupling, only one-way coupling between the droplets and a given gas velocity field is considered. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver. The third key point of the study is a detailed description of the limitations associated with each method, thus giving criteria for
NASA Astrophysics Data System (ADS)
Mišković, Olivera; Olea, Rodrigo
2011-01-01
Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.
NASA Astrophysics Data System (ADS)
Hendi, S. H.; Panahiyan, S.; Momennia, M.
2016-04-01
In this paper, we consider quadratic Maxwell invariant as a correction to the Maxwell theory and study thermodynamic behavior of the black holes in Einstein and Gauss-Bonnet gravities. We consider cosmological constant as a thermodynamic pressure to extend phase space. Next, we obtain critical values in case of variation of nonlinearity and Gauss-Bonnet parameters. Although the general thermodynamical behavior of the black hole solutions is the same as usual Van der Waals system, we show that in special case of the nonlinear electromagnetic field, there will be a turning point for the phase diagrams and usual Van der Waals is not observed. This theory of nonlinear electromagnetic field provides two critical horizon radii. We show that this unusual behavior of phase diagrams is due to existence of second critical horizon radius. It will be pointed out that the power of the gravity and nonlinearity of the matter field modify the critical values. We generalize the study by considering the effects of dimensionality on critical values and make comparisons between our models with their special sub-classes. In addition, we examine the possibility of the existence of the reentrant phase transitions through two different methods.
Miskovic, Olivera; Olea, Rodrigo
2011-01-15
Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.
NASA Astrophysics Data System (ADS)
Longoni, Gianluca
In the nuclear science and engineering field, radiation transport calculations play a key-role in the design and optimization of nuclear devices. The linear Boltzmann equation describes the angular, energy and spatial variations of the particle or radiation distribution. The discrete ordinates method (S N) is the most widely used technique for solving the linear Boltzmann equation. However, for realistic problems, the memory and computing time require the use of supercomputers. This research is devoted to the development of new formulations for the SN method, especially for highly angular dependent problems, in parallel environments. The present research work addresses two main issues affecting the accuracy and performance of SN transport theory methods: quadrature sets and acceleration techniques. New advanced quadrature techniques which allow for large numbers of angles with a capability for local angular refinement have been developed. These techniques have been integrated into the 3-D SN PENTRAN (Parallel Environment Neutral-particle TRANsport) code and applied to highly angular dependent problems, such as CT-Scan devices, that are widely used to obtain detailed 3-D images for industrial/medical applications. In addition, the accurate simulation of core physics and shielding problems with strong heterogeneities and transport effects requires the numerical solution of the transport equation. In general, the convergence rate of the solution methods for the transport equation is reduced for large problems with optically thick regions and scattering ratios approaching unity. To remedy this situation, new acceleration algorithms based on the Even-Parity Simplified SN (EP-SSN) method have been developed. A new stand-alone code system, PENSSn (Parallel Environment Neutral-particle Simplified SN), has been developed based on the EP-SSN method. The code is designed for parallel computing environments with spatial, angular and hybrid (spatial/angular) domain
NASA Technical Reports Server (NTRS)
Gopalswamy, Nat; Makela, Pertti; Yashiro, Seiji
2011-01-01
It is difficult to measure the true speed of Earth-directed CMEs from a coronagraph along the Sun-Earth line because of the occulting disk. However, the expansion speed (the speed with which the CME appears to spread in the sky plane) can be measured by such coronagraph. In order to convert the expansion speed to radial speed (which is important for space weather applications) one can use empirical relationship between the two that assumes an average width for all CMEs. If we have the width information from quadrature observations, we can confirm the relationship between expansion and radial speeds derived by Gopalswamy et al. (2009, CEAB, 33, 115,2009). The STEREO spacecraft were in quadrature with SOHO (STEREO-A ahead of Earth by 87 and STEREO-B 94 behind Earth) on 2011 February 15, when a fast Earth-directed CME occurred. The CME was observed as a halo by the Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO. The sky-plane speed was measured by SOHO/LASCO as the expansion speed, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images measured the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (Vexp ) and radial speed (Vrad ) derived previously from geometrical considerations (Gopalswamy et al. 2009): Vrad = 1/2 (1 + cot w) Vexp, where w is the half width of the CME. STEREO-B images of the CME, we found that CME had a full width of 75 degrees, so w = 37.5 degrees. This gives the relation as Vrad = 1.15 Vexp. From LASCO observations, we measured Vexp = 897 km/s, so we get the radial speed as 1033 km/s. Direct measurement of radial speed from STEREO gives 945 km/s (STEREO-A) and 1057 km/s (STEREO-B). These numbers are different only by 2.3% and 8.5% (for STEREO-A and STEREO-B, respectively) from the computed value.
Lo, Joseph; Shizgal, Bernie D
2006-11-21
Spectral methods based on nonclassical polynomials and Fourier basis functions or sinc interpolation techniques are compared for several eigenvalue problems for the Fokker-Planck and Schrodinger equations. A very rapid spectral convergence of the eigenvalues versus the number of quadrature points is obtained with the quadrature discretization method (QDM) and the appropriate choice of the weight function. The QDM is a pseudospectral method and the rate of convergence is compared with the sinc method reported by Wei [J. Chem. Phys., 110, 8930 (1999)]. In general, sinc methods based on Fourier basis functions with a uniform grid provide a much slower convergence. The paper considers Fokker-Planck equations (and analogous Schrodinger equations) for the thermalization of electrons in atomic moderators and for a quartic potential employed to model chemical reactions. The solution of the Schrodinger equation for the vibrational states of I2 with a Morse potential is also considered. PMID:17129090
NASA Technical Reports Server (NTRS)
Wang, C.-W.; Stark, W.
2005-01-01
This article considers a quaternary direct-sequence code-division multiple-access (DS-CDMA) communication system with asymmetric quadrature phase-shift-keying (AQPSK) modulation for unequal error protection (UEP) capability. Both time synchronous and asynchronous cases are investigated. An expression for the probability distribution of the multiple-access interference is derived. The exact bit-error performance and the approximate performance using a Gaussian approximation and random signature sequences are evaluated by extending the techniques used for uniform quadrature phase-shift-keying (QPSK) and binary phase-shift-keying (BPSK) DS-CDMA systems. Finally, a general system model with unequal user power and the near-far problem is considered and analyzed. The results show that, for a system with UEP capability, the less protected data bits are more sensitive to the near-far effect that occurs in a multiple-access environment than are the more protected bits.
NASA Astrophysics Data System (ADS)
Gurarii, G. Z.
2015-09-01
Extremely scarce data have been published on the structure of the geomagnetic field during the Gauss and early Matuyama chrons until recently. Only a few papers contain information about the characteristics of the field during the Gauss-Matuyama reversal, derived by studying the terrestrial sediments. This motivated us to revisit the paleomagnetism of the sedimentary rocks of Akchagyl age in the section of the Pirnuar Valley in West Kopet Dag, for the first time studied by us in the late 1960s-early 1970s. These rocks are the analog of the top Piacenzian-bottom Gelasian and span the mentioned time interval. The reanalysis was conducted with the use of the state-of-the-art paleomagnetic techniques and modern magnetostratigraphic timescale. We have studied a number of the characteristics which enabled us to distinguish the rocks whose remanence is most likely to have a depositional origin. Based on the paleomagnetic characteristics of these rocks, we reconstructed the structure of the paleomagnetic field for the studied interval (~270 ka) of the initial stage of the Gauss-Matuyama reversal and revealed the excursions at the final and initial stages of the Gauss and Matuyama chrons. This analysis has significantly updated the time constraints of the rock sedimentation in the studied section and supported the locations of the virtual geomagnetic pole during the reversal, obtained previously.
NASA Astrophysics Data System (ADS)
Petrov, Nikolai I.
2016-07-01
It is shown that the vector-vortex Laguerre-Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams with nonzero azimuthal and radial indices in a cylindrical graded-index medium is investigated. The wave shape variation with distance taking into account the spin-orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated. High efficiency transfer of a strongly focused spot through an optical waveguide over large distances takes place with a period of revival.
Alexandrescu, D; Fonea, M; Sava, N
1980-01-01
The authors made use of maps prepared in the projection system known as the "Universal Transverse Mercator" (Gauss-Kruger projection) for the study of an epidemiometric indicator in tuberculosis, namely the instantaneous prevalence of bacili carriers on December 31 1978 in the Ilfov District. The representation allows to evaluate the density of sources of infection, and as a consequence, of areas in which antiepidemic measured have to be intensified. The extension of the study to other districts could provide data for assessing the epidemiologic potential in various territories, as well as comparisons and the dynamics of the potential. The method could also be used in the study of other epidemiometric indicators. PMID:6254131
NASA Technical Reports Server (NTRS)
Boltz, F. W.
1984-01-01
An algorithm is presented for efficient p-iterative solution of the Lambert/Gauss orbit-determination problem using second-order Newton iteration. The algorithm is based on a universal transformation of Kepler's time-of-flight equation and approximate inverse solutions of this equation for short-way and long-way flight paths. The approximate solutions provide both good starting values for iteration and simplified computation of the second-order term in the iteration formula. Numerical results are presented which indicate that in many cases of practical significance (except those having collinear position vectors) the algorithm produces at least eight significant digits of accuracy with just two or three steps of iteration.
NASA Astrophysics Data System (ADS)
Maitra, Ushoshi; Mukhopadhyaya, Biswarup; Sengupta, Soumitra
2016-02-01
In the usual 5-dimensional Randall-Sundrum scenario with warped geometry of the extra compact dimension, the Goldberger-Wise mechanism for stabilisation of the radius of compactification can lead to a scalar field called the radion. The radion can have implications in TeV-scale physics, which can be especially noticeable if its vacuum expectation value (vev) is not far above a TeV. However a large mass of the first graviton excitation, which seems to be suggested by recent search limit, tends to make the radion vev, far too large in the minimal model. We show that this is not the case if a Gauss-Bonnet term, containing higher powers of the curvature, is present in the 5-dimensional action. As a result, a radion with vev in the range 1.7-4.0 TeV can be consistent with the first graviton excitation mass well above the bound set by LHC experiments.
Apostolopoulos, Pantelis S.; Brouzakis, Nikolaos; Tetradis, Nikolaos; Tzavara, Eleftheria
2007-10-15
We extend the covariant analysis of the brane cosmological evolution in order to take into account, apart from a general matter content and an induced-gravity term on the brane, a Gauss-Bonnet term in the bulk. The gravitational effect of the bulk matter on the brane evolution can be described in terms of the total bulk mass as measured by a bulk observer at the location of the brane. This mass appears in the effective Friedmann equation through a term characterized as generalized dark radiation that induces mirage effects in the evolution. We discuss the normal and self-accelerating branches of the combined system. We also derive the Raychaudhuri equation that can be used in order to determine if the cosmological evolution is accelerating.
Graviton time delay and a speed limit for small black holes in Einstein-Gauss-Bonnet theory
NASA Astrophysics Data System (ADS)
Papallo, Giuseppe; Reall, Harvey S.
2015-11-01
Camanho, Edelstein, Maldacena and Zhiboedov have shown that gravitons can experience a negative Shapiro time delay, i.e. a time advance, in Einstein-Gauss-Bonnet theory. They studied gravitons propagating in singular "shock-wave" geometries. We study this effect for gravitons propagating in smooth black hole spacetimes. For a small enough black hole, we find that gravitons of appropriate polarisation, and small impact parameter, can experience time advance. Such gravitons can also exhibit a deflection angle less than π, characteristic of a repulsive short-distance gravitational interaction. We discuss problems with the suggestion that the time advance can be used to build a "time machine". In particular, we argue that a small black hole cannot be boosted to a speed arbitrarily close to the speed of light, as would be required in such a construction.
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.
2016-08-01
A (n+1)-dimensional gravitational model with Gauss-Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, a_i ˜ exp { ( v^i t) }, i =1, dots , n , are analyzed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = sum _{k = 1}n v^k ≠ 0. We prove that under a certain restriction R imposed solutions with K(v) > 0 are stable, while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v^1 = v^2 =v^3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.
NASA Astrophysics Data System (ADS)
Hanief, M.; Wani, M. F.
2015-12-01
In this paper, surface roughness model for running-in and steady state of the wear process is proposed. In this work monotonously decreasing trend of surface roughness during running-in was assumed. The model was developed by considering the surface roughness as an explicit function of time during running-in, keeping other system parameters (velocity, load, hardness, etc.) constant. The proposed model being non-linear, optimal values of the model parameters were evaluated by Gauss-Newton (GN) algorithm. The experimental results adopted from the literature, for steel and Cu-Zn alloy specimens, were used for validation of the model. Artificial neural network (ANN) based model was also developed and was compared with the proposed model on the basis of statistical methods (coefficient of determination (R2), mean square error (MSE) and mean absolute percentage error (MAPE)).
NASA Technical Reports Server (NTRS)
Kifle, Muli; Vanderaar, Mark
1994-01-01
Union bounds and Monte Carlo simulation Bit-Error-Rate (BER) performance results are presented for various 32-ary and 64-ary Quadrature Amplitude Modulation (QAM) schemes. Filtered and unfiltered modulation formats are compared for the best packing arrangement in peak power limited systems. It is verified that circular constellations which populate as many symbols as possible at the peak magnitude offer the best performance. For example: a 32-ary QAM scheme based on concentric circles offers about 1.05 dB better peak power improvement at a BER of 10(exp -6) over the scheme optimized for average power using triangular symbol packing. This peak power improvement increases to 1.25 dB for comparable 64-ary QAM schemes. This work serves as a precursor to determine the feasibility of a combined modem/codec that can accommodate Broadband Integrated Services Digital Network (B-ISDN) at a rate of 155.52 Mbps through typical transponder bandwidths of 36 MHz and 54 MHz.
Cui, Yan; He, Yuxi; Wang, Pingshan
2014-01-01
A highly tunable and sensitive radio-frequency (RF) sensor is presented for the measurement of aqueous-solution dielectric properties. Two quadrature hybrids are utilized to achieve destructive interference that eliminates the probing signals at both measurement ports. As a result, weak signals of material-under-test (MUT) are elevated for high sensitivity detections at different frequencies. The sensor is demonstrated through measuring 2-propanol-water solution permittivity at 0.01 mole fraction concentration level from ~4 GHz to ~12 GHz. De-ionized water and methanol-water solution are used to calibrate the sensor for quantitative MUT analysis through our proposed model. Micro-meter coplanar waveguides (CPW) are fabricated as RF sensing electrodes. A polydimethylsiloxane (PDMS) microfluidic channel is employed to introduce 250 nL liquid, of which ~1 nL is effectively the MUT. The permittivity and the relaxation time of 2-propanol-water solution are obtained. Compared with our power divider based sensors, the differential reflection coefficients in this work provide additional information that complements the transmission coefficient methods. PMID:25197266
NASA Astrophysics Data System (ADS)
Kimachi, Akira; Ando, Shigeru; Doi, Motonori; Nishi, Shogo
2011-12-01
We propose a three-phase spectral matching imager (3PSMI) to realize a novel spectral matching method called quadrature spectral matching (QSM) in real time. The 3PSMI is comprised of the correlation image sensor (CIS) and wavelength-swept monochromatic illumination (WSMI) to perform QSM at each pixel on the CIS at a video frame rate. QSM consists of spectral correlation between an ac component of an object spectrum and an orthonormal pair of reference spectra, being equivalent to projecting the ac object spectrum onto a two-dimensional subspace spanned by the reference spectra. Similarity of the ac object spectrum to the reference spectra is evaluated in terms of the azimuth angle of the projection, independently of the norm of the ac object spectrum as well as spatial intensity distribution of the WSMI. A programable spectral light source is employed to implement the WSMI so that the spectral characteristics of the WSMI and CIS cancel each other and thus do not affect QSM on the 3PSMI. Experimental results confirm that the developed 3PSMI system can distinguish objects with smaller difference in spectral reflectance in real time than RGB imaging with off-the-shelf cameras.
NASA Astrophysics Data System (ADS)
El-Orany, Faisal A. A.
2005-11-01
In this paper we consider a system consisting of a two-level atom in an excited state interacting with two modes of a radiation field prepared initially in l-photon coherent states. This system is described by a two-mode multiphoton (i.e., k1,k2) Jaynes-Cummings model (JCM). For this system we investigate the occurrence of the revival-collapse phenomenon (RCP) in the evolution of the single-mode, two-mode, sum and difference quadrature squeezing. We show that there is a class of states for which all these types of squeezing exhibit RCP similar to that involved in the corresponding atomic inversion. Also we show numerically that the single-mode squeezing of the first mode for (k1,k2) = (3,1) provides RCP similar to that of the atomic inversion of the case (k1,k2) = (1,1); however, sum and difference squeezing give partial information on that case. Moreover, we show that single-mode, two-mode and sum squeezing for the case (k1,k2) = (2,2) provides information on the atomic inversion of the single-mode two-photon JCM. We derive the rescaled squeezing factors giving accurate information on the atomic inversion for all cases. The consequences of these results are that the homodyne and heterodyne detectors can be used to detect the RCP for the two-mode JCM.
NASA Astrophysics Data System (ADS)
Vikas, V.; Wang, Z. J.; Fox, R. O.
2013-09-01
Population balance equations with advection and diffusion terms can be solved using quadrature-based moment methods. Recently, high-order realizable finite-volume schemes with appropriate realizability criteria have been derived for the advection term. However, hitherto no work has been reported with respect to realizability problems for the diffusion term. The current work focuses on developing high-order realizable finite-volume schemes for diffusion. The pitfalls of existing finite-volume schemes for the diffusion term based on the reconstruction of moments are discussed, and it is shown that realizability can be guaranteed only with the 2nd-order scheme and that the realizability criterion for the 2nd-order scheme is the same as the stability criterion. However, realizability of moments cannot be guaranteed when higher-order moment-based reconstruction schemes are used. To overcome this problem, realizable high-order finite-volume schemes based on the reconstruction of weights and abscissas are proposed and suitable realizability criteria are derived. The realizable schemes can achieve higher than 2nd-order accuracy for problems with smoothly varying abscissas. In the worst-case scenario of highly nonlinear abscissas, the realizable schemes are 2nd-order accurate but have lower error magnitudes compared to existing schemes. The results obtained using the realizable high-order schemes are shown to be consistent with those obtained using the 2nd-order moment-based reconstruction scheme.
NASA Astrophysics Data System (ADS)
Smith, Elwyn; Wada, Naoya; Chujo, Wataru; Sampson, David D.
2002-06-01
High-power ultra-broadband sources such as a supercontinuum are very attractive in optical coherence tomography (OCT) and optical coherence-domain reflectometry (OCDR) due to their very high resolution potential. However, the large and extensive coherence-function sidelobes typical of such sources preclude their use in conventional OCDR and OCT systems. In addition, device or sample dispersion over such broad bandwidths may also significantly limit the achievable performance. Here we describe a novel experiment using a supercontinuum source with a static Michelson interferometer to perform OCDR at 1.55micrometers . Quadrature spectral detection is used to maximize the scanning range and to allow direct compensation for both the undesirable spectral shape of the source and for the dispersion in the system. Such a non-scanning-interferometer approach is an interesting possible alternative for very broadband, ultra-high resolution OCT systems. We demonstrate that an otherwise obscured small reflection next to a large reflection can be revealed by appropriately weighting the data to reshape the supercontinuum spectrum and compensate for dispersion. Significant reduction of the supercontinuum coherence function sidelobes is achieved, and a resolution in air of 7micrometers (FWHM) is obtained, or less than 5micrometers in media of refractive index 1.45.
0.8-5.2GHz Broad-Band SiGe-MMIC Quadrature Mixer for Software Defined Radio Receiver
NASA Astrophysics Data System (ADS)
Murakami, Keishi; Suematsu, Noriharu; Tsutsumi, Koji; Kanazawa, Gakushi; Sekine, Tomotsugu; Kubo, Hiroshi; Isota, Yoji
For the next generation wireless terminals used in the software defined radio (SDR), multi-band / multi-mode transceivers and their MMIC are required which cover the wide RF frequency range from several hundreds MHz up to several GHz. In this paper, 0.8-5.2GHz broad-band SiGe-MMIC quadrature mixer (Q-MIX) for multi-band / multi-mode direct conversion receiver has been developed. By using a static type frequency divider as a 90 degrees local (LO) power divider, measured error vector magnitude (EVM) of less than 3.1% can be achieved in the cases of 0.8/2.1GHz W-CDMA and 5.2GHz wireless Local Area Network (LAN) (IEEE 802.11a) reception. This Q-MIX also shows broad-band characteristic for base-band signal and is applicable for 4G cellular. By using fabricated Q-MIX, a multi-band / multi-mode (1.9GHz (3rd generation cellular (W-CDMA)) / 5.2GHz (4th generation cellular (Multi-Carrier (MC)-CDMA))) receiver has been developed and it has firstly demonstrated the successful reception of motion picture via W-CDMA and MC-CDMA.
NASA Astrophysics Data System (ADS)
Hort, R. D.; Revil, A.; Munakata-Marr, J.; Mao, D.
2015-07-01
Electrical resistivity measurements can potentially be used to remotely monitor fate and transport of ionic oxidants such as permanganate (MnO4-) during in situ chemical oxidation (ISCO) of contaminants like trichloroethene (TCE). Time-lapse two-dimensional bulk conductivity and induced polarization surveys conducted during a sand tank ISCO simulation demonstrated that MnO4- plume movement could be monitored in a qualitative manner using bulk conductivity tomograms, although chargeability was below sensitivity limits. We also examined changes to in-phase and quadrature electrical conductivity resulting from ion injection, MnO2 and Cl- production, and pH change during TCE and humate oxidation by MnO4- in homogeneous aqueous solutions and saturated porous media samples. Data from the homogeneous samples demonstrated that inversion of the sand tank resistivity data using a common Tikhonov regularization approach was insufficient to recover an accurate conductivity distribution within the tank. While changes to in-phase conductivity could be successfully modeled, quadrature conductivity values could not be directly related to TCE oxidation product or MnO4- concentrations at frequencies consistent with field induced polarization surveys, limiting the utility of quadrature conductivity for monitoring ISCO.
NASA Astrophysics Data System (ADS)
Tornabene, Francesco; Viola, Erasmo; Inman, Daniel J.
2009-12-01
This paper focuses on the dynamic behavior of functionally graded conical, cylindrical shells and annular plates. The last two structures are obtained as special cases of the conical shell formulation. The first-order shear deformation theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is developed within the theory of linear elasticity, when materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. Two different power-law distributions are considered for the ceramic volume fraction. The homogeneous isotropic material is inferred as a special case of functionally graded materials (FGM). The governing equations of motion, expressed as functions of five kinematic parameters, are discretized by means of the generalized differential quadrature (GDQ) method. The discretization of the system leads to a standard linear eigenvalue problem, where two independent variables are involved without using the Fourier modal expansion methodology. For the homogeneous isotropic special case, numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. Different typologies of non-uniform grid point distributions are considered. Finally, for the functionally graded material case numerical results illustrate the influence of the power-law exponent and of the power-law distribution choice on the mechanical behavior of shell structures.
Dai, Y.; Ding, M. D.; Chen, P. F.; Zhang, J.
2012-11-01
We report quadrature observations of an extreme-ultraviolet (EUV) wave event on 2011 January 27 obtained by the Extreme Ultraviolet Imager on board the Solar Terrestrial Relations Observatory, and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. Two components are revealed in the EUV wave event. A primary front is launched with an initial speed of {approx}440 km s{sup -1}. It appears that significant emission enhancement occurs in the hotter channel while deep emission reduction occurs in the cooler channel. When the primary front encounters a large coronal loop system and slows down, a secondary, much fainter, front emanates from the primary front with a relatively higher starting speed of {approx}550 km s{sup -1}. Afterward, the two fronts propagate independently with increasing separation. The primary front finally stops at a magnetic separatrix, while the secondary front travels farther until it fades out. In addition, upon the arrival of the secondary front, transverse oscillations of a prominence are triggered. We suggest that the two components are of different natures. The primary front belongs to a non-wave coronal mass ejection (CME) component, which can be reasonably explained with the field-line stretching model. The multi-temperature behavior may be caused by considerable heating due to nonlinear adiabatic compression on the CME frontal loop. As for the secondary front, it is most likely a linear fast-mode magnetohydrodynamic wave that propagates through a medium of the typical coronal temperature. X-ray and radio data provide us with complementary evidence in support of the above scenario.
NASA Astrophysics Data System (ADS)
Goguitchaichvili, Avto; Prévot, Michel; Thompson, John; Roberts, Neil
1999-08-01
We have measured the variation in the intensity of the geomagnetic field during the Gauss-Matuyama (N4-R3) polarity reversal by application of the Thelliers' method to specimens of lava flows from Hvalfjördur district in Western Iceland (Reynivallahals Mts.). Eleven lava flows all show very similar directions corresponding to an equatorial VGP (Plat=2.9°N, Plong=81.9°E, A95=4.2, K=119). Twenty-nine specimens from nine of the flows were pre-selected for palaeointensity determination on the basis that specimens from the same drill cores showed a single component of magnetisation upon thermal or AF demagnetisation, and possessed low magnetic viscosity and reversible susceptibility curves upon heating at 600-650°C. Observation that the directional data obtained in the course of the palaeointensity experiments occasionally showed substantial non-linearity indicates that a significant chemical remanent magnetization (CRM) can be acquired in the direction of the laboratory field during heating at T. For each double heating step we calculated the ratio of CRM( T) to the magnitude of the natural remanent magnetization (NRM( T)) in the direction of characteristic remanence (obtained independently from another specimen from the same core). When this ratio exceeded 15%, the paleointensity data was rejected. In addition, specimens for which the quality factor was less than 5 were rejected. Twelve reliable palaeointensity values were obtained from specimens representing five lava flows. The results confirm that the palaeointensity was substantially reduced during the N4-R3 reversal. The range of mean palaeointensity values obtained for the five flows is 8.8 to 20.5 and the overall mean is 14.8±4.6 μT. This corresponds to an equivalent VDM of 3.81±1.19 (10 22 A m 2). A comparison of all Thellier palaeointensity data from the R3 magnetozone in the Rayinivallahals Mts. area reveals a progressive although irregular increase in the palaeointensity between the Gauss
NASA Astrophysics Data System (ADS)
Zhang, Ming; Yang, Zhan-Ying; Yue, Rui-Hong
2014-10-01
Using the generalized formalism of Dalibard, Dupont-Roc and Cohen-Tannoudji we investigate the spontaneous excitation of a static atom interacting with electromagnetic vacuum fluctuations outside an Einstein Gauss-Bonnet black hole in d-dimensions. It shows that spontaneous excitation does not occur in a Boulware vacuum, while exists in an Unruh vacuum and Hartle-Hawking vacuum. As to the total rate of change of the atomic energy, it does not receive the contribution from the coupling constant of the Gauss-Bonnet term at spatial infinity only the dimensional parameter has the contribution to it. Near the event horizon, both the coupling constant and the dimension p contribute to the total rate of change of the atomic energy in all three kinds of vacuum. We discuss the contribution of the coupling constant and dimensional factor to the results in three different kinds of spacetime lastly.
Pani, Paolo; Cardoso, Vitor
2009-04-15
It is generally accepted that Einstein's theory will get some as yet unknown corrections, possibly large in the strong-field regime. An ideal place to look for these modifications is in the vicinities of compact objects such as black holes. Here, we study dilatonic black holes, which arise in the framework of Gauss-Bonnet couplings and one-loop corrected four-dimensional effective theory of heterotic superstrings at low energies. These are interesting objects as a prototype for alternative, yet well-behaved gravity theories: they evade the 'no-hair' theorem of general relativity but were proven to be stable against radial perturbations. We investigate the viability of these black holes as astrophysical objects and try to provide some means to distinguish them from black holes in general relativity. We start by extending previous works and establishing the stability of these black holes against axial perturbations. We then look for solutions of the field equations describing slowly rotating black holes and study geodesic motion around this geometry. Depending on the values of mass, dilaton charge, and angular momentum of the solution, one can have differences in the innermost-stable-circular-orbit location and orbital frequency, relative to black holes in general relativity. In the most favorable cases, the difference amounts to a few percent. Given the current state-of-the-art, we discuss the difficulty of distinguishing the correct theory of gravity from electromagnetic observations or even with gravitational-wave detectors.
NASA Astrophysics Data System (ADS)
Allocca, A.; Gatto, A.; Tacca, M.; Day, R. A.; Barsuglia, M.; Pillant, G.; Buy, C.; Vajente, G.
2015-11-01
The use of higher-order Laguerre-Gauss modes has been proposed to decrease the influence of thermal noise in future generation gravitational-wave interferometric detectors. The main obstacle for their implementation is the degeneracy of modes with same order, which highly increases the requirements on the mirror defects, beyond the state-of-the-art polishing and coating techniques. In order to increase the mirror surface quality, it is also possible to act in situ, using a thermal source, sent on the mirrors after a proper shaping. In this paper we present the results obtained on a tabletop Fabry-Pérot Michelson interferometer illuminated with a LG3 ,3 mode. We show how an incoherent light source can reduce the astigmatism of one of the mirrors, increasing the quality of the beam in one of the Fabry-Pérot cavities and then the contrast of the interferometer. The system has the potential to reduce more complex defects and also to be used in future gravitational-wave detectors using conventional Gaussian beams.
NASA Astrophysics Data System (ADS)
Shao, Xinxing; Dai, Xiangjun; He, Xiaoyuan
2015-08-01
The inverse compositional Gauss-Newton (IC-GN) algorithm is one of the most popular sub-pixel registration algorithms in digital image correlation (DIC). The IC-GN algorithm, compared with the traditional forward additive Newton-Raphson (FA-NR) algorithm, can achieve the same accuracy in less time. However, there are no clear results regarding the noise robustness of IC-GN algorithm and the computational efficiency is still in need of further improvements. In this paper, a theoretical model of the IC-GN algorithm was derived based on the sum of squared differences correlation criterion and linear interpolation. The model indicates that the IC-GN algorithm has better noise robustness than the FA-NR algorithm, and shows no noise-induced bias if the gray gradient operator is chosen properly. Both numerical simulations and experiments show good agreements with the theoretical predictions. Furthermore, a seed point-based parallel method is proposed to improve the calculation speed. Compared with the recently proposed path-independent method, our model is feasible and practical, and it can maximize the computing speed using an improved initial guess. Moreover, we compared the computational efficiency of our method with that of the reliability-guided method using a four-point bending experiment, and the results show that the computational efficiency is greatly improved. This proposed parallel IC-GN algorithm has good noise robustness and is expected to be a practical option for real-time DIC.
NASA Astrophysics Data System (ADS)
Pasqua, Antonio; Chattopadhyay, Surajit; Khurshudyan, Martiros; Aly, Ayman A.
2014-09-01
In this paper, we studied the cosmological application of the interacting Ricci Dark Energy (RDE) model in the framework of the scalar Gauss-Bonnet modified gravity model. We studied the properties of the reconstructed potential , the Strong Energy Condition (SEC), the Weak Energy Condition (WEC) and the deceleration parameter q for three different models of scale factor, i.e. the emergent, the intermediate and the logamediate one. We obtained that , for the emergent scenario, has a decreasing behavior, while, for the logamediate scenario, the potential start with an increasing behavior then, for later times, it shows a slowly decreasing behavior. Finally, for the intermediate scenario, the potential has an initial increasing behavior, then for a time of t≈1.2, it starts to decrease. We also found that both SEC and WEC are violated for all the three scale factors considered. Finally, studying the plots of q, we derived that an accelerated universe can be achieved for the three models of scale factor considered.
Ibrahim, R. S.; El-Kalaawy, O. H.
2006-10-15
The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model.
NASA Astrophysics Data System (ADS)
Wang, Yanyi; Li, Xinying; Yu, Jianjun
2016-01-01
We numerically and experimentally investigate high-speed quadrature phase shift keying (QPSK) vector signal generation based on a single Mach-Zehnder intensity modulator employing a precoding technique. We experimentally demonstrate 16-Gbaud QPSK vector signal generation at 16-GHz carrier adopting optical carrier suppression with precoding technique, and it is the highest baud rate generated by this technology. The 16-Gbaud QPSK modulated vector signal is delivered over a 20-km large effective area fiber or 2-km single-mode fiber with a bit-error-rate less than the hard-decision forward-error-correction threshold of 3.8×10-3.
Ishimura, Shota; Kikuchi, Kazuro
2015-03-01
We apply the eight-state trellis-coded modulation (TCM) using signal constellations of four-dimensional M-ary quadrature-amplitude modulation (4D-MQAM) to optical communication systems for the first time to our knowledge. In the TCM scheme, the free distance of the trellis diagram is equal to the minimum distance between constellation points in partitioned subsets, which enlarges the coding gain effectively. In fact, its asymptotic power efficiency is 3-dB larger than that of the set-partitioned 4D-MQAM (SP-4D-MQAM) format, while their spectral efficiencies are the same. Such theoretical predictions are confirmed through computer simulations on eight-state TCM with constellations of 4D-4QAM (i.e., 4D quadrature phase-shift keying: 4D-QPSK) and 4D-16QAM. In particular, eight-state TCM with 4D-QPSK constellations is practically important because of its simple encoder structure, relatively low computational cost, and high coding gain against dual-polarization QPSK (DP-QPSK) and SP-4D-QPSK. Through measurements of its bit-error rate (BER) performance, we confirm that the coding gain against DP-QPSK is about 3 dB at BER=10(-3). PMID:25836886
Kropf, Pascal; Shmuel, Amir
2016-07-01
Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested
NASA Astrophysics Data System (ADS)
Kibler, Maurice R.
2009-09-01
The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained from a polar decomposition of SU(2) and is analyzed in terms of cyclic groups, quadratic Fourier transforms, Hadamard matrices and generalized Gauss sums. Weyl pairs, generalized Pauli operators and their application to the unitary group and the Pauli group naturally arise in this approach. Dedicated to the memory of Yurii Fedorovich Smirnov.
NASA Astrophysics Data System (ADS)
Dey, Shirsendu; Lala, Arindam
2015-03-01
In this paper we have studied the onset of holographic s-wave condensate in the (4 + 1) dimensional planar Gauss-Bonnet-AdS black hole background with several non-linear corrections to the gauge field. In the probe limit, performing explicit analytic computations, with and without magnetic field, we found that these higher order corrections indeed affect various quantities characterizing the holographic superconductors. Also, performing a comparative study of the two non-linear electrodynamics it has been shown that the exponential electrodynamics has stronger effects on the formation of the scalar hair. We observe that our results agree well with those obtained numerically (Zhao et al., 2013).
Maeda, Hideki
2006-05-15
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud including the perturbative effects of quantum gravity. The n({>=}5)-dimensional action with the Gauss-Bonnet term for gravity is considered and a simple formulation of the basic equations is given for the spacetime M{approx_equal}M{sup 2}xK{sup n-2} with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with n=5 and n{>=}6. There are two families of solutions, which we call plus-branch and the minus-branch solutions. A plus-branch solution can be attached to the outside vacuum region which is asymptotically anti-de Sitter in spite of the absence of a cosmological constant. Bounce inevitably occurs in the plus-branch solution for n{>=}6, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of n=5 must be naked. On the other hand, a minus-branch solution can be attached to the outside asymptotically flat vacuum region. We show that naked singularities are massless for n{>=}6, while massive naked singularities are possible for n=5. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for n{>=}6, while it is ingoing-null for n=5. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for n{>=}10 and for n=9 depending on the parameters in the initial data, while a naked singularity is always formed for 5{<=}n{<=}8. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.
NASA Astrophysics Data System (ADS)
Espinoza-Molina, Daniela; Datcu, Mihai
2010-10-01
TerraSAR-X is the Synthetic Aperture Radar (SAR) German satellite which provides a high diversity of information due to its high-resolution. TerraSAR-X acquires daily a volume of up to 100 GB of high complexity, multi-mode SAR images, i.e. SpotLight, StripMap, and ScanSAR data, with dual or quad-polarization, and with different look angles. The high and multiple resolutions of the instrument (1m, 3m or 10m) open perspectives for new applications, that were not possible with past lower resolution sensors (20-30m). Mainly the 1m and 3m modes we expect to support a broad range of new applications related to human activities with relevant structures and objects at the 1m scale. Thus, among the most interesting scenes are: urban, industrial, and rural data. In addition, the global coverage and the relatively frequent repeat pass will definitely help to acquire extremely relevant data sets. To analyze the available TerrrSAR-X data we rely on model based methods for feature extraction and despeckling. The image information content is extracted using model-based methods based on Gauss Markov Random Field (GMRF) and Bayesian inference approach. This approach enhances the local adaptation by using a prior model, which learns the image structure and enables to estimate the local description of the structures, acting as primitive feature extraction method. However, the GMRF model-based method uses as input parameters the Model Order (MO) and the size of Estimation Window (EW). The appropriated selection of these parameters allows us to improve the classification and indexing results due to the number of well separated classes could be determined by them. Our belief is that the selection of the MO depends on the kind of information that the image contains, explaining how well the model can recognize complex structures as objects, and according to the size of EW the accuracy of the estimation is determined. In the following, we present an evaluation of the impact of the model
Sampath, Rahul S; Sundar, Hari; Veerapaneni, Shravan
2010-01-01
We present fast adaptive parallel algorithms to compute the sum of N Gaussians at N points. Direct sequential computation of this sum would take O(N{sup 2}) time. The parallel time complexity estimates for our algorithms are O(N/n{sub p}) for uniform point distributions and O( (N/n{sub p}) log (N/n{sub p}) + n{sub p}log n{sub p}) for non-uniform distributions using n{sub p} CPUs. We incorporate a plane-wave representation of the Gaussian kernel which permits 'diagonal translation'. We use parallel octrees and a new scheme for translating the plane-waves to efficiently handle non-uniform distributions. Computing the transform to six-digit accuracy at 120 billion points took approximately 140 seconds using 4096 cores on the Jaguar supercomputer. Our implementation is 'kernel-independent' and can handle other 'Gaussian-type' kernels even when explicit analytic expression for the kernel is not known. These algorithms form a new class of core computational machinery for solving parabolic PDEs on massively parallel architectures.
Goto, Nobuo; Miyazaki, Yasumitsu
2014-06-01
Optical switching of high-bit-rate quadrature-phase-shift-keying (QPSK) pulse trains using collinear acousto-optic (AO) devices is theoretically discussed. Since the collinear AO devices have wavelength selectivity, the switched optical pulse trains suffer from distortion when the bandwidth of the pulse train is comparable to the pass bandwidth of the AO device. As the AO device, a sidelobe-suppressed device with a tapered surface-acoustic-wave (SAW) waveguide and a Butterworth-type filter device with a lossy SAW directional coupler are considered. Phase distortion of optical pulse trains at 40 to 100 Gsymbols/s in QPSK format is numerically analyzed. Bit-error-rate performance with additive Gaussian noise is also evaluated by the Monte Carlo method. PMID:24922411
NASA Astrophysics Data System (ADS)
Kamimura, Tatsuya; Lee, Sang-yeop; Tanoi, Satoru; Ito, Hiroyuki; Ishihara, Noboru; Masu, Kazuya
2012-04-01
A low power-supply voltage and high-frequency quadrature voltage-controlled oscillator (QVCO) using a combination of capacitor coupling and transformer feedback techniques is presented. The capacitor coupling technique can boost the transconductance of the LC-VCO core and coupling transconductance of QVCO at high frequency. Also, this technique can improve the quality factor of the QVCO at high frequency with low power-supply voltage, compared with the conventional QVCO. In addition, the capacitor coupling QVCO with transformer feedback can improve the quality factor of QVCO. Using this topology, the QVCO is able to operate at over 10 GHz with lower power-supply voltage. Implemented in the 90 nm complementary metal oxide semiconductor (CMOS) process, the proposed QVCO measures 1-MHz-offset phase noise of -94 dBc/Hz at 13 GHz while consuming 0.68 mW from a 0.1 V power-supply.
Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.
2008-05-15
We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive global information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.