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.)
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.)
Geothermal modeling by Gauss-Legendre quadrature integration
NASA Astrophysics Data System (ADS)
Leftwich, T. E.; von Frese, R. R.; Tost, B. C.
2011-12-01
Bottom-hole temperature data and temperature dependent seismic, gravity, magnetic and other geological data are becoming increasingly available for improving our understanding of the geological structure and evolution of the Earth, aiding fossil energy exploration and CO2 sequestration efforts as well as for enhancing geothermal energy exploration. In assessing these growing data sets, there is a great need for developing methods to compute regional and local thermal fields from geologic models in spherical as well as Cartesian coordinates. We explore the utility of the elegant Gauss-Legendre quadrature formulation for numerically modeling the thermal effects (i.e., potential and field) of the spherical prism for heat productivity contrasts in radiogenic content and thermal conductivity. As an application, we investigate the potential, T, and heat flow, q, effects of real terrain on BHT observations and heat flow estimates in Ohio.
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.
A new algorithm for computing multivariate Gauss-like quadrature points.
Taylor, Mark A.; Bos, Len P.; Wingate, Beth A.
2004-06-01
The diagonal-mass-matrix spectral element method has proven very successful in geophysical applications dominated by wave propagation. For these problems, the ability to run fully explicit time stepping schemes at relatively high order makes the method more competitive then finite element methods which require the inversion of a mass matrix. The method relies on Gauss-Lobatto points to be successful, since the grid points used are required to produce well conditioned polynomial interpolants, and be high quality 'Gauss-like' quadrature points that exactly integrate a space of polynomials of higher dimension than the number of quadrature points. These two requirements have traditionally limited the diagonal-mass-matrix spectral element method to use square or quadrilateral elements, where tensor products of Gauss-Lobatto points can be used. In non-tensor product domains such as the triangle, both optimal interpolation points and Gauss-like quadrature points are difficult to construct and there are few analytic results. To extend the diagonal-mass-matrix spectral element method to (for example) triangular elements, one must find appropriate points numerically. One successful approach has been to perform numerical searches for high quality interpolation points, as measured by the Lebesgue constant (Such as minimum energy electrostatic points and Fekete points). However, these points typically do not have any Gauss-like quadrature properties. In this work, we describe a new numerical method to look for Gauss-like quadrature points in the triangle, based on a previous algorithm for computing Fekete points. Performing a brute force search for such points is extremely difficult. A common strategy to increase the numerical efficiency of these searches is to reduce the number of unknowns by imposing symmetry conditions on the quadrature points. Motivated by spectral element methods, we propose a different way to reduce the number of unknowns: We look for quadrature formula
Accurate computation of weights in classical Gauss-Christoffel quadrature rules
Yakimiw, E.
1996-12-01
For many classical Gauss-Christoffel quadrature rules there does not exist a method which guarantees a uniform level of accuracy for the Gaussian quadrature weights at all quadrature nodes unless the nodes are known exactly. More disturbing, some algebraic expressions for these weights exhibit an excessive sensitivity to even the smallest perturbations in the node location. This sensitivity rapidly increases with high order quadrature rules. Current uses of very high order quadratures are common with the advent of more powerful computers, and a loss of accuracy in the weights has become a problem and must be addressed. A simple but efficient and general method for improving the accuracy of the computation of the quadrature weights even though the nodes may carry a significant large error. In addition, a highly efficient root-finding iterative technique with superlinear converging rates for computing the nodes is developed. It uses solely the quadrature polynomials and their first derivatives. A comparison of this method with the eigenvalue method of Golub and Welsh implemented in most standard software libraries is made. The proposed method outperforms the latter from the point of view of both accuracy and efficiency. The Legendre, Lobatto, Radau, Hermite, and Laguerre quadrature rules are examined. 22 refs., 7 figs., 5 tabs.
Lattice Boltzmann models based on half-range Gauss-Hermite quadratures
NASA Astrophysics Data System (ADS)
Ambruş, Victor E.; Sofonea, Victor
2016-07-01
We discuss general features of thermal lattice Boltzmann models based on half-range Gauss quadratures, specialising to the half-range Gauss-Hermite and Gauss-Laguerre cases. The main focus of the paper is on the construction of high order half-range Hermite lattice Boltzmann (HHLB) models. The performance of the HHLB models is compared with that of Laguerre lattice Boltzmann (LLB) and full-range Hermite lattice Boltzmann (HLB) models by conducting convergence tests with respect to the quadrature order on stationary profiles of the particle number density, macroscopic velocity, temperature and heat fluxes in the two-dimensional Couette flow. The Bhatnagar-Gross-Krook (BGK) collision term is used throughout the paper. To reduce the computational costs of the numerical simulations, we use mixed lattice Boltzmann models, constructed using different quadrature methods on each Cartesian axis. For Kn ≤ 0.01, the HLB models require the least number of velocities to satisfy our convergence test. When Kn ≥ 0.05, the HLB models are outperformed in terms of number of velocities employed by both the LLB and the HHLB models. Moreover, we find that the HHLB models require less quadrature points than the LLB models at all tested values of Kn, which we attribute to the Maxwellian form of the weight function for the half-range Hermite polynomials.
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.
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
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.
NASA Astrophysics Data System (ADS)
Notaris, Sotirios
1995-03-01
Given a fixed n≥1, and a (monic) orthogonal polynomial πn(·)Dπn(·;dσ) relative to a positive measuredσ on the interval [a, b], one can define the nonnegative measure , to which correspond the (monic) orthogonal polynomials . The coefficients in the three-term recurrence relation for , whendσ is a Chebyshev measure of any of the four kinds, were obtained analytically in closed form by Gautschi and Li. Here, we give explicit formulae for the Stieltjes polynomials whendσ is any of the four Chebyshev measures. In addition, we show that the corresponding Gauss-Kronrod quadrature formulae for each of these , based on the zeros of and , have all the desirable properties of the interlacing of nodes, their inclusion in [-1, 1], and the positivity of all quadrature weights. Exceptions occur only for the Chebyshev measuredσ of the third or fourth kind andn even, in which case the inclusion property fails. The precise degree of exactness for each of these formulae is also determined.
Ambruş, Victor Eugen; Sofonea, Victor
2014-04-01
The Gauss-Laguerre quadrature method is used on the Cartesian semiaxes in the momentum space to construct a family of lattice Boltzmann models. When all quadrature orders Qx, Qy, Qz equal N+1, the Laguerre lattice Boltzmann model LLB(Qx,Qy,Qz) exactly recovers all moments up to order N of the Maxwell-Boltzmann equilibrium distribution function f(eq), calculated over any Cartesian octant of the three-dimensional momentum space. Results of Couette flow simulations at Kn=0.1, 0.5, 1.0 and in the ballistic regime are reported. Specific microfluidic effects (velocity slip, temperature jump, longitudinal heat flux) are well captured up to Kn=0.5, as demonstrated by comparison to direct simulation Monte Carlo results. Excellent agreement with analytic results is obtained in the ballistic regime.
Ambruş, Victor Eugen; Sofonea, Victor
2012-07-01
We use the spherical coordinate system in the momentum space and an appropriate discretization procedure to derive a hierarchy of lattice Boltzmann (LB) models with variable temperature. The separation of the integrals in the momentum space into angular and radial parts allows us to compute the moments of the equilibrium distribution function by means of Gauss-Legendre and Gauss-Laguerre quadratures, as well as to find the elements of the discrete momentum set for each LB model in the hierarchy. The capability of the high-order models in this hierarchy to capture specific effects in microfluidics is investigated through a computer simulation of Couette flow by using the Shakhov collision term to get the right value of the Prandtl number.
Woods, M. P.; Plenio, M. B.
2016-02-15
Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive error bounds on expectation values of system observables that have been time evolved under such discretised Hamiltonians. These bounds take on the form of a function of time and the number of discrete modes, where the discrete modes are chosen according to Gauss quadrature rules. The derivation makes use of tools from the field of Lieb-Robinson bounds and the theory of orthonormal polynomials.
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)
Bouferguene, Ahmed; Safouhi, Hassan
2006-01-01
In a previous work (Bouferguene 2005 J. Phys. A: Math. Gen. 38 3923), we have shown that in the framework of the Gaussian integral transform, multi-centre integrals over Slater type functions can be evaluated to an acceptable accuracy using a tailored Gauss quadrature in which the weight function has the form W(σ, τ z) = zνexp(-σz - τ/z). To be considered a solution worth implementing within a software for routine use in ab initio molecular simulations, the method must also prove to be at least as efficient as those methods previously published in the literature. Two major results are provided in this paper. Firstly, an improvement of the procedure used to generate the roots and weights of the Gauss-Bessel quadrature is proposed. Secondly, a computational cost analysis of the present method and the S\\bar{D} (Safouhi 2001 J. Phys. A: Math. Gen. 34 2801) based approach are compared, hence proving the equivalence of the two from a complexity point of view. In memory of Dr Mourad Ouraghi (1964-1992), Université des Sciences et Technologies Houari Boumedienne.
Gorbachev, D V; Ivanov, V I
2015-08-31
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.
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.
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
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.
Szego-Lobatto quadrature rules
NASA Astrophysics Data System (ADS)
Jagels, Carl; Reichel, Lothar
2007-03-01
Gauss-type quadrature rules with one or two prescribed nodes are well known and are commonly referred to as Gauss-Radau and Gauss-Lobatto quadrature rules, respectively. Efficient algorithms are available for their computation. Szego quadrature rules are analogs of Gauss quadrature rules for the integration of periodic functions; they integrate exactly trigonometric polynomials of as high degree as possible. Szego quadrature rules have a free parameter, which can be used to prescribe one node. This paper discusses an analog of Gauss-Lobatto rules, i.e., Szego quadrature rules with two prescribed nodes. We refer to these rules as Szego-Lobatto rules. Their properties as well as numerical methods for their computation are discussed.
NASA Astrophysics Data System (ADS)
Tsalamengas, John L.
2016-11-01
We present Gauss-Jacobi quadrature rules in terms of hypergeometric functions for the discretization of weakly singular, strongly singular, hypersingular, and nearly singular integrals that arise in integral equation formulations of potential problems for domains with sharp edges and corners. The rules are tailored to weight functions with algebraic endpoint singularities of a fairly general form, thus allowing one to easily incorporate a wide class of domains into the analysis. Numerical examples illustrate the accuracy and stability of the proposed algorithms; it is shown that the same level of high accuracy can be achieved for any choice of the external variable. The usefulness of the method is exemplified by application to the solution of a singular integral equation that arises in time-harmonic electromagnetic scattering by either closed or open perfectly conducting cylindrical objects with edges and corners, such as polygon cylinders and bent strips. Some practical aspects concerning the role of nearby singularities in achieving a highly accurate solution of singular integral equations are, also, discussed.
Crowther, Michael J; Look, Maxime P; Riley, Richard D
2014-09-28
Multilevel mixed effects survival models are used in the analysis of clustered survival data, such as repeated events, multicenter clinical trials, and individual participant data (IPD) meta-analyses, to investigate heterogeneity in baseline risk and covariate effects. In this paper, we extend parametric frailty models including the exponential, Weibull and Gompertz proportional hazards (PH) models and the log logistic, log normal, and generalized gamma accelerated failure time models to allow any number of normally distributed random effects. Furthermore, we extend the flexible parametric survival model of Royston and Parmar, modeled on the log-cumulative hazard scale using restricted cubic splines, to include random effects while also allowing for non-PH (time-dependent effects). Maximum likelihood is used to estimate the models utilizing adaptive or nonadaptive Gauss-Hermite quadrature. The methods are evaluated through simulation studies representing clinically plausible scenarios of a multicenter trial and IPD meta-analysis, showing good performance of the estimation method. The flexible parametric mixed effects model is illustrated using a dataset of patients with kidney disease and repeated times to infection and an IPD meta-analysis of prognostic factor studies in patients with breast cancer. User-friendly Stata software is provided to implement the methods. Copyright © 2014 John Wiley & Sons, Ltd.
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.
ERIC Educational Resources Information Center
Seong, Tae-Je
The similarity of item and ability parameter estimations was investigated using two numerical analysis techniques via marginal maximum likelihood estimation (MMLE) with a large simulated data set (n=1,000 examinees) and changing the number of quadrature points. MMLE estimation uses a numerical analysis technique to integrate examinees' abilities…
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
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.
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…
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…
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.
Angular quadratures for improved transport computations
Abu-Shumays, I.K.
1999-07-22
This paper introduces new octant-range, composite-type Gauss and mid-point rule angular quadrature formulas for neutron and photon transport computations. A generalization to octant-range quadratures is also introduced in order to allow for discontinuities at material interfaces for two- and three-dimensional transport problems which can be modeled with 60-degree triangular or hexagonal mesh subdivisions in the x-y plane.
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.
Quadrature effects on the accuracy of flux calculations in realistic atmospheres.
NASA Astrophysics Data System (ADS)
Box, M. A.; Trautmann, T.; Loughlin, P. E.
1993-12-01
The authors have investigated the accuracy of five different quadrature methods - equal steps in θ, equal steps in cos θ, Gaussian, double Gaussian and Gauss-Lobatto - on the accuracy of fluxes in realistic aerosol atmospheres, using the Gauss-Seidel method. In addition, a range of Gaussian quadrature stream numbers from two to 32 were compared. The atmospheric models considered are those recently presented by Lenoble, with the exception that the authors have used Henyey-Greenstein phase functions in place of Mie. The results should be easily reproduceable by any other workers interested in similar realistic atmospheres. A table of Gauss-Lobatto weights and points is provided as an appendix.
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…
Quadrature-Quadrature Phase Shift Keying.
1986-09-01
Q 2PSK for the data stream a (t) in Figure 3.1 ................................................ 27 3.3. Spectral densities of OQPSK , MSK and Q’PSK...Offset Quadrature Phase Shift Keying ( OQPSK ). Minimum Shift Keying ( vISK ), Quadrature Overlapped taised Cosine ( QOW signalling scheme, Tamed Frequency...orthogonal; hence the name %liniliur ’t Keving (AfSK) . The baseband power spectral densities S~.f) a1nd( o’,,, r QPSlK (or OQPSk . and NLSK are given by
NASA Astrophysics Data System (ADS)
McGraw, R.; Leng, L.; Zhu, W.; Riemer, N.; West, M.
2008-07-01
The method of moments (MOM) is a statistically based alternative to sectional and modal methods for aerosol simulation. The MOM is highly efficient as the aerosol distribution is represented by its lower-order moments and only these, not the full distribution itself, are tracked during simulation. Quadrature is introduced to close the moment equations under very general growth laws and to compute aerosol physical and optical properties directly from moments. In this paper the quadrature method of moments (QMOM) is used in a bivariate test tracking of aerosol mixing state. Two aerosol populations, one enriched in soot and the other in sulfate, are allowed to interact through coagulation to form a generally-mixed third particle population. Quadratures of varying complexity (including two candidate schemes for use in climate models) are described and compared with benchmark results obtained by using particle-resolved simulation. Low-order quadratures are found to be highly accurate, and Gauss and Gauss-Radau quadratures appear to give nested lower and upper bounds, respectively, to aerosol mixing rate. These results suggest that the QMOM makes it feasible to represent the generallymixed states of aerosols and track their evolution in climate models.
The Quadrature Master Equations
NASA Astrophysics Data System (ADS)
Hassan, N. J.; Pourdarvish, A.; Sadeghi, J.; Olaomi, J. O.
2017-04-01
In this paper, we derive the non-Markovian stochastic equation of motion (SEM) and master equations (MEs) for the open quantum system by using the non-Markovian stochastic Schrödinger equations (SSEs) for the quadrature unraveling in linear and nonlinear cases. The SSEs for quadrature unraveling arise as a special case of a quantum system. Also we derive the Markovian SEM and ME by using linear and nonlinear Itô SSEs for the measurement probabilities. In linear non-Markovian case, we calculate the convolutionless linear quadrature non-Markovian SEM and ME. We take advantage from example and show that corresponding theory.
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).
Digital Quadrature Modulation.
1978-01-05
imbalances between the two mixers is shown. Section 3 presents the digital quadrature modulation method and Section 4 presents two imple- mentations of the...Figure 1. Analog Quadrature Modulator. Ih output signal is given by: 4(t) 2 s1 (t) + s2 (t) N*ere 91 (t) = z(t)coswct a2 (t) - -y(t)sict (1) |r 3 Let...wawc)+Z(a+w,)+Z*(-w- )j ( 3 ) Similarly s2() -(l/4)[Z(a-w )-Z (-w~w )-Z(atwc)+Z (-w-wc)] (4) Thus the spectrum of the output it S(w) - S1 (W) + S2(w
Short note on the mass matrix for Gauss-Lobatto grid points
NASA Astrophysics Data System (ADS)
Teukolsky, Saul A.
2015-02-01
The mass matrix for Gauss-Lobatto grid points is usually approximated by Gauss-Lobatto quadrature because this leads to a diagonal matrix that is easy to invert. The exact mass matrix and its inverse are full. We show that the exact mass matrix and its inverse differ from the approximate diagonal ones by a simple rank-1 update (outer product). They can thus be applied to an arbitrary vector in O (N) operations instead of O (N2).
Discrete observability and numerical quadrature
NASA Technical Reports Server (NTRS)
Martin, Clyde F.; Wang, Xiaochang; Stamp, Mark
1991-01-01
The authors consider the problem of approximate observability of a one-dimensional diffusion equation on a finite spatial domain with spatial point measurements. The problem of the optimal selection of the measurement points is considered under three conditions: (1) no preassigned measurement nodes; (2) one preassigned node and; (3) two preassigned nodes. The main observation is that the optimal choice is related to three classical procedures in numerical analysis: (1) Gaussian quadrature; (2) Radau quadrature and; (3) Lobatto quadrature. It is shown that the existence of the Radau and Lobatto quadrature is closely related to classical root locus theory.
Discrete ordinate quadrature selection for reactor-based Eigenvalue problems
Jarrell, J. J.; Evans, T. M.; Davidson, G. G.
2013-07-01
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. (authors)
Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature
Brito, K. D.; Sprague, M. A.
2012-10-01
Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for a given model size or total computation time.
Digital quadrature phase detection
Smith, James A.; Johnson, John A.
1992-01-01
A system for detecting the phase of a frequency of phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2.pi. when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2.pi. when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention.
Digital quadrature phase detection
Smith, J.A.; Johnson, J.A.
1992-05-26
A system for detecting the phase of a frequency or phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2[pi] when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2[pi] when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention. 6 figs.
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
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.
Quadrature imposition of compatibility conditions in Chebyshev methods
NASA Technical Reports Server (NTRS)
Gottlieb, D.; Streett, C. L.
1990-01-01
Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.
Vector Helmholtz-Gauss and vector Laplace-Gauss beams.
Bandres, Miguel A; Gutiérrez-Vega, Julio C
2005-08-15
We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG beams are TE and TM Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel-Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz-Gauss beams. The general expression of the vHzG beams can be used straightforwardly to obtain vector Mathieu-Gauss and vector parabolic-Gauss beams, which to our knowledge have not yet been reported.
NASA Astrophysics Data System (ADS)
Di Fazio, Antonella; Vernucci, Antonio; Rossini, Eugenio
2003-07-01
GAUSS is a Research and Technological Development project co-funded by European Commission, within the frame of the IST (Information Society Technologies) V Programme. It is a two-year project, starting from December 2000, and successfully completed.The GAUSS Team involves a Consortium of nine European companies, including ARNI (Azienda Regionale per la Navigazione Interna, I), ASCOM (CH), ERICSSON Telecomunicazioni (I), GMV (E), TELEFONICA (E), THALES Navigation (F), TTI Norte (E), Space Engineering (I) and TELESPAZIO (I) as project co-ordinator.GAUSS objective was to design and demonstrate the feasibility of a system providing Location-based services, from the integration of Satellite Navigation and Communications, within the contexts of GALILEO and the UMTS technology. The GAUSS proposed solution supports highly reliable, near real-time two-way communication between Mobile Users and Service Centre/Provider. The services considered for GAUSS are based on exchange at low data rate transmission of small data packets carrying very accurate positioning & timing information, as typically required by Info-Mobility and Inter-Modality oriented applications. These services are characterised by bursty and unbalanced traffic, generated by a large number of Mobile Users towards a relatively small number of Service Providers, and viceversa from the Service Providers towards widely geographically sparse Mobile Users (i.e. greater amount of traffic in the return link with respect to the forward link). The GAUSS system supports both asynchronous and synchronous communication, based on: ß broad-casting (i.e. data distribution from a Service Provider to Mobile Users)ß broad-catching (i.e. data collection from MUs to a SP)ß point-to-point schemes.Resource access is based on CDMA (Code Division Multiple Access), according to the UMTS standard. A Demonstrator was built up by combining existing facilities with innovative hardware and software components, ad-hoc developed by some of
Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology.
Krishnamoorthi, Shankarjee; Sarkar, Mainak; Klug, William S
2013-11-01
We study the numerical accuracy and computational efficiency of alternative formulations of the finite element solution procedure for the monodomain equations of cardiac electrophysiology, focusing on the interaction of spatial quadrature implementations with operator splitting and 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 electrophysiological 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 nonuniform meshes having a large distribution of element sizes.
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
Refinements of some new efficient quadrature rules
NASA Astrophysics Data System (ADS)
Qayyum, A.; Shoaib, M.; Faye, I.; Kashif, A. R.
2016-11-01
In the field of Engineering and Applied Mathematical Sciences, minimizing approximation error is very important task and therefore quadrature rules are investigated regularly. In this paper, using some standard results of theoretical inequalities, e.g. Ostrowski type inequality, some new efficient quadrature rules are introduced for n-times differentiable mappings. These quadrature rules are expected to give better results comparing to the conventional quadrature rules.
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.
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.
Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes
NASA Astrophysics Data System (ADS)
Pasquetti, Richard; Rapetti, Francesca
2017-10-01
In a recent JCP paper [9], a higher order triangular spectral element method (TSEM) is proposed to address seismic wave field modeling. The main interest of this TSEM is that the mass matrix is diagonal, so that an explicit time marching becomes very cheap. This property results from the fact that, similarly to the usual SEM (say QSEM), the basis functions are Lagrange polynomials based on a set of points that shows both nice interpolation and quadrature properties. In the quadrangle, i.e. for the QSEM, the set of points is simply obtained by tensorial product of Gauss-Lobatto-Legendre (GLL) points. In the triangle, finding such an appropriate set of points is however not trivial. Thus, the work of [9] follows anterior works that started in 2000's [2,6,11] and now provides cubature nodes and weights up to N = 9, where N is the total degree of the polynomial approximation. Here we wish to evaluate the accuracy of this cubature nodes TSEM with respect to the Fekete-Gauss one, see e.g.[12], that makes use of two sets of points, namely the Fekete points and the Gauss points of the triangle for interpolation and quadrature, respectively. Because the Fekete-Gauss TSEM is in the spirit of any nodal hp-finite element methods, one may expect that the conclusions of this Note will remain relevant if using other sets of carefully defined interpolation points.
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.
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.
Differential quadrature solution of nonlinear Klein-Gordon and sine-Gordon equations
NASA Astrophysics Data System (ADS)
Pekmen, B.; Tezer-Sezgin, M.
2012-08-01
Differential quadrature method (DQM) is proposed to solve the one-dimensional quadratic and cubic Klein-Gordon equations, and two-dimensional sine-Gordon equation. We apply DQM in space direction and also blockwise in time direction. Initial and derivative boundary conditions are also approximated by DQM. DQM provides one to obtain numerical results with very good accuracy using considerably small number of grid points. Numerical solutions are obtained by using Gauss-Chebyshev-Lobatto (GCL) grid points in space intervals, and GCL grid points in each equally divided time blocks.
Automatic quadrature control and measuring system
NASA Technical Reports Server (NTRS)
Hamlet, J. F.
1973-01-01
Quadrature is separated from amplified signal by use of phase detector, with phase shifter providing appropriate reference. Output of phase detector is further amplified and filtered by dc amplifier. Output of dc amplifier provides signal to neutralize quadrature component of transducer signal.
IC quadrature filters for analog multipliers
NASA Astrophysics Data System (ADS)
Tarasov, V. P.; Timonteev, V. N.
1980-08-01
The paper considers the design of symmetric and asymmetric quadrature filters. Formulas are presented for transfer functions, nonlinear distortions, q-factor, and dynamic range for different filter connections in the direct-transmission channels. The integrated design of a highpass quadrature filter is considered.
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…
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…
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.
Doster, Timothy; Watnik, Abbie T
2016-12-20
As a means of increasing the channel capacity in free-space optical communication systems, two types of orbital angular momentum carrying beams, Bessel-Gauss and Laguerre-Gauss, are studied. In a series of numerical simulations, we show that Bessel-Gauss beams, pseudo-nondiffracting beams, outperform Laguerre-Gauss beams of various orders in channel efficiency and bit error rates.
Application of linear gauss pseudospectral method in model predictive control
NASA Astrophysics Data System (ADS)
Yang, Liang; Zhou, Hao; Chen, Wanchun
2014-03-01
This paper presents a model predictive control(MPC) method aimed at solving the nonlinear optimal control problem with hard terminal constraints and quadratic performance index. The method combines the philosophies of the nonlinear approximation model predictive control, linear quadrature optimal control and Gauss Pseudospectral method. The current control is obtained by successively solving linear algebraic equations transferred from the original problem via linearization and the Gauss Pseudospectral method. It is not only of high computational efficiency since it does not need to solve nonlinear programming problem, but also of high accuracy though there are a few discrete points. Therefore, this method is suitable for on-board applications. A design of terminal impact with a specified direction is carried out to evaluate the performance of this method. Augmented PN guidance law in the three-dimensional coordinate system is applied to produce the initial guess. And various cases for target with straight-line movements are employed to demonstrate the applicability in different impact angles. Moreover, performance of the proposed method is also assessed by comparison with other guidance laws. Simulation results indicate that this method is not only of high computational efficiency and accuracy, but also applicable in the framework of guidance design.
Gaussian Quadrature Formulae for Arbitrary Positive Measures
Fernandes, Andrew D.; Atchley, William R.
2007-01-01
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
NASA Astrophysics Data System (ADS)
Chen, Tianheng; Shu, Chi-Wang
2017-09-01
It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang and Shu (1994) [39]) and symmetric hyperbolic systems (Hou and Liu (2007) [36]), in any space dimension and for any triangulations. However, this property holds only for the square entropy and the integrations in the DG methods must be exact. It is significantly more difficult to design DG methods to satisfy entropy inequalities for a non-square convex entropy, and/or when the integration is approximated by a numerical quadrature. In this paper, we develop a unified framework for designing high order DG methods which will satisfy entropy inequalities for any given single convex entropy, through suitable numerical quadrature which is specific to this given entropy. Our framework applies from one-dimensional scalar cases all the way to multi-dimensional systems of conservation laws. For the one-dimensional case, our numerical quadrature is based on the methodology established in Carpenter et al. (2014) [5] and Gassner (2013) [19]. The main ingredients are summation-by-parts (SBP) operators derived from Legendre Gauss-Lobatto quadrature, the entropy conservative flux within elements, and the entropy stable flux at element interfaces. We then generalize the scheme to two-dimensional triangular meshes by constructing SBP operators on triangles based on a special quadrature rule. A local discontinuous Galerkin (LDG) type treatment is also incorporated to achieve the generalization to convection-diffusion equations. Extensive numerical experiments are performed to validate the accuracy and shock capturing efficacy of these entropy stable DG methods.
Spherical-earth Gravity and Magnetic Anomaly Modeling by Gauss-legendre Quadrature Integration
NASA Technical Reports Server (NTRS)
Vonfrese, R. R. B.; Hinze, W. J.; Braile, L. W.; Luca, A. J. (Principal Investigator)
1981-01-01
The anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical Earth for an arbitrary body represented by an equivalent point source distribution of gravity poles or magnetic dipoles were calculated. The distribution of equivalent point sources was determined directly from the coordinate limits of the source volume. Variable integration limits for an arbitrarily shaped body are derived from interpolation of points which approximate the body's surface envelope. The versatility of the method is enhanced by the ability to treat physical property variations within the source volume and to consider variable magnetic fields over the source and observation surface. A number of examples verify and illustrate the capabilities of the technique, including preliminary modeling of potential field signatures for Mississippi embayment crustal structure at satellite elevations.
Shang, J.S.; Andrienko, D.A.; Huang, P.G.; Surzhikov, S.T.
2014-06-01
An efficient computational capability for nonequilibrium radiation simulation via the ray tracing technique has been accomplished. The radiative rate equation is iteratively coupled with the aerodynamic conservation laws including nonequilibrium chemical and chemical–physical kinetic models. The spectral properties along tracing rays are determined by a space partition algorithm of the nearest neighbor search process, and the numerical accuracy is further enhanced by a local resolution refinement using the Gauss–Lobatto polynomial. The interdisciplinary governing equations are solved by an implicit delta formulation through the diminishing residual approach. The axisymmetric radiating flow fields over the reentry RAM-CII probe have been simulated and verified with flight data and previous solutions by traditional methods. A computational efficiency gain nearly forty times is realized over that of the existing simulation procedures.
Gaussian quadrature for multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Coussement, Jonathan; van Assche, Walter
2005-06-01
We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.
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.
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.
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.
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.
Theory of the quadrature elliptic birdcage coil.
Leifer, M C
1997-11-01
This paper presents the theory of the quadrature birdcage coil wound on an elliptic cylindrical former. A conformal transformation of the ellipse to a circular geometry is used to derive the optimal sampling of the continuous surface current distribution to produce uniform magnetic fields within an elliptic cylinder. The analysis is rigorous for ellipses of any aspect ratio and shows how to produce quadrature operation of the elliptic birdcage with a conventional hybrid combiner. Insight gained from the transformation is also used to analyze field homogeneity, find the optimal RF shield shape, and specify component values to produce the correct current distribution in practice. Measurements and images from a 16-leg elliptic birdcage coil at both low and high frequencies show good quadrature performance, homogeneity, and sensitivity.
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.
Gauss Sum Factorization with Cold Atoms
Gilowski, M.; Wendrich, T.; Mueller, T.; Ertmer, W.; Rasel, E. M.; Jentsch, Ch.; Schleich, W. P.
2008-01-25
We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193.
Comparison of two Galerkin quadrature methods
Morel, Jim E.; Warsa, James; Franke, Brian C.; ...
2017-02-21
Here, we compare two methods for generating Galerkin quadratures. In method 1, the standard SN method is used to generate the moment-to-discrete matrix and the discrete-to-moment matrix is generated by inverting the moment-to-discrete matrix. This is a particular form of the original Galerkin quadrature method. In method 2, which we introduce here, the standard SN method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. With an N-point quadrature, method 1 has the advantage that it preserves N eigenvalues and N eigenvectors of the scattering operator in a pointwise sense. Withmore » an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding SN equations while preserving N eigenvalues of the scattering operator. Our computational results indicate that these two methods are quite comparable for the test problem considered.« less
Thin-thick quadrature frequency conversion
Eimerl, D.
1985-02-07
The quadrature conversion scheme is a method of generating the second harmonic. The scheme, which uses two crystals in series, has several advantages over single-crystal or other two crystal schemes. The most important is that it is capable of high conversion efficiency over a large dynamic range of drive intensity and detuning angle.
Cosmic backreaction and Gauss's law
NASA Astrophysics Data System (ADS)
Fleury, Pierre
2017-06-01
Cosmic backreaction refers to the general question of whether a homogeneous and isotropic cosmological model is able to predict the correct expansion dynamics of our inhomogeneous Universe. One aspect of this issue concerns the validity of the continuous approximation: does a system of point masses expand the same way as a fluid does? This article shows that it is not exactly the case in Newtonian gravity, although the associated corrections vanish in an infinite Universe. It turns out that Gauss's law is a key ingredient for such corrections to vanish. Backreaction, therefore, generically arises in alternative theories of gravitation, which threatens the trustworthiness of their cosmological tests. This phenomenon is illustrated with a toy model of massive gravity.
Asymmetric Bessel-Gauss beams.
Kotlyar, V V; Kovalev, A A; Skidanov, R V; Soifer, V A
2014-09-01
We propose a three-parameter family of asymmetric Bessel-Gauss (aBG) beams with integer and fractional orbital angular momentum (OAM). The aBG beams are described by the product of a Gaussian function by the nth-order Bessel function of the first kind of complex argument, having finite energy. The aBG beam's asymmetry degree depends on a real parameter c≥0: at c=0, the aBG beam is coincident with a conventional radially symmetric Bessel-Gauss (BG) beam; with increasing c, the aBG beam acquires a semicrescent shape, then becoming elongated along the y axis and shifting along the x axis for c≫1. In the initial plane, the intensity distribution of the aBG beams has a countable number of isolated optical nulls on the x axis, which result in optical vortices with unit topological charge and opposite signs on the different sides of the origin. As the aBG beam propagates, the vortex centers undergo a nonuniform rotation with the entire beam about the optical axis (c≫1), making a π/4 turn at the Rayleigh range and another π/4 turn after traveling the remaining distance. At different values of the c parameter, the optical nulls of the transverse intensity distribution change their position, thus changing the OAM that the beam carries. An isolated optical null on the optical axis generates an optical vortex with topological charge n. A vortex laser beam shaped as a rotating semicrescent has been generated using a spatial light modulator.
NASA Astrophysics Data System (ADS)
Mittal, R. C.; Jiwari, Ram
2011-01-01
In this paper, a rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical study of a two-dimensional reaction-diffusion Brusselator system. In the Brusselator system the reaction terms arise from the mathematical modeling of chemical systems such as in enzymatic reactions, and in plasma and laser physics in multiple coupling between modes. By employing DQM, accurate results can be obtained using fewer grid points in spatial domain for a large value of T = 50. We also found that Chebyshev-Gauss-Lobatto grid points give excellent results in comparison to other grid points such as uniform grid points. Three examples are solved to illustrate the accuracy and efficiency of the DQM. Convergence and stability of the method is also examined.
Effective quadrature formula in solving linear integro-differential equations of order two
NASA Astrophysics Data System (ADS)
Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.
2017-08-01
In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.
Automatic quadrature control and measuring system. [using optical coupling circuitry
NASA Technical Reports Server (NTRS)
Hamlet, J. F. (Inventor)
1974-01-01
A quadrature component cancellation and measuring system comprising a detection system for detecting the quadrature component from a primary signal, including reference circuitry to define the phase of the quadrature component for detection is described. A Raysistor optical coupling control device connects an output from the detection system to a circuit driven by a signal based upon the primary signal. Combining circuitry connects the primary signal and the circuit controlled by the Raysistor device to subtract quadrature components. A known current through the optically sensitive element produces a signal defining the magnitude of the quadrature component.
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.
Complex source point theory of paraxial and nonparaxial cosine-Gauss and Bessel-Gauss beams.
Sheppard, Colin J R
2013-02-15
It shown how cosine-Gauss and Bessel-Gauss beams can be generated using the complex source point theory. Paraxial beams are treated first. An analytic expression is derived for the nonparaxial cosine-Gaussian beam, based on the complex source point approach, and numerical results are presented to illustrate its behavior. A way to generate nonparaxial Bessel-Gauss beams is also indicated.
Twelfth degree spline with application to quadrature.
Mohammed, P O; Hamasalh, F K
2016-01-01
In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order [Formula: see text] that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applicability and efficiency of the new method.
Numerical quadratures for approximate computation of ERBS
NASA Astrophysics Data System (ADS)
Zanaty, Peter
2013-12-01
In the ground-laying paper [3] on expo-rational B-splines (ERBS), the default numerical method for approximate computation of the integral with C∞-smooth integrand in the definition of ERBS is Romberg integration. In the present work, a variety of alternative numerical quadrature methods for computation of ERBS and other integrals with smooth integrands are studied, and their performance is compared on several benchmark examples.
NMR Experiment Factors Numbers with Gauss Sums
NASA Astrophysics Data System (ADS)
Mehring, Michael; Müller, Klaus; Averbukh, Ilya Sh.; Merkel, Wolfgang; Schleich, Wolfgang P.
2007-03-01
We factor the number 157573 using an NMR implementation of Gauss sums. Although the current implementation is classical and scales exponentially, we believe that an extension to the quantum regime using entangled states is possible.
Comparison of two Galerkin quadrature methods
Morel, J. E.; Warsa, J. S.; Franke, B. C.; Prinja, A. K.
2013-07-01
We compare two methods for generating Galerkin quadrature for problems with highly forward-peaked scattering. In Method 1, the standard Sn method is used to generate the moment-to-discrete matrix and the discrete-to-moment is generated by inverting the moment-to-discrete matrix. In Method 2, which we introduce here, the standard Sn method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. Method 1 has the advantage that it preserves both N eigenvalues and N eigenvectors (in a pointwise sense) of the scattering operator with an N-point quadrature. Method 2 has the advantage that it generates consistent angular moment equations from the corresponding S{sub N} equations while preserving N eigenvalues of the scattering operator with an N-point quadrature. Our computational results indicate that these two methods are quite comparable for the test problem considered. (authors)
Gauss-Lobatto to Bernstein polynomials transformation
NASA Astrophysics Data System (ADS)
Coluccio, Loredana; Eisinberg, Alfredo; Fedele, Giuseppe
2008-12-01
The aim of this paper is to transform a polynomial expressed as a weighted sum of discrete orthogonal polynomials on Gauss-Lobatto nodes into Bernstein form and vice versa. Explicit formulas and recursion expressions are derived. Moreover, an efficient algorithm for the transformation from Gauss-Lobatto to Bernstein is proposed. Finally, in order to show the robustness of the proposed algorithm, experimental results are reported.
The Offner imaging spectrometer in quadrature.
Prieto-Blanco, Xesús; Montero-Orille, Carlos; González-Nuñez, Héctor; Mouriz, María Dolores; Lago, Elena López; de la Fuente, Raúl
2010-06-07
This is a proposal and description of a new configuration for an Offner imaging spectrometer based on the theory of aberrations of off-plane classical-ruled spherical diffraction gratings. This new spectrometer comprises a concave mirror used in double reflection and a convex reflection grating operating in quadrature, in a concentric layout. A very simple procedure obtains designs that are anastigmatic for a given point on the entrance slit and a given wavelength. Specific examples show that the performance of this type of system improves the performance of analogous conventional in-plane systems, when compactness and/or high spectral resolution is of fundamental importance.
NASA Astrophysics Data System (ADS)
Avila, Gustavo; Carrington, Tucker
2011-08-01
In this paper we propose and test a method for computing numerically exact vibrational energy levels of a molecule with six atoms. We use a pruned product basis, a non-product quadrature, the Lanczos algorithm, and the exact normal-coordinate kinetic energy operator (KEO) with the πtμπ term. The Lanczos algorithm is applied to a Hamiltonian with a KEO for which μ is evaluated at equilibrium. Eigenvalues and eigenvectors obtained from this calculation are used as a basis to obtain the final energy levels. The quadrature scheme is designed, so that integrals for the most important terms in the potential will be exact. The procedure is tested on C2H4. All 12 coordinates are treated explicitly. We need only ˜1.52 × 108 quadrature points. A product Gauss grid with which one could calculate the same energy levels has at least 5.67 × 1013 points.
NASA Astrophysics Data System (ADS)
Gharehbaghi, Amin
2016-10-01
In this paper, a numerical solution of one-dimensional time-dependent advection-diffusion equation with variable coefficients in semi-infinite domain is presented by using the differential quadrature method. Both the explicit and implicit approaches are provided. Totally, two solute dispersion problems are employed to simulate various conditions. The inhomogeneity of the domain is supplied by the spatially dependent flow. The problem domains are modeled with Chebyshev-Gauss-Lobatto grid points. In order to examine the accuracy and the efficiency of the suggested explicit and implicit approaches, analytical solutions, which are presented in the literature, are employed. In addition, the results of the above-mentioned method are compared with outcomes of the finite difference method. The results show that both of the explicit and implicit forms of the differential quadrature method are efficient, robust and reliable. But between these two forms, numerical predictions of implicit form are more accurate than explicit form.
Anisotropic inflation in Gauss-Bonnet gravity
Lahiri, Sayantani
2016-09-19
We study anisotropic inflation with Gauss-Bonnet correction in presence of a massless vector field. In this scenario, exact anisotropic power-law inflation is realized when the inflaton potential, gauge coupling function and the Gauss-Bonnet coupling are exponential functions. We show that anisotropy becomes proportional to two slow-roll parameters of the theory and hence gets enhanced in presence of quadratic curvature corrections. The stability analysis reveals that anisotropic power-law solutions remain stable over a substantially large parameter region.
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.
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.
Nonextensive entropies derived from Gauss' principle
NASA Astrophysics Data System (ADS)
Wada, Tatsuaki
2011-05-01
Gauss' principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles.
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…
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…
Demystifying Electric Flux and Gauss's Law
ERIC Educational Resources Information Center
McManus, Jeff
2017-01-01
Many physics students have experienced the difficulty of internalizing concepts in electrostatics. After studying concrete, measurable details in mechanics, they are challenged by abstract ideas such as electric fields, flux, Gauss's law, and electric potential. There are a few well-known hands-on activities that help students get experience with…
Integrated source of broadband quadrature squeezed light.
Hoff, Ulrich B; Nielsen, Bo M; Andersen, Ulrik L
2015-05-04
An integrated silicon nitride resonator is proposed as an ultra-compact source of bright single-mode quadrature squeezed light at 850 nm. Optical properties of the device are investigated and tailored through numerical simulations, with particular attention paid to loss associated with interfacing the device. An asymmetric double layer stack waveguide geometry with inverse vertical tapers is proposed for efficient and robust fibre-chip coupling, yielding a simulated total loss of -0.75 dB/facet. We assess the feasibility of the device through a full quantum noise analysis and derive the output squeezing spectrum for intra-cavity pump self-phase modulation. Subject to standard material loss and detection efficiencies, we find that the device holds promises for generating substantial quantum noise squeezing over a bandwidth exceeding 1 GHz. In the low-propagation loss regime, approximately -6 dB squeezing is predicted for a pump power of only 75 mW.
Low-frequency quadrature mode birdcage resonator.
Borsboom, H M; Claasen-Vujcić, T; Gaykema, H J; Mehlkopf, T
1997-03-01
The birdcage resonator is frequently used in conventional MRI because of its excellent attributes. Its use in low-field MRI is restricted to field strengths higher than, for example, 0.1 T, dependent on the size of the coil. This is because of the intrinsically low inductance value of the birdcage coils. Furthermore, the sensitivity of the birdcage at low field strengths is significantly lower when compared to, for example, the solenoid. Both problems can be overcome with the multiturn technique and a novel wound birdcage coil. The quadrature mode wound birdcage coil presented in this paper can be used at frequencies as low as 100 kHz. Its sensitivity is also increased when compared to the conventional strip-ring birdcage. Homogeneity, effective volume, and methods to increase the resonator bandwidth to match the signal bandwidth are left intact. The latter is a typical low-field problem.
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.
The Goos-Hanchen shift in Helmholtz-Gauss beams
NASA Astrophysics Data System (ADS)
Jezzini, Moises A.; Gutierrez-Vega, Julio C.
2006-08-01
We present a study of the total internal reflection of a Helmholtz-Gauss beam at a plane interface between two dielectric media. The derivation is based on the decomposition of the Helmholtz-Gauss beams in terms of its constituent plane waves components. We determine the shift predicted by the classical theory of the Goos- Hänchen shift and analyze the transverse intensity patterns of the reflected waves for a variety of Helmholtz-Gauss beam including Bessel-Gauss and Cosine-Gauss beams.
A Comparison of three high-precision quadrature schemes
Bailey, David H.; Li, Xiaoye S.
2003-07-01
The authors have implemented three numerical quadrature schemes, using the new Arbitrary Precision (ARPREC) software package, with the objective of seeking a completely ''automatic'' arbitrary precision quadrature facility, namely one that does not rely on a priori information of the function to be integrated. Such a facility is required, for example, to permit the experimental identification of definite integrals based on their numerical values. The performance and accuracy of these three quadrature schemes are compared using a suite of 15 integrals, ranging from continuous, well-behaved functions on finite intervals to functions with vertical derivatives and integrable singularities at endpoints, as well as several integrals on an infinite interval.
Two-step-only quadrature phase-shifting digital holography.
Liu, Jung-Ping; Poon, Ting-Chung
2009-02-01
Conventional methods of quadrature phase-shifting holography require two holograms and either intensity distribution of the reference wave or that of the object wave to reconstruct an original object without the zero order and the twin-image noise in an on-axis holographic recording setup. We present a technique called two-step-only quadrature phase-shifting holography in which solely two quadrature-phase holograms are required. Neither reference-wave intensity nor an object-wave intensity measurement is needed in the technique.
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.
Demystifying electric flux and Gauss's law
NASA Astrophysics Data System (ADS)
McManus, Jeff
2017-04-01
Many physics students have experienced the difficulty of internalizing concepts in electrostatics. After studying concrete, measurable details in mechanics, they are challenged by abstract ideas such as electric fields, flux, Gauss's law, and electric potential. There are a few well-known hands-on activities that help students get experience with these ideas. Perhaps the most popular are field-mapping activities in many forms ranging from metal electrodes in a shallow dish of water to metal pens and conductive paper. My experience of teaching with these activities in my AP Physics course left me disappointed and my students still mystified. Over the last several years, I have developed some hands-on activities that have helped my students better understand and apply these concepts. In this column, I will describe one such activity, a flux calculation that presents an opportunity to apply Gauss's law.
Phase anomalies in Bessel-Gauss beams.
Kim, Myun-Sik; Scharf, Toralf; Assafrao, Alberto da Costa; Rockstuhl, Carsten; Pereira, Silvania F; Urbach, H Paul; Herzig, Hans Peter
2012-12-17
Bessel-Gauss beams are known as non-diffracting beams. They can be obtained by focusing an annularly shaped collimated laser beam. Here, we report for the first time on the direct measurement of the phase evolution of such beams by relying on longitudinal-differential interferometry. We found that the characteristics of Bessel-Gauss beams cause a continuously increasing phase anomaly in the spatial domain where such beams do not diverge, i.e. there is a larger phase advance of the beam when compared to a referential plane wave. Simulations are in excellent agreement with measurements. We also provide an analytical treatment of the problem that matches both experimental and numerical results and provides an intuitive explanation.
Vorticity, Stokes' Theorem and the Gauss's Theorem
NASA Astrophysics Data System (ADS)
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
Holographic isotropisation in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Casalderrey-Solana, Jorge; Ficnar, Andrej
2017-02-01
We study holographic isotropisation of homogeneous, strongly coupled, non-Abelian plasmas in Gauss-Bonnet gravity with a negative cosmological constant. We focus on small values of the Gauss-Bonnet coupling parameter λ GB and linearise the equations of motion around a time-dependent background solution with λ GB = 0. We numerically solve the linearised equations and show that the entire time evolution of the pressure anisotropy can be well approximated by the linear in λ GB corrections to the quasinormal mode expansion, even in the cases of high anisotropy. We finally show that, quite generally, the time evolution of the pressure anisotropy with the Gauss-Bonnet term is approximately shifted with respect to the evolution without it, with the sign of the shift being directly related to the sign of the λ GB parameter. Combined with the observation that negative λ GB captures qualitative features of positive gauge coupling corrections, this suggests that the latter generically increase the isotropisation time of strongly coupled plasmas.
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.
Conditional homodyne detection of light with squeezed quadrature fluctuations
Vines, Justin; Vyas, Reeta; Singh, Surendra
2006-08-15
We discuss the detection of field quadrature fluctuations in conditional homodyne detection experiments and possible sources of error in such an experiment. We also present modifications to these experiments to help eliminate such errors and extend their range of applicability.
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
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.
Radial Basis Function Based Quadrature over Smooth Surfaces
2016-03-24
weights for a particular node set. This thesis expands upon the same spherical quadrature method and applies it to an arbitrary smooth closed surface...recent technique 1 for spherical quadrature is expanded upon in Chapter II and adapted for use in approximating integrals of arbitrary smooth closed...logN) operations and O(N) memory usage. When expanding the computation of weights beyond one core, parallel scalability with number of cores was also
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.
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.
A note on Gauss-Bonnet black holes at criticality
NASA Astrophysics Data System (ADS)
Bhamidipati, Chandrasekhar; Yerra, Pavan Kumar
2017-09-01
Within the extended thermodynamics, we give a comparative study of critical heat engines for Gauss-Bonnet and charged black holes in AdS in five dimensions, in the limit of large Gauss-Bonnet parameter α and charge q, respectively. We show that the approach of efficiency of heat engines to Carnot limit in Gauss-Bonnet black holes is higher(lower) than charged black holes when corresponding parameters are small(large).
Graviton emission from a Gauss-Bonnet brane
Konya, Kenichiro
2007-05-15
We study the emission of gravitons by a homogeneous brane with the Gauss-Bonnet term into an anti-de Sitter five dimensional bulk spacetime. It is found that the graviton emission depends on the curvature scale and the Gauss-Bonnnet coupling and that the amount of emission generally decreases. Therefore nucleosynthesis constraints are easier to satisfy by including the Gauss-Bonnet term.
Normalization of optical Weber waves and Weber-Gauss beams.
Rodríguez-Lara, B M
2010-02-01
The normalization of energy divergent Weber waves and finite energy Weber-Gauss beams is reported. The well-known Bessel and Mathieu waves are used to derive the integral relations between circular, elliptic, and parabolic waves and to present the Bessel and Mathieu wave decomposition of the Weber waves. The efficiency to approximate a Weber-Gauss beam as a finite superposition of Bessel-Gauss beams is also given.
Experimental generation of Bessel-Gauss coherence functions
NASA Astrophysics Data System (ADS)
Reddy, Salla Gangi; Singh, R. P.; Miyamoto, Yoko
2017-04-01
We experimentally generate the Bessel-Gauss coherence functions using the cross-correlations between the two speckle patterns obtained using the perfect optical vortices (POV) of different orders. POV beams are generated using the Fourier transform of Bessel-Gauss beams by displaying the axicon hologram on spatial light modulator. A ground glass plate is used for scattering POV beams and the speckles are recorded. The cross-correlation function of two speckle patterns is Bessel-Gauss functions whose order is given by the difference in the orders of two POV beams used for scattering. The auto-correlation function of these speckles is Bessel-Gauss function of order zero.
Fractional Fourier transform of Lorentz-Gauss beams.
Zhou, Guoquan
2009-02-01
Lorentz-Gauss beams are introduced to describe certain laser sources that produce highly divergent beams. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz-Gauss beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz-Gauss beam passing through an FRFT system has been derived. By using the derived expression, the properties of a Lorentz-Gauss beam in the FRFT plane are graphically illustrated with numerical examples.
Gauss-Bonnet Supergravity in Six Dimensions
NASA Astrophysics Data System (ADS)
Novak, Joseph; Ozkan, Mehmet; Pang, Yi; Tartaglino-Mazzucchelli, Gabriele
2017-09-01
The supersymmetrization of curvature squared terms is important in the study of the low-energy limit of compactified superstrings where a distinguished role is played by the Gauss-Bonnet combination, which is ghost-free. In this Letter, we construct its off-shell N =(1 ,0 ) supersymmetrization in six dimensions for the first time. By studying this invariant together with the supersymmetric Einstein-Hilbert term, we confirm and extend known results of the α'-corrected string theory compactified to six dimensions. Finally, we analyze the spectrum about the AdS3×S3 solution.
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.
Surface terms and the Gauss Bonnet Hamiltonian
NASA Astrophysics Data System (ADS)
Padilla, Antonio
2003-07-01
We derive the gravitational Hamiltonian starting from the Gauss Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the Hamiltonian give a remarkably simple expression for the total energy of a spacetime. This expression is consistent with energy expressions found in Preprint hep-th/0212292. However, we can apply our results whatever the choice of background and whatever the symmetries of the spacetime.
Effective potentials in nonlinear polycrystals and quadrature formulae.
Michel, Jean-Claude; Suquet, Pierre
2017-08-01
This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.
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.
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.
Fast algorithms for Quadrature by Expansion I: Globally valid expansions
NASA Astrophysics Data System (ADS)
Rachh, Manas; Klöckner, Andreas; O'Neil, Michael
2017-09-01
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast algorithms for solving the resulting dense linear systems. Classically, these tools were developed separately. In this work, we present a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. The method allows the evaluation of layer potentials in linear-time complexity, anywhere in space, with a uniform, user-chosen level of accuracy as a black-box computational method. Providing this capability requires geometric and algorithmic considerations beyond the needs of standard FMMs as well as careful consideration of the accuracy of multipole translations. We illustrate the speed and accuracy of our method with various numerical examples.
Kinetic Plasma Simulation Using a Quadrature-based Moment Method
NASA Astrophysics Data System (ADS)
Larson, David J.
2008-11-01
The recently developed quadrature-based moment method [Desjardins, Fox, and Villedieu, J. Comp. Phys. 227 (2008)] is an interesting alternative to standard Lagrangian particle simulations. The two-node quadrature formulation allows multiple flow velocities within a cell, thus correctly representing crossing particle trajectories and lower-order velocity moments without resorting to Lagrangian methods. Instead of following many particles per cell, the Eulerian transport equations are solved for selected moments of the kinetic equation. The moments are then inverted to obtain a discrete representation of the velocity distribution function. Potential advantages include reduced computational cost, elimination of statistical noise, and a simpler treatment of collisional effects. We present results obtained using the quadrature-based moment method applied to the Vlasov equation in simple one-dimensional electrostatic plasma simulations. In addition we explore the use of the moment inversion process in modeling collisional processes within the Complex Particle Kinetics framework.
Scalar modified Bessel-Gauss beams and waves.
Seshadri, S R
2007-09-01
For modified Bessel-Gauss beams, the modulating function for the Gaussian, instead of a Bessel function of real argument, is a Bessel function of imaginary argument. The modified Bessel-Gauss beams and their full wave generalizations are treated with particular attention to the spreading properties on propagation for the azimuthal mode numbers m=0 and m=1. The spreading on propagation of the peak and the null in the radiation pattern obtained in the propagation direction for m=0 and m=1, respectively, is substantially less for the modified Bessel-Gauss waves than that for the corresponding Bessel-Gauss waves. The total power transported by the waves is determined and compared with that of the corresponding paraxial beam to assess the quality of the paraxial beam approximation for the wave. The powers in the Bessel-Gauss wave and the modified Bessel-Gauss wave are finite in contrast to that in the Bessel wave. With respect to both the spreading properties and the quality of the paraxial beam approximation, the modified Bessel-Gauss beam is an improvement over the Bessel-Gauss beam.
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.
Parallel multigrid smoothing: polynomial versus Gauss-Seidel
NASA Astrophysics Data System (ADS)
Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray
2003-07-01
Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.
Holographic p-wave superconductors from Gauss-Bonnet gravity
Cai Ronggen; Nie Zhangyu; Zhang Haiqing
2010-09-15
We study the holographic p-wave superconductors in a five-dimensional Gauss-Bonnet gravity with an SU(2) Yang-Mills gauge field. In the probe approximation, we find that when the Gauss-Bonnet coefficient grows, the condensation of the vector field becomes harder, both the perpendicular and parallel components, with respect to the direction of the condensation, of the anisotropic conductivity decrease. We also study the mass of the quasiparticle excitations, the gap frequency and the DC conductivities of the p-wave superconductor. All of them depend on the Gauss-Bonnet coefficient. In addition, we observe a strange behavior for the condensation and the relation between the gap frequency and the mass of quasiparticles when the Gauss-Bonnet coefficient is larger than 9/100, which is the upper bound for the Gauss-Bonnet coefficient from the causality of the dual field theory.
Bell's inequality for systems with quadrature phase coherence
NASA Astrophysics Data System (ADS)
Tan, S. M.; Holland, M. J.; Walls, D. F.
1990-07-01
We show that a violation of Bell's inequalities by quadrature phase measurements is not due to the interference of the two photons in a photon pair state. Rather the violation predicted by Grangier et al. for a parametric down-converter is due to the interference of the photon pair state with the vacuum. We propose new sources which violate the quadrature phase Bell's inequalities, including one which employs squeezed light and another which demonstrates the non-local properties of a single photon state.
Digital holography with a quadrature phase-shifting interferometer.
Kiire, Tomohiro; Nakadate, Suezou; Shibuya, Masato
2009-03-01
An alternative method for digital holography using a quadrature phase-shifting interferometer for high-speed measurement is presented. We show that it has image quality equal to the four-bucket method. In addition, it requires fewer imaging devices. Two quadrature phase-shifting fringe patterns are acquired in each state of an object changed temporally. The phase calculation method with these four fringe patterns gives the phase distribution of the hologram. This digital phase hologram is reconstructed to yield an object image by the Fresnel transform using digital convolutions with the fast Fourier transform algorithm. Verification results of simulations and experiments are given.
Vibration analysis of structural elements using differential quadrature method
Nassar, Mohamed; Matbuly, Mohamed S.; Ragb, Ola
2012-01-01
The method of differential quadrature is employed to analyze the free vibration of a cracked cantilever beam resting on elastic foundation. The beam is made of a functionally graded material and rests on a Winkler–Pasternak foundation. The crack action is simulated by a line spring model. Also, the differential quadrature method with a geometric mapping are applied to study the free vibration of irregular plates. The obtained results agreed with the previous studies in the literature. Further, a parametric study is introduced to investigate the effects of geometric and elastic characteristics of the problem on the natural frequencies. PMID:25685406
Offset quadrature communications with decision-feedback carrier synchronization
NASA Technical Reports Server (NTRS)
Simon, M. K.; Smith, J. G.
1974-01-01
In order to accommodate a quadrature amplitude-shift-keyed (QASK) signal, Simon and Smith (1974) have modified the decision-feedback loop which tracks a quadrature phase-shift-keyed (QPSK). In the investigation reported approaches are considered to modify the loops in such a way that offset QASK signals can be tracked, giving attention to the special case of an offset QPSK. The development of the stochastic integro-differential equation of operation for a decision-feedback offset QASK loop is discussed along with the probability density function of the phase error process.
Offset quadrature communications with decision-feedback carrier synchronization
NASA Technical Reports Server (NTRS)
Simon, M. K.; Smith, J. G.
1974-01-01
In order to accommodate a quadrature amplitude-shift-keyed (QASK) signal, Simon and Smith (1974) have modified the decision-feedback loop which tracks a quadrature phase-shift-keyed (QPSK). In the investigation reported approaches are considered to modify the loops in such a way that offset QASK signals can be tracked, giving attention to the special case of an offset QPSK. The development of the stochastic integro-differential equation of operation for a decision-feedback offset QASK loop is discussed along with the probability density function of the phase error process.
A non-uniform grid for triangular differential quadrature
NASA Astrophysics Data System (ADS)
Zhong, HongZhi; Xu, Jia
2016-12-01
The triangular differential quadrature method based on a non-uniform grid is proposed in the paper. Explicit expressions of the non-uniform grid point coordinates are given and the weighting coefficients of the triangular differential quadrature method are determined with the aid of area coordinates. Two typical examples are presented to testify the effectiveness of the non-uniform grid. It is shown that rapid convergence is achieved under the non-uniform grid in comparison with those from the uniform grid with the same order of approximation.
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.
Optimization Experiments With A Double Gauss Lens
NASA Astrophysics Data System (ADS)
Brixner, Berlyn; Klein, Morris M.
1988-05-01
This paper describes how a lens can be generated by starting from plane surfaces. Three different experiments, using the Los Alamos National Laboratory optimization procedure, all converged on the same stable prescriptions in the optimum minimum region. The starts were made first from an already optimized lens appearing in the literature, then from a powerless plane-surfaces configuration, and finally from a crude Super Angulon configuration. In each case the result was a double Gauss lens, which suggests that this type of lens may be the best compact six-glass solution for one imaging problem: an f/2 aperture and a moderate field of view. The procedures and results are discussed in detail.
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.
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…
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…
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…
Imaging with classical spherical diffraction gratings: the quadrature configuration.
Prieto-Blanco, Xesús; Montero-Orille, Carlos; González-Núñez, Héctor; Dolores Mouriz, María; López Lago, Elena; de la Fuente, Raúl
2009-11-01
We review the theory of spherical diffraction gratings with regard to their imaging properties in off-plane arrangements. Our study is restricted to gratings with equally spaced grooves, and it is focused on the quadrature configuration, where the incident and diffraction planes are orthogonal to each other. We identify regions of low astigmatism and propose some monochromator mounts.
The Gauss-Seidel Numerical Procedure for Markov Stochastic Games
2004-01-01
assumptions on the nondegeneracy of the diffusion in [6]. To date, there have not been proofs of the convergence of the Gauss- Seidel method for...Taking the sup inf in (2.3) is equivalent to solving a ma- trix game. Except for this sup inf, it is just the standard Gauss- Seidel method for iteratively...control and games for finite-state Markov chain models via value it- eration, the Gauss- Seidel method is faster than the Ja- cobi procedure. The proof of
Factorizing numbers with the Gauss sum technique: NMR implementations
Mahesh, T. S.; Rajendran, Nageswaran; Peng Xinhua; Suter, Dieter
2007-06-15
Several physics-based algorithms for factorizing large numbers were recently presented. A notable recent algorthm by Schleich et al. uses Gauss sums for distinguishing between factors and nonfactors. We demonstrate two NMR techniques that evaluate Gauss sums and thus implement their algorithm. The first one is based on differential excitation of a single spin magnetization by a cascade of rf pulses. The second method is based on spatial averaging and selective refocusing of magnetization for Gauss sums corresponding to factors. All factors of 16 637 and 52 882 363 are successfully obtained.0.
NASA Technical Reports Server (NTRS)
Simon, M. K.
1981-01-01
This paper considers the performance of quadrature partial response (QPR) in the presence of jamming. Although a QPR system employs a single sample detector in its receiver, while quadrature amplitude shift keying (or quadrature phase shift keying) requires a matched-filter type of receiver, it is shown that the coherent detection performances of the two in the presence of the intentional jammer have definite similarities.
NASA Technical Reports Server (NTRS)
Simon, M. K.
1981-01-01
This paper considers the performance of quadrature partial response (QPR) in the presence of jamming. Although a QPR system employs a single sample detector in its receiver, while quadrature amplitude shift keying (or quadrature phase shift keying) requires a matched-filter type of receiver, it is shown that the coherent detection performances of the two in the presence of the intentional jammer have definite similarities.
A Study of Gauss-Seidel-Type Methods for Simulating Large-Scale Circuits.
1984-01-01
standard Gauss-Seidel and of a modified Gauss- Seidel method with prediction are compared; and a new modified Gauss- Seidel method is proposed which...the timing analysis of MOS circuits. Keywords include: Integrated Circuits; Time-domain simulation of MOS LSI circuits; and Gauss- Seidel Method .
Slow-roll inflation with a Gauss-Bonnet correction
Guo Zongkuan; Schwarz, Dominik J.
2010-06-15
We consider slow-roll inflation for a single scalar field with an arbitrary potential and an arbitrary nonminimal coupling to the Gauss-Bonnet term. By introducing a combined hierarchy of Hubble and Gauss-Bonnet flow functions, we analytically derive the power spectra of scalar and tensor perturbations. The standard consistency relation between the tensor-to-scalar ratio and the spectral index of tensor perturbations is broken. We apply this formalism to a specific model with a monomial potential and an inverse monomial Gauss-Bonnet coupling and constrain it by the 7-year Wilkinson Microwave Anisotropy Probe data. The Gauss-Bonnet term with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio and hence may revive the quartic potential ruled out by recent cosmological data.
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}.
Domain walls in Einstein-Gauss-Bonnet bulk
Mazharimousavi, S. Habib; Halilsoy, M.
2010-10-15
We investigate the dynamics of a n-dimensional domain wall in a n+1-dimensional Einstein-Gauss-Bonnet bulk. Exact effective potential induced by the Gauss-Bonnet (GB) term on the wall is derived. In the absence of the GB term we recover the familiar gravitational and antiharmonic oscillator potentials. Inclusion of the GB correction gives rise to a minimum radius of bounce for the Friedmann-Robertson-Walker universe expanding with a negative pressure on the domain wall.
The Gauss Rifle and Magnetic Energy
NASA Astrophysics Data System (ADS)
Rabchuk, James A.
2003-03-01
With the advent of cheap and easy-to-come-by NdFeB magnets, it has become possible to design a number of simple but effective demonstrations of magnetic force. One such demonstration, dubbed the "gauss rifle," is a type of linear magnetic accelerator. It is relatively easy to assemble and involves a rapid and dramatic increase in kinetic energy of the steel ball bearings used in the demonstration. This makes the demonstration a good attention getter, setting the stage for a discussion of a number of physics topics, including conservation of energy, magnetic energy, and magnetic force. It also has the potential for becoming a laboratory experiment since the materials are relatively cheap, there is some challenge in the arrangement of the magnets, and the performance of the accelerator can be characterized by measuring the initial and final velocities of the bearings. Finally, by using freely available finite element magnetics software, it is even possible to make predictions of the final velocity for different configurations of the magnets.
Stable generation of quadrature entanglement using a ring interferometer
Eto, Yujiro; Nonaka, Akihiro; Hirano, Takuya; Zhang Yun
2009-05-15
We propose and demonstrate a scheme to stably generate quadrature-entangled optical pulses using a ring interferometer composed of an optical parametric amplifier and a dispersive media. The entangled light pulses at telecommunication wavelength are generated by combining two squeezed beams. In our scheme, the relative phase between the two beams is kept stable by the ring interferometer and is controllable using dispersive media. The amplitude and phase quadratures of the entangled beams are measured using two time-domain pulsed homodyne detectors. When the relative phase is fixed at {pi}/2, we verify the inseparability of the states by a sufficient criterion <{delta}{sup 2}[X{sub a}({phi}{sub 0})+X{sub b}({pi}-{phi}{sub 0})]>+<{delta}{sup 2}[X{sub a}({phi}{sub 0}{sup '})-X{sub b}(-{phi}{sub 0}{sup '})]>=0.64<1 where {phi}{sub 0}{sup '}-{phi}{sub 0}={pi}/2.
Quadrature-based lattice Boltzmann model for relativistic flows
NASA Astrophysics Data System (ADS)
Blaga, Robert; Ambruş, Victor E.
2017-01-01
A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.
Amplitude-weighted quadrature phase shift keying using SAW technology
NASA Astrophysics Data System (ADS)
Belkerdid, M. A.; Malocha, D. C.
1985-09-01
Surface acoustic wave (SAW) convolvers are capable of performing programmable matched filtering with the desirable properties of large processing gain, good dynamic range, broad bandwidth, small size and weight, and low power requirements. Equally powerful are the SAW-based modulators, which produce the desired pseudo-random code sequence for secure transmission in a spread-spectrum system. The SAW filter provides precise reproducible pulse shaping of the coded waveform with the same advantages of the convolver. It is very important as spectrum space becomes more crowded to optimize the spectral efficiency of transmitted information. Quadrature phase (QPSK) and minimum phase shift keying (MSK) are the two more popular quadrature modulation schemes. A new modulation technique that is composed of several amplitude-weighted QPSK signals (AWQPSK) and exhibits better bandwidth efficiency than OPSK or MSK is introduced. System analysis and performance parameters are presented for evaluation. A SAW modulator implementation is discussed and proposed.
IQ quadrature demodulation algorithm used in heterodyne detection
NASA Astrophysics Data System (ADS)
Wang, Chunhui; Qu, Yang; Tang, Yajun Pang Tiantian
2015-09-01
In order to obtain better detection results of heterodyne, we used phase IQ quadrature demodulation algorithm to process the data which detected by laser heterodyne. Based on laser heterodyne interferometer, processing the data in the interferometer phase IQ quadrature demodulation algorithm from the signal to noise ratio, sampling rate, sampling rate, filter order and cutoff frequency, verify the effects of these system parameters to the phase precision, and choose the best parameters to obtain a better phase precision through experiment as: the signal to noise ratio is 25 dB, the IF signal frequency is 98.3 MHz, 98.5 MHz, 99.1 MHz, 99.5 MHz and 100 MHz, the sampling rate is 512-2048, the cutoff frequency and order of the filter are 0.11 and 40, respectively.
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.
Solar Wind Characteristics from SOHO-Sun-Ulysses Quadrature Observations
NASA Technical Reports Server (NTRS)
Poletto, Giannina; Suess, Steve T.; Six, N. Frank (Technical Monitor)
2002-01-01
Over the past few years, we have been running SOHO (Solar and Heliospheric Observatory)-Sun-Ulysses quadrature campaigns, aimed at comparing the plasma properties at coronal altitudes with plasma properties at interplanetary distances. Coronal plasma has been observed by SOHO experiments: mainly, we used LASCO (Large Angle and Spectrometric Coronagraph Experiment) data to understand the overall coronal configuration at the time of quadratures and analyzed SUMER (Solar Ultraviolet Measurements of Emitted Radiation), CDS (Coronal Diagnostic Spectrometer) and UVCS (Ultraviolet Coronagraph Spectrometer) data to derive its physical characteristics. At interplanetary distances, SWICS (Solar Wind Ion Composition Spectrometer) and SWOOPS (Solar Wind Observation over the Poles of the Sun) aboard Ulysses provided us with interplanetary plasma data. Here we report on results from some of the campaigns. We notice that, depending on the geometry of the quadrature, i.e. on whether the radial to Ulysses traverses the corona at high or low latitudes, we are able to study different kinds of solar wind. In particular, a comparison between low-latitude and high-latitude wind, allowed us to provide evidence for differences in the acceleration of polar, fast plasma and equatorial, slow plasma: the latter occurring at higher levels and through a more extended region than fast wind. These properties are shared by both the proton and heavy ions outflows. Quadrature observations may provide useful information also on coronal vs. in situ elemental composition. To this end, we analyzed spectra taken in the corona, at altitudes ranging between approx. 1.02 and 2.2 solar radii, and derived the abundances of a number of ions, including oxygen and iron. Values of the O/Fe ratio, at coronal levels, have been compared with measurements of this ratio made by SWICS at interplanetary distances. Our results are compared with previous findings and predictions from modeling efforts.
An Application of the Quadrature-Free Discontinuous Galerkin Method
NASA Technical Reports Server (NTRS)
Lockard, David P.; Atkins, Harold L.
2000-01-01
The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.
Thin-plate spline quadrature of geodetic integrals
NASA Technical Reports Server (NTRS)
Vangysen, Herman
1989-01-01
Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.
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.
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.
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.
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.
Quadrature two-dimensional correlation spectroscopy (Q-2DCOS)
NASA Astrophysics Data System (ADS)
Noda, Isao
2016-11-01
Quadrature 2D correlation spectroscopy (Q-2DCOS) is introduced. The technique incorporates the effect of the perturbation into the traditional 2DCOS analysis by building a multivariate model, merging the information of the perturbation variable and spectral responses. By employing factors which are 90° out of phase with each other, pertinent coincidental and sequential spectral intensity variations are adequately captured for the subsequent 2D correlation analysis. Almost complete replication of the original 2DCOS results based on such a simple rank 2 model of experimental spectra suggests that only the dominant spectral intensity variation patterns in combination with its quadrature counterpart seems to be utilized in 2DCOS analysis. Using the linear perturbation variable itself as the basis for generating the primary score vector is equivalent to the least squares fitting of a quadratic polynomial with spectral intensity variations. Q-2DCOS analysis may be displayed in terms of a graphical plot on a phase plane in the vector space, so that coincidental and sequential matching of the patterns of spectral intensity variations is represented simply by the phase angle difference between two vectors. Q-2DCOS analysis is closely related to other established ideas and practices in the 2D correlation spectroscopy field, such as dynamic 2D IR dichroism, PCA 2D, quadrature orthogonal signal correction (Q-OSC), and perturbation correlation moving window (PCMW) analyses.
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).
Entanglement of Ince-Gauss Modes of Photons
NASA Astrophysics Data System (ADS)
Krenn, Mario; Fickler, Robert; Plick, William; Lapkiewicz, Radek; Ramelow, Sven; Zeilinger, Anton
2012-02-01
Ince-Gauss modes are solutions of the paraxial wave equation in elliptical coordinates [1]. They are natural generalizations both of Laguerre-Gauss and of Hermite-Gauss modes, which have been used extensively in quantum optics and quantum information processing over the last decade [2]. Ince-Gauss modes are described by one additional real parameter -- ellipticity. For each value of ellipticity, a discrete infinite-dimensional Hilbert space exists. This conceptually new degree of freedom could open up exciting possibilities for higher-dimensional quantum optical experiments. We present the first entanglement of non-trivial Ince-Gauss Modes. In our setup, we take advantage of a spontaneous parametric down-conversion process in a non-linear crystal to create entangled photon pairs. Spatial light modulators (SLMs) are used as analyzers. [1] Miguel A. Bandres and Julio C. Guti'errez-Vega ``Ince Gaussian beams", Optics Letters, Vol. 29, Issue 2, 144-146 (2004) [2] Adetunmise C. Dada, Jonathan Leach, Gerald S. Buller, Miles J. Padgett, and Erika Andersson, ``Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities", Nature Physics 7, 677-680 (2011)
Two-frame algorithm to design quadrature filters in phase shifting interferometry.
Mosiño, J F; Gutiérrez-García, J C; Gutiérrez-García, T A; Macías-Preza, J M
2010-11-22
The main purpose of this paper is to present a method to design tunable quadrature filters in phase shifting interferometry. From a general tunable two-frame algorithm introduced, a set of individual filters corresponding to each quadrature conditions of the filter is obtained. Then, through a convolution algorithm of this set of filters the desired symmetric quadrature filter is recovered. Finally, the method is applied to obtain several tunable filters, like four and five-frame algorithms.
Gauss-Bonnet chameleon mechanism of dark energy
Ito, Yusaku; Nojiri, Shin'ichi
2009-05-15
As a model of the current accelerated expansion of the Universe, we consider a model of the scalar-Einstein-Gauss-Bonnet gravity. This model includes the propagating scalar modes, which might give a large correction to the Newton law. In order to avoid this problem, we propose an extension of the chameleon mechanism where the scalar mode becomes massive due to the coupling with the Gauss-Bonnet term. Since the Gauss-Bonnet invariant does not vanish near the Earth or in the Solar System, even in the vacuum, the scalar mode is massive even in the vacuum and the correction to the Newton law could be small. We also discuss the possibility that the model could describe simultaneously the inflation in the early Universe, in addition to the current accelerated expansion.
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.
Gravitational perfect fluid collapse in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Abbas, G.; Tahir, M.
2017-08-01
The Einstein Gauss-Bonnet theory of gravity is the low-energy limit of heterotic super-symmetric string theory. This paper deals with gravitational collapse of a perfect fluid in Einstein-Gauss-Bonnet gravity by considering the Lemaitre-Tolman-Bondi metric. For this purpose, the closed form of the exact solution of the equations of motion has been determined by using the conservation of the stress-energy tensor and the condition of marginally bound shells. It has been investigated that the presence of a Gauss-Bonnet coupling term α >0 and the pressure of the fluid modifies the structure and time formation of singularity. In this analysis a singularity forms earlier than a horizon, so the end state of the collapse is a naked singularity depending on the initial data. But this singularity is weak and timelike, which goes against the investigation of general relativity.
Magnetic brane solutions in Gauss-Bonnet-Maxwell massive gravity
NASA Astrophysics Data System (ADS)
Hendi, Seyed Hossein; Eslam Panah, Behzad; Panahiyan, Shahram; Momennia, Mehrab
2017-09-01
Magnetic branes of Gauss-Bonnet-Maxwell theory in the context of massive gravity is studied in detail. Exact solutions are obtained and their interesting geometrical properties are investigated. It is argued that although these horizonless solutions are free of curvature singularity, they enjoy a cone-like geometry with a conic singularity. In order to investigate the effects of various parameters on the geometry of conic singularity, its corresponding deficit angle is studied. It will be shown that despite the effects of Gauss-Bonnet gravity on the solutions, deficit angle is free of Gauss-Bonnet parameter. On the other hand, the effects of massive gravity, cosmological constant and electrical charge on the deficit angle will be explored. Also, a brief discussion related to possible geometrical phase transition of these topological objects is given.
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
Real-time single analog output for quadrature phase interferometry
NASA Astrophysics Data System (ADS)
Barraud, C.; Garcia, L.; Cross, B.; Charlaix, E.
2017-04-01
We present a dynamic displacement sensor based on a quadrature phase interferometer, providing a real-time analog output of the differential displacement between two mobile surfaces. The sensor offers a sub-picometer resolution with a sensitivity essentially uniform over a distance range extending to several micrometers, and can be used to measure the amplitude and phase of very small oscillations in nano-mechanical testing. We demonstrate its use in nano-rheology, by studying the flow in nanometric liquid films at very small strain rates.
Principles and improvements of quadrature-based QKD
NASA Astrophysics Data System (ADS)
Hu, Wenhao; Shu, Di; Wang, Daqing; Liu, Yu
2010-11-01
An overview of quadrature-based quantum key distribution is provided. Beginning from the comparison between single-photon schema and continuous variable schema, the article focuses on the classical and state-of-art protocols. Protocols' main procedures and security analysis are introduced, which includes the methods under individual attack and collective attack. Then recent development of unconditional security proof is introduced including the optimality of Gaussian attack and de Finetti theorem. Introduction towards discrete modulated schemas' security proof is also made. At last, the article discusses experimental realization of various protocols and the main trend in this field.
Photoacoustic tomography using a Michelson interferometer with quadrature phase detection
NASA Astrophysics Data System (ADS)
Speirs, Rory W.; Bishop, Alexis I.
2013-07-01
We present a pressure sensor based on a Michelson interferometer, for use in photoacoustic tomography. Quadrature phase detection is employed allowing measurement at any point on the mirror surface without having to retune the interferometer, as is typically required by Fabry-Perot type detectors. This opens the door to rapid full surface detection, which is necessary for clinical applications. Theory relating acoustic pressure to detected acoustic particle displacements is used to calculate the detector sensitivity, which is validated with measurement. Proof-of-concept tomographic images of blood vessel phantoms have been taken with sub-millimeter resolution at depths of several millimeters.
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.
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.
Quadrature phase interferometer used to calibrate dial indicator calibrators
NASA Astrophysics Data System (ADS)
Huang, Shau-Chi; Liou, Huay-Chung; Peng, Gwo-Sheng; Lu, Ming-Feng
2001-10-01
To calibrate dial indicators, gage blocks or dial indicator calibrators are usually used. For better accuracy and resolution, interferometers are used to calibrate dial indicator calibrators. Systematic errors of laser interferometers can be classified into three categories of intrinsic errors, environment errors and installation errors. Intrinsic errors include laser wavelength error, electronic error and optics nonlinearity. In order to achieve nanometer accuracy, minimizing intrinsic error is crucial. In this paper, we will address the problems of minimizing the optics nonlinearity error and describe the discrete-time signal processing method to minimize the electronic error, nonlinearity error and drift by simply using quadrature phase interferometer for nanometer accuracy and linearity.
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.
Xiong, Xiao-Gen; Yanai, Takeshi
2017-07-11
The Projector Augmented Wave (PAW) method developed by Blöchl is well recognized as an efficient, accurate pseudopotential approach in solid-state density functional theory (DFT) calculations with the plane-wave basis. Here we present an approach to incorporate the PAW method into the Gauss-type function (GTF) based DFT implementation, which is widely used for molecular quantum chemistry calculations. The nodal and high-exponent GTF components of valence molecular orbitals (MOs) are removed or pseudized by the ultrasoft PAW treatment, while there is elaborate transparency to construct an accurate and well-controlled pseudopotential from all-electron atomic description and to reconstruct an all-electron form of valence MOs from the pseudo MOs. The smoothness of the pseudo MOs should benefit the efficiency of GTF-based DFT calculations in terms of elimination of high-exponent primitive GTFs and reduction of grid points in the numerical quadrature. The processes of the PAW method are divided into basis-independent and -dependent parts. The former is carried out using the previously developed PAW libraries libpaw and atompaw. The present scheme is implemented by incorporating libpaw into the conventional GTF-based DFT solver. The details of the formulations and implementations of GTF-related PAW procedures are presented. The test calculations are shown for illustrating the performance. With the near-complete GTF basis at the cc-pVQZ level, the total energies obtained using our PAW method with suited frozen core treatments converge to those with the conventional all-electron GTF-based method with a rather small absolute error.
Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory.
Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen
2011-04-15
We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.
Fast convolution quadrature for the wave equation in three dimensions
NASA Astrophysics Data System (ADS)
Banjai, L.; Kachanovska, M.
2014-12-01
This work addresses the numerical solution of time-domain boundary integral equations arising from acoustic and electromagnetic scattering in three dimensions. The semidiscretization of the time-domain boundary integral equations by Runge-Kutta convolution quadrature leads to a lower triangular Toeplitz system of size N. This system can be solved recursively in an almost linear time (O(Nlog2N)), but requires the construction of O(N) dense spatial discretizations of the single layer boundary operator for the Helmholtz equation. This work introduces an improvement of this algorithm that allows to solve the scattering problem in an almost linear time. The new approach is based on two main ingredients: the near-field reuse and the application of data-sparse techniques. Exponential decay of Runge-Kutta convolution weights wnh(d) outside of a neighborhood of d≈nh (where h is a time step) allows to avoid constructing the near-field (i.e. singular and near-singular integrals) for most of the discretizations of the single layer boundary operators (near-field reuse). The far-field of these matrices is compressed with the help of data-sparse techniques, namely, H-matrices and the high-frequency fast multipole method. Numerical experiments indicate the efficiency of the proposed approach compared to the conventional Runge-Kutta convolution quadrature algorithm.
Wormholes in dilatonic Einstein-Gauss-Bonnet theory.
Kanti, Panagiota; Kleihaus, Burkhard; Kunz, Jutta
2011-12-30
We construct traversable wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions, without needing any form of exotic matter. We determine their domain of existence, and show that these wormholes satisfy a generalized Smarr relation. We demonstrate linear stability with respect to radial perturbations for a subset of these wormholes.
Bounce universe from string-inspired Gauss-Bonnet gravity
Bamba, Kazuharu; Makarenko, Andrey N.; Myagky, Alexandr N.; Odintsov, Sergei D. E-mail: andre@tspu.edu.ru E-mail: odintsov@ieec.uab.es
2015-04-01
We explore cosmology with a bounce in Gauss-Bonnet gravity where the Gauss-Bonnet invariant couples to a dynamical scalar field. In particular, the potential and and Gauss-Bonnet coupling function of the scalar field are reconstructed so that the cosmological bounce can be realized in the case that the scale factor has hyperbolic and exponential forms. Furthermore, we examine the relation between the bounce in the string (Jordan) and Einstein frames by using the conformal transformation between these conformal frames. It is shown that in general, the property of the bounce point in the string frame changes after the frame is moved to the Einstein frame. Moreover, it is found that at the point in the Einstein frame corresponding to the point of the cosmological bounce in the string frame, the second derivative of the scale factor has an extreme value. In addition, it is demonstrated that at the time of the cosmological bounce in the Einstein frame, there is the Gauss-Bonnet coupling function of the scalar field, although it does not exist in the string frame.
Gauss-Legendre Sky Pixelization (glesp) for CMB Maps
NASA Astrophysics Data System (ADS)
Doroshkevich, A. G.; Naselsky, P. D.; Verkhodanov, O. V.; Novikov, D. I.; Turchaninov, V. I.; Novikov, I. D.; Christensen, P. R.; Chiang, L.-Y.
A new scheme of sky pixelization is developed for CMB maps. The scheme is based on the Gauss-Legendre polynomials zeros and allows one to create strict orthogonal expansion of the map. A corresponding code has been implemented and comparison with other methods has been done.
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.
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…
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…
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…
Efficient Modified Filon-Type Quadrature for Highly Oscillatory Bessel Transformations
NASA Astrophysics Data System (ADS)
Xiang, S.
2008-10-01
In this paper, we consider efficient modified Filon-type method for the integration of systems containing Bessel function and gives error analysis for these quadratures. Preliminary numerical results show the effectiveness and accuracy of the quadrature for large arguments of integral systems.
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).
D'Onofrio, Giuseppe; Pirozzi, Enrica
2017-05-01
We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.
Holographic superconductors with various condensates in Einstein-Gauss-Bonnet gravity
Pan Qiyuan; Wang Bin; Papantonopoulos, Eleftherios; Oliveira, Jeferson de; Pavan, A. B.
2010-05-15
We study holographic superconductors in Einstein-Gauss-Bonnet gravity. We consider two particular backgrounds: a d-dimensional Gauss-Bonnet-AdS black hole and a Gauss-Bonnet-AdS soliton. We discuss in detail the effects that the mass of the scalar field, the Gauss-Bonnet coupling and the dimensionality of the AdS space have on the condensation formation and conductivity. We also study the ratio {omega}{sub g}/T{sub c} for various masses of the scalar field and Gauss-Bonnet couplings.
2006-09-01
7 A. QUADRATURE MIRROR FILTER BANK AS PART OF AN LPI ELINT DETECTION SYSTEM ...implementation for a real-time Quadrature Mirror Filter Bank on an SRC-6 reconfigurable computer system . A Quadrature Mirror Filter (QMF) Bank is a type...of wavelet decomposition filter system used for Digital Signal Processing (DSP). The use of a Quadrature Mirror Filter Bank as part of a larger
NASA Astrophysics Data System (ADS)
Agachev, J. R.; Galimyanov, A. F.
2016-11-01
In this paper the method of mechanical quadrature solutions fractional integral equation. Computational scheme quadrature method is based on the quadrature formula of rectangles with equidistant nodes, which is the formula of the highest trigonometric degree of accuracy, using a regularizing parameter. This decision is taken for the approximate trigonometric interpolation polynomial constructed from the values that make up the solution of the quadrature method. The substantiation of the method in Holder spaces.
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.
Convolution quadrature for the wave equation with impedance boundary conditions
NASA Astrophysics Data System (ADS)
Sauter, S. A.; Schanz, M.
2017-04-01
We consider the numerical solution of the wave equation with impedance boundary conditions and start from a boundary integral formulation for its discretization. We develop the generalized convolution quadrature (gCQ) to solve the arising acoustic retarded potential integral equation for this impedance problem. For the special case of scattering from a spherical object, we derive representations of analytic solutions which allow to investigate the effect of the impedance coefficient on the acoustic pressure analytically. We have performed systematic numerical experiments to study the convergence rates as well as the sensitivity of the acoustic pressure from the impedance coefficients. Finally, we apply this method to simulate the acoustic pressure in a building with a fairly complicated geometry and to study the influence of the impedance coefficient also in this situation.
Analysis and applications of quadrature hybrids as RF circulators
Hanna, S.M.; Keane, J.
1993-12-31
The operation of a quadrature hybrid as a power combiner is analyzed. The analytical results are compared with data measured experimentally using a 211 MHz cavity. Graphical solution of the measured cases are in good agreement with analytical predictions. The use of the 90{degree}-hybrid as an RF circulator is also analyzed. The active operation of the harmonic cavity in the NSLS VUV-ring is used to demonstrate this application. This fourth-harmonic cavity is used to change the shape of the bucket potential to lengthen a stored bunch. Thus, a longer stored-beam lifetime can be achieved without compromising the high brightness of the VUV photon beam. If operated actively, the harmonic cavity would present a mismatched load to an RF generator. Thus, a need exists for a circulator. Similarities in operation between the 90{degree}-hybrid and a circulator are discussed.
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.
Experimental generation of broadband quadrature entanglement using laser pulses
Zhang, Yun; Furuta, Tatsuya; Okubo, Ryuhi; Takahashi, Kosuke; Hirano, Takuya
2007-07-15
We report on the generation of broadband pulsed quadrature entanglement by combining two squeezed vacua, which are generated from two degenerate optical parametric amplifiers (OPAs), on a beam splitter. With a single pass through OPA, in which a periodically poled lithium niobate waveguide is used as a nonlinear material, the noise reduction of 3.4{+-}0.2 dB below the shot noise limit is observed with a bandwidth of more than 200 MHz. The entanglement correlation or EPR correlation is confirmed with a sufficient criterion <{delta}{sup 2}(X{sub a}+X{sub b})>+<{delta}{sup 2}(Y{sub a}-Y{sub b})>=1.28<2.
Induced polarization of volcanic rocks - 1. Surface versus quadrature conductivity
NASA Astrophysics Data System (ADS)
Revil, A.; Le Breton, M.; Niu, Q.; Wallin, E.; Haskins, E.; Thomas, D. M.
2017-02-01
We performed complex conductivity measurements on 28 core samples from the hole drilled for the Humu'ula Groundwater Research Project (Hawai'i Island, HI, USA). The complex conductivity measurements were performed at 4 different pore water conductivities (0.07, 0.5, 1.0 or 2.0, and 10 S m-1 prepared with NaCl) over the frequency range 1 mHz to 45 kHz at 22 ± 1 °C. The in-phase conductivity data are plotted against the pore water conductivity to determine, sample by sample, the intrinsic formation factor and the surface conductivity. The intrinsic formation factor is related to porosity by Archie's law with an average value of the cementation exponent m of 2.45, indicating that only a small fraction of the connected pore space controls the transport properties. Both the surface and quadrature conductivities are found to be linearly related to the cation exchange capacity of the material, which was measured with the cobalt hexamine chloride method. Surface and quadrature conductivities are found to be proportional to each other like for sedimentary siliclastic rocks. A Stern layer polarization model is used to explain these experimental results. Despite the fact that the samples contain some magnetite (up to 5 per cent wt.), we were not able to identify the effect of this mineral on the complex conductivity spectra. These results are very encouraging in showing that galvanometric induced polarization measurements can be used in volcanic areas to separate the bulk from the surface conductivity and therefore to define some alteration attributes. Such a goal cannot be achieved with resistivity alone.
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.
Induced polarization of volcanic rocks. 1Surface versus quadrature conductivity
NASA Astrophysics Data System (ADS)
Revil, A.; Breton, M. Le; Niu, Q.; Wallin, E.; Haskins, E.; Thomas, D. M.
2016-11-01
We performed complex conductivity measurements on 28 core samples from the hole drilled for the Humu´ula Groundwater Research Project (Hawai´i Island, HI, USA). The complex conductivity measurements were performed at 4 different pore water conductivities (0.07, 0.5, 1.0 or 2.0, and 10 S m-1 prepared with NaCl) over the frequency range 1 mHz to 45 kHz at 22 ± 1°C. The in-phase conductivity data are plotted against the pore water conductivity to determine, sample by sample, the intrinsic formation factor and the surface conductivity. The intrinsic formation factor is related to porosity by Archie's law with an average value of the cementation exponent m of 2.45, indicating that only a small fraction of the connected pore space controls the transport properties. Both the surface and quadrature conductivities are found to be linearly related to the cation exchange capacity of the material, which was measured with the cobalt hexamine chloride method. Surface and quadrature conductivities are found to be proportional to each other like for sedimentary siliclastic rocks. A Stern layer polarization model is used to explain these experimental results. Despite the fact that the samples contain some magnetite (up to 5% wt.), we were not able to identify the effect of this mineral on the complex conductivity spectra. These results are very encouraging in showing that galvanometric induced polarization measurements can be used in volcanic areas to separate the bulk from the surface conductivity and therefore to define some alteration attributes. Such a goal cannot be achieved with resistivity alone.
Quasinormal modes of Einstein-Gauss-Bonnet-dilaton black holes
NASA Astrophysics Data System (ADS)
Blázquez-Salcedo, Jose Luis; Khoo, Fech Scen; Kunz, Jutta
2017-09-01
We study quasinormal modes of static Einstein-Gauss-Bonnet-dilaton black holes. Both axial and polar perturbations are considered and studied from l =0 to l =3 . We emphasize the difference in the spectrum between the Schwarzschild solutions and dilatonic black holes. At large Gauss-Bonnet coupling constant, a small secondary branch of black holes is present, when the dilaton coupling is sufficiently strong. The modes of the primary branch can differ from the Schwarzschild modes up to 10%. The secondary branch is unstable and possesses long-lived modes. We address the possible effects of these modes on future observations of gravitational waves emitted during the ringdown phase of astrophysical black holes.
Bouncing loop quantum cosmology in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Haro, J.; Makarenko, A. N.; Myagky, A. N.; Odintsov, S. D.; Oikonomou, V. K.
2015-12-01
We develop an effective Gauss-Bonnet extension of loop quantum cosmology, by introducing holonomy corrections in modified F (G ) theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of loop quantum gravity theories, and we result in having leading order corrections to the classical F (G ) theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes it possible to find the loop quantum cosmology corrected F (G ) theory that can realize various cosmological scenarios. We exemplify our theoretical constructions by using bouncing cosmologies, and we investigate which loop quantum cosmology corrected Gauss-Bonnet modified gravities can successfully realize such cosmologies.
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.
Debye screening versus Gauss law in electrostatics: Finite size effects
NASA Astrophysics Data System (ADS)
Dubey, Ritesh Kumar; Menon, V. J.; Mishra, M.; Tripathi, D. N.
2007-10-01
We revisit the well-known topics of self- and induced-screening in an otherwise isotropic neutral plasma/colloid. It is pointed out that the standard Debye-Hückel (DH) theory (ignoring finite size effects) suffers from many ambiguities related to net ionic numbers, total charge of the system, role of the electrostatic Gauss law, short-distance behaviour of the potential and incorrectly normalized pair correlation functions. We give a new formulation (incorporating finite size effects) such that ionic numbers are maintained, the total charge of the system has physically correct value, the Gauss law boundary conditions are rigorously obeyed, short-distance behaviour of the potential is guaranteed automatically, and correlation functions are correctly normalized. Numerical differences between the two approaches show up if the screening length μ-1 becomes comparable to the size R of the system.
Noether symmetries in Gauss-Bonnet-teleparallel cosmology.
Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F
2016-01-01
A generalized teleparallel cosmological model, [Formula: see text], containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant [Formula: see text], is studied in the framework of the Noether symmetry approach. As [Formula: see text] gravity, where [Formula: see text] is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, [Formula: see text] contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function [Formula: see text] and to derive exact cosmological solutions.
Holographic p-wave superfluid in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Liu, Shancheng; Pan, Qiyuan; Jing, Jiliang
2017-02-01
We construct the holographic p-wave superfluid in Gauss-Bonnet gravity via a Maxwell complex vector field model and investigate the effect of the curvature correction on the superfluid phase transition in the probe limit. We obtain the rich phase structure and find that the higher curvature correction hinders the condensate of the vector field but makes it easier for the appearance of translating point from the second-order transition to the first-order one or for the emergence of the Cave of Winds. Moreover, for the supercurrents versus the superfluid velocity, we observe that our results near the critical temperature are independent of the Gauss-Bonnet parameter and agree well with the Ginzburg-Landau prediction.
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.
Noether symmetries in Gauss-Bonnet-teleparallel cosmology
NASA Astrophysics Data System (ADS)
Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F.
2016-11-01
A generalized teleparallel cosmological model, f(T_{G},T), containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant T_{{G}}, is studied in the framework of the Noether symmetry approach. As f({G}, R) gravity, where {G} is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, f(T_{G},T) contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function f(T_{G},T) and to derive exact cosmological solutions.
The LHCb Simulation Application, Gauss: Design, Evolution and Experience
NASA Astrophysics Data System (ADS)
Clemencic, M.; Corti, G.; Easo, S.; Jones, C. R.; Miglioranzi, S.; Pappagallo, M.; Robbe, P.; LHCb Collaboration
2011-12-01
The LHCb simulation application, Gauss, is based on the Gaudi framework and on experiment basic components such as the Event Model and Detector Description. Gauss also depends on external libraries for the generation of the primary events (PYTHIA 6, EvtGen, etc.) and on GEANT4 for particle transport in the experimental setup. The application supports the production of different types of events from minimum bias to B physics signals and particle guns. It is used for purely generator-level studies as well as full simulations. Gauss is used both directly by users and in massive central productions on the grid. The design and implementation of the application and its evolution due to evolving requirements will be described as in the case of the recently adopted Python-based configuration or the possibility of taking into account detectors conditions via a Simulation Conditions database. The challenge of supporting at the same time the flexibililty needed for the different tasks for which it is used, from evaluation of physics reach to background modeling, together with the stability and reliabilty of the code will also be described.
Long life of Gauss-Bonnet corrected black holes
Konoplya, R. A.; Zhidenko, A.
2010-10-15
Dictated by the string theory and various higher dimensional scenarios, black holes in D>4-dimensional space-times must have higher curvature corrections. The first and dominant term is quadratic in curvature, and called the Gauss-Bonnet (GB) term. We shall show that although the Gauss-Bonnet correction changes black hole's geometry only softly, the emission of gravitons is suppressed by many orders even at quite small values of the GB coupling. The huge suppression of the graviton emission is due to the multiplication of the two effects: the quick cooling of the black hole when one turns on the GB coupling and the exponential decreasing of the gray-body factor of the tensor type of gravitons at small and moderate energies. At higher D the tensor gravitons emission is dominant, so that the overall lifetime of black holes with Gauss-Bonnet corrections is many orders larger than was expected. This effect should be relevant for the future experiments at the Large Hadron Collider (LHC).
Uncontracted Rys Quadrature Implementation of up to G Functions on Graphical Processing Units.
Asadchev, Andrey; Allada, Veerendra; Felder, Jacob; Bode, Brett M; Gordon, Mark S; Windus, Theresa L
2010-03-09
An implementation is presented of an uncontracted Rys quadrature algorithm for electron repulsion integrals, including up to g functions on graphical processing units (GPUs). The general GPU programming model, the challenges associated with implementing the Rys quadrature on these highly parallel emerging architectures, and a new approach to implementing the quadrature are outlined. The performance of the implementation is evaluated for single and double precision on two different types of GPU devices. The performance obtained is on par with the matrix-vector routine from the CUDA basic linear algebra subroutines (CUBLAS) library.
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.
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.
Optimal displacement in apparent motion and quadrature models of motion sensing
NASA Technical Reports Server (NTRS)
Watson, Andrew B.
1990-01-01
A grating appears to move if it is displaced by some amount between two brief presentations, or between multiple successive presentations. A number of recent experiments have examined the influence of displacement size upon either the sensitivity to motion, or upon the induced motion aftereffect. Several recent motion models are based upon quadrature filters that respond in opposite quadrants in the spatiotemporal frequency plane. Predictions of the quadrature model are derived for both two-frame and multiframe displays. Quadrature models generally predict an optimal displacement of 1/4 cycle for two-frame displays, but in the multiframe case the prediction depends entirely on the frame rate.
NASA Astrophysics Data System (ADS)
Simon, M. K.; Li, L.
2003-08-01
We show that MIL-STD shaped offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope modulation, can be represented in the form of a cross-correlated trellis-coded quadrature modulation, a generic structure containing both memory and cross-correlation between the in-phase and quadrature-phase channels. Such a representation allows identification of the optimum form of receiver for MIL-STD SOQPSK and at the same time, through modification of the equivalent I and Q encoders to recursive types, allows for it to be embedded as the inner code of a serial or parallel (turbo-like) concatenated coding structure together with iterative decoding.
Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light.
Dwyer, S; Barsotti, L; Chua, S S Y; Evans, M; Factourovich, M; Gustafson, D; Isogai, T; Kawabe, K; Khalaidovski, A; Lam, P K; Landry, M; Mavalvala, N; McClelland, D E; Meadors, G D; Mow-Lowry, C M; Schnabel, R; Schofield, R M S; Smith-Lefebvre, N; Stefszky, M; Vorvick, C; Sigg, D
2013-08-12
Squeezed states of light are an important tool for optical measurements below the shot noise limit and for optical realizations of quantum information systems. Recently, squeezed vacuum states were deployed to enhance the shot noise limited performance of gravitational wave detectors. In most practical implementations of squeezing enhancement, relative fluctuations between the squeezed quadrature angle and the measured quadrature (sometimes called squeezing angle jitter or phase noise) are one limit to the noise reduction that can be achieved. We present calculations of several effects that lead to quadrature fluctuations, and use these estimates to account for the observed quadrature fluctuations in a LIGO gravitational wave detector. We discuss the implications of this work for quantum enhanced advanced detectors and even more sensitive third generation detectors.
Adaptive Quadrature for Item Response Models. Research Report. ETS RR-06-29
ERIC Educational Resources Information Center
Haberman, Shelby J.
2006-01-01
Adaptive quadrature is applied to marginal maximum likelihood estimation for item response models with normal ability distributions. Even in one dimension, significant gains in speed and accuracy of computation may be achieved.
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.
Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method
NASA Technical Reports Server (NTRS)
Lockard, David P.; Atkins, Harold L.
1999-01-01
The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.
A Quadrature Free Discontinuous Galerkin Conservative Level Set Scheme
NASA Astrophysics Data System (ADS)
Czajkowski, Mark; Desjardins, Olivier
2010-11-01
In an effort to improve the scalability and accuracy of the Accurate Conservative Level Set (ACLS) scheme [Desjardins et al., J COMPUT PHYS 227 (2008)], a scheme based on the quadrature free discontinuous Galerkin (DG) methodology has been developed. ACLS relies on a hyperbolic tangent level set function that is transported and reinitialized using conservative schemes in order to alleviate mass conservation issues known to plague level set methods. DG allows for an arbitrarily high order representation of the interface by using a basis of high order polynomials while only using data from the faces of neighboring cells. The small stencil allows DG to have excellent parallel scalability. The diffusion term present in the conservative reinitialization equation is handled using local DG method [Cockburn et al., SIAM J NUMER ANAL 39, (2001)] while the normals are computed from a limited form of the level set function in order to avoid spurious oscillations. The resulting scheme is shown to be both robust, accurate, and highly scalable, making it a method of choice for large-scale simulations of multiphase flows with complex interfacial topology.
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.
Velocity envelope of vector flow estimation with spatial quadrature
NASA Astrophysics Data System (ADS)
Kerr, Richard F.; Anderson, Martin E.
2003-05-01
We present the results of two studies investigating the optimal aperture configuration for maximized lateral blood flow velocity estimation using Heterodyned Spatial Quadrature. Our objective was to determine the maximum velocities that can be estimated at Doppler angles of 90 degrees and 60 degrees with a bias of less than 5% for both uniform scatterer motion in a tissue-mimicking phantom and blood-mimicking fluid circulated through a wall-less vessel flow phantom. Constant flow rates ranging from 3.0 to 18.0 ml/sec were applied in the flow phantom, producing expected peak velocities of 15.0 to 89.8 cm/sec under laminar flow conditions. Velocity estimates were obtained at each flow rate using 256 trials, with each trial consisting of an ensemble of 32 vectors. For an f/1 receive geometry with bi-lobed Hamming apodization, all peak flow velocities tested were estimated to within 5% of their expected values for both 90 degree and 60 degree Doppler angles. An f/2 receive geometry featuring bi-lobed Blackman apodization generally provided accurate lateral velocity estimates up to 71.9 cm/sec for a Doppler angle of 90 degrees, and accurate lateral component estimates up to 50.1 cm/sec for a 60 degree Doppler angle. The implications of these findings will be discussed.
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.
Carrier Synchronization of Offset Quadrature Phase-Shift Keying
NASA Astrophysics Data System (ADS)
Simon, M. K.
1998-01-01
This article contains analyses of the performance of various carrier synchronization loops for offset quadrature phase-shift-keying (OQPSK) modulation, all motivated in one form or another by the maximum a posteriori (MAP) estimation of carrier phase. When they are implemented as either high or low signal-to-noise ratio (SNR) approximations to the generic implementation suggested by the MAP estimation of carrier phase for an OQPSK signal, it is shown that the loops behave more like biphase than quadriphase loops in that they only exhibit a 180-deg phase ambiguity rather than the 90-deg phase ambiguity typical of the latter. This phase ambiguity advantage coupled with the mean-square tracking-error performance advantage that results and its ultimate effect on average error probability performance offer a potentially significant justification for using OQPSK rather than QPSK even on a linear transmission channel, where it often is reasoned (based on the assumption of an ideal environment) that the two modulation schemes perform identically.
Radiation transport modeling using extended quadrature method of moments
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.
Comparision of adaptive quadrature mirror filter subband coding systems
NASA Astrophysics Data System (ADS)
Buschmann, Jonathan E.; Marcozzi, Elena; Raveglia, Dalmazio
1990-06-01
We investigate high quality coding systems by exploiting both statistical andpsychovisual video signal properties. Source image filtering via Quadrature Mirror Filters (QMF) and quantization of the obtained subbands, seem suitable to exploit both these signal properties. All the investigated QMF filters are separable, non-recursive, and oftwo different types. The first type consists of linear phase filters which allow, after synthesis, exact cancellation of all aliasing, but the overall characteristic of the analysis-synthesis system has amplitudeonly approximately constant The secondtype is constitutedby more sophisticated filters which allow exact signal reconsiruction and, naturally, cancellation of all aliasing; however, the single filters constituting the bank can be nonlinear phase filters. These can be implemented by a lattice structure which induces, and thereby guarantees, perfectreconstruction even ifthelatticeparameters arecoarsely quantized. Uniform quantizers havebeenchosen for all subbands, with DPCM for the lowest frequency band and PCM for the higher frequency bands. Certain quantizer parameters are adapted to the type of filter used. Additional parameters are adaptively adjusted according to the statistics of the subbands. This work aims at finding a satisfactory compromise between the characteristics of the QMF filter bank and those of the coders.
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
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.
Generalizing higher-order Bessel-Gauss beams: analytical description and demonstration.
Schimpf, Damian N; Schulte, Jan; Putnam, William P; Kärtner, Franz X
2012-11-19
We report on a novel class of higher-order Bessel-Gauss beams in which the well-known Bessel-Gauss beam is the fundamental mode and the azimuthally symmetric Laguerre-Gaussian beams are special cases. We find these higher-order Bessel-Gauss beams by superimposing decentered Hermite-Gaussian beams. We show analytically and experimentally that these higher-order Bessel-Gauss beams resemble higher-order eigenmodes of optical resonators consisting of aspheric mirrors. This work is relevant for the many applications of Bessel-Gauss beams in particular the more recently proposed high-intensity Bessel-Gauss enhancement cavities for strong-field physics applications.
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
2016-01-07
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.
Calculation method for a quadrature phase-shifting interferometer and its applications.
Nakadate, Suezou; Sawada, Shinya; Kiire, Tomohiro; Shibuya, Masato; Yatagai, Toyohiko
2013-01-01
A calculation method for a quadrature phase-shifting interferometer is presented, and its applications to specular and speckle interferometers and digital holography are described. Two sets of quadrature phase-shifted interferograms are acquired, and the calculation method proposed gives the phase distribution of the interferograms. The principle of the calculation method with error analysis and experimental results for specular and speckle interferometers and digital holography are also given.
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
Generation of Arbitrary Quadrature Signals Using One Dual-Drive Modulator
NASA Astrophysics Data System (ADS)
Ho, Keang-Po; Cuei, Han-Wei
2005-02-01
Regardless of the number of constellation points, all quadrature-amplitude modulation (QAM) signals can be generated using a single dual-drive Mach-Zehnder modulator. When the general method is applied to quadrature-phase-shift-keying (QPSK) signals, three different QPSK transmitters are shown with drive signals having four, three, or two levels. The usage of only one dual-drive modulator greatly simplifies the design of QAM and QPSK transmitters.
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.
Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere.
Zhou, Guoquan; Chu, Xiuxiang
2010-01-18
The propagation of a Lorentz-Gauss beam in turbulent atmosphere is investigated. Based on the extended Huygens-Fresnel integral and the Hermite-Gaussian expansion of a Lorentz function, analytical formulae for the average intensity and the effective beam size of a Lorentz-Gauss beam are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a Lorentz-Gauss beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a Lorentz-Gauss beam in turbulent atmosphere are also discussed in detail.
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.
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).
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.
Light trajectory in Bessel-Gauss vortex beams.
Xie, Chen; Giust, Remo; Jukna, Vytautas; Furfaro, Luca; Jacquot, Maxime; Lacourt, Pierre-Ambroise; Froehly, Luc; Dudley, John; Couairon, Arnaud; Courvoisier, Francois
2015-07-01
We investigate the early stage of propagation of Bessel-Gauss vortex beams where a transition regime shows a progressive lateral expansion of the main intensity ring before reaching a diffraction-free regime. The eikonal equation is used to characterize the beam structure. The beam is featured by a family of hyperboloids with variable waists, generating a tapered tubular caustic. Our analytical results are in excellent agreement with numerical and experimental results. We show the transition regime can be well eliminated by using hollow input beams.
Nonsingular Universes in Gauss-Bonnet Gravity’s Rainbow
NASA Astrophysics Data System (ADS)
Hendi, Seyed Hossein; Momennia, Mehrab; Eslam Panah, Behzad; Faizal, Mir
2016-08-01
In this paper, we study the rainbow deformation of Friedmann-Robertson-Walker (FRW) cosmology in both Einstein gravity and Gauss-Bonnet (GB) gravity. We demonstrate that the singularity in FRW cosmology can be removed because of the rainbow deformation of the FRW metric. We obtain the general constraints required for FRW cosmology to be free of singularities. We observe that the inclusion of GB gravity can significantly change the constraints required to obtain nonsingular universes. We use rainbow functions motivated by the hard spectra of gamma-ray bursts to deform FRW cosmology and explicitly demonstrate that such a deformation removes the singularity in FRW cosmology.
Nonlinear diffraction from high-order Hermite-Gauss beams.
Kalinowski, Ksawery; Shapira, Asia; Libster-Hershko, Ana; Arie, Ady
2015-01-01
We investigate experimentally and theoretically the nonlinearly diffracted second harmonic light from the first-order Hermite-Gauss beam. We investigate the cases of loosely and tightly focused beams in a periodically poled lithium niobate crystal in the temperature range near the birefringent phase matching. Unlike the case of fundamental Gaussian beam, the nonlinear diffracted beam is spatially structured. Its shape depends on the focusing conditions and on the crystal temperature. Furthermore, for the case of tight focusing, the diffracted beam structure depends on the beam's position with respect to the domain wall.
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).
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.
Quadrature Amplitude Modulation Division for Multiuser MISO Broadcast Channels
NASA Astrophysics Data System (ADS)
Dong, Zheng; Zhang, Yan-Yu; Zhang, Jian-Kang; Gao, Xiang-Chuan
2016-12-01
This paper considers a discrete-time multiuser multiple-input single-output (MISO) Gaussian broadcast channel~(BC), in which channel state information (CSI) is available at both the transmitter and the receivers. The flexible and explicit design of a uniquely decomposable constellation group (UDCG) is provided based on pulse amplitude modulation (PAM) and rectangular quadrature amplitude modulation (QAM) constellations. With this, a modulation division (MD) transmission scheme is developed for the MISO BC. The proposed MD scheme enables each receiver to uniquely and efficiently detect their desired signals from the superposition of mutually interfering cochannel signals in the absence of noise. In our design, the optimal transmitter beamforming problem is solved in a closed-form for two-user MISO BC using max-min fairness as a design criterion. Then, for a general case with more than two receivers, we develop a user-grouping-based beamforming scheme, where the grouping method, beamforming vector design and power allocation problems are addressed by using weighted max-min fairness. It is shown that our proposed approach has a lower probability of error compared with the zero-forcing (ZF) method when the Hermitian angle between the two channel vectors is small in a two-user case. In addition, simulation results also reveal that for the general channel model with more than two users, our user-grouping-based scheme significantly outperforms the ZF, time division (TD), minimum mean-square error (MMSE) and signal-to-leakage-and-noise ratio (SLNR) based techniques in moderate and high SNR regimes when the number of users approaches to the number of base station (BS) antennas and it degrades into the ZF scheme when the number of users is far less than the number of BS antennas in Rayleigh fading channels.
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.
Unified solutions of extended Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Keskin, A. I.; Açıkgöz, I.
2016-12-01
We study some scale factor power-law solutions of the field equations of the extended Gauss Bonnet gravity in the spatial FRW (Friedmann-Robertson-Walker) universe. We consider the lagrangian density given by F ( R, G ) =f ( G ) + R + α R2 which exhibits a modification comparing with the modified Gauss Bonnet gravity. After constructing the Friedmann equations and finding the power-law solution we obtain the real valued of our model describing a mechanism that shows transitions among three stages of the universe (inflation, deceleration, acceleration) in an unified way. In particular, in this unified solution we obtained an inflation model without using any scalar field description when α>0, and also we verified our early time inflationary scenario using observational parameters, i.e. ns, r. Further, we research for the power-law solution of our model when the universe is in the phantom phase. Here, it is observed that the acceleration of the universe in phantom region is composed of two phases which congruent with the recent observations.
Phase space of modified Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Carloni, Sante; Mimoso, José P.
2017-08-01
We investigate the evolution of non-vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f( R) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.
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.
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.
Driving corrugated donut rotors with Laguerre-Gauss beams.
Loke, Vincent L Y; Asavei, Theodor; Stilgoe, Alexander B; Nieminen, Timo A; Rubinsztein-Dunlop, Halina
2014-08-11
Tightly-focused laser beams that carry angular momentum have been used to trap and rotate microrotors. In particular, a Laguerre-Gauss mode laser beam can be used to transfer its orbital angular momentum to drive microrotors. We increase the torque efficiency by a factor of about 2 by designing the rotor such that its geometry is compatible with the driving beam, when driving the rotation with the optimum beam, rather than beams of higher or lower orbital angular momentum. Based on Floquet's theorem, the order of discrete rotational symmetry of the rotor can be made to couple with the azimuthal mode of the Laguerre-Gauss beam. We design corrugated donut rotors, that have a flat disc-like profile, with the help of the discrete dipole approximation and the T-matrix methods in parallel with experimental demonstrations of stable trapping and torque measurement. We produce and test such a rotor using two-photon photopolymerization. With a rotor that has 8-fold discrete rotational symmetry, an outer radius of 1.85 μm and a hollow core radius of 0.5 μm, we were able to transfer approximately 0.3 h̄ per photon of the orbital angular momentum from an LG04 beam.
Image segmentation using hidden Markov Gauss mixture models.
Pyun, Kyungsuk; Lim, Johan; Won, Chee Sun; Gray, Robert M
2007-07-01
Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.
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
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.
Controllable light capsules employing modified Bessel-Gauss beams.
Gong, Lei; Liu, Weiwei; Zhao, Qian; Ren, Yuxuan; Qiu, Xingze; Zhong, Mincheng; Li, Yinmei
2016-07-08
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.
Phase space of modified Gauss-Bonnet gravity.
Carloni, Sante; Mimoso, José P
2017-01-01
We investigate the evolution of non-vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f(R) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.
A new sum analogous to Gauss sums and its fourth power mean.
Ru, Shaofeng; Zhang, Wenpeng
2014-01-01
The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
NASA Astrophysics Data System (ADS)
Muthuvalu, Mohana Sundaram
2016-06-01
In this paper, performance analysis of the preconditioned Gauss-Seidel iterative methods for solving dense linear system arise from Fredholm integral equations of the second kind is investigated. The formulation and implementation of the preconditioned Gauss-Seidel methods are presented. Numerical results are included in order to verify the performance of the methods.
The convergence of the modified Gauss-Seidel methods for consistent linear systems
NASA Astrophysics Data System (ADS)
Li, Wen
2003-05-01
In this paper we present a convergence analysis for the modified Gauss-Seidel methods given in Gunawardena et al. (Linear Algebra Appl. 154-156 (1991) 125) and Kohno et al. (Linear Algebra Appl. 267 (1997) 113) for consistent linear systems. We prove that the modified Gauss-Seidel method converges for some values of the parameters in the preconditioned matrix.
Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves.
Reivelt, Kaido; Saari, Peeter
2004-06-01
We show that the field of the optically feasible luminal localized wave solutions of the scalar homogeneous wave equation can be modeled by means of Bessel-Gauss pulses. As the Bessel-Gauss pulses have a closed-form expression, this fact may be of great value in numerical simulations of various experimental situations.
2011-09-01
and location measurements , GPS must take into consideration the ionospheric environment and does so by computing the electron content in the path...VERIFICATION OF GLOBAL ASSIMILATION OF IONOSPHERIC MEASUREMENTS GAUSS MARKOV (GAIM-GM) MODEL FORECAST ACCURACY THESIS...United States. AFIT/GAP/ENP/11-S01 VERIFICATION OF GLOBAL ASSIMILATION OF IONOSPHERIC MEASUREMENTS GAUSS MARKOV (GAIM
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.
2014-01-01
We consider a family {τm : m ≥ 2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τm, we solve a Gauss-Kuzmin-type problem. PMID:24707226
Lascu, Dan
2014-01-01
We consider a family {τ m : m ≥ 2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τ m , we solve a Gauss-Kuzmin-type problem.
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
Design and application of quadrature compensation patterns in bulk silicon micro-gyroscopes.
Ni, Yunfang; Li, Hongsheng; Huang, Libin
2014-10-29
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.
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
Gauss-Bonnet braneworld cosmological effect on relic density of dark matter
Okada, Nobuchika; Okada, Satomi
2009-05-15
In Gauss-Bonnet braneworld cosmology, the Friedmann equation of our four-dimensional Universe on 3-brane is modified in a high energy regime (Gauss-Bonnet regime), while the standard expansion law is reproduced in low energies (standard regime). We investigate the Gauss-Bonnet braneworld cosmological effect on the thermal relic density of cold dark matter when the freeze-out of the dark matter occurs in the Gauss-Bonnet regime. We find that the resultant relic density is considerably reduced when the transition temperature, which connects the Gauss-Bonnet regime with the standard regime, is low enough. This result is in sharp contrast with the result previously obtained in the Randall-Sundrum braneworld cosmology, where the relic density is enhanced.
Bessel-Gauss beam enhancement cavities for high-intensity applications.
Putnam, William P; Schimpf, Damian N; Abram, Gilberto; Kärtner, Franz X
2012-10-22
We introduce Bessel-Gauss beam enhancement cavities that may circumvent the major obstacles to more efficient cavity-enhanced high-field physics such as high-harmonic generation. The basic properties of Bessel-Gauss beams are reviewed and their transformation properties through simple optical systems (consisting of spherical and conical elements) are presented. A general Bessel-Gauss cavity design strategy is outlined, and a particular geometry, the confocal Bessel-Gauss cavity, is analyzed in detail. We numerically simulate the confocal Bessel-Gauss cavity and present an example cavity with 300 MHz repetition rate supporting an effective waist of 33 μm at the focus and an intensity ratio from the focus to the cavity mirror surfaces of 1.5 × 10(4).
Black holes in the Einstein-Gauss-Bonnet theory and the geometry of their thermodynamics—II
NASA Astrophysics Data System (ADS)
Biswas, Ritabrata; Chakraborty, Subenoy
2010-03-01
In the present work we study (i) the charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as the Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) the black hole in EGB gravity with a Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
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.
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.
Membrane paradigm for Einstein-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Jacobson, Ted; Mohd, Arif; Sarkar, Sudipta
2017-03-01
We construct the membrane paradigm for black objects in Einstein-Gauss-Bonnet gravity in spacetime dimensions ≥5 . As in the case of general relativity, the horizon can be modeled as a membrane endowed with fluidlike properties. We derive the stress tensor for this membrane fluid and study the perturbation around static backgrounds with constant curvature horizon cross section, for which the stress tensor can be regularized with the usual redshift factor, and expressed in the form of a Newtonian viscous fluid with pressure, shear viscosity and bulk viscosity. We evaluate the transport coefficients for black holes with constant curvature horizons and negative or zero cosmological constant. For the black brane geometry our result for the ratio of shear viscosity to entropy density agrees with that obtained previously in different frameworks.
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.
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.
Exponential fitted Gauss, Radau and Lobatto methods of low order
NASA Astrophysics Data System (ADS)
Martín-Vaquero, J.; Vigo-Aguiar, J.
2008-08-01
Several exponential fitting Runge-Kutta methods of collocation type are derived as a generalization of the Gauss, Radau and Lobatto traditional methods of two steps. The new methods are capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential and ordinary polynomials. Theorems of the truncation error reveal the good behavior of the new methods for stiff problems. Plots of their absolute stability regions that include the whole of the negative real axis are provided. A different procedure to find the parameter of the method is proposed. The variable step Radau method of two stages is derived. Finally, numerical examples underscore the efficiency of the proposed codes, especially when they are integrating stiff problems.
Nonparaxial Bessel and Bessel-Gauss pincers light-sheets
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2017-01-01
Nonparaxial optical Bessel and Bessel-Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
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.
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.
Extended Gauss-Bonnet gravities in Weyl geometry
NASA Astrophysics Data System (ADS)
Beltrán Jiménez, Jose; Koivisto, Tomi S.
2014-07-01
In this paper we consider an extended Gauss-Bonnet gravity theory in arbitrary dimensions and in a space provided with a Weyl connection, which is torsion-free but non-metric-compatible, the non-metricity tensor being determined by a vector field. The action considered consists of the usual Einstein-Hilbert action plus all the terms quadratic in the curvature that reduce to the usual Gauss-Bonnet term for vanishing Weyl connection, i.e., when only the Levi-Civita part of the connection is present. We expand the action in terms of Riemannian quantities and obtain vector-tensor theories. We find that all the free parameters only appear in the kinetic term of the vector field, so two branches are possible: one with a propagating vector field and another one where the vector field does not propagate. We focus on the propagating case. We find that in four dimensions, the theory is equivalent to Einstein's gravity plus a Proca field. This field is naturally decoupled from matter, so it represents a natural dark matter candidate. Also for d = 4, we discuss a non-trivial cubic term in the curvature that can be constructed without spoiling the second-order nature of the field equations, because it leads to the vector-tensor Horndeski interaction. In arbitrary dimensions, the theory becomes more involved. We show that, even though the vector field presents kinetic interactions which do not have U\\left( 1 \\right) symmetry, there are no additional propagating degrees of freedom with respect to the usual massive case. We show that, interestingly, this relies on the fact that the corresponding Stückelberg field belongs to a specific class within the general Horndeski theories. Finally, since Weyl geometries provide the natural ground on which to build scale invariant theories, we apply the usual Weyl gauging in order to make the Horndeski action locally scale invariant, and discuss new terms that can be added.
NASA Astrophysics Data System (ADS)
Suzuki, Meisaku; Kanno, Atsushi; Yamamoto, Naokatsu; Sotobayashi, Hideyuki
2016-02-01
The effects of in-phase/quadrature-phase (IQ) imbalances are evaluated with a direct IQ down-converter in the W-band (75-110 GHz). The IQ imbalance of the converter is measured within a range of +/-10 degrees in an intermediate frequency of DC-26.5 GHz. 1-8-G-baud quadrature phase-shift keying (QPSK) signals are transmitted successfully with observed bit error rates within a forward error correction limit of 2×10-3 using radio over fiber (RoF) techniques. The direct down-conversion technique is applicable to next-generation high-speed wireless access communication systems in the millimeter-wave band.
Carrier synchronization and detection of QASK signal sets. [Quadrature Amplitude Shift Keying
NASA Technical Reports Server (NTRS)
Simon, M. K.; Smith, J. G.
1974-01-01
A carrier regeneration loop which generates highly coherent quadrature reference signals for quadrature amplitude-shift keying (QASK) demodulation is presented. The loop employs the principle of decision feedback and has a structure analogous to a decision feedback loop for quadriphase signals suggested earlier in the literature. The error probability performance of QASK is computed in the presence of the noisy carrier reference signals provided by the above loop. It is demonstrated that when the ratio of data rate to loop bandwidth is 50 or greater, then for all practical purposes, ideal QASK error probability performance is achieved.
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.
Wang, Jin; Kroh, Marcel; Theurer, Abongwa; Zawadzki, Crispin; Schmidt, Detlef; Ludwig, Reinhold; Lauermann, Matthias; Zhang, Ziyang; Beling, Andreas; Matiss, Andreas; Schubert, Colja; Steffan, Andreas; Keil, Norbert; Grote, Norbert
2011-12-12
A dual-quadrature coherent receiver based on a polymer planar lightwave circuit (PLC) is presented. This receiver comprises two separate optical 90°-hybrid chips made of polymer waveguides and hybridly integrated with InGaAs/InP photodiode (PD) arrays. The packaged receiver was successfully operated in 112 Gbit/s dual-polarization quadrature phase-shift keying (QPSK) transmission experiments. In back-to-back configuration the OSNR requirement for a BER value of 10(-3) was 15.1 dB which has to be compared to a theoretical limit of 13.8 dB.
A method to design tunable quadrature filters in phase shifting interferometry.
Mosiño, J F; Doblado, D Malacara; Hernández, D Malacara
2009-08-31
The main purpose of this paper is to present a method to design tunable quadrature filters in phase shifting interferometry. The algorithm is obtained from a generalized Fourier transform of a symmetrical quadrature filter. This formalism allows us to represent the detuning phase shift error and bias modulation as geometrical conditions. Therefore, the design of the filter becomes a set of solvable linear equations. Hence, to prove our method, several general tunable filters, like three and four frame algorithms, are obtained. Finally, from our results we reproduce particular symmetrical four frame algorithms reported in literature.
Spherically symmetric brane in a bulk of f(R) and Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Chakraborty, Sumanta; SenGupta, Soumitra
2016-11-01
Effective gravitational field equations on a four-dimensional brane embedded in a five-dimensional bulk have been considered. Using the Einstein-Hilbert action along with the Gauss-Bonnet correction term, we have derived static spherically symmetric vacuum solution to the effective field equations, first order in the Gauss-Bonnet coupling parameter. The solution so obtained, has one part corresponding to general relativity with an additional correction term, proportional to the Gauss-Bonnet coupling parameter. The correction term modifies the spacetime structure, in particular, the location of the event horizon. Proceeding further, we have derived effective field equations for f(R) gravity with Gauss-Bonnet correction term and a static spherically symmetric solution has been obtained. In this case the Gauss-Bonnet term modifies both the event and cosmological horizon of the spacetime. There exists another way of obtaining the brane metric—expanding the bulk gravitational field equations in the ratio of bulk to brane curvature scale and assuming a separable bulk metric ansatz. It turns out that static, spherically symmetric solutions obtained from this perturbative method can be matched exactly, with the solutions derived earlier. This will hold for Einstein-Hilbert plus Gauss-Bonnet as well as for f(R) with the Gauss-Bonnet correction. Implications of these results are discussed.
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.
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.
The time delay in strong gravitational lensing with Gauss-Bonnet correction
Man, Jingyun; Cheng, Hongbo E-mail: hbcheng@ecust.edu.cn
2014-11-01
The time delay between two relativistic images in the strong gravitational lensing governed by Gauss-Bonnet gravity is studied. We make a complete analytical derivation of the expression of time delay in presence of Gauss-Bonnet coupling. With respect to Schwarzschild, the time delay decreases as a consequence of the shrinking of the photon sphere. As the coupling increases, the second term in the time delay expansion becomes more relevant. Thus time delay in strong limit encodes some new information about geometry in five-dimensional spacetime with Gauss-Bonnet correction.
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.
Discrete-Gauss states and the generation of focusing dark beams
NASA Astrophysics Data System (ADS)
Ferrando, Albert
2014-08-01
Discrete-Gauss states are a new class of Gaussian solutions of the free Schrödinger equation owning discrete rotational symmetry. They are obtained by acting with a discrete deformation operator onto Laguerre-Gauss modes. We present a general analytical construction of these states and show the necessary and sufficient condition for them to host embedded dark beam structures. We unveil the intimate connection between discrete rotational symmetry, orbital angular momentum, and the generation of focusing dark beams. The distinguishing features of focusing dark beams are discussed. The potential applications of discrete-Gauss states in advanced optical trapping and quantum information processing are also briefly discussed.
Power spectra from an inflaton coupled to the Gauss-Bonnet term
Guo Zongkuan; Schwarz, Dominik J.
2009-09-15
We consider power-law inflation with a Gauss-Bonnet correction inspired by string theory. We analyze the stability of cosmological perturbations and obtain the allowed parameter space. We find that for Gauss-Bonnet-dominated inflation ultraviolet instabilities of either scalar or tensor perturbations show up on small scales. The Gauss-Bonnet correction with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio in the potential-dominated case. We place tight constraints on the model parameters by making use of the WMAP 5-year data.
Serbes, Gorkem; Aydin, Nizamettin
2014-01-01
Quadrature signals are dual-channel signals obtained from the systems employing quadrature demodulation. Embolic Doppler ultrasound signals obtained from stroke-prone patients by using Doppler ultrasound systems are quadrature signals caused by emboli, which are particles bigger than red blood cells within circulatory system. Detection of emboli is an important step in diagnosing stroke. Most widely used parameter in detection of emboli is embolic signal-to-background signal ratio. Therefore, in order to increase this ratio, denoising techniques are employed in detection systems. Discrete wavelet transform has been used for denoising of embolic signals, but it lacks shift invariance property. Instead, dual-tree complex wavelet transform having near-shift invariance property can be used. However, it is computationally expensive as two wavelet trees are required. Recently proposed modified dual-tree complex wavelet transform, which reduces the computational complexity, can also be used. In this study, the denoising performance of this method is extensively evaluated and compared with the others by using simulated and real quadrature signals. The quantitative results demonstrated that the modified dual-tree-complex-wavelet-transform-based denoising outperforms the conventional discrete wavelet transform with the same level of computational complexity and exhibits almost equal performance to the dual-tree complex wavelet transform with almost half computational cost.
Bogdanov, Yu. I. Avosopyants, G. V.; Belinskii, L. V.; Katamadze, K. G.; Kulik, S. P.; Lukichev, V. F.
2016-08-15
We describe a new method for reconstructing the quantum state of the electromagnetic field from the results of mutually complementary optical quadrature measurements. This method is based on the root approach and displaces squeezed Fock states are used as the basis. Theoretical analysis and numerical experiments demonstrate the considerable advantage of the developed tools over those described in the literature.
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.
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.
Light-controlled resistors provide quadrature signal rejection for high-gain servo systems
NASA Technical Reports Server (NTRS)
Mc Cauley, D. D.
1967-01-01
Servo amplifier feedback system, in which the phase sensitive detection, low pass filtering, and multiplication functions required for quadrature rejection, are preformed by light-controlled photoresistors, eliminates complex circuitry. System increases gain, improves signal-to-noise ratio, and eliminates the necessity for compensation.
Bostock, M J; Holland, D J; Nietlispach, D
2017-06-01
NMR spectroscopy is central to atomic resolution studies in biology and chemistry. Key to this approach are multidimensional experiments. Obtaining such experiments with sufficient resolution, however, is a slow process, in part since each time increment in every indirect dimension needs to be recorded twice, in quadrature. We introduce a modified compressed sensing (CS) algorithm enabling reconstruction of data acquired with random acquisition of quadrature components in gradient-selection NMR. We name this approach random quadrature detection (RQD). Gradient-selection experiments are essential to the success of modern NMR and with RQD, a 50 % reduction in the number of data points per indirect dimension is possible, by only acquiring one quadrature component per time point. Using our algorithm (CSRQD), high quality reconstructions are achieved. RQD is modular and combined with non-uniform sampling we show that this provides increased flexibility in designing sampling schedules leading to improved resolution with increasing benefits as dimensionality of experiments increases, with particular advantages for 4- and higher dimensional experiments.
Holographic Van der Waals-like phase transition in the Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
He, Song; Li, Li-Fang; Zeng, Xiao-Xiong
2017-02-01
The Van der Waals-like phase transition is observed in temperature-thermal entropy plane in spherically symmetric charged Gauss-Bonnet-AdS black hole background. In terms of AdS/CFT, the non-local observables such as holographic entanglement entropy, Wilson loop, and two point correlation function of very heavy operators in the field theory dual to spherically symmetric charged Gauss-Bonnet-AdS black hole have been investigated. All of them exhibit the Van der Waals-like phase transition for a fixed charge parameter or Gauss-Bonnet parameter in such gravity background. Further, with choosing various values of charge or Gauss-Bonnet parameter, the equal area law and the critical exponent of the heat capacity are found to be consistent with phase structures in temperature-thermal entropy plane.
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.
GaussFit - A system for least squares and robust estimation
NASA Technical Reports Server (NTRS)
Jefferys, W. H.; Fitzpatrick, M. J.; Mcarthur, B. E.
1988-01-01
GaussFit is a new computer program for solving least-squares and robust estimation problems. It has a number of unique features, including a complete programming language designed especially to formulate estimation problems, a built-in compiler and interpreter to support the programming language, and a built-in algebraic manipulator for calculating the required partial derivatives analytically. These features make GaussFit very easy to use, so that even complex problems can be set up and solved with minimal effort. GaussFit can correctly handle many cases of practical interest: nonlinear models, exact constraints, correlated observations, and models where the equations of condition contain more than one observed quantity. An experimental robust estimation capability is built into GaussFit so that data sets contaminated by outliers can be handled simply and efficiently.
GLESP 2.0: Gauss-Legendre Sky Pixelization for CMB Analysis
NASA Astrophysics Data System (ADS)
Doroshkevich, A. G.; Naselsky, P. D.; Verkhodanov, O. V.; Novikov, D. I.; Turchaninov, V. I.; Novikov, I. D.; Christensen, P. R.; Chiang, L.-Y.
2011-03-01
GLESP is a pixelization scheme for the cosmic microwave background (CMB) radiation maps. This scheme is based on the Gauss-Legendre polynomials zeros and allows one to create strict orthogonal expansion of the map.
Warm starting the projected Gauss-Seidel algorithm for granular matter simulation
NASA Astrophysics Data System (ADS)
Wang, Da; Servin, Martin; Berglund, Tomas
2016-03-01
The effect on the convergence of warm starting the projected Gauss-Seidel solver for nonsmooth discrete element simulation of granular matter are investigated. It is found that the computational performance can be increased by a factor 2-5.
A New Preconditioner on Gauss-Seidel Method for H-Matrices
NASA Astrophysics Data System (ADS)
Darvishi, M. T.; Azimbeigi, M.
2009-09-01
In order to accelerate the convergency of Gauss-Seidel method to solve systems of linear equations when the coefficient matrix is an H-matrix, a new preconditioner is introduced. The convergency of the new preconditioned method is proved.
Generation of pulsed Bessel-Gauss beams using passive axicon-theoretical and experimental studies.
Parsa, Shahrzad; Fallah, Hamid Reza; Ramezani, Mohsen; Soltanolkotabi, Mahmood
2012-10-20
We studied the conditions for generating passive Bessel-Gauss beams by using an axicon. We designed an appropriate Gaussian resonator and extracted a quasi-fundamental Gaussian mode from a pulsed Nd:YAG laser pumped by a Xenon flash lamp and measured its parameters, such as propagation factor, divergence angle, and Rayleigh range. Then we generated passive Bessel-Gauss beams using an axicon and investigated their propagation properties, theoretically and experimentally. For example, for the axicon of 1°, the output energy and the Rayleigh range of the generated Bessel-Gauss beams were measured to be 58 mJ and 229.3 mm, respectively. We compared these properties with our results of the Gaussian mode. Finally, by using axicons with different apex angles, and also by changing the beam spot size on the axicon, we generated Bessel-Gauss beams and studied their properties theoretically and experimentally.
Design Improvement and Implementation of 3D Gauss-Markov Mobility Model
2013-02-19
AFFTC-PA-12430 Design Improvement and Implementation of 3D Gauss-Markov Mobility Model Mohammed Alenazi, Cenk Sahin , and James P.G. Sterbenz...0019 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Mohammed Alenazi, Cenk Sahin , and James P.G. Sterbenz 5d. PROJECT...Gauss-Markov Mobility Model Mohammed Alenazi and Cenk Sahin Faculty Advisor: James P.G. Sterbenz Department of Electrical Engineering & Computer Science
A new approach to exact solutions construction in scalar cosmology with a Gauss-Bonnet term
NASA Astrophysics Data System (ADS)
Fomin, I. V.; Chervon, S. V.
2017-08-01
We study the cosmological model based on Einstein-Gauss-Bonnet gravity with non-minimal coupling of a scalar field to a Gauss-Bonnet term in four-dimensional (4D) Friedmann universe. We show how constructing the exact solutions by the method based on a confrontation of the Hubble parameter in the model under consideration is achieved with that in a standard scalar field inflationary cosmology.
Shear viscosity from Gauss-Bonnet gravity with a dilaton coupling
Cai Ronggen; Nie Zhangyu; Sun Yawen; Ohta, Nobuyoshi
2009-03-15
We calculate the shear viscosity of field theories with gravity duals of Gauss-Bonnet gravity with a nontrivial dilaton using anti-de Sitter/conformal field theory. We find that the dilaton field has a nontrivial contribution to the ratio of shear viscosity over entropy density, and, after imposing a causal constraint for the boundary field theory, the new lower bound 4/25{pi}, obtained from pure Gauss-Bonnet gravity, may have a small violation.
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.
Stability of the Einstein static universe in modified Gauss-Bonnet gravity
Boehmer, Christian G.; Lobo, Francisco S. N.
2009-03-15
We analyze the stability of the Einstein static universe by considering linear homogeneous perturbations in the context of f(G) modified Gauss-Bonnet theories of gravity. By considering a generic form of f(G), the stability region of the Einstein static universe is parametrized by the linear equation of state parameter w=p/{rho} and the second derivative f{sup ''}(G) of the Gauss-Bonnet term.
Charged black hole solutions in Gauss-Bonnet-massive gravity
NASA Astrophysics Data System (ADS)
Hendi, S. H.; Panahiyan, S.; Panah, B. Eslam
2016-01-01
Motivated by high interest in the close relation between string theory and black hole solutions, in this paper, we take into account the Einstein-Gauss-Bonnet Lagrangian in the context of massive gravity. We examine the possibility of black hole in this regard, and discuss the types of horizons. Next, we calculate conserved and thermodynamic quantities and check the validity of the first law of thermodynamics. In addition, we investigate the stability of these black holes in context of canonical ensemble. We show that number, type and place of phase transition points may be significantly affected by different parameters. Next, by considering cosmological constant as thermodynamical pressure, we will extend phase space and calculate critical values. Then, we construct thermodynamical spacetime by considering mass as thermodynamical potential. We study geometrical thermodynamics of these black holes in context of heat capacity and extended phase space. We show that studying heat capacity, geometrical thermodynamics and critical behavior in extended phase space lead to consistent results. Finally, we will employ a new method for obtaining critical values and show that the results of this method are consistent with those of other methods.
Laguerre-Gauss basis functions in observer models
NASA Astrophysics Data System (ADS)
Burgess, Arthur E.
2003-05-01
Observer models based on linear classifiers with basis functions (channels) are useful for evaluation of detection performance with medical images. They allow spatial domain calculations with a covariance matrix of tractable size. The term "channelized Fisher-Hotelling observer" will be used here. It is also called the "channelized Hotelling observer" model. There are an infinite number of basis function (channel ) sets that could be employed. Examples of channel sets that have been used include: difference of Gaussian (DOG) filters, difference of Mesa (DOM) filters and Laguerre-Gauss (LG) basis functions. Another option, sums of LG functions (LGS), will also be presented here. This set has the advantage of having no DC response. The effect of the number of images used to estimate model observer performance will be described, for both filtered 1/f3 noise and GE digital mammogram backgrounds. Finite sample image sets introduce both bias and variance to the estimate. The results presented here agree with previous work on linear classifiers. The LGS basis set gives a small but statistically significant reduction in bias. However, this may not be of much practical benefit. Finally, the effect of varying the number of basis functions included in the set will be addressed. It was found that four LG bases or three LGS bases are adequate.
Shadows of Einstein-dilaton-Gauss-Bonnet black holes
NASA Astrophysics Data System (ADS)
Cunha, Pedro V. P.; Herdeiro, Carlos A. R.; Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen
2017-05-01
We study the shadows of the fully non-linear, asymptotically flat Einstein-dilaton-Gauss-Bonnet (EdGB) black holes (BHs), for both static and rotating solutions. We find that, in all cases, these shadows are smaller than for comparable Kerr BHs, i.e. with the same total mass and angular momentum under similar observation conditions. In order to compare both cases we provide quantitative shadow parameters, observing in particular that the differences in the shadows mean radii are never larger than the percent level. Therefore, generically, EdGB BHs cannot be excluded by (near future) shadow observations alone. On the theoretical side, we find no clear signature of some exotic features of EdGB BHs on the corresponding shadows, such as the regions of negative (Komar, say) energy density outside the horizon. We speculate that this is due to the fact that the Komar energy interior to the light rings (or more precisely, the surfaces of constant radial coordinate that intersect the light rings in the equatorial plane) is always smaller than the ADM mass, and consequently the corresponding shadows are smaller than those of comparable Kerr BHs. The analysis herein provides a clear example that it is the light ring impact parameter, rather than its ;size;, that determines a BH shadow.
Nonlinear dynamics in the Einstein-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Shinkai, Hisa-aki; Torii, Takashi
2017-08-01
We numerically investigated how nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms. We especially monitored the processes of appearances of a singularity (or black hole) in two models: (i) a perturbed wormhole throat in spherically symmetric space-time, and (ii) colliding scalar pulses in plane-symmetric space-time. We used a dual-null formulation for evolving the field equations, which enables us to locate the trapping horizons directly, and also enables us to follow close to the large-curvature region due to its causal integrating scheme. We observed that the fate of a perturbed wormhole is either a black hole or an expanding throat depending on the total energy of the structure, and its threshold depends on the coupling constant of the GB terms (αGB ). We also observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude also depends on αGB. For both models, the normal corrections (αGB>0 ) work for avoiding the appearance of singularity, although it is inevitable. We also found that in the critical situation for forming a black hole, the existence of the trapped region in the Einstein-GB gravity does not directly indicate the formation of a black hole.
The rich structure of Gauss-Bonnet holographic superconductors
NASA Astrophysics Data System (ADS)
Barclay, Luke
2011-10-01
We study fully backreacting, Gauss-Bonnet (GB) holographic superconductors in 5 bulk spacetime dimensions. We explore the system's dependence on the scalar mass for both positive and negative GB coupling, α. We find that when the mass approaches the Breitenlohner-Freedman (BF) bound and α → L 2 /4 the effect of backreaction is to increase the critical temperature, T c, of the system: the opposite of its effect in the rest of parameter space. We also find that reducing α below zero increases T c and that the effect of backreaction is diminished. We study the zero temperature limit, proving that this system does not permit regular solutions for a non-trivial, tachyonic scalar field and constrain possible solutions for fields with positive masses. We investigate singular, zero temperature solutions in the Einstein limit but find them to be incompatible with the concept of GB gravity being a perturbative expansion of Einstein gravity. We study the conductivity of the system, finding that the inclusion of backreaction hinders the development of poles in the conductivity that are associated with quasi-normal modes approaching the real axis from elsewhere in the complex plane.
Hawking radiation via tunneling from a d-dimensional black hole in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Li, Gu-Qiang; Mo, Jie-Xiong
2017-04-01
We extend the Parikh-Wilczek method from Einstein gravity spacetime to Gauss-Bonnet modified gravity and study the tunneling radiation of particles across the event horizon of a d-dimensional Gauss-Bonnet Anti de-Sitter black hole. The emission rate of a particle is calculated. It is shown that the emission rate of massive particles takes the same functional form as that of massless particles although that their motion equations tunneling across the horizon are different. It is also shown that the emission spectrum deviates from the pure thermal spectrum but is consistent with an underlying unitary theory. In addition, significant but interesting phenomenon is demonstrated when Gauss-Bonnet term is present. The expression of the emission rate for a black hole in Gauss-Bonnet gravity differs from that for a black hole in Einstein gravity. After adopting the conventional tunneling rate, we obtain the expression of the entropy of the Gauss-Bonnet black hole, which is in accordance with the early results but does not obey the area law. So the research of tunneling radiation in this paper may serve as a new perspective of understanding the thermodynamics of black holes in Gauss-Bonnet gravity.
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.
Constraining scalar-Gauss-Bonnet inflation by reheating, unitarity, and Planck data
NASA Astrophysics Data System (ADS)
Bhattacharjee, Srijit; Maity, Debaprasad; Mukherjee, Rupak
2017-01-01
We revisit the inflationary dynamics in detail for theories with Gauss-Bonnet gravity coupled to scalar functions, in light of the Planck data. Considering the chaotic inflationary scenario, we constrain the parameters of two models involving inflaton-Gauss-Bonnet coupling by current Planck data. For nonzero inflaton-Gauss-Bonnet coupling β , an inflationary analysis provides us a big cosmologically viable region in the space of (m , β ), where m is the mass of the inflaton. However, we study further on constraining β arising from reheating considerations and unitarity of tree-level amplitude involving 2-graviton →2 -graviton (h h →h h ) scattering. Our analysis, particularly on reheating significantly reduces the parameter space of (m , β ) for all models. The quadratic Gauss-Bonnet coupling parameter turns out to be more strongly constrained than that of the linear coupling. For the linear Gauss-Bonnet coupling function, we obtain β ≲1 03, with the condition β (m /MP)2≃10-4. However, the study of the Higgs inflation scenario in the presence of a Gauss-Bonnet term turns out to be completely disfavored.
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.
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
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.
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.
On the implementation of a modified Sag-Szekeres quadrature method
Lyness, J.N.; Delves, L.M.
1997-07-01
The authors describe a modified Sag-Szekeres multidimensional quadrature algorithm and discuss its implementation as a general-purpose library procedure on serial and parallel architectures. Examples illustrate its effectiveness for both smooth and singular integrands. The procedure has been implemented as a parallel library routine, running on transputer-based systems, as part of Esprit project P2528: Supernode II; (see Plowman (1992)). This routine is scheduled to appear in the quadrature section of the Liverpool-NAG Transputer Software Library. The authors give here some results obtained using this routine, to demonstrate the rapid convergence obtained with both smooth and singular integrands, and to demonstrate the routine`s effectiveness on a parallel NIMD architecture.
Rivera-Ortega, Uriel; Meneses-Fabian, Cruz; Rodriguez-Zurita, Gustavo
2013-07-29
A new method in interferometry based on on-off non-quadrature amplitude modulation for object phase retrieval is presented. Although the technique introduces inhomogeneous visibility and phase variations in the interferogram, it is shown that the phase retrieval of a given object is still possible. This method is implemented by using three beams and two Mach-Zehnder interferometers in series. One of the arms of the system is used as a probe beam and the other two are used as reference beams, yielding from their sum the conventional reference beam of a two-beam interferometer. We demonstrate that, if there is a phase difference within the range of (0,π) between these two beams, the effect of modulation in both amplitude and phase is generated for the case of on-off non-quadrature amplitude modulation. An analytical discussion is provided to sustain this method. Numerical and experimental results are also shown.
Quadrature demodulation with synchronous difference for interferometric fiber-optic gyroscopes.
Wang, Zinan; Yang, Yi; Li, Yongxiao; Yu, Xiaoqi; Zhang, Zhenrong; Li, Zhengbin
2012-11-05
We propose a novel method of quadrature demodulation with synchronous difference for suppressing noise in interferometric fiber-optic gyroscopes (IFOGs). For an IFOG with sine wave phase modulation, an in-phase result and a quadrature result are obtained simultaneously by coherent detection. Eigenfrequency modulation is used and a phase shift of 45° is set between the modulation signal and the reference signal, so that two results have the same expectation of amplitude but with opposite signs. A synchronous difference procedure is carried out for output, in which signals are added up and common noise between two results is eliminated. Theoretical analysis and experimental results show that both short term noise and long term instability of the IFOG are reduced by this method. In experimental comparison with the traditional demodulation method on the same IFOG with a 1982 m fiber coil, this method reduces the bias drift from 0.040°/h to 0.004°/h.
Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.
Oettinger, D; Mendoza, M; Herrmann, H J
2013-07-01
We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.
Accuracy-preserving source term quadrature for third-order edge-based discretization
NASA Astrophysics Data System (ADS)
Nishikawa, Hiroaki; Liu, Yi
2017-09-01
In this paper, we derive a family of source term quadrature formulas for preserving third-order accuracy of the node-centered edge-based discretization for conservation laws with source terms on arbitrary simplex grids. A three-parameter family of source term quadrature formulas is derived, and as a subset, a one-parameter family of economical formulas is identified that does not require second derivatives of the source term. Among the economical formulas, a unique formula is then derived that does not require gradients of the source term at neighbor nodes, thus leading to a significantly smaller discretization stencil for source terms. All the formulas derived in this paper do not require a boundary closure, and therefore can be directly applied at boundary nodes. Numerical results are presented to demonstrate third-order accuracy at interior and boundary nodes for one-dimensional grids and linear triangular/tetrahedral grids over straight and curved geometries.
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)
Noncritical quadrature squeezing in two-transverse-mode optical parametric oscillators
Navarrete-Benlloch, Carlos; Roldan, Eugenio; Valcarcel, German J. de; Romanelli, Alejandro
2010-04-15
In this article we explore the quantum properties of a degenerate optical parametric oscillator when it is tuned to the first family of transverse modes at the down-converted frequency. Recently we found [C. Navarrete-Benlloch et al., Phys. Rev. Lett. 100, 203601 (2008)] that above threshold a TEM{sub 10} mode following a random rotation in the transverse plane emerges in this system (we denote it as the bright mode), breaking thus its rotational invariance. Then, owing to the mode orientation being undetermined, we showed that the phase quadrature of the transverse mode orthogonal to this one (denoted as the dark mode) is perfectly squeezed at any pump level and without an increase in the fluctuations on its amplitude quadrature (which seems to contradict the uncertainty principle). In this article we go further in the study of this system and analyze some important features not considered previously. First we show that the apparent violation of the uncertainty principle is just that -'apparent' - as the conjugate pair of the squeezed quadrature is not another quadrature but the orientation of the bright mode (which is completely undetermined in the long term). We also study a homodyne scheme in which the local oscillator is not perfectly matched to the dark mode, as this could be impossible in real experiments due to the random rotation of the mode, showing that even in this case large levels of noise reduction can be obtained (also including the experimentally unavoidable phase fluctuations). Finally, we show that neither the adiabatic elimination of the pump variables nor the linearization of the quantum equations are responsible for the remarkable properties of the dark mode (which we prove analytically and through numerical simulations, respectively), which were simplifying assumptions used in Navarrete-Benlloch et al. [Phys. Rev. Lett. 100, 203601 (2008)]. These studies show that the production of noncritically squeezed light through spontaneous rotational
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.
Pozar, Tomaz; Gregorcic, Peter; Mozina, Janez
2011-03-20
We present the influence of alignment and the real properties of optical components on the performance of a two-detector homodyne displacement-measuring quadrature laser interferometer. An experimental method, based on the optimization of visibility and sensitivity, was established and theoretically described to assess the performance and stability of the interferometer. We show that the optimal performance of such interferometers is achieved with the iterative alignment procedure described.
Požar, Tomaž; Gregorčič, Peter; Možina, Janez
2011-03-20
We present the influence of alignment and the real properties of optical components on the performance of a two-detector homodyne displacement-measuring quadrature laser interferometer. An experimental method, based on the optimization of visibility and sensitivity, was established and theoretically described to assess the performance and stability of the interferometer. We show that the optimal performance of such interferometers is achieved with the iterative alignment procedure described.
Multiple bit differential detection of offset quadrature phase-shift-keying
NASA Technical Reports Server (NTRS)
Simon, M.
2003-01-01
Analogous to multiple symbol differential detectionof quadrature phase-shift-keying (QPSK), a multiple bit differential detection scheme is described for offset QPSK that also exhibits continuous improvement in performance with increasing observation interval. Being derived from maximum-likelihood (ML) considerations, the proposed scheme is purported to be the most power efficient scheme for such a modulation and detection method. Extension of the results to shaped offset QPSK is also possible.
Modified exponential based differential quadrature scheme to solve convection diffusion equation
NASA Astrophysics Data System (ADS)
Arora, Geeta; Kataria, Pooja
2017-07-01
This paper proffers differential quadrature scheme to obtain approximate solution of one dimensional advection diffusion equation with Dirichlet's boundary conditions. The scheme uses modified exponential cubic spline basis functions to obtain the numerical results. The method uses less computational effort and produces more accurate results. In the numerical problems, L∞ and L2 errors show the relative performance of the method for different time levels. The results shown by the method are in good approximation with the exact solution.
NASA Astrophysics Data System (ADS)
Wang, Dongdong; Li, Xiwei; Pan, Feixu
2017-01-01
A simple and unified finite element formulation is presented for superconvergent eigenvalue computation of wave equations ranging from 1D to 3D. In this framework, a general method based upon the so called α mass matrix formulation is first proposed to effectively construct 1D higher order mass matrices for arbitrary order elements. The finite elements discussed herein refer to the Lagrangian type of Lobatto elements that take the Lobatto points as nodes. Subsequently a set of quadrature rules that exactly integrate the 1D higher order mass matrices are rationally derived, which are termed as the superconvergent quadrature rules. More importantly, in 2D and 3D cases, it is found that the employment of these quadrature rules via tensor product simultaneously for the mass and stiffness matrix integrations of Lobatto elements produces a unified superconvergent formulation for the eigenvalue or frequency computation without wave propagation direction dependence, which usually is a critical issue for the multidimensional higher order mass matrix formulation. Consequently the proposed approach is capable of computing arbitrary frequencies in a superconvergent fashion. Meanwhile, numerical implementation of the proposed method for multidimensional problems is trivial. The effectiveness of the proposed methodology is systematically demonstrated by a series of numerical examples. Numerical results revealed that a superconvergence with 2(p+1)th order of frequency accuracy is achieved by the present unified formulation for the pth order Lobatto element.
Output field-quadrature measurements and squeezing in ultrastrong cavity-QED
NASA Astrophysics Data System (ADS)
Stassi, Roberto; Savasta, Salvatore; Garziano, Luigi; Spagnolo, Bernardo; Nori, Franco
2016-12-01
We study the squeezing of output quadratures of an electro-magnetic field escaping from a resonator coupled to a general quantum system with arbitrary interaction strengths. The generalized theoretical analysis of output squeezing proposed here is valid for all the interaction regimes of cavity-quantum electrodynamics: from the weak to the strong, ultrastrong, and deep coupling regimes. For coupling rates comparable or larger then the cavity resonance frequency, the standard input-output theory for optical cavities fails to calculate the variance of output field-quadratures and predicts a non-negligible amount of output squeezing, even if the system is in its ground state. Here we show that, for arbitrary interaction strength and for general cavity-embedded quantum systems, no squeezing can be found in the output-field quadratures if the system is in its ground state. We also apply the proposed theoretical approach to study the output squeezing produced by: (i) an artificial two-level atom embedded in a coherently-excited cavity; and (ii) a cascade-type three-level system interacting with a cavity field mode. In the latter case the output squeezing arises from the virtual photons of the atom-cavity dressed states. This work extends the possibility of predicting and analyzing the results of continuous-variable optical quantum-state tomography when optical resonators interact very strongly with other quantum systems.
NASA Astrophysics Data System (ADS)
Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.
2016-03-01
We present the Clenshaw-Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw-Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order to exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N3) planewave results. Finally, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.
Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.
2015-12-02
We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order tomore » exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N3) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.« less
Adaptive Gaussian quadrature detection for continuous-variable quantum key distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, L.; Imre, S.
2016-03-01
We propose the adaptive quadrature detection for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD scheme uses Gaussian subcarrier continuous variables for the information conveying and Gaussian sub-channels for the transmission. The proposed multicarrier detection scheme dynamically adapts to the subchannel conditions using a corresponding statistics which is provided by our sophisticated sub-channel estimation procedure. The sub-channel estimation phase determines the transmittance coefficients of the sub-channels, which information are used further in the adaptive quadrature decoding process. We define a technique to estimate the transmittance conditions of the sub-channels. We introduce the terms of single and collective adaptive quadrature detection. We prove the achievable error probabilities, the signal-to-noise ratios, and quantify the attributes of the framework. The adaptive detection scheme allows to utilize the extra resources of multicarrier CVQKD and to maximize the amount of transmittable valuable information in diverse measurement and transmission conditions. The framework is particularly convenient for experimental CVQKD scenarios.
Adaptive Quadrature Detection for Multicarrier Continuous-Variable Quantum Key Distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, Laszlo; Imre, Sandor
2015-03-01
We propose the adaptive quadrature detection for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD scheme uses Gaussian subcarrier continuous variables for the information conveying and Gaussian sub-channels for the transmission. The proposed multicarrier detection scheme dynamically adapts to the sub-channel conditions using a corresponding statistics which is provided by our sophisticated sub-channel estimation procedure. The sub-channel estimation phase determines the transmittance coefficients of the sub-channels, which information are used further in the adaptive quadrature decoding process. We define the technique called subcarrier spreading to estimate the transmittance conditions of the sub-channels with a theoretical error-minimum in the presence of a Gaussian noise. We introduce the terms of single and collective adaptive quadrature detection. We also extend the results for a multiuser multicarrier CVQKD scenario. We prove the achievable error probabilities, the signal-to-noise ratios, and quantify the attributes of the framework. The adaptive detection scheme allows to utilize the extra resources of multicarrier CVQKD and to maximize the amount of transmittable information. This work was partially supported by the GOP-1.1.1-11-2012-0092 (Secure quantum key distribution between two units on optical fiber network) project sponsored by the EU and European Structural Fund, and by the COST Action MP1006.
NASA Astrophysics Data System (ADS)
Arce-Guevara, Valdemar E.; Alba-Cadena, Alfonso; Mendez, Martín O.
Quadrature bandpass filters take a real-valued signal and output an analytic signal from which the instantaneous amplitude and phase can be computed. For this reason, they represent a useful tool to extract time-varying, narrow-band information from electrophysiological signals such as electroencephalogram (EEG) or electrocardiogram. One of the defining characteristics of quadrature filters is its null response to negative frequencies. However, when the frequency band of interest is close to 0 Hz, a careless filter design could let through negative frequencies, producing distortions in the amplitude and phase of the output. In this work, three types of quadrature filters (Ideal, Gabor and Sinusoidal) have been evaluated using both artificial and real EEG signals. For the artificial signals, the performance of each filter was measured in terms of the distortion in amplitude and phase, and sensitivity to noise and bandwidth selection. For the real EEG signals, a qualitative evaluation of the dynamics of the synchronization between two EEG channels was performed. The results suggest that, while all filters under study behave similarly under noise, they differ in terms of their sensitivity to bandwidth choice. In this study, the Sinusoidal filter showed clear advantages for the estimation of low-frequency EEG synchronization.
On the power spectral density of quadrature modulated signals. [satellite communication
NASA Technical Reports Server (NTRS)
Yan, T. Y.
1981-01-01
The conventional (no-offset) quadriphase modulation technique suffers from the fact that hardlimiting will restore the frequency sidelobes removed by proper filtering. Thus, offset keyed quadriphase modulation techniques are often proposed for satellite communication with bandpass hardlimiting. A unified theory is developed which is capable of describing the power spectral density before and after the hardlimiting process. Using the in-phase and the quadrature phase channel with arbitrary pulse shaping, analytical results are established for generalized quadriphase modulation. In particular MSK, OPSK or the recently introduced overlapped raised cosine keying all fall into this general category. It is shown that for a linear communication channel, the power spectral density of the modulated signal remains unchanged regardless of the offset delay. Furthermore, if the in phase and the quadrature phase channel have identical pulse shapes without offset, the spectrum after bandpass hardlimiting will be identical to that of the conventional QPSK modulation. Numerical examples are given for various modulation techniques. A case of different pulse shapes in the in phase and the quadrature phase channel is also considered.
NASA Astrophysics Data System (ADS)
Wang, Dongdong; Li, Xiwei; Pan, Feixu
2016-11-01
A simple and unified finite element formulation is presented for superconvergent eigenvalue computation of wave equations ranging from 1D to 3D. In this framework, a general method based upon the so called α mass matrix formulation is first proposed to effectively construct 1D higher order mass matrices for arbitrary order elements. The finite elements discussed herein refer to the Lagrangian type of Lobatto elements that take the Lobatto points as nodes. Subsequently a set of quadrature rules that exactly integrate the 1D higher order mass matrices are rationally derived, which are termed as the superconvergent quadrature rules. More importantly, in 2D and 3D cases, it is found that the employment of these quadrature rules via tensor product simultaneously for the mass and stiffness matrix integrations of Lobatto elements produces a unified superconvergent formulation for the eigenvalue or frequency computation without wave propagation direction dependence, which usually is a critical issue for the multidimensional higher order mass matrix formulation. Consequently the proposed approach is capable of computing arbitrary frequencies in a superconvergent fashion. Meanwhile, numerical implementation of the proposed method for multidimensional problems is trivial. The effectiveness of the proposed methodology is systematically demonstrated by a series of numerical examples. Numerical results revealed that a superconvergence with 2(p+1)th order of frequency accuracy is achieved by the present unified formulation for the pth order Lobatto element.
Features of warped geometry in presence of Gauss-Bonnet coupling
NASA Astrophysics Data System (ADS)
Choudhury, Sayantan; SenGupta, Soumitra
2013-02-01
We study the role of the Gauss-Bonnet corrections and two loop higher genus contribution to the gravity action on the Kaluza-Klien modes and their interactions for different bulk fields which enable one to study various phenomenological implications of string loop corrected Gauss-Bonnet modified warped geometry model in one canvas. We have explicitly derived a phenomenological bound on the Gauss-Bonnet parameter so that the required Planck to TeV scale hierarchy can be achieved through the warp factor in the light of recently discovered Higgs like boson at 125GeV. Moreover due to the presence of small perturbative Gauss-Bonnet as well as string loop corrections we have shown that the warping solution can be obtained for both de-Sitter and anti-de-Sitter bulk which is quite distinct from Randall-Sundrum scenario. Finally we have evaluated various interactions among these bulk fields and determined the coupling parameters and the Kaluza-Klien mode masses which is crucial to understand the phenomenology of a string two loop corrected Einstein-Gauss-Bonnet warp geometry.
Nonparaxial propagation of Lorentz-Gauss beams in uniaxial crystal orthogonal to the optical axis.
Wang, Xun; Liu, Zhirong; Zhao, Daomu
2014-04-01
Analytical expressions for the three components of nonparaxial propagation of a polarized Lorentz-Gauss beam in uniaxial crystal orthogonal to the optical axis are derived and used to investigate its propagation properties in uniaxial crystal. The influences of the initial beam parameters and the parameters of the uniaxial crystal on the evolution of the beam-intensity distribution in the uniaxial crystal are examined in detail. Results show that the statistical properties of a nonparaxial Lorentz-Gauss beam in a uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam's parameters and the parameters of the crystal: the beam waist sizes-w(0), w(0x), and w(0y)-not only affect the size and shape of the beam profile in uniaxial crystal but also determine the nonparaxial effect of a Lorentz-Gauss beam; the beam profile of a Lorentz-Gauss beam in uniaxial crystal is elongated in the x or y direction, which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index; with increasing deviation of the ratio from unity, the extension of the beam profile augments. The results indicate that uniaxial crystal provides an effective and convenient method for modulating the Lorentz-Gauss beams. Our results may be valuable in some fields, such as optical trapping and nonlinear optics, where a light beam with a special profile and polarization is required.
Eliminating chromatic aberration in Gauss-type lens design using a novel genetic algorithm.
Fang, Yi-Chin; Tsai, Chen-Mu; Macdonald, John; Pai, Yang-Chieh
2007-05-01
Two different types of Gauss lens design, which effectively eliminate primary chromatic aberration, are presented using an efficient genetic algorithm (GA). The current GA has to deal with too many targets in optical global optimization so that the performance is not much improved. Generally speaking, achromatic aberrations have a great relationship with variable glass sets for all elements. For optics whose design is roughly convergent, glass sets for optics will play a significant role in axial and lateral color aberration. Therefore better results might be derived from the optimal process of eliminating achromatic aberration, which could be carried out by finding feasible glass sets in advance. As an alternative, we propose a new optimization process by using a GA and involving theories of geometrical optics in order to select the best optical glass combination. Two Gauss-type lens designs are employed in this research. First, a telephoto lens design is sensitive to axial aberration because of its long focal length, and second, a wide-angle Gauss design is complicated by lateral color aberration at the extreme corners because Gauss design is well known not to deal well with wide-angle problems. Without numbers of higher chief rays passing the element, it is difficult to correct lateral color aberration altogether for the Gauss design. The results and conclusions show that the attempts to eliminate primary chromatic aberrations were successful.
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.
Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum
Dotti, Gustavo; Oliva, Julio; Troncoso, Ricardo
2010-07-15
The classification of a certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in d{>=}5 dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for d>5. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximally symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum.
Warm-tachyon Gauss-Bonnet inflation in the light of Planck 2015 data
NASA Astrophysics Data System (ADS)
Motaharfar, Meysam; Sepangi, Hamid Reza
2016-11-01
We study a warm-tachyon inflationary model non-minimally coupled to a Gauss-Bonnet term. The general conditions required for reliability of the model are obtained by considerations of a combined hierarchy of Hubble and Gauss-Bonnet flow functions. The perturbed equations are comprehensively derived in the longitudinal gauge in the presence of slow-roll and quasi-stable conditions. General expressions for observable quantities of interest such as the tensor-to-scalar ratio, scalar spectral index and its running are found in the high dissipation regime. Finally, the model is solved using exponential and inverse power-law potentials, which satisfy the properties of a tachyon potential, with parameters of the model being constrained within the framework of the Planck 2015 data. We show that the Gauss-Bonnet coupling constant controls termination of inflation in such a way as to be in good agreement with the Planck 2015 data.
A soliton and a black hole are in Gauss-Bonnet gravity: Who wins?
NASA Astrophysics Data System (ADS)
Wong, Anson W. C.; Mann, Robert B.
2012-12-01
We study here the phase-transitional evolution between the Eguchi-Hanson soliton, the orbifolded Schwarzschild anti-de Sitter black hole, and orbifolded thermal anti-de Sitter space in Gauss-Bonnet gravity for a small Gauss-Bonnet coefficient α. Novel phase structure is uncovered for both negative and positive α with spacetime configurations that are stable in Gauss-Bonnet gravity without being so in Einsteinian gravity. The evolutionary tracks taken towards such stable configurations are guided by quantum tunneling and can be represented with a phase diagram constructed by comparing the Euclidean actions of each of our states as a function of α and the black hole radius rb. According to the AdS/CFT correspondence dictionary, it is expected that some generalized version of closed-string tachyon condensation will exhibit the phase behavior found here.
Testing Einstein-dilaton-Gauss-Bonnet gravity with the reflection spectrum of accreting black holes
NASA Astrophysics Data System (ADS)
Zhang, Hao; Zhou, Menglei; Bambi, Cosimo; Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen
2017-05-01
Einstein-dilaton-Gauss-Bonnet gravity is a theoretically well-motivated alternative theory of gravity emerging as a low-energy four-dimensional model from heterotic string theory. Its rotating black hole solutions are known numerically and can have macroscopic deviations from the Kerr black holes of Einstein's gravity. Einstein-dilaton-Gauss-Bonnet gravity can thus be tested with observations of astrophysical black holes. In the present paper, we simulate observations of the reflection spectrum of thin accretion disks with present and future x-ray facilities to understand whether x-ray reflection spectroscopy can distinguish the black holes in Einstein-dilaton-Gauss-Bonnet gravity from those in Einstein's gravity. We find that this is definitively out of reach for present x-ray missions, but it may be achieved with the next generation of facilities.
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.
Dynamics of a Flat Multidimensional Anisotropic Universe in the Gauss-Bonnet Gravity
NASA Astrophysics Data System (ADS)
Toporensky, Alexey; Kirnos, Ilya; Pavluchenko, Sergyey
We consider a flat anisotropic metric in (4+1)- and (5+1)-dimensional space-time in Gauss-Bonnet gravity. In the present presentation we are interesting in the behavior mostly in the vicinity of the cosmological singularity, which allows us to take into account only corrections of the highest possible order. In our case it is the Gauss-Bonnet contribution, so we neglect Einstein terms. In the absence of matter sources this problem have been studied in Ref. 1,2, in the present presentation we take matter into account. The full Einstein - Gauss-Bonnet system shows a complicated behavior even in the vacuum case3,4 and we leave investigation of such system with matter for a future work.
Gauss-bonnet black holes and possibilities for their experimental search
NASA Astrophysics Data System (ADS)
Alexeyev, S. O.; Rannu, K. A.
2012-03-01
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 1015 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.
Enhanced instability of de Sitter space in Einstein-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Parikh, Maulik
2011-08-01
We show that the addition of a topological Gauss-Bonnet term to the gravitational action can greatly increase the instability of four-dimensional de Sitter space by favoring the nucleation of black holes. The pair-production rate given by the Euclidean action for the instanton takes the form exp(ΔS) where S is the entropy in Einstein-Gauss-Bonnet theory. The coefficient of the Gauss-Bonnet term in the action sets a stability bound on the curvature of empty de Sitter space. For that coefficient in the low-energy effective action of heterotic string theory, the maximal curvature of de Sitter space is, in general, much lower than the Planck scale.
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.
Holographic phase transitions of p-wave superconductors in Gauss-Bonnet gravity with backreaction
Cai Ronggen; Nie Zhangyu; Zhang Haiqing
2011-03-15
We investigate the phase transitions of holographic p-wave superconductors in (4+1)-dimensional Einstein-Yang-Mills-Gauss-Bonnet theories, in a grand canonical ensemble. Turning on the backreaction of the Yang-Mills field, it is found that the condensations of vector order parameter become harder if the Gauss-Bonnet coefficient grows up or the backreaction becomes stronger. In particular, the vector order parameter exhibits the features of first order and second order phase transitions, while only the second order phase transition is observed in the probe limit. We discuss the roles that the Gauss-Bonnet term and the backreaction play in changing the order of phase transition.
Inhomogeneous dust collapse in 5D Einstein-Gauss-Bonnet gravity
Jhingan, S.; Ghosh, Sushant G.
2010-01-15
We consider a Lemaitre-Tolman-Bondi type space-time in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms, and present an exact solution in closed form. It turns out that the presence of the coupling constant of the Gauss-Bonnet terms {alpha}>0 completely changes the causal structure of the singularities from the analogous general relativistic case. The gravitational collapse of inhomogeneous dust in the five-dimensional Gauss-Bonnet extended Einstein equations leads to formation of a massive, but weak, timelike singularity which is forbidden in general relativity. Interestingly, this is a counterexample to three conjectures, viz., cosmic censorship conjecture, hoop conjecture, and Seifert's conjecture.
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.
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
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.
Addendum to ''Thin-shell wormholes supported by ordinary matter in Einstein-Gauss-Bonnet gravity''
Simeone, Claudio
2011-04-15
Thin-shell wormholes are constructed starting from the exotic branch of the Wiltshire spherically symmetric solution of Einstein-Gauss-Bonnet gravity. The energy-momentum tensor of the shell is studied, and it is shown that configurations supported by matter satisfying the energy conditions exist for certain values of the parameters. Differing from the previous result associated with the normal branch of the Wiltshire solution, this is achieved for small positive values of the Gauss-Bonnet parameter and for vanishing charge.
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.
Tachyon Cosmology with Gauss-Bonnet and Non-Minimal Kinetic Couplings
NASA Astrophysics Data System (ADS)
Banijamali, A.
2016-05-01
We consider a tachyonic model of dark energy in which scalar field non-minimally coupled with curvature and kinetic part of its Lagrangian density. Additionally the model contains the Gauss-Bonnet coupling to the scalar field through an arbitrary function. The non-minimal Gauss-Bonnet coupling function and scalar field potential have been obtained for power-law solution and then for a dynamically varying equation of state. We have extracted the required condition for the so-called phantom divide line crossing in the model and represented such a crossing numerically.
An evaluation of the Gauss-Radau algorithm for the simulation of chemical dynamics
Bolton, K.; Nordholm, S. Chalmers Univ. of Technology, Goeteborg )
1994-08-01
The Verlet, Verlet leap frog, Gear fixed time step, Gear variable time step, Runge-Kutta, and Gauss-Radau algorithms have been compared using trajectory data obtained from the integration of a one-dimensional diatomic chain under constant pressure. Investigation into the times of local and normal mode relaxation and conservation of the constants of the motion facilitated comparison of the integration techniques. It has been found that the Gauss-Radau algorithm, which is not widely used in the simulation of chemical dynamics, generally affords a higher accuracy at an improved efficiency. 14 refs., 10 figs., 11 tabs.
Gauss-Bonnet correction to the R-current correlator in N =4 theory at strong coupling
NASA Astrophysics Data System (ADS)
Bu, Yanyan
2014-04-01
We consider higher-curvature corrections to the R-current correlator by studying the propagation of a U(1) field in Einstein-Gauss-Bonnet gravity with a negative cosmological constant. We numerically solve the Maxwell equations and plot an R-current spectral function with lightlike momenta, which contains pivotal information of thermal photon emission. We also analytically compute the R-current correlator in the long-distance limit by using the holographic membrane paradigm. In the high-energy regime, the inelastic scattering between R-current and gauge theory plasma is expected to happen, which will reveal the structure of the plasma at strong coupling. It turns out that the Gauss-Bonnet correction effectively rescales all physical quantities considered here by some functions of the Gauss-Bonnet coefficient. In particular, the Gauss-Bonnet terms will enhance or weaken signatures calculated here in accordance with the sign of the Gauss-Bonnet coefficient.
A new estimation method for two-step-only quadrature phase-shifting digital holography
NASA Astrophysics Data System (ADS)
Zhang, Shuqun; Zhou, Jianyang
2015-01-01
Two-step-only quadrature phase-shifting digital holography can reconstruct the original complex object using only two holograms without the additional recording of the reference wave intensity and the object wave intensity. Its success depends on the accurate estimation of the reference wave intensity from the two acquired holograms. The previous estimation method is relatively computational expensive. In this paper, we present a novel simple and effective method for estimating the reference wave intensity with low computational load. Simulation results are presented to demonstrate the effectiveness and speedup of the proposed method.
Quadrature-Free Implementation of the Discontinuous Galerkin Method for Hyperbolic Equations
NASA Technical Reports Server (NTRS)
Atkins, H. L.; Shu, Chi-Wang
1996-01-01
A discontinuous Galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions. This approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent to the discontinuous Galerkin method. Test problems include both linear and nonlinear one-dimensional scalar advection of botH smooth and discontinuous initial value problems, two-dimensional scalar advection of smooth initial value problems discretized by using unstructured grids with varying degrees of smoothness and regularity, and two-dimensional linear Euler solutions on unstructured grids.
Quadrature-Free Implementation of the Discontinuous Galerkin Method for Hyperbolic Equations
NASA Technical Reports Server (NTRS)
Atkins, H. L.; Shu, Chi-Wang
1996-01-01
A discontinuous Galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions. This approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent to the discontinuous Galerkin method. Test problems include both linear and nonlinear one-dimensional scalar advection of botH smooth and discontinuous initial value problems, two-dimensional scalar advection of smooth initial value problems discretized by using unstructured grids with varying degrees of smoothness and regularity, and two-dimensional linear Euler solutions on unstructured grids.
Bottrill, K R H; Hesketh, G; Jones, L; Parmigiani, F; Richardson, D J; Petropoulos, P
2017-01-23
We demonstrate all-optical regeneration of both the phase and the amplitude of a 10 GBaud quadrature phase shift keying (QPSK) signal using two nonlinear stages. First we regenerate the phase using a wavelength converting phase sensitive amplifier and then we regenerate the amplitude using a saturated single-pump parametric amplifier, returning the signal to its original wavelength at the same time. We exploit the conjugating nature of the two processing stages to eliminate the intrinsic SPM distortion of the system, further improving performance.
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.
Improving noiseless linear amplification for optical quantum communication with quadrature squeezing
NASA Astrophysics Data System (ADS)
Yang, Song; Zhang, ShengLi; Zou, XuBo; Bi, SiWen; Lin, XuLing
2013-02-01
Quantum noiseless linear amplification (NLA) is an important tool for long-distance optical quantum communication. In this paper, we show that NLA with linear optics and photon counts can be further improved by applying quadrature squeezing. Moreover, we find that such enhancement through squeezing can be observed even when a photon dichotic on-off detector and a pseudo-single-photon state are applied to the amplification process. Such a result could find more applications in already-known NLA-related quantum information tasks.
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.
Ten-no, Seiichiro
2004-07-01
A rational generator, which fulfills the cusp conditions for singlet and triplet electron pairs, is proposed and applied to explicitly correlated second order Møller-Plesset perturbation theory calculations. It is shown that the generator in conjunction with frozen geminals improves the convergence of correlation energy without introducing any variational parameters in explicitly correlated functions. A new scheme for three-electron integrals based on numerical quadratures is also illustrated. The method is tested for the convergence of reaction enthalpies with various basis sets. (c) 2004 American Institute of Physics.
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.
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.
NASA Astrophysics Data System (ADS)
Kato, Kentaro; Hirota, Osamu
2005-08-01
The quadrature amplitude modulation (QAM) signal of coherent state of light is applied to the quantum stream cipher by Y-00 protocol. We first discuss on the performance of the square-root measurement (SRM) for the QAM signals in comparison with the optimum receiver. It is shown that the quantum stream cipher with the QAM signals is designed by using the SRM, taking account of the ciphertext-only attack and the known/chosen plain attack. Furthermore, the modification of the quantum stream cipher with the QAM signals is considered.
Cui, Junning; He, Zhangqiang; Tan, Jiubin; Sun, Tao
2016-10-03
The deviation of wave plates' optical axes from their intended angles, which may result from either instability or assembly error, is the main cause of quadrature phase error in homodyne quadrature laser interferometers (HQLIs). The quadrature phase error sensitivity to wave plate angle deviations, which is an effective measure of HQLI robustness, is further amplified by beam splitter imperfections. In this paper, a new HQLI design involving non-polarization beam splitting is presented, and a method of making this HQLI robust by yawing the wave plates in the measurement and reference arms is proposed. The theoretical analysis results indicate that ultra-low quadrature phase error sensitivities to wave plate angle deviations can be realized and that non-polarizing beam splitter imperfections can be adequately compensated for. The experimental results demonstrate that the proposed method can reduce the quadrature phase error sensitivity by more than 1 order of magnitude, from a theoretical value of 1.4°/1° to 0.05°/1°.
Exact vs. Gauss-Seidel numerical solutions of the non-LTE radiation transfer problem
NASA Astrophysics Data System (ADS)
Quang, Carine; Paletou, Frédéric; Chevallier, Loïc
2004-12-01
Although published in 1995 (Trujillo Bueno & Fabiani Bendicho, ApJ 455, 646), the Gauss-Seidel method for solving the non-LTE radiative transfer problem has deserved too little attention in the astrophysical community yet. Further tests of the performances and of the accuracy of the numerical scheme are provided.
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…
NASA Astrophysics Data System (ADS)
Jing, Jiliang; Pan, Qiyuan; Chen, Songbai
2012-10-01
The behaviors of the holographic superconductors/insulator transition are studied by introducing a charged scalar field coupled with a logarithmic electromagnetic field in both the Einstein-Gauss-Bonnet AdS black hole and soliton. For the Einstein-Gauss-Bonnet AdS black hole, we find that: i) the larger coupling parameter of logarithmic electrodynamic field b makes it easier for the scalar hair to be condensed; ii) the ratio of the gap frequency in conductivity ωg to the critical temperature Tc depends on both b and the Gauss-Bonnet constant α; and iii) the critical exponents are independent of the b and α. For the Einstein-Gauss-Bonnet AdS soliton, we show that the system is the insulator phase when the chemical potential μ is small, but there is a phase transition and the AdS soliton reaches the superconductor (or superfluid) phase when μ is larger than critical chemical potential. A special property should be noted is that the critical chemical potential is not changed by the coupling parameter b but depends on α.
A Gauss-Bonnet Cosmology with an Effective Time-Dependent Scalar Potential
NASA Astrophysics Data System (ADS)
El-Nabulsi, Rami Ahmad
2017-05-01
A special class of a Gauss-Bonnet minimal power-law cosmology characterised by an effective time-dependent scalar field potential is explored in this communication. Some new features related to the late-time cosmological dynamics are observed and discussed accordingly.
Observational constraints on braneworld inflation: The effect of a Gauss-Bonnet term
Tsujikawa, Shinji; Sami, M.; Maartens, Roy
2004-09-15
High-energy modifications to general relativity introduce changes to the perturbations generated during inflation, and the latest high-precision cosmological data can be used to place constraints on such modified inflation models. Recently it was shown that Randall-Sundrum-type braneworld inflation leads to tighter constraints on quadratic and quartic potentials than in general relativity. We investigate how this changes with a Gauss-Bonnet correction term, which can be motivated by string theory. Randall-Sundrum models preserve the standard consistency relation between the tensor spectral index and the tensor-to-scalar ratio. The Gauss-Bonnet term breaks this relation, and also modifies the dynamics and perturbation amplitudes at high energies. We find that the Gauss-Bonnet term tends to soften the Randall-Sundrum constraints. The observational compatibility of the quadratic potential is strongly improved. For a broad range of energy scales, the quartic potential is rescued from marginal rejection. Steep inflation driven by an exponential potential is excluded in the Randall-Sundrum case, but the Gauss-Bonnet term leads to marginal compatibility for sufficient e-folds.
Thin-shell wormholes supported by ordinary matter in Einstein-Gauss-Bonnet gravity
Richarte, Martin G.; Simeone, Claudio
2007-10-15
The generalized Darmois-Israel formalism for Einstein-Gauss-Bonnet theory is applied to construct thin-shell Lorentzian wormholes with spherical symmetry. We calculate the energy localized on the shell, and we find that for certain values of the parameters wormholes could be supported by matter not violating the energy conditions.
Boundary causality versus hyperbolicity for spherical black holes in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia
2017-07-01
We explore the constraints boundary causality places on the allowable Gauss-Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss-Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss-Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss-Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.
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…
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…
On the structure of quadratic Gauss sums in the Talbot effect.
Fernández-Pousa, Carlos R
2017-05-01
We report on the detailed derivation of the Gauss sums leading to the weighting phase factors in the fractional Talbot effect. In contrast to previous approaches, the derivation is directly based on the two coprime integers p and q that define the fractional Talbot effect so that, using standard techniques from the number theory, the computation is reduced, up to a global phase, to the trivial completion of the exponential of the square of a sum. In addition, it is shown that the Gauss sums can be reduced to only two cases, depending on the parity of integer q. Explicit and simpler expressions for the two forms of the Talbot weighting phases are also provided. The Gauss sums are presented as a discrete Fourier transform pair between quadratic phase sequences showing perfect periodic autocorrelation and a connection with the theory of biunimodular sequences is presented. In addition, the Talbot weighting factors of orders 1/q and 2/q are reduced to a closed form, and the equivalence to existing characterizations of Talbot weighting phases is also discussed. The relationship with one-dimensional multilevel phase structures is exemplified by the study of Talbot array illuminators. These results simplify and extend the description of the role played by Gauss sums in the fractional Talbot effect, providing a compact synthesis of previous results.
Basic full-wave generalization of the real-argument Hermite-Gauss beam.
Seshadri, S R
2010-05-01
The linearly polarized real-argument Hermite-Gauss beam is investigated by the Fourier transform method. The complex power is obtained and the reactive power of the paraxial beam is found to be zero. The complex space source required for the full-wave generalization of the real-argument Hermite-Gauss beam is deduced. The resulting basic full real-argument Hermite-Gauss wave is determined. The real and the reactive powers of the full wave are evaluated. The reactive power of the basic full real-argument Hermite-Gauss wave is infinite, and the reasons for this singularity are described. The real power depends on kw(0), m, and n, where k is the wavenumber, w(0) is the e-folding distance of the Gaussian part of the input distribution, and m and n are the mode numbers. The variation in the real power with respect to changes in kw(0) for specified m and n as well as with respect to changes in m and n for a specified kw(0) is examined.
Generation of J0-Bessel-Gauss beam by a heterogeneous refractive index map.
San-Roman-Alerigi, Damian P; Ng, Tien K; Zhang, Yaping; Ben Slimane, Ahmed; Alsunaidi, Mohammad; Ooi, Boon S
2012-07-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J(0)-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si(1-y)O(y)/Si(1-x-y)Ge(x)C(y) platform or by photo-refractive media. The proposed device is 200 μm in length and 25 μm in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J(0)-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers.
ERIC Educational Resources Information Center
Cudeck, Robert; And Others
1993-01-01
An implementation of the Gauss-Newton algorithm for the analysis of covariance structure that is specifically adapted for high-level computer languages is reviewed. This simple method for estimating structural equation models is useful for a variety of standard models, as is illustrated. (SLD)
Beam propagation factors and kurtosis parameters of a Lorentz-Gauss vortex beam.
Zhou, Guoquan
2014-06-01
Based on the second-order and the higher-order moments, analytical expressions for the beam propagation factors of a Lorentz-Gauss vortex beam with l=1 have been derived, and analytical propagation expressions for the kurtosis parameters of a Lorentz-Gauss vortex beam with l=1 through a paraxial and real ABCD optical system have also been presented. The M² factor is determined by the parameters a and b and decreases with increasing the parameter a or b. The M² factor is validated to be larger than 2. The kurtosis parameters depend on the diffraction-free ranges of the Lorentz part, the parameters a and b, and the ratio A/B. The kurtosis parameters of a Lorentz-Gauss vortex beam propagating in free space are demonstrated in different reference planes. In the far field, the kurtosis parameter K decreases with increasing one of the parameters a and b. Upon propagation, the kurtosis parameter K first decreases, then increases, and finally tends to a saturated value. In any case, the kurtosis parameter K is larger than 2. This research is beneficial to optical trapping, guiding, and manipulation of microscopic particles and atoms using Lorentz-Gauss vortex beams.
A Modified Gauss-Jordan Procedure as an Alternative to Iterative Procedures in Multiple Regression.
ERIC Educational Resources Information Center
Roscoe, John T.; Kittleson, Howard M.
Correlation matrices involving linear dependencies are common in educational research. In such matrices, there is no unique solution for the multiple regression coefficients. Although computer programs using iterative techniques are used to overcome this problem, these techniques possess certain disadvantages. Accordingly, a modified Gauss-Jordan…
Vallone, Giuseppe
2015-04-15
Circular beams were introduced as a very general solution to the paraxial wave equation carrying orbital angular momentum. Here, we study their properties by looking at their normalization and their expansion in terms of Laguerre-Gauss modes. We also study their far-field divergence and, for particular cases of the beam parameters, their possible experimental generation.
A Modified Gauss-Jordan Procedure as an Alternative to Iterative Procedures in Multiple Regression.
ERIC Educational Resources Information Center
Roscoe, John T.; Kittleson, Howard M.
Correlation matrices involving linear dependencies are common in educational research. In such matrices, there is no unique solution for the multiple regression coefficients. Although computer programs using iterative techniques are used to overcome this problem, these techniques possess certain disadvantages. Accordingly, a modified Gauss-Jordan…
ERIC Educational Resources Information Center
Cudeck, Robert; And Others
1993-01-01
An implementation of the Gauss-Newton algorithm for the analysis of covariance structure that is specifically adapted for high-level computer languages is reviewed. This simple method for estimating structural equation models is useful for a variety of standard models, as is illustrated. (SLD)
Goos-Hanchen and Imbert-Fedorov shifts for Hermite-Gauss beams.
Prajapati, Chandra; Ranganathan, D
2012-07-01
We study the lateral Goos-Hanchen and the transverse Imbert-Fedorov shift produced during the reflection of Hermite-Gauss beams H(m0) or H(0m) at a plane interface. The vector angular spectrum method for a light beam in terms of a two-form angular spectrum consisting of the two orthogonal polarized components was used. We have carried out a detailed numerical calculation of these shifts at different angles of incidence, over the whole range of incidence without making the usual approximations. The shift variation as a function of refractive index and order of the Hermite-Gauss beam is studied. We also compare the shift variations with the orientation of the lobes of the Hermite-Gauss beam. We observed that the shifts are nearly equal for the two cases H(m0) (lobe oriented in the plane of incidence) and H(0m) (lobe oriented perpendicular to plane of incidence). These are the first quantitative estimates of the shifts for Hermite-Gauss beams as per our knowledge and are relevant for all cases of slab geometry.
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.
Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations
Fierce, Laura; McGraw, Robert L.
2017-07-26
Here, sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the quadrature method of moments. Given a set of moment constraints, we show how linear programming, combined with an entropy-inspired cost function, can be used to construct optimized quadrature representations of aerosol distributions. The sparse representations derived from this approach accurately reproduce cloud condensation nuclei (CCN) activity for realistically complex distributions simulated by a particleresolved model. Additionally, the linear programming techniques described in this study can be used to bound key aerosolmore » properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy approach described here is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a particle-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.« less
Compressive optical image encryption with two-step-only quadrature phase-shifting digital holography
NASA Astrophysics Data System (ADS)
Li, Jun; Li, Hongbing; Li, Jiaosheng; Pan, Yangyang; Li, Rong
2015-06-01
An image encryption method which combines two-step-only quadrature phase-shifting digital holography with compressive sensing (CS) has been proposed in the fully optical domain. An object image is firstly encrypted to two on-axis quadrature-phase holograms using the two random phase masks in the Mach-Zehnder interferometer. Then, the two encrypted images are highly compressed to a one-dimensional signal using the single-pixel compressive holographic imaging in the optical domain. At the receiving terminal, the two compressive encrypted holograms are exactly reconstructed from much less than the Nyquist sampling number of observations by solving an optimization problem, and the original image can be decrypted with only two reconstructed holograms and the correct keys. This method largely decreases holograms data volume for the current optical image encryption system, and it is also suitable for some special optical imaging cases such as different wavelengths imaging and weak light imaging. Numerical simulation is performed to demonstrate the feasibility and validity of this novel image encryption method.
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)
NASA Astrophysics Data System (ADS)
Shoupeng, Song; Zhou, Jiang
2017-03-01
Converting ultrasonic signal to ultrasonic pulse stream is the key step of finite rate of innovation (FRI) sparse sampling. At present, ultrasonic pulse-stream-forming techniques are mainly based on digital algorithms. No hardware circuit that can achieve it has been reported. This paper proposes a new quadrature demodulation (QD) based circuit implementation method for forming an ultrasonic pulse stream. Elaborating on FRI sparse sampling theory, the process of ultrasonic signal is explained, followed by a discussion and analysis of ultrasonic pulse-stream-forming methods. In contrast to ultrasonic signal envelope extracting techniques, a quadrature demodulation method (QDM) is proposed. Simulation experiments were performed to determine its performance at various signal-to-noise ratios (SNRs). The circuit was then designed, with mixing module, oscillator, low pass filter (LPF), and root of square sum module. Finally, application experiments were carried out on pipeline sample ultrasonic flaw testing. The experimental results indicate that the QDM can accurately convert ultrasonic signal to ultrasonic pulse stream, and reverse the original signal information, such as pulse width, amplitude, and time of arrival. This technique lays the foundation for ultrasonic signal FRI sparse sampling directly with hardware circuitry.
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.
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.
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.
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.
Digital Detection and Processing of Multiple Quadrature Harmonics for EPR Spectroscopy
Ahmad, R.; Som, S.; Kesselring, E.; Kuppusamy, P.; Zweier, J.L.; Potter, L.C.
2010-01-01
A quadrature digital receiver and associated signal estimation procedure are reported for L-band electron paramagnetic resonance (EPR) spectroscopy. The approach provides simultaneous acquisition and joint processing of multiple harmonics in both in-phase and out-of-phase channels. The digital receiver, based on a high-speed dual-channel analog-to-digital converter, allows direct digital down-conversion with heterodyne processing using digital capture of the microwave reference signal. Thus, the receiver avoids noise and nonlinearity associated with analog mixers. Also, the architecture allows for low-Q anti-alias filtering and does not require the sampling frequency to be time-locked to the microwave reference. A noise model applicable for arbitrary contributions of oscillator phase noise is presented, and a corresponding maximum-likelihood estimator of unknown parameters is also reported. The signal processing is applicable for Lorentzian lineshape under nonsaturating conditions. The estimation is carried out using a convergent iterative algorithm capable of jointly processing the in-phase and out-of-phase data in the presence of phase noise and unknown microwave phase. Cramér-Rao bound analysis and simulation results demonstrate a significant reduction in linewidth estimation error using quadrature detection, for both low and high values of phase noise. EPR spectroscopic data are also reported for illustration. PMID:20971667
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.
Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation
NASA Astrophysics Data System (ADS)
Ly-Gagnon, Dany-Sebastien; Tsukamoto, Satoshi; Katoh, Kazuhiro; Kikuchi, Kazuro
2006-01-01
This paper describes a coherent optical receiver for demodulating optical quadrature phase-shift keying (QPSK) signals. At the receiver, a phase-diversity homodyne detection scheme is employed without locking the phase of the local oscillator (LO). To handle the carrier phase drift, the carrier phase is estimated with digital signal processing (DSP) on the homodyne-detected signal. Such a scheme presents the following major advantages over the conventional optical differential detection. First, its bit error rate (BER) performance is better than that of differential detection. This higher sensitivity can extend the reach of unrepeated transmission systems and reduce crosstalk between multiwavelength channels. Second, the optoelectronic conversion process is linear, so that the whole optical signal information can be postprocessed in the electrical domain. Third, this scheme is applicable to multilevel modulation formats such as M-array PSK and quadrature amplitude modulation (QAM). The performance of the receiver is evaluated through various simulations and experiments. As a result, an unrepeated transmission over 210 km with a 20-Gb/s optical QPSK signal is achieved. Moreover, in wavelength-division multiplexing (WDM) environment, coherent detection allows the filtering of a desired wavelength channel to reside entirely in the electrical domain, taking advantage of the sharp cutoff characteristics of electrical filters. The experiments show the feasibility to transmit polarization-multiplexed 40-Gb/s QPSK signals over 200 km with channel spacing of 16 GHz, leading to a spectral efficiency as high as 2.5 b/s/Hz.
NASA Astrophysics Data System (ADS)
Kavehrad, M.; Sundberg, C.-E.; McLane, P. J.
The performance of cross-coupled, M-ary Quadrature Amplitude Modulation (QAM) systems is determined when bandwidth efficient trellis codes are used to combat interference. Performance with and without compensation for cross-coupled interference is presented. It is found that simple trellis codes can maintain the error probability at an acceptable level for cross-coupling parameters that render uncoded systems unusable. Up to two dimensional trellis codes are considered for four dimensional QAM signals. The average probability of the most likely error events is calculated by using the method of moments. The results are applicable to any digital communication system using multidimensional quadrature amplitude modulation, e.g., voiceband modems and cross-polarized radio systems. In the paper the analysis is restricted to nondispersive cross-coupling models. In most cases the coding gain is larger than in the absence of cross-coupling interference. Specifically, it is found that simple trellis codes have coding gains of more than 5 dB in cross-coupling interference compared to 3 dB for a Gaussian channel. This is obtained for schemes compared at equal bandwidth.
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.
Digital detection and processing of multiple quadrature harmonics for EPR spectroscopy.
Ahmad, R; Som, S; Kesselring, E; Kuppusamy, P; Zweier, J L; Potter, L C
2010-12-01
A quadrature digital receiver and associated signal estimation procedure are reported for L-band electron paramagnetic resonance (EPR) spectroscopy. The approach provides simultaneous acquisition and joint processing of multiple harmonics in both in-phase and out-of-phase channels. The digital receiver, based on a high-speed dual-channel analog-to-digital converter, allows direct digital down-conversion with heterodyne processing using digital capture of the microwave reference signal. Thus, the receiver avoids noise and nonlinearity associated with analog mixers. Also, the architecture allows for low-Q anti-alias filtering and does not require the sampling frequency to be time-locked to the microwave reference. A noise model applicable for arbitrary contributions of oscillator phase noise is presented, and a corresponding maximum-likelihood estimator of unknown parameters is also reported. The signal processing is applicable for Lorentzian lineshape under nonsaturating conditions. The estimation is carried out using a convergent iterative algorithm capable of jointly processing the in-phase and out-of-phase data in the presence of phase noise and unknown microwave phase. Cramér-Rao bound analysis and simulation results demonstrate a significant reduction in linewidth estimation error using quadrature detection, for both low and high values of phase noise. EPR spectroscopic data are also reported for illustration.
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).
Dadhich, Naresh; Pons, Josep M
We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.
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
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
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
ERIC Educational Resources Information Center
Smith, H. V.
2008-01-01
A method is derived for the numerical evaluation of the error term arising in some Gauss-type formulae modified so as to approximate Cauchy Principal Value integrals. The method uses Chebyshev polynomials of the first kind. (Contains 1 table.)
ERIC Educational Resources Information Center
Smith, H. V.
2008-01-01
A method is derived for the numerical evaluation of the error term arising in some Gauss-type formulae modified so as to approximate Cauchy Principal Value integrals. The method uses Chebyshev polynomials of the first kind. (Contains 1 table.)
Hong-Ou-Mandel interference of entangled Hermite-Gauss modes
NASA Astrophysics Data System (ADS)
Zhang, Yingwen; Prabhakar, Shashi; Rosales-Guzmán, Carmelo; Roux, Filippus S.; Karimi, Ebrahim; Forbes, Andrew
2016-09-01
Hong-Ou-Mandel (HOM) interference is demonstrated experimentally for entangled photon pairs in the Hermite-Gauss (HG) basis. We use two Dove prisms in one of the paths of the photons to manipulate the entangled quantum state that enters the HOM interferometer. It is demonstrated that, when entangled photon pairs are in a symmetric Bell state in the Laguerre-Gauss (LG) basis, they will remain symmetric after decomposing them into the HG basis, thereby resulting in no coincidence events after the HOM interference. On the other hand, if the photon pairs are in an antisymmetric Bell state in the LG basis, then they will also be antisymmetric in the HG basis, thereby producing only coincidence events as a result of the HOM interference.
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.
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.
History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term
NASA Astrophysics Data System (ADS)
Debnath, Subhra; Ruz, Soumendra Nath; Mandal, Ranajit; Sanyal, Abhik Kumar
2017-05-01
Gauss-Bonnet-dilatonic coupling in four dimensions plays an important role to explain late-time cosmic evolution. However, this term is an outcome of the low energy string effective action and thus ought to be important in the early universe too. Unfortunately, a phase-space formulation of such a theory does not exist in the literature due to branching. We therefore consider a modified theory of gravity, which contains a nonminimally coupled scalar-tensor sector in addition to a higher-order scalar curvature invariant term with Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation with late-time cosmic acceleration. The quantum version of the theory is also well behaved.
Phase transition for black holes in dilatonic Einstein-Gauss-Bonnet theory of gravitation
NASA Astrophysics Data System (ADS)
Khimphun, Sunly; Lee, Bum-Hoon; Lee, Wonwoo
2016-11-01
We study the thermodynamic properties of a black hole and the Hawking-Page phase transition in the asymptotically anti-de Sitter spacetime in the dilatonic Einstein-Gauss-Bonnet theory of gravitation. We show how the higher-order curvature terms can influence both the thermodynamic properties and the phase transition. We evaluate both heat capacity and free energy difference to determine the local and global thermodynamic stabilities, respectively. We find that the phase transition occurs from the thermal anti-de Sitter to a small spherical black hole geometry and occurs to a hyperbolic black hole geometry in the (dilatonic) Einstein-Gauss-Bonnet theory of gravitation unlike those in Einstein's theory of gravitation.
Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term
NASA Astrophysics Data System (ADS)
Koh, Seoktae; Lee, Bum-Hoon; Tumurtushaa, Gansukh
2017-06-01
We consider inflationary models with a Gauss-Bonnet term to reconstruct the scalar-field potentials and the Gauss-Bonnet coupling functions. Both expressions are derived from the observationally favored configurations of ns and r . Our result implies that, for the reconstructed potentials and coupling functions, the blue tilt of inflationary tensor fluctuations can be realized. To achieve a blue tilt for the inflationary tensor fluctuations, a scalar field must climb up its potential before rolling down. We further investigate the properties of propagation of the perturbation modes in Friedmann-Robertson-Walker spacetime. For the reconstructed configurations that give rise to the blue tilt for the inflationary tensor fluctuations, we show that the ghosts and instabilities are absent with the superluminal propagation speeds for the scalar perturbation modes, whereas the propagation speeds of the tensor perturbations are subluminal.
Higher-dimensional thin-shell wormholes in Einstein-Yang-Mills-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Mazharimousavi, S. Habib; Halilsoy, M.; Amirabi, Z.
2011-01-01
We present thin-shell wormhole solutions in the Einstein-Yang-Mills-Gauss-Bonnet (EYMGB) theory in higher dimensions d >= 5. Exact black hole solutions are employed for this purpose where the radius of the thin shell lies outside the event horizon. For some reasons the cases d = 5 and d > 5 are treated separately. The surface energy-momentum of the thin shell creates surface pressures to resist against collapse and rendering stable wormholes possible. We test the stability of the wormholes against spherical perturbations through a linear energy-pressure relation and plot stability regions. Apart from this restricted stability we investigate the possibility of normal (i.e. non-exotic) matter which satisfies the energy conditions. For negative values of the Gauss-Bonnet (GB) parameter we obtain such physical wormholes.
Modified teleparallel theories of gravity: Gauss-Bonnet and trace extensions.
Bahamonde, Sebastian; Böhmer, Christian G
2016-01-01
We investigate modified theories of gravity in the context of teleparallel geometries with possible Gauss-Bonnet contributions. The possible coupling of gravity with the trace of the energy-momentum tensor is also taken into account. This is motivated by the various different theories formulated in the teleparallel approach and the metric approach without discussing the exact relationship between them. Our formulation clarifies the connections between different well-known theories. For instance, we are able to formulate the correct teleparallel equivalent of Gauss-Bonnet modified general relativity, amongst other results. Finally, we are able to identify modified gravity models which have not been studied in the past. These appear naturally within our setup and would make a interesting starting point for further studies.
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.
Application of Gauss-Seidel multilevel control to a single axis torsional model
NASA Technical Reports Server (NTRS)
Chichester, F. D.
1981-01-01
An approach to the application of multilevel control techniques for large space structures is presented. Gauss-Seidel second level controls and an extension of standard linear quadratic regulator techniques are applied to a model consisting of a flexible space vehicle comprising three rigid bodies rotating about a common axis. The method incorporates second order derivatives with respect to time, entailing the use of a two level hierarchy of subsystems. Gauss-Seidel second level control formulations were chosen to avoid the necessity of having as many controls as constraints or using gradient techniques in the choice of the Hamiltonian. The modular nature of the resulting control system allows applications for spacecraft with larger numbers of modules.
The preconditioned Gauss-Seidel method faster than the SOR method
NASA Astrophysics Data System (ADS)
Niki, Hiroshi; Kohno, Toshiyuki; Morimoto, Munenori
2008-09-01
In recent years, a number of preconditioners have been applied to linear systems [A.D. Gunawardena, S.K. Jain, L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154-156 (1991) 123-143; T. Kohno, H. Kotakemori, H. Niki, M. Usui, Improving modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113-123; H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+Smax), J. Comput. Appl. Math. 145 (2002) 373-378; H. Kotakemori, H. Niki, N. Okamoto, Accelerated iteration method for Z-matrices, J. Comput. Appl. Math. 75 (1996) 87-97; M. Usui, H. Niki, T.Kohno, Adaptive Gauss-Seidel method for linear systems, Internat. J. Comput. Math. 51(1994)119-125 [10
Application of Gauss-Seidel multilevel control to a single axis torsional model
NASA Technical Reports Server (NTRS)
Chichester, F. D.
1981-01-01
An approach to the application of multilevel control techniques for large space structures is presented. Gauss-Seidel second level controls and an extension of standard linear quadratic regulator techniques are applied to a model consisting of a flexible space vehicle comprising three rigid bodies rotating about a common axis. The method incorporates second order derivatives with respect to time, entailing the use of a two level hierarchy of subsystems. Gauss-Seidel second level control formulations were chosen to avoid the necessity of having as many controls as constraints or using gradient techniques in the choice of the Hamiltonian. The modular nature of the resulting control system allows applications for spacecraft with larger numbers of modules.
Gauss-Bonnet black holes and holographic heat engines beyond large N
NASA Astrophysics Data System (ADS)
Johnson, Clifford V.
2016-11-01
Working in the extended black hole thermodynamics where a dynamical cosmological constant defines a thermodynamic pressure p, we study the efficiency of heat engines that perform mechanical work via the pdV terms now present in the First Law. Here the black hole itself is the working substance, and we focus on a judiciously chosen engine cycle. We work in Gauss-Bonnet-Einstein-Maxwell gravity with negative cosmological constant and, using a high temperature expansion, compare the results for these ‘holographic’ heat engines to that of previously studied cases with no Gauss-Bonnet sector. From the dual holographic large N field theory perspective, this amounts to studying the effects of a class of 1/N corrections to the efficiency of the cycle.
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.
BV weak solutions to Gauss-Codazzi system for isometric immersions
NASA Astrophysics Data System (ADS)
Christoforou, Cleopatra
The isometric immersion problem for surfaces embedded into R is studied via the fluid dynamic framework introduced in Chen et al. (2010) [6] as a system of balance laws of mixed-type. The techniques developed in the theory of weak solutions of bounded variation in continuum physics are employed to deal with the isometric immersions in the setting of differential geometry. The so-called BV framework is formed that establishes convergence of approximate solutions of bounded variation to the Gauss-Codazzi system and yields the C isometric realization of two-dimensional surfaces into R. Local and global existence results are established for weak solutions of small bounded variation to the Gauss-Codazzi system for negatively curved surfaces that admit equilibrium configurations. As an application, the case of catenoidal shell of revolution is provided.
Quintessence background for 5D Einstein-Gauss-Bonnet black holes
NASA Astrophysics Data System (ADS)
Ghosh, Sushant G.; Amir, Muhammed; Maharaj, Sunil D.
2017-08-01
As we know that the Lovelock theory is an extension of the general relativity to the higher-dimensions, in this theory the first- and the second-order terms correspond to general relativity and the Einstein-Gauss-Bonnet gravity, respectively. We obtain a 5D black hole solution in Einstein-Gauss-Bonnet gravity surrounded by the quintessence matter, and we also analyze their thermodynamical properties. Owing to the quintessence corrected black hole, the thermodynamic quantities have also been corrected except for the black hole entropy, and a phase transition is achievable. The phase transition for the thermodynamic stability is characterized by a discontinuity in the specific heat at r=r_C, with the stable (unstable) branch for r < (>) r_C.
Zhang, Yufeng; Shi, Xinling; Zhang, Kexin; Chen, Jianhua
2009-03-01
A novel approach based on the phasing-filter (PF) technique and the empirical mode decomposition (EMD) algorithm is proposed to preserve quadrature Doppler signal components from bidirectional slow blood flow close to the vessel wall. Bidirectional mixed Doppler ultrasound signals, which were echoed from the forward and reverse moving blood and vessel wall, were initially separated to avoid the phase distortion of quadrature Doppler signals (which is induced from direct decomposition by the nonlinear EMD processing). Separated unidirectional mixed Doppler signals were decomposed into intrinsic mode functions (IMFs) using the EMD algorithm and the relevant IMFs that contribute to blood flow components were identified and summed to give the blood flow signals, whereby only the components from the bidirectional slow blood flow close to the vessel wall were retained independently. The complex quadrature Doppler blood flow signal was reconstructed from a combination of the extracted unidirectional Doppler blood flow signals. The proposed approach was applied to simulated and clinical Doppler signals. It is concluded from the experimental results that this approach is practical for the preservation of quadrature Doppler signal components from the bidirectional slow blood flow close to the vessel wall, and may provide more diagnostic information for the diagnosis and treatment of vascular diseases.
Zero-IF and near-zero-IF quadrature demodulators with high tolerance to I-Q imbalance
NASA Astrophysics Data System (ADS)
Gu, Jian
2002-08-01
This paper deals with quadrature demodulators used for Zero Intermediate Frequency (ZIF) and Near Zero Intermediate frequency (NZIF) receivers. ZIF and NZIF receivers are more sensitive to circuitry mismatch, which causes I-Q imbalance. With IQ-Balancing (IQB) technology, any adverse effect of frequency-dependent I-Q imbalance can be removed and quadrature receivers can have high tolerance to the I-Q imbalance. The paper first provides detailed description of the IQB technology for a simple I-Q network. Then the paper shows that any I-Q operations (ideal or non-ideal) can be described by an I-Q network and that the I-Q network can be described by a set of 2-by-2 matrixes, each of which defines the imbalance condition at a given frequency. As a result, the IQB technology can be applied to the I-Q network to remove any adverse effect. The paper then explains how the IQB technology can be used with a quadrature demodulator for ZIF/NZIF receivers for any modulation schemes. Finally, two application examples are included to show how the proposed quadrature demodulator can make ZIF/NZIF receivers have much higher tolerance to I-Q imbalance. System simulation results are provided for a ZIF receiver for OFDM signals and a NZIF receiver for GMSK signals.
Direct 3D Quadratures for the DPM Polarizatioin Potential on MIMD Computers.
NASA Astrophysics Data System (ADS)
Gibson, Thomas L.
1996-05-01
The Distributed Positron Model (DPM) has been successfully used to calculate accurate, parameter-independent polarization potentials for use in low-energy positron-Atom(T.L. Gibson, J. Phys. B) 23, 767-776 (1990) and positron-Molecule(T.L. Gibson, J. Phys. B) 25, 1321-1336 (1992) scattering. However, the DPM is computationally intensive with most of the CPU-time going into the calculation of large sets of modified nuclear attraction integrals. A direct, three-dimensional quadrature scheme has been developed for use on MIMD computers such as the INTEL Delta and Paragon systems(Supported by the Caltech Concurrent Supercomputing Consortium.). An overview of the parallel approach used and comparisons of the time to generate these integral sets on various computers will be given.
NASA Astrophysics Data System (ADS)
Doble, J. E.
1984-10-01
British Telecom is running a field trial of a spectrally efficient (4.2 bits/Hz) reduced bandwidth quadrature phase shift keyed digital radio system for the lower 6 GHz and 4 GHz bands in a part of the UK that is subject to above average multipath activity. Some of the observations made during a two-year period are described together with the improvements made to the antennas and the methods likely to be used in predicting system performance in other locations. The current method of predicting multipath fading is examined and found wanting in its application to digital system planning. An alternative is put forward and an example of its use is given.
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". .
Rerucha, Simon; Buchta, Zdenek; Sarbort, Martin; Lazar, Josef; Cip, Ondrej
2012-10-19
We have proposed an approach to the interference phase extraction in the homodyne laser interferometry. The method employs a series of computational steps to reconstruct the signals for quadrature detection from an interference signal from a non-polarising interferometer sampled by a simple photodetector. The complexity trade-off is the use of laser beam with frequency modulation capability. It is analytically derived and its validity and performance is experimentally verified. The method has proven to be a feasible alternative for the traditional homodyne detection since it performs with comparable accuracy, especially where the optical setup complexity is principal issue and the modulation of laser beam is not a heavy burden (e.g., in multi-axis sensor or laser diode based systems).
Reconfigurable microwave photonic in-phase and quadrature detector for frequency agile radar.
Emami, Hossein; Sarkhosh, Niusha
2014-06-01
A microwave photonic in-phase and quadrature detector is conceived and practically demonstrated. The detector has the ability to become electronically reconfigured to operate at any frequency over a wide range. This makes it an excellent candidate for frequency agile radars and other electronic warfare systems based on frequency hopping. The detector exhibits a very low amplitude and phase imbalance, which removes the need for any imbalance compensation technique. The system is designed based on the transversal filtering concept and reconfigurability is achieved via wavelength control in a dispersive fiber. The system operation was demonstrated over a frequency range of 3.5-35 GHz, with a maximum of -32 dB amplitude imbalance.
Efficient calculation of degenerate atomic rates by numerical quadrature on GPUs
NASA Astrophysics Data System (ADS)
Aslanyan, V.; Aslanyan, A. G.; Tallents, G. J.
2017-10-01
The rates of atomic processes in cold, dense plasma are governed strongly by effects of quantum degeneracy. The electrons follow Fermi-Dirac statistics and their high density limits the number of quantum states available for occupation after a collision. These factors preclude a direct solution to the usual rate coefficient integrals. We summarize the formulation of this problem and present a simple, but efficient method of evaluating collisional rate coefficients via direct numerical integration. Numerical quadrature has an intrinsically high level of parallelism, ideally suited for graphics processor units. GPUs are particularly suited to this problem because of the large number of integrals which must be carried out simultaneously for a given atomic model. A CUDA code to calculate the rates of significant atomic processes as part of a collisional-radiative model is presented and discussed. This approach may be readily extended to other applications where rapid and repeated evaluation of many integrals is required.
NASA Technical Reports Server (NTRS)
Deepak, A.; Fluellen, A.
1978-01-01
An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.
Phase quadrature discrimination based on three-pump four-wave mixing in nonlinear optical fibers.
Baillot, Maxime; Gay, Mathilde; Peucheret, Christophe; Michel, Joindot; Chartier, Thierry
2016-11-14
We theoretically and experimentally study the principle of phase-sensitive frequency conversion in a highly-nonlinear fiber using three pump waves. This mechanism, originally demonstrated with four continuous-wave pumps and a signal wave, is based on four-wave mixing and enables to convert the two quadrature components of the signal to different frequencies. In this work, we derive a set of two simple equations to describe this mechanism and find analytic solutions. We show that only three pumps are required, instead of four as originally proposed. We give simple relations to determine the initial conditions for the power levels and the phases of the pumps. To validate this approach, we perform an experimental demonstration of the three-pump scheme and find excellent agreement with the theory.
Parallel-quadrature phase-shifting digital holographic microscopy using polarization beam splitter
NASA Astrophysics Data System (ADS)
Das, Bhargab; Yelleswarapu, Chandra S.; Rao, D. V. G. L. N.
2012-11-01
We present a digital holography microscopy technique based on a parallel-quadrature phase-shifting method. Two π/2 phase-shifted holograms are recorded simultaneously using polarization phase-shifting principle, slightly off-axis recording geometry, and two identical CCD sensors. The parallel phase-shifting is realized by combining circularly polarized object beam with a 45° degree polarized reference beam through a polarizing beam splitter. DC term is eliminated by subtracting the two holograms from each other and the object information is reconstructed after selecting the frequency spectrum of the real image. Both amplitude and phase object reconstruction results are presented. Simultaneous recording eliminates phase errors caused by mechanical vibrations and air turbulences. The slightly off-axis recording geometry with phase-shifting allows a much larger dimension of the spatial filter for reconstruction of the object information. This leads to better reconstruction capability than traditional off-axis holography.
Parallel-quadrature phase-shifting digital holographic microscopy using polarization beam splitter.
Das, Bhargab; Yelleswarapu, Chandra S; Rao, Dvgln
2012-11-01
We present a digital holography microscopy technique based on parallel-quadrature phase-shifting method. Two π/2 phase-shifted holograms are recorded simultaneously using polarization phase-shifting principle, slightly off-axis recording geometry, and two identical CCD sensors. The parallel phase-shifting is realized by combining circularly polarized object beam with a 45° degree polarized reference beam through a polarizing beam splitter. DC term is eliminated by subtracting the two holograms from each other and the object information is reconstructed after selecting the frequency spectrum of the real image. Both amplitude and phase object reconstruction results are presented. Simultaneous recording eliminates phase errors caused by mechanical vibrations and air turbulences. The slightly off-axis recording geometry with phase-shifting allows a much larger dimension of the spatial filter for reconstruction of the object information. This leads to better reconstruction capability than traditional off-axis holography.
Mixed-precision evaluation of two-electron integrals by Rys quadrature
NASA Astrophysics Data System (ADS)
Asadchev, Andrey; Gordon, Mark S.
2012-08-01
A mixed precision implementation of two-electron integrals is demonstrated to have two benefits: (a) computations can be performed reliably in 32-bit precision on architectures for which 32-bit precision is significantly faster than 64-bit precision (e.g. graphical processing units), and (b) numerical results that match those using higher than 64-bit precision can be recovered without a significant penalty associated with performing the entire computation in higher precision. A justification is presented for using mixed precision in the Rys two-electron integral quadrature algorithm, together with timings and numerical results using a variety of floating-point types. The code discussed here presents a systematic way to control the accuracy of the Rys algorithm, regardless of the types and numbers of integrals.
Tomic, Milos C.; Djinovic, Zoran V.; Petricevic, Slobodan J.
2017-01-01
We propose and experimentally prove an algorithm for demodulation of interferometric signals, modified for use in a totally implantable hearing aid device. A fiber optic configuration, which generates two quasi-quadrature signals by a passive 3x3 coupler, for a non-contact detection of the middle ear ossicle vibration is employed. We simulated the ossicle vibration and large movements and demonstrated the effectiveness of the algorithm to compensate changes of the signal DC values and the phase shift introduced by the coupler. Applying the proposed algorithm we obtained the output signal stability better than 0.5 dB, and the system equivalent input noise of about 31 dB (A) SPL @ 1 kHz. PMID:28717576
NASA Astrophysics Data System (ADS)
Cigeroglu, Ender; Samandari, Hamed
2014-11-01
Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.
A Note on Multigrid Theory for Non-nested Grids and/or Quadrature
NASA Technical Reports Server (NTRS)
Douglas, C. C.; Douglas, J., Jr.; Fyfe, D. E.
1996-01-01
We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.
Stress fields around two pores in an elastic body: exact quadrature domain solutions.
Crowdy, Darren
2015-08-08
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.
Performance of quadrature overlapped raised-cosine modulation over nonlinear satellite channels
NASA Technical Reports Server (NTRS)
Divsalar, D.; Simon, M. K.
1981-01-01
This paper considers the performance evaluation of Staggered Quadrature Overlapped Raised Cosine (SQORC) signal transmission through wideband nonlinear satellite channels in the presence of uplink and downlink additive Gaussian noise. Expressions for the bit error rate are derived for a general transponder model with AM-AM and AM-PM conversion. It is shown that the bit error rate of SQORC is one-half of the sum of the bit error rate of MSK at 2/3 of the uplink signal-to-noise ratio and the bit error rate of Quadriphase Phase-Shift Keying QPSK at 4/3 of the uplink signal-to-noise ratio, whereas the spectrum of SQROC is the product of MSK and QPSK spectra. Numerical results are presented for a transponder which is modelled as a hard limiter.
A novel approach to estimating the Doppler shift frequency from quadrature mixer output
NASA Astrophysics Data System (ADS)
Wang, M. Y.; Liu, A. D.; Zhou, C.; Hu, J. Q.; Li, H.; Lan, T.; Xie, J. L.; Ding, W. X.; Liu, W. D.; Yu, C. X.
2017-07-01
Doppler backscattering systems (DBSs) have been widely used in magnetic confinement fusion devices to measure the density fluctuations and propagation velocity of turbulence. However, the received signals of a DBS usually include both zero-order reflection and backscattering components, which results in interference in calculating the Doppler shift frequency from the backscattering components. A novel method is introduced here for estimating the Doppler shift frequency by separating the zero-order reflection and backscattering components using the cross-phase spectrum between the I-signal and Q-signal from a quadrature mixer, based on the difference in symmetrical characteristics between the zero-order reflection and backscattering signal spectra. It is proven that this method is more effective than traditional approaches, such as multiple signal classification and fast Fourier transformation, for extracting Doppler shift information.
Parallel-quadrature phase-shifting digital holographic microscopy using polarization beam splitter
Das, Bhargab; Yelleswarapu, Chandra S; Rao, DVGLN
2012-01-01
We present a digital holography microscopy technique based on parallel-quadrature phase-shifting method. Two π/2 phase-shifted holograms are recorded simultaneously using polarization phase-shifting principle, slightly off-axis recording geometry, and two identical CCD sensors. The parallel phase-shifting is realized by combining circularly polarized object beam with a 45° degree polarized reference beam through a polarizing beam splitter. DC term is eliminated by subtracting the two holograms from each other and the object information is reconstructed after selecting the frequency spectrum of the real image. Both amplitude and phase object reconstruction results are presented. Simultaneous recording eliminates phase errors caused by mechanical vibrations and air turbulences. The slightly off-axis recording geometry with phase-shifting allows a much larger dimension of the spatial filter for reconstruction of the object information. This leads to better reconstruction capability than traditional off-axis holography. PMID:23109732
Atom-assisted quadrature squeezing of a mechanical oscillator inside a dispersive cavity
NASA Astrophysics Data System (ADS)
Chauhan, Anil Kumar; Biswas, Asoka
2016-08-01
We present a hybrid optomechanical scheme to achieve dynamical squeezing of position quadrature of a mesoscopic mechanical oscillator, that can be externally controlled by classical fields. A membrane-in-the-middle setup is employed, in which an atom in Λ configuration is considered to be trapped on either side of the membrane inside the cavity. We show that a considerable amount of squeezing (beyond the 3-dB limit) can be achieved and maintained at a transient time scale that is not affected by the spontaneous emission of the atom. Squeezing depends upon the initial preparation of atomic states. Further, a strong effective coupling (larger than the relevant decay rates) between the atom and the oscillator can be attained by using large control fields that pump the atom and the cavity. The effects of cavity decay and the phononic bath on squeezing are studied. The results are supported by the detailed analytical calculations.
Fast numerical solution for fractional diffusion equations by exponential quadrature rule
NASA Astrophysics Data System (ADS)
Zhang, Lu; Sun, Hai-Wei; Pang, Hong-Kui
2015-10-01
After spatial discretization to the fractional diffusion equation by the shifted Grünwald formula, it leads to a system of ordinary differential equations, where the resulting coefficient matrix possesses the Toeplitz-like structure. An exponential quadrature rule is employed to solve such a system of ordinary differential equations. The convergence by the proposed method is theoretically studied. In practical computation, the product of a Toeplitz-like matrix exponential and a vector is calculated by the shift-invert Arnoldi method. Meanwhile, the coefficient matrix satisfies a condition that guarantees the fast approximation by the shift-invert Arnoldi method. Numerical results are given to demonstrate the efficiency of the proposed method.
Electrostatic stiffness correction for quadrature error in decoupled dual-mass MEMS gyroscope
NASA Astrophysics Data System (ADS)
Li, Hongsheng; Cao, Huiliang; Ni, Yunfang
2014-07-01
This paper proposes an electrostatic stiffness correction method for the quadrature error (QUER) in a decoupled dual-mass gyroscope structure. The QUER is caused by the imperfections during the structure manufacturing process, and the two masses usually have different QUERs. The harm contribution to the Coriolis signal is analyzed and quantified. The generating forms of QUER motion in both masses are analyzed, the correction electrodes' working principle is introduced, and a single mass individual correction method is proposed. The QUER stiffness correction system is designed based on a PI controller, and the experiments are arranged to verify the theoretical analysis. The bias stability decreases from 2.06 to 0.64 deg/h after the QUER correction, and the parameters of scale factor such as nonlinearly, asymmetry, and repeatability, reduce from 143, 557, and 210 ppm to 84, 242, and 175 ppm, respectively.
NASA Astrophysics Data System (ADS)
Kavehrad, Mohsen; Sundberg, Carl-Erik W.
1987-04-01
Average bit error probabilities for M-ary quadrature amplitude modulation (MQAM) systems are evaluated using a truncated union bound to calculate an approximate upper bound on the average bit error probability. Coded BPSK and QSPK are studied in a dual-polarized channel with and without an interference compensator. Trellis-coded MQAM signals are also examined. A new technique, dual-channel polarization hopping, which provides diversity gains when applied to coded cross-coupled channels is proposed. Average bit error probabilities for convolutionally coded QAM schemes in cross-coupled interference channels are derived. It is concluded that trellis-coded QAM schemes give larger coding gains in cross-coupled interference channels than in Gaussian noise and the choice of optimum code for the trellis-coded QAM scheme depends on the expected interference level.
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
Eikonal instability of Gauss-Bonnet-(anti-)-de Sitter black holes
NASA Astrophysics Data System (ADS)
Konoplya, R. A.; Zhidenko, A.
2017-05-01
Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, [J. High Energy Phys. 07 (2016) 151, 10.1007/JHEP07(2016)151] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown [Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), 10.1103/PhysRevLett.114.071102], that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [Frolov, Phys. Rev. Lett. 115, 051102 (2015), 10.1103/PhysRevLett.115.051102]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.
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.
Clinical Profile of Statin Intolerance in the Phase 3 GAUSS-2 Study.
Cho, Leslie; Rocco, Michael; Colquhoun, David; Sullivan, David; Rosenson, Robert S; Dent, Ricardo; Xue, Allen; Scott, Rob; Wasserman, Scott M; Stroes, Erik
2016-06-01
Recent evidence suggests that statin intolerance may be more common than reported in randomized trials. However, the statin-intolerant population is not well characterized. The goal of this report is to characterize the population enrolled in the phase 3 Goal Achievement after Utilizing an anti-PCSK9 antibody in Statin Intolerant Subjects Study (GAUSS-2; NCT 01763905). GAUSS-2 compared evolocumab, a fully human monoclonal antibody to proprotein convertase subtilisin/kexin type 9 (PCSK9) to ezetimibe in hypercholesterolemic patients who discontinued statin therapy due to statin-associated muscle symptoms (SAMS). GAUSS-2 was a 12-week, double-blind, placebo-controlled, randomized study that enrolled patients with elevated LDL-C who were either not on a statin or able to tolerate only a low-dose due to SAMS. Patients had received ≥2 statins and were unable to tolerate any statin dose or increase in dose above a specified weekly dose due to SAMS. Three hundred seven patients (mean [SD] age, 62 [10] years; 54 % males) were randomized 2:1 (evolocumab:ezetimibe). Mean (SD) LDL-C was 4.99 (1.51) mmol/L. Patients had used ≥2 (100 %), ≥3 (55 %), or ≥4 (21 %) statins. Coronary artery disease was present in 29 % of patients. Statin-intolerant symptoms were myalgia in 80 % of patients, weakness in 39 %, and more serious complications in 20 %. In 98 % of patients, SAMS interfered with normal daily activity; in 52 %, symptoms precluded moderate exertion. Evaluation of the GAUSS-2 trial population of statin-intolerant patients demonstrates that most patients were high risk with severely elevated LDL-C and many had statin-associated muscle symptoms that interfered with their quality of life.
On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Wilson, Mitsuru
2017-01-01
We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.
Dynamical manipulation of Cosine-Gauss beams in a graphene plasmonic waveguide.
He, Xueqing; Ning, Tigang; Li, Rujiang; Pei, Li; Zheng, Jingjing; Li, Jing
2017-06-12
In this paper, we theoretically propose for the first time that graphene monolayer can be used to manipulate the Cosine-Gauss beams (CGBs). We show that both the transverse oscillation period and propagation length of a CGB can be dynamically manipulated by utilizing the tunability of the graphene's chemical potential. The graphene-based planar plasmonic waveguide provides a good platform to investigate the propagation properties of CGBs, which is potentially compatible to the microelectronic technology.
Rotation of large asymmetrical absorbing objects by Laguerre-Gauss beams.
Herne, Catherine M; Capuzzi, Kristina M; Sobel, Emily; Kropas, Ryan T
2015-09-01
In this Letter, we show the manipulation and rotation of opaque graphite through adhesion with optically trapped polystyrene spheres. The absorbing graphite is rotated by the orbital angular momentum transfer from a Laguerre-Gauss laser mode and is trapped due to the presence of refracting spheres. This technique is effective for trapping and rotating absorbing objects of all sizes, including those larger than the laser mode.
GAUSS IX. Interactive Analysis of Gamm-ray Spectra from GE Semiconductor Detectors
Egger, A.E.
1997-01-01
GAUSS IX is a tool to interactively analyze gamma-ray spectra from Ge Semicondutor detectors. The user has full control over the view of the spectrum being analyzed and the location of the peaks and peak regions. Analysis is performed at user request to the requested peak regions. The fit of a peak region can be previewed before archival or deletion. An iterative procedure is available for calibrating the energy and width equations.
NASA Astrophysics Data System (ADS)
Kirnos, I. V.; Makarenko, A. N.; Pavluchenko, S. A.; Toporensky, A. V.
2010-11-01
We investigate dynamics of (4 + 1) and (5 + 1) dimensional flat anisotropic Universe filled with a perfect fluid in the Gauss-Bonnet gravity. An analytical solutions valid for particular values of the equation of state parameter w = 1/3 have been found. For other values of w structure of cosmological singularity have been studied numerically. We found that for w > 1/3 the singularity is isotropic. Several important differences between (4 + 1) and (5 + 1) dimensional cases are discussed.
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.
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.
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.
Quadrature mechatronic actuator (QMA) drives for heavy ship doors and machinery
NASA Astrophysics Data System (ADS)
Knowles, Gareth J.; Bird, Ross W.; Goehrig, Michael J.; Knoll, William C.; Hoffman, Heath; Park, Jaedo
2004-07-01
An important part of the Navy objectives is to be both more efficient and enable manpower reduction is to reduce maintenance, reduce manpower, and eliminate pollutants through creating a more all-electric ship environment. However, placement of both non-centralized and centralized hydraulic systems for control of heavy machinery, large bay doors, articulated systems such as rudders for controlling air flow to the skirt system (such as in Landing Craft Air Cushion (LCAC) is extremely challenging. At the base of the design approach to a Mechatronic Motion System is the fact that such applications do not require high precision. What is required is that the actuator delivers sufficient thrust power without increasing the existing actuator weight and be a self-contained unit. To address this need, QorTek and PSU have been developing a new concept of an entirely new kind of motion system actuator that has few parts, enormous thrust capability for its compact size, and is amenable to affordable manufacture. The new Quadrature Mechatronic Actuator (QMA) is a hydraulic replacement that will match hydraulic force-displacement capabilities in a fully solid-state design. Quadrature Mechatronic Actuators will look very similar to the existing hydraulic actuators currently used on LCAC. These compact self-contained units represent a one-for-one substitute for existing equipment. The Mechatronic Actuator itself will be lighter and slightly smaller than its hydraulic actuator equivalent and use one or more internal hybrid solid-state drivers that are internally coupled to a linear translator.
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.
Quantum Gauss-Jordan Elimination and Simulation of Accounting Principles on Quantum Computers
NASA Astrophysics Data System (ADS)
Diep, Do Ngoc; Giang, Do Hoang; Van Minh, Nguyen
2017-06-01
The paper is devoted to a version of Quantum Gauss-Jordan Elimination and its applications. In the first part, we construct the Quantum Gauss-Jordan Elimination (QGJE) Algorithm and estimate the complexity of computation of Reduced Row Echelon Form (RREF) of N × N matrices. The main result asserts that QGJE has computation time is of order 2 N/2. The second part is devoted to a new idea of simulation of accounting by quantum computing. We first expose the actual accounting principles in a pure mathematics language. Then, we simulate the accounting principles on quantum computers. We show that, all accounting actions are exhousted by the described basic actions. The main problems of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation, we use our constructed Quantum Gauss-Jordan Elimination to solve the problems and the complexity of quantum computing is a square root order faster than the complexity in classical computing.
Steganalysis of content-adaptive JPEG steganography based on Gauss partial derivative filter bank
NASA Astrophysics Data System (ADS)
Zhang, Yi; Liu, Fenlin; Yang, Chunfang; Luo, Xiangyang; Song, Xiaofeng; Lu, Jicang
2017-01-01
A steganalysis feature extraction method based on Gauss partial derivative filter bank is proposed in this paper to improve the detection performance for content-adaptive JPEG steganography. Considering that the embedding changes of content-adaptive steganographic schemes are performed in the texture and edge regions, the proposed method generates filtered images comprising rich texture and edge information using Gauss partial derivative filter bank, and histograms of absolute values of filtered subimages are extracted as steganalysis features. Gauss partial derivative filter bank can represent texture and edge information in multiple orientations with less computation load than conventional methods and prevent redundancy in different filtered images. These two properties are beneficial in the extraction of low-complexity sensitive features. The results of experiments conducted on three selected modern JPEG steganographic schemes-uniform embedding distortion, JPEG universal wavelet relative distortion, and side-informed UNIWARD-indicate that the proposed feature set is superior to the prior art feature sets-discrete cosine transform residual, phase aware rich model, and Gabor filter residual.
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.
Equations of motion as covariant Gauss law: The Maxwell-Chern-Simons case
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; Momen, Arshad; de Queiroz, Amilcar R.
2017-08-01
Time-independent gauge transformations are implemented in the canonical formalism by the Gauss law which is not covariant. The covariant form of Gauss law is conceptually important for studying the asymptotic properties of the gauge fields. For QED in 3 + 1 dimensions, we have developed a formalism for treating the equations of motion (EOM) themselves as constraints, that is, constraints on states using Peierls’ quantization.1 They generate spacetime dependent gauge transformations. We extend these results to the Maxwell-Chern-Simons (MCS) Lagrangian. The surprising result is that the covariant Gauss law commutes with all observables: the gauge invariance of the Lagrangian gets trivialized upon quantization. The calculations do not fix a gauge. We also consider a novel gauge condition on the test functions (not on quantum fields) which we name the “quasi-self-dual gauge” condition. It explicitly shows the mass spectrum of the theory. In this version, no freedom remains for the gauge transformations: EOM commute with all observables and are in the center of the algebra of observables.
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.