A fast algorithm for forward-modeling of gravitational fields in spherical coordinates with 3D Gauss-Legendre quadrature

NASA Astrophysics Data System (ADS)

Zhao, G.; Liu, J.; Chen, B.; Guo, R.; Chen, L.

2017-12-01

Forward modeling of gravitational fields at large-scale requires to consider the curvature of the Earth and to evaluate the Newton's volume integral in spherical coordinates. To acquire fast and accurate gravitational effects for subsurface structures, subsurface mass distribution is usually discretized into small spherical prisms (called tesseroids). The gravity fields of tesseroids are generally calculated numerically. One of the commonly used numerical methods is the 3D Gauss-Legendre quadrature (GLQ). However, the traditional GLQ integration suffers from low computational efficiency and relatively poor accuracy when the observation surface is close to the source region. We developed a fast and high accuracy 3D GLQ integration based on the equivalence of kernel matrix, adaptive discretization and parallelization using OpenMP. The equivalence of kernel matrix strategy increases efficiency and reduces memory consumption by calculating and storing the same matrix elements in each kernel matrix just one time. In this method, the adaptive discretization strategy is used to improve the accuracy. The numerical investigations show that the executing time of the proposed method is reduced by two orders of magnitude compared with the traditional method that without these optimized strategies. High accuracy results can also be guaranteed no matter how close the computation points to the source region. In addition, the algorithm dramatically reduces the memory requirement by N times compared with the traditional method, where N is the number of discretization of the source region in the longitudinal direction. It makes the large-scale gravity forward modeling and inversion with a fine discretization possible.

Multilevel mixed effects parametric survival models using adaptive Gauss-Hermite quadrature with application to recurrent events and individual participant data meta-analysis.

PubMed

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.

Discrete Ordinate Quadrature Selection for Reactor-based Eigenvalue Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jarrell, Joshua J; Evans, Thomas M; Davidson, Gregory G

2013-01-01

In this paper we analyze the effect of various quadrature sets on the eigenvalues of several reactor-based problems, including a two-dimensional (2D) fuel pin, a 2D lattice of fuel pins, and a three-dimensional (3D) reactor core problem. While many quadrature sets have been applied to neutral particle discrete ordinate transport calculations, the Level Symmetric (LS) and the Gauss-Chebyshev product (GC) sets are the most widely used in production-level reactor simulations. Other quadrature sets, such as Quadruple Range (QR) sets, have been shown to be more accurate in shielding applications. In this paper, we compare the LS, GC, QR, and themore » 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.« less

Discrete ordinate quadrature selection for reactor-based Eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 themore » 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)« less

Gauss-Legendre quadrature method used to evaluate the spatio-temporal intensity of ultrashort pulses in the focal region of lenses.

PubMed

García-Martínez, L; Rosete-Aguilar, M; Garduño-Mejia, J

2012-01-20

We analyze the spatio-temporal intensity of sub-20 femtosecond pulses with a carrier wavelength of 810 nm along the optical axis of low numerical aperture achromatic and apochromatic doublets designed in the IR region by using the scalar diffraction theory. The diffraction integral is solved by expanding the wave number around the carrier frequency of the pulse in a Taylor series up to third order, and then the integral over the frequencies is solved by using the Gauss-Legendre quadrature method. The numerical errors in this method are negligible by taking 96 nodes and the computational time is reduced by 95% compared to the integration method by rectangles. We will show that the third-order group velocity dispersion (GVD) is not negligible for 10 fs pulses at 810 nm propagating through the low numerical aperture doublets, and its effect is more important than the propagation time difference (PTD). This last effect, however, is also significant. For sub-20 femtosecond pulses, these two effects make the use of a pulse shaper necessary to correct for second and higher-order GVD terms and also the use of apochromatic optics to correct the PTD effect. The design of an apochromatic doublet is presented in this paper and the spatio-temporal intensity of the pulse at the focal region of this doublet is compared to that given by the achromatic doublet. © 2012 Optical Society of America

Quadrature-quadrature phase-shift keying

NASA Astrophysics Data System (ADS)

Saha, Debabrata; Birdsall, Theodore G.

1989-05-01

Quadrature-quadrature phase-shift keying (Q2PSK) is a spectrally efficient modulation scheme which utilizes available signal space dimensions in a more efficient way than two-dimensional schemes such as QPSK and MSK (minimum-shift keying). It uses two data shaping pulses and two carriers, which are pairwise quadrature in phase, to create a four-dimensional signal space and increases the transmission rate by a factor of two over QPSK and MSK. However, the bit error rate performance depends on the choice of pulse pair. With simple sinusoidal and cosinusoidal data pulses, the Eb/N0 requirement for Pb(E) = 10 to the -5 is approximately 1.6 dB higher than that of MSK. Without additional constraints, Q2PSK does not maintain constant envelope. However, a simple block coding provides a constant envelope. This coded signal substantially outperforms MSKS and TFM (time-frequency multiplexing) in bandwidth efficiency. Like MSK, Q2PSK also has self-clocking and self-synchronizing ability. An optimum class of pulse shapes for use in Q2PSK-format is presented. One suboptimum realization achieves the Nyquist rate of 2 bits/s/Hz using binary detection.

A computational approach for hypersonic nonequilibrium radiation utilizing space partition algorithm and Gauss quadrature

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.

Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

PubMed

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.

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.

Differentially coherent quadrature-quadrature phase shift keying (Q2PSK)

NASA Astrophysics Data System (ADS)

Saha, Debabrata; El-Ghandour, Osama

The quadrature-quadrature phase-shift-keying (Q2PSK) signaling scheme uses the vertices of a hypercube of dimension four. A generalized Q2PSK signaling format for differentially coherent detection at the receiver is considered. Performance in the presence of additive white Gaussian noise (AWGN) is analyzed. The symbol error rate is found to be approximately twice the symbol error rate in a quaternary DPSK system operating at the same Eb/Nb. However, the bandwidth efficiency of differential Q2PSK is substantially higher than that of quaternary DPSK.

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.

General implementation of arbitrary nonlinear quadrature phase gates

NASA Astrophysics Data System (ADS)

Marek, Petr; Filip, Radim; Ogawa, Hisashi; Sakaguchi, Atsushi; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.

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.

Quadrature demultiplexing using a degenerate vector parametric amplifier.

PubMed

Lorences-Riesgo, Abel; Liu, Lan; Olsson, Samuel L I; Malik, Rohit; Kumpera, Aleš; Lundström, Carl; Radic, Stojan; Karlsson, Magnus; Andrekson, Peter A

2014-12-01

We report on quadrature demultiplexing of a quadrature phase-shift keying (QPSK) signal into two cross-polarized binary phase-shift keying (BPSK) signals with negligible penalty at bit-error rate (BER) equal to 10(-9). The all-optical quadrature demultiplexing is achieved using a degenerate vector parametric amplifier operating in phase-insensitive mode. We also propose and demonstrate the use of a novel and simple phase-locked loop (PLL) scheme based on detecting the envelope of one of the signals after demultiplexing in order to achieve stable quadrature decomposition.

Comparison of two Galerkin quadrature methods

DOE PAGES

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 S N 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 S N 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 pointwisemore » sense. With an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding S N 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

Comparison of two Galerkin quadrature methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morel, Jim E.; Warsa, James; Franke, Brian C.

Here, we compare two methods for generating Galerkin quadratures. In method 1, the standard S N 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 S N 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 pointwisemore » sense. With an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding S N 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

Virtual source for a Mathieu-Gauss beam

NASA Astrophysics Data System (ADS)

Dan, Li; Zhijun, Ren; Suyu, Deng

2017-05-01

We introduce a group of virtual sources for generating 2nth-order even Mathieu-Gauss beams based on the beam superposition. Integral and differential representations are derived for a 2nth-order even Mathieu-Gauss wave and the solution yields a corresponding 2nth-order even paraxial Mathieu-Gauss beam in an appropriate limit. The first three orders of nonparaxial corrections for the on-axis field of the 2nth-order even paraxial Mathieu-Gauss beam are obtained using the integral representation.

Coherent detection of frequency-hopped quadrature modulations in the presence of jamming. II - QPR Class I modulation. [Quadrature Partial Response

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.

Colon Cancer Risk Assessment - Gauss Program

Cancer.gov

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.

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.

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.

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.

Experimental generation of Hermite-Gauss and Ince-Gauss beams through kinoform phase holograms

NASA Astrophysics Data System (ADS)

Mellado-Villaseñor, Gabriel; Aguirre-Olivas, Dilia; Sánchez-de-la-Llave, David; Arrizón, Victor

2015-08-01

We generate Hermite-Gauss and Ince-Gauss beams by using kinoform phase holograms encoded onto a liquid crystal display. The phase transmittance of this holograms coincide with the phases of such beams. Scale versions of the desired beams appear at the Fourier domain of the KPHs. When an appropriated pupil size is employed, the method synthesizes HG and IG beams with relatively high accuracy and high efficiency. It is noted that experimental and numerical results are agreement with the theory.

GAUSS Project Trials Results

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

Effective potentials in nonlinear polycrystals and quadrature formulae

NASA Astrophysics Data System (ADS)

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. A 471, 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.

Effective potentials in nonlinear polycrystals and quadrature formulae.

PubMed

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. A 471 , 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.

Quadrature mixture LO suppression via DSW DAC noise dither

DOEpatents

Dubbert, Dale F [Cedar Crest, NM; Dudley, Peter A [Albuquerque, NM

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.

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)

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.

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

PubMed

Stuebner, Michael; Haider, Mansoor A

2010-06-18

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

An improved technique for determining reflection from semi-infinite atmospheres with linearly anisotropic phase functions. [radiative transfer

NASA Technical Reports Server (NTRS)

Fricke, C. L.

1975-01-01

A solution to the problem of reflection from a semi-infinite atmosphere is presented, based upon Chandrasekhar's H-function method for linearly anisotropic phase functions. A modification to the Gauss quadrature formula which gives about the same accuracy with 10 points as the conventional Gauss quadrature does with 100 points was developed. A computer program achieving this solution is described and results are presented for several illustrative cases.

Performance improvement of coherent free-space optical communication with quadrature phase-shift keying modulation using digital phase estimation.

PubMed

Li, Xueliang; Geng, Tianwen; Ma, Shuang; Li, Yatian; Gao, Shijie; Wu, Zhiyong

2017-06-01

The performance of coherent free-space optical (CFSO) communication with phase modulation is limited by both phase fluctuations and intensity scintillations induced by atmospheric turbulence. To improve the system performance, one effective way is to use digital phase estimation. In this paper, a CFSO communication system with quadrature phase-shift keying modulation is studied. With consideration of the effects of log-normal amplitude fluctuations and Gauss phase fluctuations, a two-stage Mth power carrier phase estimation (CPE) scheme is proposed. The simulation results show that the phase noise can be suppressed greatly by this scheme, and the system symbol error rate performance with the two-stage Mth power CPE can be three orders lower than that of the single-stage Mth power CPE. Therefore, the two-stage CPE we proposed can contribute to the performance improvements of the CFSO communication system and has determinate guidance sense to its actual application.

General n-dimensional quadrature transform and its application to interferogram demodulation.

PubMed

Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis

2003-05-01

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.

Quadrature rules with multiple nodes for evaluating integrals with strong singularities

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2006-05-01

We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.

Scalar field collapse in Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Banerjee, Narayan; Paul, Tanmoy

2018-02-01

We consider a "scalar-Einstein-Gauss-Bonnet" theory in four dimension, where the scalar field couples non-minimally with the Gauss-Bonnet (GB) term. This coupling with the scalar field ensures the non-topological character of the GB term. In this scenario, we examine the possibility for collapsing of the scalar field. Our result reveals that such a collapse is possible in the presence of Gauss-Bonnet gravity for suitable choices of parametric regions. The singularity formed as a result of the collapse is found to be a curvature singularity which is hidden from the exterior by an apparent horizon.

Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

NASA Astrophysics Data System (ADS)

Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo

2018-05-01

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which uses the Chern-Weil theorem plus a dimensional continuation process, such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The boundary term constructed in this paper allows to deal with a general background and is not equivalent to the Gibbons-Hawking-Myers boundary term. However, we show that they coincide if one replaces the background of the Katz procedure by a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients, the expected mass of the Boulware-Deser black hole.

Differential detection in quadrature-quadrature phase shift keying (Q2PSK) systems

NASA Astrophysics Data System (ADS)

El-Ghandour, Osama M.; Saha, Debabrata

1991-05-01

A generalized quadrature-quadrature phase shift keying (Q2PSK) signaling format is considered for differential encoding and differential detection. Performance in the presence of additive white Gaussian noise (AWGN) is analyzed. Symbol error rate is found to be approximately twice the symbol error rate in a quaternary DPSK system operating at the same Eb/N0. However, the bandwidth efficiency of differential Q2PSK is substantially higher than that of quaternary DPSK. When the error is due to AWGN, the ratio of double error rate to single error rate can be very high, and the ratio may approach zero at high SNR. To improve error rate, differential detection through maximum-likelihood decoding based on multiple or N symbol observations is considered. If N and SNR are large this decoding gives a 3-dB advantage in error rate over conventional N = 2 differential detection, fully recovering the energy loss (as compared to coherent detection) if the observation is extended to a large number of symbol durations.

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.

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.

Computation of the Complex Probability Function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trainer, Amelia Jo; Ledwith, Patrick John

The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the n th degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.

Development in understanding of Gauss-Krüger projection and its outcomes

NASA Astrophysics Data System (ADS)

Masaharu, Hiroshi

2018-05-01

The role of Gauss and Krüger is made clear in developing Gauss-Krüger projection. Gauss developed the projection and Krüger had brought Gauss's posthumous work into the open. From studying such historical issues, useful projection formula was found and this is now implemented for actual usage in surveying in Japan.

Directional dual-tree complex wavelet packet transforms for processing quadrature signals.

PubMed

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.

Quadratures with multiple nodes, power orthogonality, and moment-preserving spline approximation

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.

2001-01-01

Quadrature formulas with multiple nodes, power orthogonality, and some applications of such quadratures to moment-preserving approximation by defective splines are considered. An account on power orthogonality (s- and [sigma]-orthogonal polynomials) and generalized Gaussian quadratures with multiple nodes, including stable algorithms for numerical construction of the corresponding polynomials and Cotes numbers, are given. In particular, the important case of Chebyshev weight is analyzed. Finally, some applications in moment-preserving approximation of functions by defective splines are discussed.

Gauss-Bonnet chameleon mechanism of dark energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 couldmore » 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.« less

Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods

PubMed Central

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

Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods.

PubMed

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.

Noncritical quadrature squeezing through spontaneous polarization symmetry breaking.

PubMed

Garcia-Ferrer, Ferran V; Navarrete-Benlloch, Carlos; de Valcárcel, Germán J; Roldán, Eugenio

2010-07-01

We discuss the possibility of generating noncritical quadrature squeezing by spontaneous polarization symmetry breaking. We first consider Type II frequency-degenerate optical parametric oscillators but discard them for a number of reasons. Then we propose a four-wave-mixing cavity, in which the polarization of the output mode is always linear but has an arbitrary orientation. We show that in such a cavity, complete noise suppression in a quadrature of the output field occurs, irrespective of the parameter values.

Radiating black hole solutions in Einstein-Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dominguez, Alfredo E.; Instituto Universitario Aeronautico, Avenida Fuerza Aerea km 6.5.; Gallo, Emanuel

2006-03-15

In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as the Gauss-Bonnet versions of the Bonnor-Vaidya (de Sitter/anti-de Sitter) solution, a global monopole, and the Husain black holes. We also present a more general version of this theorem in which less restrictive conditionsmore » on the energy-momentum tensor are imposed. As an application of this theorem, we present the exact solution describing a black hole radiating a charged null fluid in a Born-Infeld nonlinear electrodynamics.« less

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.

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.

The use of rational functions in numerical quadrature

NASA Astrophysics Data System (ADS)

Gautschi, Walter

2001-08-01

Quadrature problems involving functions that have poles outside the interval of integration can profitably be solved by methods that are exact not only for polynomials of appropriate degree, but also for rational functions having the same (or the most important) poles as the function to be integrated. Constructive and computational tools for accomplishing this are described and illustrated in a number of quadrature contexts. The superiority of such rational/polynomial methods is shown by an analysis of the remainder term and documented by numerical examples.

Bounce universe from string-inspired Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bamba, Kazuharu; Makarenko, Andrey N.; Myagky, Alexandr N.

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 movedmore » 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.« less

Development and Evaluation of a Hydrostatic Dynamical Core Using the Spectral Element/Discontinuous Galerkin Methods

DTIC Science & Technology

2014-04-01

The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...and DG horizontal discretization employs high-order nodal basis functions 29 associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...Inside 235 each element we build ( 1)N + Gauss-Lobatto- Legendre (GLL) quadrature points, where N 236 indicate the polynomial order of the basis

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.

The AGS Ggamma Meter and Calibrating the Gauss Clock

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 themore » 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).« less

Propagation of partially coherent Lorentz-Gauss vortex beam through oceanic turbulence.

PubMed

Liu, Dajun; Yin, Hongming; Wang, Guiqiu; Wang, Yaochuan

2017-11-01

The partially coherent Lorentz-Gauss vortex beam generated by a Schell-model source has been introduced. Based on the extended Huygens-Fresnel principle, the cross-spectral density function of a partially coherent Lorentz-Gauss vortex beam propagating in oceanic turbulence is derived. The influences of coherence length, topological charge M, and oceanic turbulence on the spreading properties and position of the coherence vortex for a partially coherent Lorentz-Gauss vortex beam are analyzed in detail. The results show that a partially coherent Lorentz-Gauss vortex beam propagating in stronger oceanic turbulence will evolve into a Gaussian-like beam more rapidly as the propagation distance increases, and the number of coherent vortices will change.

Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lahiri, Sayantani, E-mail: sayantani.lahiri@gmail.com

2017-01-01

In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by amore » non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.« less

Entangled singularity patterns of photons in Ince-Gauss modes

NASA Astrophysics Data System (ADS)

Krenn, Mario; Fickler, Robert; Huber, Marcus; Lapkiewicz, Radek; Plick, William; Ramelow, Sven; Zeilinger, Anton

2013-01-01

Photons with complex spatial mode structures open up possibilities for new fundamental high-dimensional quantum experiments and for novel quantum information tasks. Here we show entanglement of photons with complex vortex and singularity patterns called Ince-Gauss modes. In these modes, the position and number of singularities vary depending on the mode parameters. We verify two-dimensional and three-dimensional entanglement of Ince-Gauss modes. By measuring one photon and thereby defining its singularity pattern, we nonlocally steer the singularity structure of its entangled partner, while the initial singularity structure of the photons is undefined. In addition we measure an Ince-Gauss specific quantum-correlation function with possible use in future quantum communication protocols.

Thin-thick quadrature frequency conversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

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.

Design and application of quadrature compensation patterns in bulk silicon micro-gyroscopes.

PubMed

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.

The time delay in strong gravitational lensing with Gauss-Bonnet correction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Man, Jingyun; Cheng, Hongbo, E-mail: jingyunman@mail.ecust.edu.cn, 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.

Multisite EPR oximetry from multiple quadrature harmonics.

PubMed

Ahmad, R; Som, S; Johnson, D H; Zweier, J L; Kuppusamy, P; Potter, L C

2012-01-01

Multisite continuous wave (CW) electron paramagnetic resonance (EPR) oximetry using multiple quadrature field modulation harmonics is presented. First, a recently developed digital receiver is used to extract multiple harmonics of field modulated projection data. Second, a forward model is presented that relates the projection data to unknown parameters, including linewidth at each site. Third, a maximum likelihood estimator of unknown parameters is reported using an iterative algorithm capable of jointly processing multiple quadrature harmonics. The data modeling and processing are applicable for parametric lineshapes under nonsaturating conditions. Joint processing of multiple harmonics leads to 2-3-fold acceleration of EPR data acquisition. For demonstration in two spatial dimensions, both simulations and phantom studies on an L-band system are reported. Copyright © 2011 Elsevier Inc. All rights reserved.

Quadrature transmit array design using single-feed circularly polarized patch antenna for parallel transmission in MR imaging.

PubMed

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.

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.

Crossing of the phantom divide using tachyon-Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sadeghi, J.; Banijamali, A.; Milani, F.

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.

Disentangling Complexity in Bayesian Automatic Adaptive Quadrature

NASA Astrophysics Data System (ADS)

Adam, Gheorghe; Adam, Sanda

2018-02-01

The paper describes a Bayesian automatic adaptive quadrature (BAAQ) solution for numerical integration which is simultaneously robust, reliable, and efficient. Detailed discussion is provided of three main factors which contribute to the enhancement of these features: (1) refinement of the m-panel automatic adaptive scheme through the use of integration-domain-length-scale-adapted quadrature sums; (2) fast early problem complexity assessment - enables the non-transitive choice among three execution paths: (i) immediate termination (exceptional cases); (ii) pessimistic - involves time and resource consuming Bayesian inference resulting in radical reformulation of the problem to be solved; (iii) optimistic - asks exclusively for subrange subdivision by bisection; (3) use of the weaker accuracy target from the two possible ones (the input accuracy specifications and the intrinsic integrand properties respectively) - results in maximum possible solution accuracy under minimum possible computing time.

Causal structures in Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Izumi, Keisuke

2014-08-01

We analyze causal structures in Gauss-Bonnet gravity. It is known that Gauss-Bonnet gravity potentially has superluminal propagation of gravitons due to its noncanonical kinetic terms. In a theory with superluminal modes, an analysis of causality based on null curves makes no sense, and thus, we need to analyze them in a different way. In this paper, using the method of the characteristics, we analyze the causal structure in Gauss-Bonnet gravity. We have the result that, on a Killing horizon, gravitons can propagate in the null direction tangent to the Killing horizon. Therefore, a Killing horizon can be a causal edge as in the case of general relativity; i.e. a Killing horizon is the "event horizon" in the sense of causality. We also analyze causal structures on nonstationary solutions with (D-2)-dimensional maximal symmetry, including spherically symmetric and flat spaces. If the geometrical null energy condition, RABNANB≥0 for any null vector NA, is satisfied, the radial velocity of gravitons must be less than or equal to that of light. However, if the geometrical null energy condition is violated, gravitons can propagate faster than light. Hence, on an evaporating black hole where the geometrical null energy condition is expected not to hold, classical gravitons can escape from the "black hole" defined with null curves. That is, the causal structures become nontrivial. It may be one of the possible solutions for the information loss paradox of evaporating black holes.

Noether symmetries in Gauss-Bonnet-teleparallel cosmology.

PubMed

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.

Unique Properties and Prospects: Quantum Theory of the Orbital Angular Momentum of Ince-Gauss Beams

NASA Astrophysics Data System (ADS)

Plick, William; Krenn, Mario; Fickler, Robert; Ramelow, Sven; Zeilinger, Anton

2012-02-01

The Ince-Gauss modes represent a new addition to the standard solutions to the paraxial wave equation. Parametrized by the ellipticity of the beam, they span the solution space between the Hermite-Gauss and the Laguerre-Gauss modes. These beams may be decomposed in either basis, and single photons in the Ince-Gauss modes exist naturally as superpositions of either Laguerre-Gauss or Hermite-Gauss modes. We present the fully quantum theory of the orbital angular momentum of these beams. Interesting features that arise are: stable beams with fractional orbital angular momentum, non-monotonic behavior of the OAM with respect to ellipticity, and the possibility of orthogonal modes possessing the same OAM. We believe that these modes may open up a fully new parameter space for quantum informatics and communication, and thus are worthy of thorough study.

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.

Evaluation of quadrature-phase-shift-keying signal characteristics in W-band radio-over-fiber transmission using direct in-phase/quadrature-phase conversion technique

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.

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

NASA Astrophysics Data System (ADS)

Casalderrey-Solana, Jorge; Gushterov, Nikola I.; Meiring, Ben

2018-04-01

We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter λGB. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of N=4 Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of λGB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorbachev, D V; Ivanov, V I

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.

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.

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.

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…

Brane universes with Gauss-Bonnet-induced-gravity

NASA Astrophysics Data System (ADS)

Brown, Richard A.

2007-04-01

The DGP brane world model allows us to get the observed late time acceleration via modified gravity, without the need for a “dark energy” field. This can then be generalised by the inclusion of high energy terms, in the form of a Gauss-Bonnet bulk. This is the basis of the Gauss-Bonnet-Induced-Gravity (GBIG) model explored here with both early and late time modifications to the cosmological evolution. Recently the simplest GBIG models (Minkowski bulk and no brane tension) have been analysed. Two of the three possible branches in these models start with a finite density “Big-Bang” and with late time acceleration. Here we present a comprehensive analysis of more general models where we include a bulk cosmological constant and brane tension. We show that by including these factors it is possible to have late time phantom behaviour.

Research on atmospheric transmission distortion of Gauss laser using multiple phase screen method

NASA Astrophysics Data System (ADS)

Zhang, Yizhuo; Wang, Qiushi; Gu, Haidong

2018-02-01

The laser beam is attenuated, broadened, defocused and may even be deflected from its initial propagation direction as it propagates through the atmosphere. It leads to the decrease of the laser intensity of the receiving surface. Gauss beam is the fundamental components of all possible laser waveforms. Therefore, research on the transmission of the Gauss laser has far-reaching consequences in optical communication, weaponry, target designation, ranging, remote sensing and other applications that require transmission of laser beams through the atmosphere. In this paper, we propose a laboratory simulation method using multi-phase screen to calculate the effects of atmospheric turbulence. Theoretical analysis of Gauss laser transmission in the atmosphere is given. By calculating the propagation of the Gauss beam TEM00, the far field intensity and phase distribution is shown. By the given method, the optical setup is presented and used for optimizing the adaptive optics algorithm.

A multivariate quadrature based moment method for LES based modeling of supersonic combustion

NASA Astrophysics Data System (ADS)

Donde, Pratik; Koo, Heeseok; Raman, Venkat

2012-07-01

The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.

Average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence

NASA Astrophysics Data System (ADS)

Liu, Dajun; Wang, Guiqiu; Wang, Yaochuan

2018-01-01

Based on the Huygens-Fresnel integral and the relationship of Lorentz distribution and Hermite-Gauss function, the average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence have been investigated by using numerical examples. The influences of beam parameters and oceanic turbulence on the propagation properties are also discussed in details. It is shown that the partially coherent Lorentz-Gauss beam with smaller coherence length will spread faster in oceanic turbulence, and the stronger oceanic turbulence will accelerate the spreading of partially coherent Lorentz-Gauss beam in oceanic turbulence.

Stochastic sampling of quadrature grids for the evaluation of vibrational expectation values

NASA Astrophysics Data System (ADS)

López Ríos, Pablo; Monserrat, Bartomeu; Needs, Richard J.

2018-02-01

The thermal lines method for the evaluation of vibrational expectation values of electronic observables [B. Monserrat, Phys. Rev. B 93, 014302 (2016), 10.1103/PhysRevB.93.014302] was recently proposed as a physically motivated approximation offering balance between the accuracy of direct Monte Carlo integration and the low computational cost of using local quadratic approximations. In this paper we reformulate thermal lines as a stochastic implementation of quadrature-grid integration, analyze the analytical form of its bias, and extend the method to multiple-point quadrature grids applicable to any factorizable harmonic or anharmonic nuclear wave function. The bias incurred by thermal lines is found to depend on the local form of the expectation value, and we demonstrate that the use of finer quadrature grids along selected modes can eliminate this bias, while still offering an ˜30 % lower computational cost than direct Monte Carlo integration in our tests.

Greybody factors for a spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole

NASA Astrophysics Data System (ADS)

Zhang, Cheng-Yong; Li, Peng-Cheng; Chen, Bin

2018-02-01

We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and nonminimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the nonminimally coupling constant, the spacetime dimension, the cosmological constant, and the Gauss-Bonnet coefficient in detail. We find that the nonminimal coupling may suppress the greybody factor and the Gauss-Bonnet coupling could enhance it, but they both suppress the energy emission rate of Hawking radiation.

Discrete variable representation in electronic structure theory: quadrature grids for least-squares tensor hypercontraction.

PubMed

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.

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.

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…

Explorations of the Gauss-Lucas Theorem

ERIC Educational Resources Information Center

Brilleslyper, Michael A.; Schaubroeck, Beth

2017-01-01

The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…

Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory.

PubMed

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.

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…

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.

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.

Notes on the boundaries of quadrature domains

NASA Astrophysics Data System (ADS)

Verma, Kaushal

2018-03-01

We highlight an intrinsic connection between classical quadrature domains and the well-studied theme of removable singularities of analytic sets in several complex variables. Exploiting this connection provides a new framework to recover several basic properties of such domains, namely the algebraicity of their boundary, a better understanding of the associated defining polynomial and the possible boundary singularities that can occur.

Phase space of modified Gauss-Bonnet gravity.

PubMed

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.

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.

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.

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…

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

Convergence and Applications of a Gossip-Based Gauss-Newton Algorithm

NASA Astrophysics Data System (ADS)

Li, Xiao; Scaglione, Anna

2013-11-01

The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares problems. In this paper, we propose a multi-agent distributed version of this algorithm, named Gossip-based Gauss-Newton (GGN) algorithm, which can be applied in general problems with non-convex objectives. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.

Characterization of high order spatial discretizations and lumping techniques for discontinuous finite element SN transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, P. G.; Ragusa, J. C.; Morel, J. E.

2013-07-01

We examine several possible methods of mass matrix lumping for discontinuous finite element discrete ordinates transport using a Lagrange interpolatory polynomial trial space. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping in a purely absorbing 1-D slab cell for the linear discontinuous approximation, we show that when used with higher degree interpolatory polynomial trial spaces, traditional lumping does yield strictly positive outflows and does not increase in accuracy with an increase in trial space polynomial degree. As an alternative, we examine methods which are 'self-lumping'. Self-lumping methods yield diagonal mass matrices by using numerical quadrature restrictedmore » to the Lagrange interpolatory points. Using equally-spaced interpolatory points, self-lumping is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows in pure absorbers for odd power polynomials in 1-D slab geometry. By changing interpolatory points from the traditional equally-spaced points to the quadrature points of the Gauss-Legendre or Lobatto-Gauss-Legendre quadratures, it is possible to generate solution representations with a diagonal mass matrix and a strictly positive outflow for any degree polynomial solution representation in a pure absorber medium in 1-D slab geometry. Further, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to the quadrature points of high order accuracy numerical quadrature schemes. (authors)« less

Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu Yapeng; Sun Peng; Zhang Jianhui

2011-06-15

Using the AdS/CFT correspondence, we study the hydrodynamics with conserved current from the dual Maxwell-Gauss-Bonnet gravity. After constructing the perturbative solution to the first order based on the boosted black brane solution in the bulk Maxwell-Gauss-Bonnet gravity, we extract the stress tensor and conserved current of the dual conformal fluid on its boundary, and also find the effect of the Gauss-Bonnet term on the dual conformal fluid. Our results show that the Gauss-Bonnet term can affect the parameters such as the shear viscosity {eta}, entropy density s, thermal conductivity {kappa} and electrical conductivity {sigma}. However, it does not affect themore » so-called Wiedemann-Franz law which relates {kappa} to {sigma}, while it affects the ratio {eta}/s. In addition, another interesting result is that {eta}/s can also be affected by the bulk Maxwell field in our case, which is consistent with some previous results predicted through the Kubo formula. Moreover, the anomalous magnetic and vortical effects by adding the Chern-Simons term are also considered in our case in the Maxwell-Gauss-Bonnet gravity.« less

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.

Gauss-Kronrod-Trapezoidal Integration Scheme for Modeling Biological Tissues with Continuous Fiber Distributions

PubMed Central

Hou, Chieh; Ateshian, Gerard A.

2015-01-01

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 analysis. Second, fibers may not be in tension in some regions on the unit sphere, where the integration becomes a waste. Third, if tensed fiber bundles span a small region compared to the area of the elements on the sphere, a significant discretization error arises. This study presents an integration scheme specialized to the CFD framework, which significantly mitigates the first drawback of the FEI scheme, while eliminating the second and third completely. Here, integration is performed only over the regions of the unit sphere where fibers are in tension. Gauss-Kronrod quadrature is used across latitudes and the trapezoidal scheme across longitudes. Over a wide range of strain states, fiber material properties, and fiber angular distributions, results demonstrate that this new scheme always outperforms FEI, sometimes by orders of magnitude in the number of computational steps and relative accuracy of the stress calculation. PMID:26291492

A double-quadrature radiofrequency coil design for proton-decoupled carbon-13 magnetic resonance spectroscopy in humans at 7T.

PubMed

Serés Roig, Eulalia; Magill, Arthur W; Donati, Guillaume; Meyerspeer, Martin; Xin, Lijing; Ipek, Ozlem; Gruetter, Rolf

2015-02-01

Carbon-13 magnetic resonance spectroscopy ((13) C-MRS) is challenging because of the inherent low sensitivity of (13) C detection and the need for radiofrequency transmission at the (1) H frequency while receiving the (13) C signal, the latter requiring electrical decoupling of the (13) C and (1) H radiofrequency channels. In this study, we added traps to the (13) C coil to construct a quadrature-(13) C/quadrature-(1) H surface coil, with sufficient isolation between channels to allow simultaneous operation at both frequencies without compromise in coil performance. Isolation between channels was evaluated on the bench by measuring all coupling parameters. The quadrature mode of the quadrature-(13) C coil was assessed using in vitro (23) Na gradient echo images. The signal-to-noise ratio (SNR) was measured on the glycogen and glucose resonances by (13) C-MRS in vitro, compared with that obtained with a linear-(13) C/quadrature-(1) H coil, and validated by (13) C-MRS in vivo in the human calf at 7T. Isolation between channels was better than -30 dB. The (23) Na gradient echo images indicate a region where the field is strongly circularly polarized. The quadrature coil provided an SNR enhancement over a linear coil of 1.4, in vitro and in vivo. It is feasible to construct a double-quadrature (13) C-(1) H surface coil for proton decoupled sensitivity enhanced (13) C-NMR spectroscopy in humans at 7T. © 2014 Wiley Periodicals, Inc.

Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave.

PubMed

Lin, Jiao; Dellinger, Jean; Genevet, Patrice; Cluzel, Benoit; de Fornel, Frederique; Capasso, Federico

2012-08-31

A new surface wave is introduced, the cosine-Gauss beam, which does not diffract while it propagates in a straight line and tightly bound to the metallic surface for distances up to 80 μm. The generation of this highly localized wave is shown to be straightforward and highly controllable, with varying degrees of transverse confinement and directionality, by fabricating a plasmon launcher consisting of intersecting metallic gratings. Cosine-Gauss beams have potential for applications in plasmonics, notably for efficient coupling to nanophotonic devices, opening up new design possibilities for next-generation optical interconnects.

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…

Gravitational quasinormal modes of static Einstein-Gauss-Bonnet anti-de Sitter black holes

NASA Astrophysics Data System (ADS)

Ma, Hong; Li, Jin

2018-04-01

In this paper, we describe quasinormal modes (QNMs) for gravitational perturbations of Einstein-Gauss-Bonnet black holes (BHs) in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime (flat, de Sitter (dS) and anti-de Sitter (AdS)). Our attention is concentrated on discussing the (in)stability of Einstein-Gauss-Bonnet AdS BHs through the temporal evolution of all types of gravitational perturbation fields (tensor, vector and scalar). It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore, the influences of the Gauss-Bonnet coupling parameter α, the number of dimensions n and the angular momentum quantum number l on the Einstein-Gauss-Bonnet AdS BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of α. This indicates that QNM frequencies become increasingly unstable with large α. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between α and properties of Einstein-Gauss-Bonnet AdS BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds. Supported by FAPESP (2012/08934-0), National Natural Science Foundation of China (11205254, 11178018, 11375279, 11605015), the Natural Science Foundation Project of CQ CSTC (2011BB0052), and the Fundamental Research Funds for the Central Universities (106112016CDJXY300002, 106112017CDJXFLX0014, CDJRC10300003)

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…

A conservative staggered-grid Chebyshev multidomain method for compressible flows

NASA Technical Reports Server (NTRS)

Kopriva, David A.; Kolias, John H.

1995-01-01

We present a new multidomain spectral collocation method that uses staggered grids for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute.

From entropy-maximization to equality-maximization: Gauss, Laplace, Pareto, and Subbotin

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2014-12-01

The entropy-maximization paradigm of statistical physics is well known to generate the omnipresent Gauss law. In this paper we establish an analogous socioeconomic model which maximizes social equality, rather than physical disorder, in the context of the distributions of income and wealth in human societies. We show that-on a logarithmic scale-the Laplace law is the socioeconomic equality-maximizing counterpart of the physical entropy-maximizing Gauss law, and that this law manifests an optimized balance between two opposing forces: (i) the rich and powerful, striving to amass ever more wealth, and thus to increase social inequality; and (ii) the masses, struggling to form more egalitarian societies, and thus to increase social equality. Our results lead from log-Gauss statistics to log-Laplace statistics, yield Paretian power-law tails of income and wealth distributions, and show how the emergence of a middle-class depends on the underlying levels of socioeconomic inequality and variability. Also, in the context of asset-prices with Laplace-distributed returns, our results imply that financial markets generate an optimized balance between risk and predictability.

On the frequency spectra of the core magnetic field Gauss coefficients

NASA Astrophysics Data System (ADS)

Lesur, Vincent; Wardinski, Ingo; Baerenzung, Julien; Holschneider, Matthias

2018-03-01

From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k-2 slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.

Collapsing spherical star in Scalar-Einstein-Gauss-Bonnet gravity with a quadratic coupling

NASA Astrophysics Data System (ADS)

Chakrabarti, Soumya

2018-04-01

We study the evolution of a self interacting scalar field in Einstein-Gauss-Bonnet theory in four dimension where the scalar field couples non minimally with the Gauss-Bonnet term. Considering a polynomial coupling of the scalar field with the Gauss-Bonnet term, a self-interaction potential and an additional perfect fluid distribution alongwith the scalar field, we investigate different possibilities regarding the outcome of the collapsing scalar field. The strength of the coupling and choice of the self-interaction potential serves as the pivotal initial conditions of the models presented. The high degree of non-linearity in the equation system is taken care off by using a method of invertibe point transformation of anharmonic oscillator equation, which has proven itself very useful in recent past while investigating dynamics of minimally coupled scalar fields.

A MIMO radar quadrature and multi-channel amplitude-phase error combined correction method based on cross-correlation

NASA Astrophysics Data System (ADS)

Yun, Lingtong; Zhao, Hongzhong; Du, Mengyuan

2018-04-01

Quadrature and multi-channel amplitude-phase error have to be compensated in the I/Q quadrature sampling and signal through multi-channel. A new method that it doesn't need filter and standard signal is presented in this paper. And it can combined estimate quadrature and multi-channel amplitude-phase error. The method uses cross-correlation and amplitude ratio between the signal to estimate the two amplitude-phase errors simply and effectively. And the advantages of this method are verified by computer simulation. Finally, the superiority of the method is also verified by measure data of outfield experiments.

Digital quadrature phase detection

DOEpatents

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

DOEpatents

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.

Pre-correction of distorted Bessel-Gauss beams without wavefront detection

NASA Astrophysics Data System (ADS)

Fu, Shiyao; Wang, Tonglu; Zhang, Zheyuan; Zhai, Yanwang; Gao, Chunqing

2017-12-01

By utilizing the property of the phase's rapid solution of the Gerchberg-Saxton algorithm, we experimentally demonstrate a scheme to correct distorted Bessel-Gauss beams resulting from inhomogeneous media as weak turbulent atmosphere with good performance. A probe Gaussian beam is employed and propagates coaxially with the Bessel-Gauss modes through the turbulence. No wavefront sensor but a matrix detector is used to capture the probe Gaussian beams, and then, the correction phase mask is computed through inputting such probe beam into the Gerchberg-Saxton algorithm. The experimental results indicate that both single and multiplexed BG beams can be corrected well, in terms of the improvement in mode purity and the mitigation of interchannel cross talk.

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.

Fractional Fourier transform of Lorentz-Gauss vortex beams

NASA Astrophysics Data System (ADS)

Zhou, GuoQuan; Wang, XiaoGang; Chu, XiuXiang

2013-08-01

An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.

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.

Feasibility of heart rate variability measurement from quadrature Doppler radar using arctangent demodulation with DC offset compensation.

PubMed

Massagram, Wansuree; Hafner, Noah M; Park, Byung-Kwan; Lubecke, Victor M; Host-Madsen, Anders; Boric-Lubecke, Olga

2007-01-01

This paper describes the experimental results of the beat-to-beat interval measurement from a quadrature Doppler radar system utilizing arctangent demodulation with DC offset compensation techniques. The comparison in SDNN and in RMSDD of both signals demonstrates the potential of using quadrature Doppler radar for HRV analysis.

A Gauss-Kronrod-Trapezoidal integration scheme for modeling biological tissues with continuous fiber distributions.

PubMed

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.

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

NASA Technical Reports Server (NTRS)

Sidi, Avram; Pennline, James A.

1999-01-01

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

NASA Technical Reports Server (NTRS)

Sidi, Avram; Pennline, James A.

1999-01-01

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Comparisons between real and complex Gauss wavelet transform methods of three-dimensional shape reconstruction

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.

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

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.

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.

Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dotti, Gustavo; Instituto de Fisica Enrique Gaviola, CONICET, Cordoba; Oliva, Julio

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 maximallymore » 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.« less

The Gauss-Bonnet operator of an infinite graph

NASA Astrophysics Data System (ADS)

Anné, Colette; Torki-Hamza, Nabila

2015-06-01

We propose a general condition, to ensure essential self-adjointness for the Gauss-Bonnet operator , based on a notion of completeness as Chernoff. This gives essential self-adjointness of the Laplace operator both for functions and 1-forms on infinite graphs. This is used to extend Flanders result concerning solutions of Kirchhoff's laws.

Image segmentation using hidden Markov Gauss mixture models.

PubMed

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

PubMed Central

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

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.

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

Charged Rényi entropies in CFTs with Einstein-Gauss-Bonnet holographic duals

NASA Astrophysics Data System (ADS)

Pastras, Georgios; Manolopoulos, Dimitrios

2014-11-01

We calculate the Rényi entropy S q ( μ, λ), for spherical entangling surfaces in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings λ, larger than specific value, but still allowed by causality, we observe a violation of the inequality , which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction of the behaviour of the analytic continuation of S q ( μ, λ) for imaginary chemical potential, between negative and non-negative λ.

Neural Correlates of Phrase Quadrature Perception in Harmonic Rhythm: An EEG Study Using a Brain-Computer Interface.

PubMed

Fernández-Soto, Alicia; Martínez-Rodrigo, Arturo; Moncho-Bogani, José; Latorre, José Miguel; Fernández-Caballero, Antonio

2018-06-01

For the sake of establishing the neural correlates of phrase quadrature perception in harmonic rhythm, a musical experiment has been designed to induce music-evoked stimuli related to one important aspect of harmonic rhythm, namely the phrase quadrature. Brain activity is translated to action through electroencephalography (EEG) by using a brain-computer interface. The power spectral value of each EEG channel is estimated to obtain how power variance distributes as a function of frequency. The results of processing the acquired signals are in line with previous studies that use different musical parameters to induce emotions. Indeed, our experiment shows statistical differences in theta and alpha bands between the fulfillment and break of phrase quadrature, an important cue of harmonic rhythm, in two classical sonatas.

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.

Solving radiative transfer with line overlaps using Gauss-Seidel algorithms

NASA Astrophysics Data System (ADS)

Daniel, F.; Cernicharo, J.

2008-09-01

Context: The improvement in observational facilities requires refining the modelling of the geometrical structures of astrophysical objects. Nevertheless, for complex problems such as line overlap in molecules showing hyperfine structure, a detailed analysis still requires a large amount of computing time and thus, misinterpretation cannot be dismissed due to an undersampling of the whole space of parameters. Aims: We extend the discussion of the implementation of the Gauss-Seidel algorithm in spherical geometry and include the case of hyperfine line overlap. Methods: We first review the basics of the short characteristics method that is used to solve the radiative transfer equations. Details are given on the determination of the Lambda operator in spherical geometry. The Gauss-Seidel algorithm is then described and, by analogy to the plan-parallel case, we see how to introduce it in spherical geometry. Doing so requires some approximations in order to keep the algorithm competitive. Finally, line overlap effects are included. Results: The convergence speed of the algorithm is compared to the usual Jacobi iterative schemes. The gain in the number of iterations is typically factors of 2 and 4 for the two implementations made of the Gauss-Seidel algorithm. This is obtained despite the introduction of approximations in the algorithm. A comparison of results obtained with and without line overlaps for N2H^+, HCN, and HNC shows that the J=3-2 line intensities are significantly underestimated in models where line overlap is neglected.

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.

Dynamic analysis of multirigid-body system based on the Gauss principle

NASA Astrophysics Data System (ADS)

Lilov, L.; Lorer, M.

Two different approaches can be used for solving the basic dynamic problem in the case of a multirigid body system. The first approach is based on the derivation of the nonlinear equations of motion of the mechanical system, while the second approach is concerned with the direct derivation of the unknown accelerations. Using the Gauss principle, the accelerations can be determined by using the condition for the minimum of a functional. The present investigation is concerned with an algorithm for a dynamical study of a multibody system on the basis of the Gauss principle. The system may contain an arbitrary number of closed loops. The main purpose of the proposed algorithm is the investigation of the dynamics of industrial manipulators, robots, and similar mechanisms.

GAUSS Market Analysis for Integrated Satellite Communication and Navigation Location Based services

NASA Astrophysics Data System (ADS)

Di Fazio, Antonella; Dricot, Fabienne; Tata, Francesco

2003-07-01

The demand for mobile information services coupled with positioning technologies for delivering value- added services that depend on a user's location has rapidly increased during last years. In particular, services and applications related with improved mobility safety and transport efficiency look very attractive.Solutions for location services vary in respect of positioning accuracy and the technical infrastructure required, and the associated investment in terminals and networks. From the analysis of the state-of-the art, it comes that various technologies are currently available on the European market, while mobile industry is gearing up to launch a wide variety of location services like tracking, alarming and locating.Nevertheless, when addressing safety of life as well as security applications, severe hurdles have to be posed in the light of existing technologies. Existing navigation (e.g. GPS) and communication systems are not able to completely satisfy the needs and requirements of safety-of-life-critical applications. As a matter of fact, the GPS system's main weaknesses today is its lack of integrity, which means its inability to warn users of a malfunction in a reasonable time, while the other positioning techniques do not provide satisfactory accuracy as well, and terrestrial communication networks are not capable to cope with stringent requirement in terms of service reliability and coverage.In this context, GAUSS proposes an innovative satellite-based solution using novel technology and effective tools for addressing mobility challenges in a cost efficient manner, improving safety and effectiveness.GAUSS (Galileo And UMTS Synergetic System) is a Research and Technological Development project co- funded by European Commission, within the frame of the 5th IST Programme. The project lasted two years, and it was successfully completed in November 2002. GAUSS key concept is the integration of Satellite Navigation GNSS and UMTS communication technology, to

Addendum to ''Thin-shell wormholes supported by ordinary matter in Einstein-Gauss-Bonnet gravity''

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

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.

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.

On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology [Formula: see text].

PubMed

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.

How Can Multivariate Item Response Theory Be Used in Reporting of Susbcores? Research Report. ETS RR-10-09

ERIC Educational Resources Information Center

Haberman, Shelby J.; Sinharay, Sandip

2010-01-01

Recently, there has been increasing interest in reporting diagnostic scores. This paper examines reporting of subscores using multidimensional item response theory (MIRT) models. An MIRT model is fitted using a stabilized Newton-Raphson algorithm (Haberman, 1974, 1988) with adaptive Gauss-Hermite quadrature (Haberman, von Davier, & Lee, 2008).…

Clinical Profile of Statin Intolerance in the Phase 3 GAUSS-2 Study.

PubMed

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.

Planar quadrature RF transceiver design using common-mode differential-mode (CMDM) transmission line method for 7T MR imaging.

PubMed

Li, Ye; Yu, Baiying; Pang, Yong; Vigneron, Daniel B; Zhang, Xiaoliang

2013-01-01

The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR) in magnetic resonance (MR) imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM) technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM) and the differential mode (DM) of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays.

Stability of anti-de sitter space in Einstein-Gauss-Bonnet gravity.

PubMed

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.

Accurate cell counts in live mouse embryos using optical quadrature and differential interference contrast microscopy

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.

Competing s-wave orders from Einstein-Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Li, Zhi-Hong; Fu, Yun-Chang; Nie, Zhang-Yu

2018-01-01

In this paper, the holographic superconductor model with two s-wave orders from 4 + 1 dimensional Einstein-Gauss-Bonnet gravity is explored in the probe limit. At different values of the Gauss-Bonnet coefficient α, we study the influence of tuning the mass and charge parameters of the bulk scalar field on the free energy curve of condensed solution with signal s-wave order, and compare the difference of tuning the two different parameters while the changes of the critical temperature are the same. Based on the above results, it is indicated that the two free energy curves of different s-wave orders can have one or two intersection points, where two typical phase transition behaviors of the s + s coexistent phase, including the reentrant phase transition near the Chern-Simons limit α = 0.25, can be found. We also give an explanation to the nontrivial behavior of the Tc- α curves near the Chern-Simons limit, which might be heuristic to understand the origin of the reentrant behavior near the Chern-Simons limit.

Propagation of partially coherent Lorentz and Lorentz-Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere

NASA Astrophysics Data System (ADS)

Zhao, Chengliang; Cai, Yangjian

2011-05-01

Based on the generalized Huygens-Fresnel integral, propagation of partially coherent Lorentz and Lorentz-Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere was investigated. Analytical propagation formulae were derived for the cross-spectral densities of partially coherent Lorentz and Lorentz-Gauss beams. As an application example, the focusing properties of partially coherent Gaussian, Lorentz and Lorentz-Gauss beams in a turbulent atmosphere and in free space were studied numerically and comparatively. It is found that the focusing properties of such beams are closely related to the initial coherence length and the structure constant of turbulence. By choosing a suitable initial coherence length, a partially coherent Lorentz beam can be focused more tightly than a Gaussian or Lorentz-Gauss beam in free space or in a turbulent atmosphere with small structure constant at the geometrical focal plane.

Best quadrature formula on Sobolev class with Chebyshev weight

NASA Astrophysics Data System (ADS)

Xie, Congcong

2008-05-01

Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KWr[-1,1] with Chebyshev weight. The given function information means that the values of a function f[set membership, variant]KWr[-1,1] and its derivatives up to r-1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples.

Development of a Double-Gauss Lens Based Setup for Optoacoustic Applications

PubMed Central

Choi, Hojong; Ryu, Jae-Myung; Yeom, Jung-Yeol

2017-01-01

In optoacoustic (photoacoustic) systems, different echo signal intensities such as amplitudes, center frequencies, and bandwidths need to be compensated by utilizing variable gain or time-gain compensation amplifiers. However, such electronic components can increase system complexities and signal noise levels. In this paper, we introduce a double-Gauss lens to generate a large field of view with uniform light intensity due to the low chromatic aberrations of the lens, thus obtaining uniform echo signal intensities across the field of view of the optoacoustic system. In order to validate the uniformity of the echo signal intensities in the system, an in-house transducer was placed at various positions above a tissue sample and echo signals were measured and compared with each other. The custom designed double-Gauss lens demonstrated negligible light intensity variation (±1.5%) across the illumination field of view (~2 cm diameter). When the transducer was used to measure echo signal from an eye of a bigeye tuna within a range of ±1 cm, the peak-to-peak amplitude, center frequency, and their −6 dB bandwidth variations were less than 2 mV, 1 MHz, and 6%, respectively. The custom designed double-Gauss lens can provide uniform light beam across a wide area while generating insignificant echo signal variations, and thus can lower the burden of the receiving electronics or signal processing in the optoacoustic system. PMID:28273794

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.

Nested sparse grid collocation method with delay and transformation for subsurface flow and transport problems

NASA Astrophysics Data System (ADS)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-06-01

In numerical modeling of subsurface flow and transport problems, formation properties may not be deterministically characterized, which leads to uncertainty in simulation results. In this study, we propose a sparse grid collocation method, which adopts nested quadrature rules with delay and transformation to quantify the uncertainty of model solutions. We show that the nested Kronrod-Patterson-Hermite quadrature is more efficient than the unnested Gauss-Hermite quadrature. We compare the convergence rates of various quadrature rules including the domain truncation and domain mapping approaches. To further improve accuracy and efficiency, we present a delayed process in selecting quadrature nodes and a transformed process for approximating unsmooth or discontinuous solutions. The proposed method is tested by an analytical function and in one-dimensional single-phase and two-phase flow problems with different spatial variances and correlation lengths. An additional example is given to demonstrate its applicability to three-dimensional black-oil models. It is found from these examples that the proposed method provides a promising approach for obtaining satisfactory estimation of the solution statistics and is much more efficient than the Monte-Carlo simulations.

Design and implementation of quadrature bandpass sigma-delta modulator used in low-IF RF receiver

NASA Astrophysics Data System (ADS)

Ge, Binjie; Li, Yan; Yu, Hang; Feng, Xiaoxing

2018-05-01

This paper presents the design and implementation of quadrature bandpass sigma-delta modulator. A pole movement method for transforming real sigma-delta modulator to a quadrature one is proposed by detailed study of the relationship of noise-shaping center frequency and integrator pole position in sigma-delta modulator. The proposed modulator uses sampling capacitor sharing switched capacitor integrator, and achieves a very small feedback coefficient by a series capacitor network, and those two techniques can dramatically reduce capacitor area. Quantizer output-dependent dummy capacitor load for reference voltage buffer can compensate signal-dependent noise that is caused by load variation. This paper designs a quadrature bandpass Sigma-Delta modulator for 2.4 GHz low IF receivers that achieve 69 dB SNDR at 1 MHz BW and -1 MHz IF with 48 MHz clock. The chip is fabricated with SMIC 0.18 μm CMOS technology, it achieves a total power current of 2.1 mA, and the chip area is 0.48 mm2. Project supported by the National Natural Science Foundation of China (Nos. 61471245, U1201256), the Guangdong Province Foundation (No. 2014B090901031), and the Shenzhen Foundation (Nos. JCYJ20160308095019383, JSGG20150529160945187).

Creating aperiodic photonic structures by synthesized Mathieu-Gauss beams

NASA Astrophysics Data System (ADS)

Vasiljević, Jadranka M.; Zannotti, Alessandro; Timotijević, Dejan V.; Denz, Cornelia; Savić, Dragana M. Jović

2017-08-01

We demonstrate a kind of aperiodic photonic structure realized using the interference of multiple Mathieu-Gauss beams. Depending on the beam configurations, their mutual distances, angles of rotation, or phase relations we are able to observe different classes of such aperiodic optically induced refractive index structures. Our experimental approach is based on the optical induction in a single parallel writing process.

Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method

NASA Astrophysics Data System (ADS)

Schanz, Martin; Ye, Wenjing; Xiao, Jinyou

2016-04-01

Transient problems can often be solved with transformation methods, where the inverse transformation is usually performed numerically. Here, the discrete Fourier transform in combination with the exponential window method is compared with the convolution quadrature method formulated as inverse transformation. Both are inverse Laplace transforms, which are formally identical but use different complex frequencies. A numerical study is performed, first with simple convolution integrals and, second, with a boundary element method (BEM) for elastodynamics. Essentially, when combined with the BEM, the discrete Fourier transform needs less frequency calculations, but finer mesh compared to the convolution quadrature method to obtain the same level of accuracy. If further fast methods like the fast multipole method are used to accelerate the boundary element method the convolution quadrature method is better, because the iterative solver needs much less iterations to converge. This is caused by the larger real part of the complex frequencies necessary for the calculation, which improves the conditions of system matrix.

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

DOE PAGES

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

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fierce, Laura; McGraw, Robert L.

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

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

Some spectral approximation of one-dimensional fourth-order problems

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Maday, Yvon

1989-01-01

Some spectral type collocation method well suited for the approximation of fourth-order systems are proposed. The model problem is the biharmonic equation, in one and two dimensions when the boundary conditions are periodic in one direction. It is proved that the standard Gauss-Lobatto nodes are not the best choice for the collocation points. Then, a new set of nodes related to some generalized Gauss type quadrature formulas is proposed. Also provided is a complete analysis of these formulas including some new issues about the asymptotic behavior of the weights and we apply these results to the analysis of the collocation method.

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…

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.

PubMed

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.

On the Study of a Quadrature DCSK Modulation Scheme for Cognitive Radio

NASA Astrophysics Data System (ADS)

Quyen, Nguyen Xuan

The past decade has witnessed a boom of wireless communications which necessitate an increasing improvement of data rate, error-rate performance, bandwidth efficiency, and information security. In this work, we propose a quadrature (IQ) differential chaos-shift keying (DCSK) modulation scheme for the application in cognitive radio (CR), named CR-IQ-DCSK, which offers the above improvement. Chaotic signal is generated in frequency domain and then converted into time domain via an inverse Fourier transform. The real and imaginary components of the frequency-based chaotic signal are simultaneously used in in-phase and quadrature branches of an IQ modulator, where each branch conveys two bits by means of a DCSK-based modulation. Schemes and operating principle of the modulator and demodulator are proposed and described. Analytical BER performance for the proposed schemes over a typical multipath Rayleigh fading channel is derived and verified by numerical simulations. Results show that the proposed scheme outperforms DCSK, CDSK and performs better with the increment of the number of channel paths.

Efficient Jacobi-Gauss collocation method for solving initial value problems of Bratu type

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.

2013-09-01

In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J {/n (α,β)}( x) with α, β ∈ (-1, ∞), x ∈ [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.

General aspects of Gauss-Bonnet models without potential in dimension four

DOE Office of Scientific and Technical Information (OSTI.GOV)

Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com

In the present work, the isotropic and homogenous solutions with spatial curvature k =0 of four dimensional Gauss-Bonnet models are characterized. The main assumption is that the scalar field φ which is coupled to the Gauss-Bonnet term has no potential [1]–[2]. Some singular and some eternal solutions are described. The evolution of the universe is given in terms of a curve γ=( H (φ), φ) which is the solution of a polynomial equation P ( H {sup 2}, φ)=0 with φ dependent coefficients. In addition, it is shown that the initial conditions in these models put several restrictions on themore » evolution. For instance, an universe initially contracting will be contracting always for future times and an universe that is expanding was always expanding at past times. Thus, there are no cyclic cosmological solutions for this model. These results are universal, that is, independent on the form of the coupling f (φ) between the scalar field and the Gauss-Bonnet term. In addition, a proof that at a turning point φ-dot →0 a singularity necessarily emerges is presented, except for some specific choices of the coupling. This is valid unless the Hubble constant H → 0 at this point. This proof is based on the Raychaudhuri equation for the model. The description presented here is in part inspired in the works [3]–[4]. However, the mathematical methods that are implemented are complementary of those in these references, and they may be helpful for study more complicated situations in a future.« less

Cross-quadrature modulation with the Raman-induced Kerr effect

NASA Astrophysics Data System (ADS)

Levenson, M. D.; Holland, M. J.; Walls, D. F.; Manson, P. J.; Fisk, P. T. H.; Bachor, H. A.

1991-08-01

The Raman-enhanced third-order optical nonlinearity of calcite potentially can support resonant back-action-evading measurement of the optical-field amplitude. In a preliminary experiment, we have observed cross-quadrature modulation transfer between an amplitude-modulated pump beam and an unmodulated probe beam tuned near the Stokes frequency. The theory of Holland et al. [Phys. Rev. A 42, 2995 (1990)] is extended to the case for which intracavity losses are significant in an attempt to account for the observations.

Spectral Quadrature method for accurate O ( N ) electronic structure calculations of metals and insulators

DOE PAGES

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(N 3) 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

High-accuracy 3D Fourier forward modeling of gravity field based on the Gauss-FFT technique

NASA Astrophysics Data System (ADS)

Zhao, Guangdong; Chen, Bo; Chen, Longwei; Liu, Jianxin; Ren, Zhengyong

2018-03-01

The 3D Fourier forward modeling of 3D density sources is capable of providing 3D gravity anomalies coincided with the meshed density distribution within the whole source region. This paper firstly derives a set of analytical expressions through employing 3D Fourier transforms for calculating the gravity anomalies of a 3D density source approximated by right rectangular prisms. To reduce the errors due to aliasing and imposed periodicity as well as edge effects in the Fourier domain modeling, we develop the 3D Gauss-FFT technique to the 3D gravity anomalies forward modeling. The capability and adaptability of this scheme are tested by simple synthetic models. The results show that the accuracy of the Fourier forward methods using the Gauss-FFT with 4 Gaussian-nodes (or more) is comparable to that of the spatial modeling. In addition, the "ghost" source effects in the 3D Fourier forward gravity field due to imposed periodicity of the standard FFT algorithm are remarkably depressed by the application of the 3D Gauss-FFT algorithm. More importantly, the execution times of the 4 nodes Gauss-FFT modeling are reduced by two orders of magnitude compared with the spatial forward method. It demonstrates that the improved Fourier method is an efficient and accurate forward modeling tool for the gravity field.

Study of quadrature FIR filters for extraction of low-frequency instantaneous information in biophysical signals

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.

Field-quadrature and photon-number correlations produced by parametric processes.

PubMed

McKinstrie, C J; Karlsson, M; Tong, Z

2010-09-13

In a previous paper [Opt. Express 13, 4986 (2005)], formulas were derived for the field-quadrature and photon-number variances produced by multiple-mode parametric processes. In this paper, formulas are derived for the quadrature and number correlations. The number formulas are used to analyze the properties of basic devices, such as two-mode amplifiers, attenuators and frequency convertors, and composite systems made from these devices, such as cascaded parametric amplifiers and communication links. Amplifiers generate idlers that are correlated with the amplified signals, or correlate pre-existing pairs of modes, whereas attenuators decorrelate pre-existing modes. Both types of device modify the signal-to-noise ratios (SNRs) of the modes on which they act. Amplifiers decrease or increase the mode SNRs, depending on whether they are operated in phase-insensitive (PI) or phase-sensitive (PS) manners, respectively, whereas attenuators always decrease these SNRs. Two-mode PS links are sequences of transmission fibers (attenuators) followed by two-mode PS amplifiers. Not only do these PS links have noise figures that are 6-dB lower than those of the corresponding PI links, they also produce idlers that are (almost) completely correlated with the signals. By detecting the signals and idlers, one can eliminate the effects of electronic noise in the detectors.

Beam shape coefficients calculation for an elliptical Gaussian beam with 1-dimensional quadrature and localized approximation methods

NASA Astrophysics Data System (ADS)

Wang, Wei; Shen, Jianqi

2018-06-01

The use of a shaped beam for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively. Numerical techniques for evaluating the BSCs of a shaped beam, such as the quadrature, the localized approximation (LA), the integral localized approximation (ILA) methods, have been developed within the framework of generalized Lorenz-Mie theory (GLMT). The quadrature methods usually employ the 2-/3-dimensional integrations. In this work, the expressions of the BSCs for an elliptical Gaussian beam (EGB) are simplified into the 1-dimensional integral so as to speed up the numerical computation. Numerical results of BSCs are used to reconstruct the beam field and the fidelity of the reconstructed field to the given beam field is estimated. It is demonstrated that the proposed method is much faster than the 2-dimensional integrations and it can acquire more accurate results than the LA method. Limitations of the quadrature method and also the LA method in the numerical calculation are analyzed in detail.

Two new modified Gauss-Seidel methods for linear system with M-matrices

NASA Astrophysics Data System (ADS)

Zheng, Bing; Miao, Shu-Xin

2009-12-01

In 2002, H. Kotakemori et al. proposed the modified Gauss-Seidel (MGS) method for solving the linear system with the preconditioner [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner () J. Comput. Appl. Math. 145 (2002) 373-378]. Since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row. In the present paper, to deal with this drawback, we propose two new preconditioners. The convergence and comparison theorems of the modified Gauss-Seidel methods with these two preconditioners for solving the linear system are established. The convergence rates of the new proposed preconditioned methods are compared. In addition, numerical experiments are used to show the effectiveness of the new MGS methods.

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.

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).

The effect of the Gauss-Bonnet term on Hawking radiation from arbitrary dimensional black brane

NASA Astrophysics Data System (ADS)

Kuang, Xiao-Mei; Saavedra, Joel; Övgün, Ali

2017-09-01

We investigate the probabilities of the tunneling and the radiation spectra of massive spin-1 particles from arbitrary dimensional Gauss-Bonnet-Axions (GBA) Anti-de Sitter (AdS) black branes, via using the WKB approximation to the Proca spin-1 field equation. The tunneling probabilities and Hawking temperature of the arbitrary dimensional GBA AdS black brane is calculated via the Hamilton-Jacobi approach. We also compute the Hawking temperature via the Parikh-Wilczek tunneling approach. The results obtained from the two methods are consistent. In our setup, the Gauss-Bonnet (GB) coupling affects the Hawking temperature if and only if the momentum of the axion fields is non-vanishing.

Stability of Gauss-Bonnet black holes in anti-de Sitter space-time against scalar field condensation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brihaye, Yves; Hartmann, Betti

We study the stability of static, hyperbolic Gauss-Bonnet black holes in (4+1)-dimensional anti-de Sitter (AdS) space-time against the formation of scalar hair. Close to extremality the black holes possess a near-horizon topology of AdS{sub 2}xH{sup 3} such that within a certain range of the scalar field mass one would expect that they become unstable to the condensation of an uncharged scalar field. We confirm this numerically and observe that there exists a family of hairy black hole solutions labeled by the number of nodes of the scalar field function. We construct explicit examples of solutions with a scalar field thatmore » possesses zero nodes, one node, and two nodes, respectively, and show that the solutions with nodes persist in the limit of Einstein gravity, i.e. for vanishing Gauss-Bonnet coupling. We observe that the interval of the mass for which scalar field condensation appears decreases with increasing Gauss-Bonnet coupling and/or with increasing node number.« less

Rotation of large asymmetrical absorbing objects by Laguerre-Gauss beams.

PubMed

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.

Imaging of trabecular meshwork using Bessel-Gauss light sheet with fluorescence

NASA Astrophysics Data System (ADS)

Jie Jeesmond Hong, Xun; Shinoj, V. K.; Murukeshan, V. M.; Baskaran, M.; Aung, Tin

2017-03-01

Ocular imaging technology that holds promise for both fundamental investigation and clinical detection of glaucoma is still a challenging research area. A direct view of the trabecular meshwork (TM) with high resolution is not generally possible because the iridocorneal angle region is obstructed by the sclera overlap. The best approach to observe the aqueous outflow system (AOS) is therefore to view from the opposite angle. In this research work, we developed two imaging systems for the high resolution ex vivo studies of the AOS inside porcine eye, based on a Gaussian illuminated and a digitally scanned Bessel-Gauss beam light sheet fluorescence configurations. The digitally scanned Bessel-Gauss beam is able to overcome the trade-off between the length and thickness of the Gaussian light sheet to give better imaging performance. It has adequate spatial resolution to resolve critical anatomical structures such as the TM, thereby enabling objective information about the AOS. This non-contact and non-invasive imaging methodology with excellent safety profile is expected to be well received by vision researchers and clinicians in the evaluation and management of glaucoma.

SOHO-Ulysses Coordinated Studies During the Two Extended Quadratures and the Alignment of 2007-2008

NASA Technical Reports Server (NTRS)

Suess, S. T.; Poletto, G.

2007-01-01

During SOHO-Sun-Ulysses quadratures the geometry of the configuration makes it possible to sample "in situ" the plasma parcels that are remotely observed in the corona. Although the quadrature position occurs at a well defined instant in time, we typically take data while Ulysses is within +/- 5 degrees of the limb, with the understanding that plasma sampled by Ulysses over this time interval can all be traced to its source in the corona. The relative positions of SOHO and Ulysses in winter 2007 (19 Dec 2006-28 May 2007) are unusual: the SOHO-Sun-Ulysses included angle is always between 85 and 95 degrees - the quadrature lasts for 5 months! This provides an opportunity for extended observations of specific observing objectives. In addition, in summer 2007, Ulysses (at 1.34 AU) is in near-radial alignment with Earth/ACE/Wind and SOHO, allowing us to analyze radial gradients and propagation in the solar wind and inner heliosphere. Our own quadrature campaigns rely heavily on LASCO and UVCS coronal observations: LASCO giving the overall context above 2 solar radii while the UVCS spectrograph acquired data from - 1.5 to, typically, 4-5 solar radii. In the past, coronal parameters have been derived from data acquired by these two experiments and compared with "in situ" data of Ulysses' SWOOPS and SWICS. Data from other experiments like EIT, CDS, SUMER, Sac Peak Fe XIV maps, magnetic field maps from the Wilcox solar magnetograph, MLSO, from MDI, and from the Ulysses magnetograph experiment have been, and will be, used to complement LASCO/UVCS/SWOOPS and SWICS data. We anticipate that observations by ACE/WIND/STEREO/Hinode and other missions will be relevant as well. During the IHY campaigns, Ulysses will be 52-80 degrees south in winter 2007, near sunspot minimum. Hence, our own scientific objective will be to sample high speed wind or regions of transition between slow and fast wind. This might be a very interesting situation - not met in previous quadratures - allowing

Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories

NASA Astrophysics Data System (ADS)

Antoniou, G.; Bakopoulos, A.; Kanti, P.

2018-04-01

In the context of the Einstein-scalar-Gauss-Bonnet theory, with a general coupling function between the scalar field and the quadratic Gauss-Bonnet term, we investigate the existence of regular black-hole solutions with scalar hair. Based on a previous theoretical analysis, which studied the evasion of the old and novel no-hair theorems, we consider a variety of forms for the coupling function (exponential, even and odd polynomial, inverse polynomial, and logarithmic) that, in conjunction with the profile of the scalar field, satisfy a basic constraint. Our numerical analysis then always leads to families of regular, asymptotically flat black-hole solutions with nontrivial scalar hair. The solution for the scalar field and the profile of the corresponding energy-momentum tensor, depending on the value of the coupling constant, may exhibit a nonmonotonic behavior, an unusual feature that highlights the limitations of the existing no-hair theorems. We also determine and study in detail the scalar charge, horizon area, and entropy of our solutions.

Digital Detection and Processing of Multiple Quadrature Harmonics for EPR Spectroscopy

PubMed Central

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.

Noise-cancelling quadrature magnetic position, speed and direction sensor

DOEpatents

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.

Reduction of quantum systems and the local Gauss law

NASA Astrophysics Data System (ADS)

Stienstra, Ruben; van Suijlekom, Walter D.

2018-05-01

We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004).

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.

Optimization experiments with a double Gauss lens

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brixner, B.; Klein, M.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 fieldmore » of view. The procedures and results are discussed in detail.« less

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.

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.

Block Gauss elimination followed by a classical iterative method for the solution of linear systems

NASA Astrophysics Data System (ADS)

Alanelli, Maria; Hadjidimos, Apostolos

2004-02-01

In the last two decades many papers have appeared in which the application of an iterative method for the solution of a linear system is preceded by a step of the Gauss elimination process in the hope that this will increase the rates of convergence of the iterative method. This combination of methods has been proven successful especially when the matrix A of the system is an M-matrix. The purpose of this paper is to extend the idea of one to more Gauss elimination steps, consider other classes of matrices A, e.g., p-cyclic consistently ordered, and generalize and improve the asymptotic convergence rates of some of the methods known so far.

Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing

NASA Astrophysics Data System (ADS)

Voss, Paul L.; Köprülü, Kahraman G.; Kumar, Prem

2006-04-01

We present a quantum theory of nondegenerate phase-sensitive parametric amplification in a χ(3) nonlinear medium. The nonzero response time of the Kerr (χ(3)) nonlinearity determines the quantum-limited noise figure of χ(3) parametric amplification, as well as the limit on quadrature squeezing. This nonzero response time of the nonlinearity requires coupling of the parametric process to a molecular vibration phonon bath, causing the addition of excess noise through spontaneous Raman scattering. We present analytical expressions for the quantum-limited noise figure of frequency nondegenerate and frequency degenerate χ(3) parametric amplifiers operated as phase-sensitive amplifiers. We also present results for frequency nondegenerate quadrature squeezing. We show that our nondegenerate squeezing theory agrees with the degenerate squeezing theory of Boivin and Shapiro as degeneracy is approached. We have also included the effect of linear loss on the phase-sensitive process.

Dual-mass vibratory rate gyroscope with suppressed translational acceleration response and quadrature-error correction capability

NASA Technical Reports Server (NTRS)

Clark, William A. (Inventor); Juneau, Thor N. (Inventor); Lemkin, Mark A. (Inventor); Roessig, Allen W. (Inventor)

2001-01-01

A microfabricated vibratory rate gyroscope to measure rotation includes two proof-masses mounted in a suspension system anchored to a substrate. The suspension has two principal modes of compliance, one of which is driven into oscillation. The driven oscillation combined with rotation of the substrate about an axis perpendicular to the substrate results in Coriolis acceleration along the other mode of compliance, the sense-mode. The sense-mode is designed to respond to Coriolis accelerationwhile suppressing the response to translational acceleration. This is accomplished using one or more rigid levers connecting the two proof-masses. The lever allows the proof-masses to move in opposite directions in response to Coriolis acceleration. The invention includes a means for canceling errors, termed quadrature error, due to imperfections in implementation of the sensor. Quadrature-error cancellation utilizes electrostatic forces to cancel out undesired sense-axis motion in phase with drive-mode position.

Parallelization of Lower-Upper Symmetric Gauss-Seidel Method for Chemically Reacting Flow

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jost, Gabriele; Chang, Sherry

2005-01-01

Development of technologies for exploration of the solar system has revived an interest in computational simulation of chemically reacting flows since planetary probe vehicles exhibit non-equilibrium phenomena during the atmospheric entry of a planet or a moon as well as the reentry to the Earth. Stability in combustion is essential for new propulsion systems. Numerical solution of real-gas flows often increases computational work by an order-of-magnitude compared to perfect gas flow partly because of the increased complexity of equations to solve. Recently, as part of Project Columbia, NASA has integrated a cluster of interconnected SGI Altix systems to provide a ten-fold increase in current supercomputing capacity that includes an SGI Origin system. Both the new and existing machines are based on cache coherent non-uniform memory access architecture. Lower-Upper Symmetric Gauss-Seidel (LU-SGS) relaxation method has been implemented into both perfect and real gas flow codes including Real-Gas Aerodynamic Simulator (RGAS). However, the vectorized RGAS code runs inefficiently on cache-based shared-memory machines such as SGI system. Parallelization of a Gauss-Seidel method is nontrivial due to its sequential nature. The LU-SGS method has been vectorized on an oblique plane in INS3D-LU code that has been one of the base codes for NAS Parallel benchmarks. The oblique plane has been called a hyperplane by computer scientists. It is straightforward to parallelize a Gauss-Seidel method by partitioning the hyperplanes once they are formed. Another way of parallelization is to schedule processors like a pipeline using software. Both hyperplane and pipeline methods have been implemented using openMP directives. The present paper reports the performance of the parallelized RGAS code on SGI Origin and Altix systems.

An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles

DTIC Science & Technology

2012-06-01

Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre -Gauss-Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...low order polynomials patched together in such away so that the resulting trajectory has several continuous derivatives at all points. In [7], Murray...claims that splines are ideal for optimal control problems because each segment of the spline’s piecewise polynomials approximate the trajectory

Digital detection and processing of multiple quadrature harmonics for EPR spectroscopy.

PubMed

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. Copyright © 2010 Elsevier Inc. All rights reserved.

Scalar hair around charged black holes in Einstein-Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Grandi, Nicolás; Landea, Ignacio Salazar

2018-02-01

We explore charged black hole solutions in Einstein-Gauss-Bonnet gravity in five dimensions, with a charged scalar hair. We interpret such hairy black holes as the final state of the superradiant instability previously reported for this system. We explore the relation of the hairy black hole solutions with the nonbackreacting quasibound states and scalar clouds, as well as with the boson star solutions.

Maximum likelihood orientation estimation of 1-D patterns in Laguerre-Gauss subspaces.

PubMed

Di Claudio, Elio D; Jacovitti, Giovanni; Laurenti, Alberto

2010-05-01

A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

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.

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.

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…

Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals.

PubMed

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 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

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.

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

PubMed

Hudson, H M; Ma, J; Green, P

1994-01-01

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

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.

Two integrator loop quadrature oscillators: A review.

PubMed

Soliman, Ahmed M

2013-01-01

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.

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.

Application of Quantum Gauss-Jordan Elimination Code to Quantum Secret Sharing Code

NASA Astrophysics Data System (ADS)

Diep, Do Ngoc; Giang, Do Hoang; Phu, Phan Huy

2017-12-01

The QSS codes associated with a MSP code are based on finding an invertible matrix V, solving the system vATMB (s a) = s. We propose a quantum Gauss-Jordan Elimination Procedure to produce such a pivotal matrix V by using the Grover search code. The complexity of solving is of square-root order of the cardinal number of the unauthorized set √ {2^{|B|}}.

Application of Quantum Gauss-Jordan Elimination Code to Quantum Secret Sharing Code

NASA Astrophysics Data System (ADS)

Diep, Do Ngoc; Giang, Do Hoang; Phu, Phan Huy

2018-03-01

The QSS codes associated with a MSP code are based on finding an invertible matrix V, solving the system vATMB (s a)=s. We propose a quantum Gauss-Jordan Elimination Procedure to produce such a pivotal matrix V by using the Grover search code. The complexity of solving is of square-root order of the cardinal number of the unauthorized set √ {2^{|B|}}.

Quadrature formula for evaluating left bounded Hadamard type hypersingular integrals

NASA Astrophysics Data System (ADS)

Bichi, Sirajo Lawan; Eshkuvatov, Z. K.; Nik Long, N. M. A.; Okhunov, Abdurahim

2014-12-01

Left semi-bounded Hadamard type Hypersingular integral (HSI) of the form H(h,x) = 1/π √{1+x/1-x }∫-1 **1√{1-t/1+t }h(t)/(t-x)2 dt,x∈(-1.1), Where h(t) is a smooth function is considered. The automatic quadrature scheme (AQS) is constructed by approximating the density function h(t) by the truncated Chebyshev polynomials of the fourth kind. Numerical results revealed that the proposed AQS is highly accurate when h(t) is choosing to be the polynomial and rational functions. The results are in line with the theoretical findings.

Evaluation of the non-Gaussianity of two-mode entangled states over a bosonic memory channel via cumulant theory and quadrature detection

NASA Astrophysics Data System (ADS)

Xiang, Shao-Hua; Wen, Wei; Zhao, Yu-Jing; Song, Ke-Hui

2018-04-01

We study the properties of the cumulants of multimode boson operators and introduce the phase-averaged quadrature cumulants as the measure of the non-Gaussianity of multimode quantum states. Using this measure, we investigate the non-Gaussianity of two classes of two-mode non-Gaussian states: photon-number entangled states and entangled coherent states traveling in a bosonic memory quantum channel. We show that such a channel can skew the distribution of two-mode quadrature variables, giving rise to a strongly non-Gaussian correlation. In addition, we provide a criterion to determine whether the distributions of these states are super- or sub-Gaussian.

High-power CO(2) laser with a Gauss-core resonator for high-speed cutting of thin metal sheets.

PubMed

Takenaka, Y; Nishimae, J; Tanaka, M; Motoki, Y

1997-01-01

A novel resonator, the Gauss-core resonator, based on a stable resonator configuration designed to yield a highly focusing beam operating in a large-volume TEM(00) mode, is presented. A 6.2 kW linearly polarized output beam with an M(2) factor of 1.7 is obtained experimentally for a high-power cw CO(2) laser. The capability of the Gauss-core resonator to process laser materials is also studied. We can cut 1-mm-thick mild (soft) steel with a maximum cutting speed of 58 m/min at 5.6 kW and 0.2-mm-thick steel 145 m/min at 2.8 kW.

GPU-accelerated Modeling and Element-free Reverse-time Migration with Gauss Points Partition

NASA Astrophysics Data System (ADS)

Zhen, Z.; Jia, X.

2014-12-01

Element-free method (EFM) has been applied to seismic modeling and migration. Compared with finite element method (FEM) and finite difference method (FDM), it is much cheaper and more flexible because only the information of the nodes and the boundary of the study area are required in computation. In the EFM, the number of Gauss points should be consistent with the number of model nodes; otherwise the accuracy of the intermediate coefficient matrices would be harmed. Thus when we increase the nodes of velocity model in order to obtain higher resolution, we find that the size of the computer's memory will be a bottleneck. The original EFM can deal with at most 81×81 nodes in the case of 2G memory, as tested by Jia and Hu (2006). In order to solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP), and utilize the GPUs to improve the computation efficiency. Considering the characteristics of the Gaussian points, the GPP method doesn't influence the propagation of seismic wave in the velocity model. To overcome the time-consuming computation of the stiffness matrix (K) and the mass matrix (M), we also use the GPUs in our computation program. We employ the compressed sparse row (CSR) format to compress the intermediate sparse matrices and try to simplify the operations by solving the linear equations with the CULA Sparse's Conjugate Gradient (CG) solver instead of the linear sparse solver 'PARDISO'. It is observed that our strategy can significantly reduce the computational time of K and Mcompared with the algorithm based on CPU. The model tested is Marmousi model. The length of the model is 7425m and the depth is 2990m. We discretize the model with 595x298 nodes, 300x300 Gauss cells and 3x3 Gauss points in each cell. In contrast to the computational time of the conventional EFM, the GPUs-GPP approach can substantially improve the efficiency. The speedup ratio of time consumption of computing K, M is 120 and the

Quadrature demodulation based circuit implementation of pulse stream for ultrasonic signal FRI sparse sampling

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.

Performance Analysis of Direct-Sequence Code-Division Multiple-Access Communications with Asymmetric Quadrature Phase-Shift-Keying Modulation

NASA Technical Reports Server (NTRS)

Wang, C.-W.; Stark, W.

2005-01-01

This article considers a quaternary direct-sequence code-division multiple-access (DS-CDMA) communication system with asymmetric quadrature phase-shift-keying (AQPSK) modulation for unequal error protection (UEP) capability. Both time synchronous and asynchronous cases are investigated. An expression for the probability distribution of the multiple-access interference is derived. The exact bit-error performance and the approximate performance using a Gaussian approximation and random signature sequences are evaluated by extending the techniques used for uniform quadrature phase-shift-keying (QPSK) and binary phase-shift-keying (BPSK) DS-CDMA systems. Finally, a general system model with unequal user power and the near-far problem is considered and analyzed. The results show that, for a system with UEP capability, the less protected data bits are more sensitive to the near-far effect that occurs in a multiple-access environment than are the more protected bits.

Single-grid spectral collocation for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte

1988-01-01

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

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.

Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds

NASA Astrophysics Data System (ADS)

Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung

2016-06-01

We describe a Lie Algebra on the moduli space of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions {{F}g^alg, g ≥ 1}, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.

The process of learning in neural net models with Poisson and Gauss connectivities.

PubMed

Sivridis, L; Kotini, A; Anninos, P

2008-01-01

In this study we examined the dynamic behavior of isolated and non-isolated neural networks with chemical markers that follow a Poisson or Gauss distribution of connectivity. The Poisson distribution shows higher activity in comparison to the Gauss distribution although the latter has more connections that obliterated due to randomness. We examined 57 hematoxylin and eosin stained sections from an equal number of autopsy specimens with a diagnosis of "cerebral matter within normal limits". Neural counting was carried out in 5 continuous optic fields, with the use of a simple optical microscope connected to a computer (software programmer Nikon Act-1 vers-2). The number of neurons that corresponded to a surface was equal to 0.15 mm(2). There was a gradual reduction in the number of neurons as age increased. A mean value of 45.8 neurons /0.15 mm(2) was observed within the age range 21-25, 33 neurons /0.15 mm(2) within the age range 41-45, 19.3 neurons /0.15 mm(2) within the age range 56-60 years. After the age of 60 it was observed that the number of neurons per unit area stopped decreasing. A correlation was observed between these experimental findings and the theoretical neural model developed by professor Anninos and his colleagues. Equivalence between the mean numbers of neurons of the above mentioned age groups and the highest possible number of synaptic connections per neuron (highest number of synaptic connections corresponded to the age group 21-25) was created. We then used both inhibitory and excitatory post-synaptic potentials and applied these values to the Poisson and Gauss distributions, whereas the neuron threshold was varied between 3 and 5. According to the obtained phase diagrams, the hysteresis loops decrease as age increases. These findings were significant as the hysteresis loops can be regarded as the basis for short-term memory.

On the properties of circular beams: normalization, Laguerre-Gauss expansion, and free-space divergence.

PubMed

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.

Calculation of photoionization differential cross sections using complex Gauss-type orbitals.

PubMed

Matsuzaki, Rei; Yabushita, Satoshi

2017-09-05

Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2 . In the calculations of H2 , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

SQDFT: Spectral Quadrature method for large-scale parallel O(N) Kohn-Sham calculations at high temperature

NASA Astrophysics Data System (ADS)

Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj; Pask, John E.

2018-03-01

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for O(N) Kohn-Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw-Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw-Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. We further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect O(N) scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.

Double-Referential Holography and Spatial Quadrature Amplitude Modulation

NASA Astrophysics Data System (ADS)

Zukeran, Keisuke; Okamoto, Atsushi; Takabayashi, Masanori; Shibukawa, Atsushi; Sato, Kunihiro; Tomita, Akihisa

2013-09-01

We proposed a double-referential holography (DRH) that allows phase-detection without external additional beams. In the DRH, phantom beams, prepared in the same optical path as signal beams and preliminary multiplexed in a recording medium along with the signal, are used to produce interference fringes on an imager for converting a phase into an intensity distribution. The DRH enables stable and high-accuracy phase detection independent of the fluctuations and vibrations of the optical system owing to medium shift and temperature variation. Besides, the collinear arrangement of the signal and phantom beams leads to the compactness of the optical data storage system. We conducted an experiment using binary phase modulation signals for verifying the DRH operation. In addition, 38-level spatial quadrature amplitude modulation signals were successfully reproduced with the DRH by numerical simulation. Furthermore, we verified that the distributed phase-shifting method moderates the dynamic range consumption for the exposure of phantom beams.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

2014-02-01

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

Dataset for petroleum based stock markets and GAUSS codes for SAMEM.

PubMed

Khalifa, Ahmed A A; Bertuccelli, Pietro; Otranto, Edoardo

2017-02-01

This article includes a unique data set of a balanced daily (Monday, Tuesday and Wednesday) for oil and natural gas volatility and the oil rich economies' stock markets for Saudi Arabia, Qatar, Kuwait, Abu Dhabi, Dubai, Bahrain and Oman, using daily data over the period spanning Oct. 18, 2006-July 30, 2015. Additionally, we have included unique GAUSS codes for estimating the spillover asymmetric multiplicative error model (SAMEM) with application to Petroleum-Based Stock Market. The data, the model and the codes have many applications in business and social science.

Evaluating the potential for quantitative monitoring of in situ chemical oxidation of aqueous-phase TCE using in-phase and quadrature electrical conductivity

NASA Astrophysics Data System (ADS)

Hort, R. D.; Revil, A.; Munakata-Marr, J.; Mao, D.

2015-07-01

Electrical resistivity measurements can potentially be used to remotely monitor fate and transport of ionic oxidants such as permanganate (MnO4-) during in situ chemical oxidation (ISCO) of contaminants like trichloroethene (TCE). Time-lapse two-dimensional bulk conductivity and induced polarization surveys conducted during a sand tank ISCO simulation demonstrated that MnO4- plume movement could be monitored in a qualitative manner using bulk conductivity tomograms, although chargeability was below sensitivity limits. We also examined changes to in-phase and quadrature electrical conductivity resulting from ion injection, MnO2 and Cl- production, and pH change during TCE and humate oxidation by MnO4- in homogeneous aqueous solutions and saturated porous media samples. Data from the homogeneous samples demonstrated that inversion of the sand tank resistivity data using a common Tikhonov regularization approach was insufficient to recover an accurate conductivity distribution within the tank. While changes to in-phase conductivity could be successfully modeled, quadrature conductivity values could not be directly related to TCE oxidation product or MnO4- concentrations at frequencies consistent with field induced polarization surveys, limiting the utility of quadrature conductivity for monitoring ISCO.

Numerical study on the selective excitation of Helmholtz-Gauss beams in end-pumped solid-state digital lasers with the control of the laser gain transverse position provided by off-axis end pumping

NASA Astrophysics Data System (ADS)

Tsai, Ko-Fan; Chu, Shu-Chun

2018-03-01

This study proposes a complete and unified method for selective excitation of any specified nearly nondiffracting Helmholtz-Gauss (HzG) beam in end-pumped solid-state digital lasers. Four types of the HzG beams: cosine-Gauss beams, Bessel-Gauss beams, Mathieu-Gauss beams, and, in particular, parabolic-Gauss beams are successfully demonstrated to be generated with the proposed methods. To the best of the authors’ knowledge, parabolic-Gauss beams have not yet been directly generated from any kind of laser system. The numerical results of this study show that one can successfully achieve any lasing HzG beams directly from the solid-state digital lasers with only added control of the laser gain transverse position provided by off-axis end pumping. This study also presents a practical digital laser set-up for easily manipulating off-axis pumping in order to achieve the control of the laser gain transverse gain position in digital lasers. The reported results in this study provide advancement of digital lasers in dynamically generating nondiffracting beams. The control of the digital laser cavity gain position creates the possibility of achieving real-time selection of more laser modes in digital lasers, and it is worth further investigation in the future.

Detecting photons in the dark region of Laguerre-Gauss beams.

PubMed

Klimov, Vasily; Bloch, Daniel; Ducloy, Martial; Rios Leite, Jose R

2009-06-08

We show that a photon detector, sensitive to the magnetic field or to the gradient of electric field, can help to characterize the quantum properties of spatially-dependent optical fields. We discuss the excitation of an atom through magnetic dipole or electric quadrupole transitions with the photons of a Bessel beam or a Laguerre-Gauss (LG) beams. These spiral beams are shown to be not true hollow beams, due to the presence of magnetic fields and gradients of electric fields on beam axis. This approach paves the way to an analysis at the quantum level of the propagating light beams having a complicated spatial structure.

Ricci-Gauss-Bonnet holographic dark energy

NASA Astrophysics Data System (ADS)

Saridakis, Emmanuel N.

2018-03-01

We present a model of holographic dark energy in which the infrared cutoff is determined by both the Ricci and the Gauss-Bonnet invariants. Such a construction has the significant advantage that the infrared cutoff, and consequently the holographic dark energy density, does not depend on the future or the past evolution of the universe, but only on its current features, and moreover it is determined by invariants, whose role is fundamental in gravitational theories. We extract analytical solutions for the behavior of the dark energy density and equation-of-state parameters as functions of the redshift. These reveal the usual thermal history of the universe, with the sequence of radiation, matter and dark energy epochs, resulting in the future to a complete dark energy domination. The corresponding dark energy equation-of-state parameter can lie in the quintessence or phantom regime, or experience the phantom-divide crossing during the cosmological evolution, and its asymptotic value can be quintessencelike, phantomlike, or be exactly equal to the cosmological-constant value. Finally, we extract the constraints on the model parameters that arise from big bang nucleosynthesis.

The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Harada, Kyouji; Morimoto, Munenori; Sakakihara, Michio

2004-03-01

Several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the Gauss-Seidel method. In this article, on the basis of nonnegative matrix, comparisons between some splittings for such preconditioned matrices are derived. Simple numerical examples are also given.

A 9-Bit 50 MSPS Quadrature Parallel Pipeline ADC for Communication Receiver Application

NASA Astrophysics Data System (ADS)

Roy, Sounak; Banerjee, Swapna

2018-03-01

This paper presents the design and implementation of a pipeline Analog-to-Digital Converter (ADC) for superheterodyne receiver application. Several enhancement techniques have been applied in implementing the ADC, in order to relax the target specifications of its building blocks. The concepts of time interleaving and double sampling have been used simultaneously to enhance the sampling speed and to reduce the number of amplifiers used in the ADC. Removal of a front end sample-and-hold amplifier is possible by employing dynamic comparators with switched capacitor based comparison of input signal and reference voltage. Each module of the ADC comprises two 2.5-bit stages followed by two 1.5-bit stages and a 3-bit flash stage. Four such pipeline ADC modules are time interleaved using two pairs of non-overlapping clock signals. These two pairs of clock signals are in phase quadrature with each other. Hence the term quadrature parallel pipeline ADC has been used. These configurations ensure that the entire ADC contains only eight operational-trans-conductance amplifiers. The ADC is implemented in a 0.18-μm CMOS process and supply voltage of 1.8 V. The proto-type is tested at sampling frequencies of 50 and 75 MSPS producing an Effective Number of Bits (ENOB) of 6.86- and 6.11-bits respectively. At peak sampling speed, the core ADC consumes only 65 mW of power.

A 9-Bit 50 MSPS Quadrature Parallel Pipeline ADC for Communication Receiver Application

NASA Astrophysics Data System (ADS)

Roy, Sounak; Banerjee, Swapna

2018-06-01

This paper presents the design and implementation of a pipeline Analog-to-Digital Converter (ADC) for superheterodyne receiver application. Several enhancement techniques have been applied in implementing the ADC, in order to relax the target specifications of its building blocks. The concepts of time interleaving and double sampling have been used simultaneously to enhance the sampling speed and to reduce the number of amplifiers used in the ADC. Removal of a front end sample-and-hold amplifier is possible by employing dynamic comparators with switched capacitor based comparison of input signal and reference voltage. Each module of the ADC comprises two 2.5-bit stages followed by two 1.5-bit stages and a 3-bit flash stage. Four such pipeline ADC modules are time interleaved using two pairs of non-overlapping clock signals. These two pairs of clock signals are in phase quadrature with each other. Hence the term quadrature parallel pipeline ADC has been used. These configurations ensure that the entire ADC contains only eight operational-trans-conductance amplifiers. The ADC is implemented in a 0.18-μm CMOS process and supply voltage of 1.8 V. The proto-type is tested at sampling frequencies of 50 and 75 MSPS producing an Effective Number of Bits (ENOB) of 6.86- and 6.11-bits respectively. At peak sampling speed, the core ADC consumes only 65 mW of power.

Phantom-like behavior of a DGP-inspired Scalar-Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nozari, Kourosh; Azizi, Tahereh; Setare, M.R., E-mail: knozari@umz.ac.ir, E-mail: t.azizi@umz.ac.ir, E-mail: rezakord@ipm.ir

2009-10-01

We study the phantom-like behavior of a DGP-inspired braneworld scenario where curvature correction on the brane is taken into account. We include a possible modification of the induced gravity on the brane by incorporating higher order curvature terms of Gauss-Bonnet type. We investigate the cosmological implications of the model and we show that the normal branch of the scenario self-accelerates in this modified scenario without introducing any dark energy component. Also, a phantom-like behavior can be realized in this model without introducing any phantom field that suffers from serious difficulties such as violation of the null energy condition.

Adaptive Square-Root Cubature-Quadrature Kalman Particle Filter for satellite attitude determination using vector observations

NASA Astrophysics Data System (ADS)

Kiani, Maryam; Pourtakdoust, Seid H.

2014-12-01

A novel algorithm is presented in this study for estimation of spacecraft's attitudes and angular rates from vector observations. In this regard, a new cubature-quadrature particle filter (CQPF) is initially developed that uses the Square-Root Cubature-Quadrature Kalman Filter (SR-CQKF) to generate the importance proposal distribution. The developed CQPF scheme avoids the basic limitation of particle filter (PF) with regards to counting the new measurements. Subsequently, CQPF is enhanced to adjust the sample size at every time step utilizing the idea of confidence intervals, thus improving the efficiency and accuracy of the newly proposed adaptive CQPF (ACQPF). In addition, application of the q-method for filter initialization has intensified the computation burden as well. The current study also applies ACQPF to the problem of attitude estimation of a low Earth orbit (LEO) satellite. For this purpose, the undertaken satellite is equipped with a three-axis magnetometer (TAM) as well as a sun sensor pack that provide noisy geomagnetic field data and Sun direction measurements, respectively. The results and performance of the proposed filter are investigated and compared with those of the extended Kalman filter (EKF) and the standard particle filter (PF) utilizing a Monte Carlo simulation. The comparison demonstrates the viability and the accuracy of the proposed nonlinear estimator.

SQDFT: Spectral Quadrature method for large-scale parallel O ( N ) Kohn–Sham calculations at high temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method formore » $$\\mathscr{O}(N)$$ Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. Here, we further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $$\\mathscr{O}(N)$$ scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.« less

SQDFT: Spectral Quadrature method for large-scale parallel O ( N ) Kohn–Sham calculations at high temperature

DOE PAGES

Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj; ...

2017-12-07

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method formore » $$\\mathscr{O}(N)$$ Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. Here, we further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $$\\mathscr{O}(N)$$ scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.« less

S4 solution of the transport equation for eigenvalues using Legendre polynomials

NASA Astrophysics Data System (ADS)

Öztürk, Hakan; Bülbül, Ahmet

2017-09-01

Numerical solution of the transport equation for monoenergetic neutrons scattered isotropically through the medium of a finite homogeneous slab is studied for the determination of the eigenvalues. After obtaining the discrete ordinates form of the transport equation, separated homogeneous and particular solutions are formed and then the eigenvalues are calculated using the Gauss-Legendre quadrature set. Then, the calculated eigenvalues for various values of the c0, the mean number of secondary neutrons per collision, are given in the tables.

Information entropy of Gegenbauer polynomials and Gaussian quadrature

NASA Astrophysics Data System (ADS)

Sánchez-Ruiz, Jorge

2003-05-01

In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.

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 Gauss-Newton full-waveform inversion in PML-truncated domains using scalar probing waves

NASA Astrophysics Data System (ADS)

Pakravan, Alireza; Kang, Jun Won; Newtson, Craig M.

2017-12-01

This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss-Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush-Kuhn-Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss-Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.

Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams.

PubMed

Peet, Viktor

2011-08-01

For a light beam focused through a biaxial crystal along one of its optical axes, the effect of internal conical refraction in the crystal leads to the formation in the focal image plane of two bright rings separated by a dark ring. It is shown that, with circularly polarized Laguerre-Gauss LG(0)(ℓ) beams entering the crystal, this classical double-ring pattern is transformed into a multiring one consisting of ℓ+2 bright rings. © 2011 Optical Society of America

Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling.

PubMed

Silva, Hector O; Sakstein, Jeremy; Gualtieri, Leonardo; Sotiriou, Thomas P; Berti, Emanuele

2018-03-30

We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well.

Differential quadrature method of nonlinear bending of functionally graded beam

NASA Astrophysics Data System (ADS)

Gangnian, Xu; Liansheng, Ma; Wang, Youzhi; Quan, Yuan; Weijie, You

2018-02-01

Using the third-order shear deflection beam theory (TBT), nonlinear bending of functionally graded (FG) beams composed with various amounts of ceramic and metal is analyzed utilizing the differential quadrature method (DQM). The properties of beam material are supposed to accord with the power law index along to thickness. First, according to the principle of stationary potential energy, the partial differential control formulae of the FG beams subjected to a distributed lateral force are derived. To obtain numerical results of the nonlinear bending, non-dimensional boundary conditions and control formulae are dispersed by applying the DQM. To verify the present solution, several examples are analyzed for nonlinear bending of homogeneous beams with various edges. A minute parametric research is in progress about the effect of the law index, transverse shear deformation, distributed lateral force and boundary conditions.

Prostate multimodality image registration based on B-splines and quadrature local energy.

PubMed

Mitra, Jhimli; Martí, Robert; Oliver, Arnau; Lladó, Xavier; Ghose, Soumya; Vilanova, Joan C; Meriaudeau, Fabrice

2012-05-01

Needle biopsy of the prostate is guided by Transrectal Ultrasound (TRUS) imaging. The TRUS images do not provide proper spatial localization of malignant tissues due to the poor sensitivity of TRUS to visualize early malignancy. Magnetic Resonance Imaging (MRI) has been shown to be sensitive for the detection of early stage malignancy, and therefore, a novel 2D deformable registration method that overlays pre-biopsy MRI onto TRUS images has been proposed. The registration method involves B-spline deformations with Normalized Mutual Information (NMI) as the similarity measure computed from the texture images obtained from the amplitude responses of the directional quadrature filter pairs. Registration accuracy of the proposed method is evaluated by computing the Dice Similarity coefficient (DSC) and 95% Hausdorff Distance (HD) values for 20 patients prostate mid-gland slices and Target Registration Error (TRE) for 18 patients only where homologous structures are visible in both the TRUS and transformed MR images. The proposed method and B-splines using NMI computed from intensities provide average TRE values of 2.64 ± 1.37 and 4.43 ± 2.77 mm respectively. Our method shows statistically significant improvement in TRE when compared with B-spline using NMI computed from intensities with Student's t test p = 0.02. The proposed method shows 1.18 times improvement over thin-plate splines registration with average TRE of 3.11 ± 2.18 mm. The mean DSC and the mean 95% HD values obtained with the proposed method of B-spline with NMI computed from texture are 0.943 ± 0.039 and 4.75 ± 2.40 mm respectively. The texture energy computed from the quadrature filter pairs provides better registration accuracy for multimodal images than raw intensities. Low TRE values of the proposed registration method add to the feasibility of it being used during TRUS-guided biopsy.

Artificial immune system for effective properties optimization of magnetoelectric composites

NASA Astrophysics Data System (ADS)

Poteralski, Arkadiusz; Dziatkiewicz, Grzegorz

2018-01-01

The optimization problem of the effective properties for magnetoelectric composites is considered. The effective properties are determined by the semi-analytical Mori-Tanaka approach. The generalized Eshelby tensor components are calculated numerically by using the Gauss quadrature method for the integral representation of the inclusion problem. The linear magnetoelectric constitutive equation is used. The effect of orientation of the electromagnetic materials components is taken into account. The optimization problem of the design is formulated and the artificial immune system is applied to solve it.

A robust hidden Markov Gauss mixture vector quantizer for a noisy source.

PubMed

Pyun, Kyungsuk Peter; Lim, Johan; Gray, Robert M

2009-07-01

Noise is ubiquitous in real life and changes image acquisition, communication, and processing characteristics in an uncontrolled manner. Gaussian noise and Salt and Pepper noise, in particular, are prevalent in noisy communication channels, camera and scanner sensors, and medical MRI images. It is not unusual for highly sophisticated image processing algorithms developed for clean images to malfunction when used on noisy images. For example, hidden Markov Gauss mixture models (HMGMM) have been shown to perform well in image segmentation applications, but they are quite sensitive to image noise. We propose a modified HMGMM procedure specifically designed to improve performance in the presence of noise. The key feature of the proposed procedure is the adjustment of covariance matrices in Gauss mixture vector quantizer codebooks to minimize an overall minimum discrimination information distortion (MDI). In adjusting covariance matrices, we expand or shrink their elements based on the noisy image. While most results reported in the literature assume a particular noise type, we propose a framework without assuming particular noise characteristics. Without denoising the corrupted source, we apply our method directly to the segmentation of noisy sources. We apply the proposed procedure to the segmentation of aerial images with Salt and Pepper noise and with independent Gaussian noise, and we compare our results with those of the median filter restoration method and the blind deconvolution-based method, respectively. We show that our procedure has better performance than image restoration-based techniques and closely matches to the performance of HMGMM for clean images in terms of both visual segmentation results and error rate.

Quadrature transmit coil for breast imaging at 7 tesla using forced current excitation for improved homogeneity.

PubMed

McDougall, Mary Preston; Cheshkov, Sergey; Rispoli, Joseph; Malloy, Craig; Dimitrov, Ivan; Wright, Steven M

2014-11-01

To demonstrate the use of forced current excitation (FCE) to create homogeneous excitation of the breast at 7 tesla, insensitive to the effects of asymmetries in the electrical environment. FCE was implemented on two breast coils: one for quadrature (1) H imaging and one for proton-decoupled (13) C spectroscopy. Both were a Helmholtz-saddle combination, with the saddle tuned to 298 MHz for imaging and 75 MHz for spectroscopy. Bench measurements were acquired to demonstrate the ability to force equal currents on elements in the presence of asymmetric loading to improve homogeneity. Modeling and temperature measurements were conducted per safety protocol. B1 mapping, imaging, and proton-decoupled (13) C spectroscopy were demonstrated in vivo. Using FCE to ensure balanced currents on elements enabled straightforward tuning and maintaining of isolation between quadrature elements of the coil. Modeling and bench measurements confirmed homogeneity of the field, which resulted in images with excellent fat suppression and in broadband proton-decoupled carbon-13 spectra. FCE is a straightforward approach to ensure equal currents on multiple coil elements and a homogeneous excitation field, insensitive to the effects of asymmetries in the electrical environment. This enabled effective breast imaging and proton-decoupled carbon-13 spectroscopy at 7T. © 2014 Wiley Periodicals, Inc.

Improved algorithm for calculating the Chandrasekhar function

NASA Astrophysics Data System (ADS)

Jablonski, A.

2013-02-01

algorithms by selecting ranges of the argument omega in which the performance is the fastest. Reasons for the new version: Some of the theoretical models describing electron transport in condensed matter need a source of the Chandrasekhar H function values with an accuracy of at least 10 decimal places. Additionally, calculations of this function should be as fast as possible since frequent calls to a subroutine providing this function are made (e.g., numerical evaluation of a double integral with a complicated integrand containing the H function). Both conditions were satisfied in the algorithm previously published [1]. However, it has been found that a proper selection of the quadrature in an integral representation of the Chandrasekhar function may considerably decrease the running time. By suitable selection of the number of abscissas in Gauss-Legendre quadrature, the execution time was decreased by a factor of more than 20. Simultaneously, the accuracy of results has not been affected. Summary of revisions: (1) As in previous work [1], two integral representations of the Chandrasekhar function, H(x,omega), were considered: the expression published by Dudarev and Whelan [2] and the expression published by Davidović et al. [3]. The algorithms implementing these representations were designated A and B, respectively. All integrals in these implementations were previously calculated using Romberg quadrature. It has been found, however, that the use of Gauss-Legendre quadrature considerably improved the performance of both algorithms. Two conditions have to be satisfied. (i) The number of abscissas, N, has to be rather large, and (ii) the abscissas and corresponding weights should be determined with accuracy as high as possible. The abscissas and weights are available for N=16, 20, 24, 32, 40, 48, 64, 80, and 96 with accuracy of 20 decimal places [4], and all these values were introduced into a new procedure GAUSS replacing procedure ROMBERG. Due to the fact that the

Reconfigurable microwave photonic in-phase and quadrature detector for frequency agile radar.

PubMed

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.

SOHO-Ulysses Coordinated Studies During the Two Extended Quadratures and the Radial Alignment of 2007-2008

NASA Technical Reports Server (NTRS)

Suess, S. T.; Poletto, G.

2007-01-01

During quadrature, plasma seen on the limb of the Sun, along the radi al direction to Ulysses, by SOHO or STEREO can be sampled in situ as lt later passes Ulysses. A figure shows a coronagraph image, the rad ial towards Ulysses at 58 deg. S. and the SOHO/UVCS slit positions d uring one set of observations. A CME subsequently occurred and passed Ulysses (at 3/4 AU) 15 days later.

The RKGL method for the numerical solution of initial-value problems

NASA Astrophysics Data System (ADS)

Prentice, J. S. C.

2008-04-01

We introduce the RKGL method for the numerical solution of initial-value problems of the form y'=f(x,y), y(a)=[alpha]. The method is a straightforward modification of a classical explicit Runge-Kutta (RK) method, into which Gauss-Legendre (GL) quadrature has been incorporated. The idea is to enhance the efficiency of the method by reducing the number of times the derivative f(x,y) needs to be computed. The incorporation of GL quadrature serves to enhance the global order of the method by, relative to the underlying RK method. Indeed, the RKGL method has a global error of the form Ahr+1+Bh2m, where r is the order of the RK method and m is the number of nodes used in the GL component. In this paper we derive this error expression and show that RKGL is consistent, convergent and strongly stable.

(q,{mu}) and (p,q,{zeta})-exponential functions: Rogers-Szego'' polynomials and Fourier-Gauss transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hounkonnou, Mahouton Norbert; Nkouankam, Elvis Benzo Ngompe

2010-10-15

From the realization of q-oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szego polynomials as well as their relevant properties. We also compute the matrix elements associated with the (p,q)-oscillator algebra (a generalization of the q-one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.

Nonsingular solutions and instabilities in Einstein-scalar-Gauss-Bonnet cosmology

NASA Astrophysics Data System (ADS)

Sberna, Laura; Pani, Paolo

2017-12-01

It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times.

Vacuum energy in Einstein-Gauss-Bonnet anti-de Sitter gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kofinas, Georgios; Olea, Rodrigo

2006-10-15

A finite action principle for Einstein-Gauss-Bonnet anti-de Sitter gravity is achieved by supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions. For even dimensions, this term is given by the boundary contribution in the Euler theorem with a coupling constant fixed, demanding the spacetime to have constant (negative) curvature in the asymptotic region. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. A well-posed variational principle leads to an appropriate definition of energy and other conserved quantities using the Noether theorem, andmore » to a correct description of black hole thermodynamics. In particular, this procedure assigns a nonzero energy to anti-de Sitter spacetime in all odd dimensions.« less

On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for C*-Dynamical Systems

NASA Astrophysics Data System (ADS)

Fathizadeh, Farzad; Gabriel, Olivier

2016-02-01

The analog of the Chern-Gauss-Bonnet theorem is studied for a C^*-dynamical system consisting of a C^*-algebra A equipped with an ergodic action of a compact Lie group G. The structure of the Lie algebra g of G is used to interpret the Chevalley-Eilenberg complex with coefficients in the smooth subalgebra A subset A as noncommutative differential forms on the dynamical system. We conformally perturb the standard metric, which is associated with the unique G-invariant state on A, by means of a Weyl conformal factor given by a positive invertible element of the algebra, and consider the Hermitian structure that it induces on the complex. A Hodge decomposition theorem is proved, which allows us to relate the Euler characteristic of the complex to the index properties of a Hodge-de Rham operator for the perturbed metric. This operator, which is shown to be selfadjoint, is a key ingredient in our construction of a spectral triple on A and a twisted spectral triple on its opposite algebra. The conformal invariance of the Euler characteristic is interpreted as an indication of the Chern-Gauss-Bonnet theorem in this setting. The spectral triples encoding the conformally perturbed metrics are shown to enjoy the same spectral summability properties as the unperturbed case.

New developments of the Extended Quadrature Method of Moments to solve Population Balance Equations

NASA Astrophysics Data System (ADS)

Pigou, Maxime; Morchain, Jérôme; Fede, Pascal; Penet, Marie-Isabelle; Laronze, Geoffrey

2018-07-01

Population Balance Models have a wide range of applications in many industrial fields as they allow accounting for heterogeneity among properties which are crucial for some system modelling. They actually describe the evolution of a Number Density Function (NDF) using a Population Balance Equation (PBE). For instance, they are applied to gas-liquid columns or stirred reactors, aerosol technology, crystallisation processes, fine particles or biological systems. There is a significant interest for fast, stable and accurate numerical methods in order to solve for PBEs, a class of such methods actually does not solve directly the NDF but resolves their moments. These methods of moments, and in particular quadrature-based methods of moments, have been successfully applied to a variety of systems. Point-wise values of the NDF are sometimes required but are not directly accessible from the moments. To address these issues, the Extended Quadrature Method of Moments (EQMOM) has been developed in the past few years and approximates the NDF, from its moments, as a convex mixture of Kernel Density Functions (KDFs) of the same parametric family. In the present work EQMOM is further developed on two aspects. The main one is a significant improvement of the core iterative procedure of that method, the corresponding reduction of its computational cost is estimated to range from 60% up to 95%. The second aspect is an extension of EQMOM to two new KDFs used for the approximation, the Weibull and the Laplace kernels. All MATLAB source codes used for this article are provided with this article.

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.

Electronically Tunable Differential Integrator: Linear Voltage Controlled Quadrature Oscillator.

PubMed

Nandi, Rabindranath; Pattanayak, Sandhya; Venkateswaran, Palaniandavar; Das, Sagarika

2015-01-01

A new electronically tunable differential integrator (ETDI) and its extension to voltage controlled quadrature oscillator (VCQO) design with linear tuning law are proposed; the active building block is a composite current feedback amplifier with recent multiplication mode current conveyor (MMCC) element. Recently utilization of two different kinds of active devices to form a composite building block is being considered since it yields a superior functional element suitable for improved quality circuit design. The integrator time constant (τ) and the oscillation frequency (ω o ) are tunable by the control voltage (V) of the MMCC block. Analysis indicates negligible phase error (θ e ) for the integrator and low active ω o -sensitivity relative to the device parasitic capacitances. Satisfactory experimental verifications on electronic tunability of some wave shaping applications by the integrator and a double-integrator feedback loop (DIFL) based sinusoid oscillator with linear f o variation range of 60 KHz~1.8 MHz at low THD of 2.1% are verified by both simulation and hardware tests.

Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories

NASA Astrophysics Data System (ADS)

Antoniou, G.; Bakopoulos, A.; Kanti, P.

2018-03-01

We consider a general Einstein-scalar-Gauss-Bonnet theory with a coupling function f (ϕ ) . We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically flat solution may be easily constructed under mild assumptions for f (ϕ ). We show that the existing no-hair theorems are easily evaded, and a large number of regular black-hole solutions with scalar hair are then presented for a plethora of coupling functions f (ϕ ).

Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories.

PubMed

Antoniou, G; Bakopoulos, A; Kanti, P

2018-03-30

We consider a general Einstein-scalar-Gauss-Bonnet theory with a coupling function f(ϕ). We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically flat solution may be easily constructed under mild assumptions for f(ϕ). We show that the existing no-hair theorems are easily evaded, and a large number of regular black-hole solutions with scalar hair are then presented for a plethora of coupling functions f(ϕ).

Regular black holes in Einstein-Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Ghosh, Sushant G.; Singh, Dharm Veer; Maharaj, Sunil D.

2018-05-01

Einstein-Gauss-Bonnet theory, a natural generalization of general relativity to a higher dimension, admits a static spherically symmetric black hole which was obtained by Boulware and Deser. This black hole is similar to its general relativity counterpart with a curvature singularity at r =0 . We present an exact 5D regular black hole metric, with parameter (k >0 ), that interpolates between the Boulware-Deser black hole (k =0 ) and the Wiltshire charged black hole (r ≫k ). Owing to the appearance of the exponential correction factor (e-k /r2), responsible for regularizing the metric, the thermodynamical quantities are modified, and it is demonstrated that the Hawking-Page phase transition is achievable. The heat capacity diverges at a critical radius r =rC, where incidentally the temperature is maximum. Thus, we have a regular black hole with Cauchy and event horizons, and evaporation leads to a thermodynamically stable double-horizon black hole remnant with vanishing temperature. The entropy does not satisfy the usual exact horizon area result of general relativity.

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.

Volumetric formulation for a class of kinetic models with energy conservation.

PubMed

Sbragaglia, M; Sugiyama, K

2010-10-01

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum, and energy. Issues related to boundary condition problems and improvements based on grid refinement are also investigated.

Legendre modified moments for Euler's constant

NASA Astrophysics Data System (ADS)

Prévost, Marc

2008-10-01

Polynomial moments are often used for the computation of Gauss quadrature to stabilize the numerical calculation of the orthogonal polynomials, see [W. Gautschi, Computational aspects of orthogonal polynomials, in: P. Nevai (Ed.), Orthogonal Polynomials-Theory and Practice, NATO ASI Series, Series C: Mathematical and Physical Sciences, vol. 294. Kluwer, Dordrecht, 1990, pp. 181-216 [6]; W. Gautschi, On the sensitivity of orthogonal polynomials to perturbations in the moments, Numer. Math. 48(4) (1986) 369-382 [5]; W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Statist. Comput. 3(3) (1982) 289-317 [4

An incremental block-line-Gauss-Seidel method for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Napolitano, M.; Walters, R. W.

1985-01-01

A block-line-Gauss-Seidel (LGS) method is developed for solving the incompressible and compressible Navier-Stokes equations in two dimensions. The method requires only one block-tridiagonal solution process per iteration and is consequently faster per step than the linearized block-ADI methods. Results are presented for both incompressible and compressible separated flows: in all cases the proposed block-LGS method is more efficient than the block-ADI methods. Furthermore, for high Reynolds number weakly separated incompressible flow in a channel, which proved to be an impossible task for a block-ADI method, solutions have been obtained very efficiently by the new scheme.

Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?

NASA Astrophysics Data System (ADS)

Benincasa, Dionigi M. T.

2011-07-01

We investigate the relation between the two dimensional Causal Set action, Script S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.

Utah State University Global Assimilation of Ionospheric Measurements Gauss-Markov Kalman filter model of the ionosphere: Model description and validation

NASA Astrophysics Data System (ADS)

Scherliess, L.; Schunk, R. W.; Sojka, J. J.; Thompson, D. C.; Zhu, L.

2006-11-01

The Utah State University Gauss-Markov Kalman Filter (GMKF) was developed as part of the Global Assimilation of Ionospheric Measurements (GAIM) program. The GMKF uses a physics-based model of the ionosphere and a Gauss-Markov Kalman filter as a basis for assimilating a diverse set of real-time (or near real-time) observations. The physics-based model is the Ionospheric Forecast Model (IFM), which accounts for five ion species and covers the E region, F region, and the topside from 90 to 1400 km altitude. Within the GMKF, the IFM derived ionospheric densities constitute a background density field on which perturbations are superimposed based on the available data and their errors. In the current configuration, the GMKF assimilates slant total electron content (TEC) from a variable number of global positioning satellite (GPS) ground sites, bottomside electron density (Ne) profiles from a variable number of ionosondes, in situ Ne from four Defense Meteorological Satellite Program (DMSP) satellites, and nighttime line-of-sight ultraviolet (UV) radiances measured by satellites. To test the GMKF for real-time operations and to validate its ionospheric density specifications, we have tested the model performance for a variety of geophysical conditions. During these model runs various combination of data types and data quantities were assimilated. To simulate real-time operations, the model ran continuously and automatically and produced three-dimensional global electron density distributions in 15 min increments. In this paper we will describe the Gauss-Markov Kalman filter model and present results of our validation study, with an emphasis on comparisons with independent observations.

Instrument Reflections and Scene Amplitude Modulation in a Polychromatic Microwave Quadrature Interferometer

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". .

A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes

NASA Technical Reports Server (NTRS)

Carpenter, Russell; Lee, Taesul

2008-01-01

Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.

Parallel-quadrature phase-shifting digital holographic microscopy using polarization beam splitter

PubMed Central

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

Achromatic registration of quadrature components of the optical spectrum in spectral domain optical coherence tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shilyagin, P A; Gelikonov, G V; Gelikonov, V M

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 phasemore » 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)« less

Fast large-scale clustering of protein structures using Gauss integrals.

PubMed

Harder, Tim; Borg, Mikael; Boomsma, Wouter; Røgen, Peter; Hamelryck, Thomas

2012-02-15

Clustering protein structures is an important task in structural bioinformatics. De novo structure prediction, for example, often involves a clustering step for finding the best prediction. Other applications include assigning proteins to fold families and analyzing molecular dynamics trajectories. We present Pleiades, a novel approach to clustering protein structures with a rigorous mathematical underpinning. The method approximates clustering based on the root mean square deviation by first mapping structures to Gauss integral vectors--which were introduced by Røgen and co-workers--and subsequently performing K-means clustering. Compared to current methods, Pleiades dramatically improves on the time needed to perform clustering, and can cluster a significantly larger number of structures, while providing state-of-the-art results. The number of low energy structures generated in a typical folding study, which is in the order of 50,000 structures, can be clustered within seconds to minutes.

Iron line spectroscopy with Einstein-dilaton-Gauss-Bonnet black holes

NASA Astrophysics Data System (ADS)

Nampalliwar, Sourabh; Bambi, Cosimo; Kokkotas, Kostas D.; Konoplya, Roman A.

2018-06-01

Einstein-dilaton-Gauss-Bonnet gravity is a well-motivated alternative theory of gravity that emerges naturally from string theory. While black hole solutions have been known in this theory in numerical form for a while, an approximate analytical metric was obtained recently by some of us, which allows for faster and more detailed analysis. Here we test the accuracy of the analytical metric in the context of X-ray reflection spectroscopy. We analyze innermost stable circular orbits (ISCO) and relativistically broadened iron lines and find that both the ISCO and iron lines are determined sufficiently accurately up to the limit of the approximation. We also find that, though the ISCO increases by about 7% as dilaton coupling increases from zero to extremal values, the redshift at ISCO changes by less than 1%. Consequently, the shape of the iron line is much less sensitive to the dilaton charge than expected.

Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.

PubMed

April, Alexandre

2011-10-01

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

Improvements in sub-grid, microphysics averages using quadrature based approaches

NASA Astrophysics Data System (ADS)

Chowdhary, K.; Debusschere, B.; Larson, V. E.

2013-12-01

Sub-grid variability in microphysical processes plays a critical role in atmospheric climate models. In order to account for this sub-grid variability, Larson and Schanen (2013) propose placing a probability density function on the sub-grid cloud microphysics quantities, e.g. autoconversion rate, essentially interpreting the cloud microphysics quantities as a random variable in each grid box. Random sampling techniques, e.g. Monte Carlo and Latin Hypercube, can be used to calculate statistics, e.g. averages, on the microphysics quantities, which then feed back into the model dynamics on the coarse scale. We propose an alternate approach using numerical quadrature methods based on deterministic sampling points to compute the statistical moments of microphysics quantities in each grid box. We have performed a preliminary test on the Kessler autoconversion formula, and, upon comparison with Latin Hypercube sampling, our approach shows an increased level of accuracy with a reduction in sample size by almost two orders of magnitude. Application to other microphysics processes is the subject of ongoing research.

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE PAGES

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

2018-03-20

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Simple inflationary models in Gauss-Bonnet brane-world cosmology

NASA Astrophysics Data System (ADS)

Okada, Nobuchika; Okada, Satomi

2016-06-01

In light of the recent Planck 2015 results for the measurement of the cosmic microwave background (CMB) anisotropy, we study simple inflationary models in the context of the Gauss-Bonnet (GB) brane-world cosmology. The brane-world cosmological effect modifies the power spectra of scalar and tensor perturbations generated by inflation and causes a dramatic change for the inflationary predictions of the spectral index (n s) and the tensor-to-scalar ratio (r) from those obtained in the standard cosmology. In particular, the predicted r values in the inflationary models favored by the Planck 2015 results are suppressed due to the GB brane-world cosmological effect, which is in sharp contrast with inflationary scenario in the Randall-Sundrum brane-world cosmology, where the r values are enhanced. Hence, these two brane-world cosmological scenarios are distinguishable. With the dramatic change of the inflationary predictions, the inflationary scenario in the GB brane-world cosmology can be tested by more precise measurements of n s and future observations of the CMB B-mode polarization.

Physical process first law and increase of horizon entropy for black holes in Einstein-Gauss-Bonnet gravity.

PubMed

Chatterjee, Ayan; Sarkar, Sudipta

2012-03-02

We establish the physical process version of the first law by studying small perturbations of a stationary black hole with a regular bifurcation surface in Einstein-Gauss-Bonnet gravity. Our result shows that when the stationary black hole is perturbed by a matter stress energy tensor and finally settles down to a new stationary state, the Wald entropy increases as long as the matter satisfies the null energy condition.

Phase space analysis for a scalar-tensor model with kinetic and Gauss-Bonnet couplings

NASA Astrophysics Data System (ADS)

Granda, L. N.; Loaiza, E.

2016-09-01

We study the phase space for a scalar-tensor string inspired model of dark energy with nonminimal kinetic and Gauss-Bonnet couplings. The form of the scalar potential and of the coupling terms is of the exponential type, which gives rise to appealing cosmological solutions. The critical points describe a variety of cosmological scenarios that go from a matter or radiation dominated universe to a dark energy dominated universe. Trajectories were found in the phase space departing from unstable or saddle fixed points and arriving at the stable scalar field dominated point corresponding to late-time accelerated expansion.

Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

NASA Astrophysics Data System (ADS)

Mišković, Olivera; Olea, Rodrigo

2011-01-01

Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.

Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miskovic, Olivera; Olea, Rodrigo; Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso

2011-01-15

Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, itmore » extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.« less

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

NASA Technical Reports Server (NTRS)

Liu, J. J. F.; Alford, R. L.

1979-01-01

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

A structure preserving Lanczos algorithm for computing the optical absorption spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao, Meiyue; Jornada, Felipe H. da; Lin, Lin

2016-11-16

We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

Solving fractional optimal control problems within a Chebyshev-Legendre operational technique

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.

2017-06-01

In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

A New Closed Form Approximation for BER for Optical Wireless Systems in Weak Atmospheric Turbulence

NASA Astrophysics Data System (ADS)

Kaushik, Rahul; Khandelwal, Vineet; Jain, R. C.

2018-04-01

Weak atmospheric turbulence condition in an optical wireless communication (OWC) is captured by log-normal distribution. The analytical evaluation of average bit error rate (BER) of an OWC system under weak turbulence is intractable as it involves the statistical averaging of Gaussian Q-function over log-normal distribution. In this paper, a simple closed form approximation for BER of OWC system under weak turbulence is given. Computation of BER for various modulation schemes is carried out using proposed expression. The results obtained using proposed expression compare favorably with those obtained using Gauss-Hermite quadrature approximation and Monte Carlo Simulations.

Quantum statistical relation for black holes in nonlinear electrodynamics coupled to Einstein-Gauss-Bonnet AdS gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miskovic, Olivera; Olea, Rodrigo

2011-03-15

We consider curvature-squared corrections to Einstein-Hilbert gravity action in the form of a Gauss-Bonnet term in D>4 dimensions. In this theory, we study the thermodynamics of charged static black holes with anti-de Sitter (AdS) asymptotics, and whose electric field is described by nonlinear electrodynamics. These objects have received considerable attention in recent literature on gravity/gauge dualities. It is well-known that, within the framework of anti-de Sitter/conformal field theory (AdS/CFT) correspondence, there exists a nonvanishing Casimir contribution to the internal energy of the system, manifested as the vacuum energy for global AdS spacetime in odd dimensions. Because of this reason, wemore » derive a quantum statistical relation directly from the Euclidean action and not from the integration of the first law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists, in addition to the bulk action, of counterterms that depend on both extrinsic and intrinsic curvatures of the boundary (Kounterterm series). This procedure results in a consistent inclusion of the vacuum energy and chemical potential in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless of the explicit form of the nonlinear electrodynamics Lagrangian.« less

Pulsed Traveling-wave Quadrature Squeezing Using Quasi-phase Matched Lithium Niobate Crystals

NASA Astrophysics Data System (ADS)

Chen, Chao-Hsiang

Interests in generating higher quantum noise squeezing in order to develop methods to enhance optical measurement below the shot-noise limit in various applications has grown in recent years. The noise suppression from squeezing can improve the SNR in coherent optical systems when the returning signal power is weak, such as optical coherence tomography, LADAR, confocal microscopy and low-light coherent imaging. Unlike the generation of squeezing with a continuous wave, which is currently developed mainly for gravitational wave detection in LIGO project, the study of pulsed-traveling waves is focused on industrial, medical and other commercial interests. This dissertation presents the experimental results of pulsed traveling wave squeezing. The intention of the study is to explore the possibility of using quasi-phase matched crystals to generate the highest possible degree of quadrature squeezing. In order to achieve this goal, efforts to test the various effects from spatial Gaussian modes and relative beam waist placement for the second-harmonic pump were carried out in order to further the understanding of limiting factors to pulsed traveling wave squeezing. 20mm and 30mm-long periodically poled lithium noibate (PPLN) crystals were used in the experiment to generate a squeezed vacuum state. A maximum of 4.2+/-0.2dB quadrature squeezing has been observed, and the measured anti-squeezing exceeds 20dB.The phase sensitive amplification (PSA) gain and de-gain performance were also measured to compare the results of measured squeezing. The PPLN crystals can produce high conversion efficiency of second-harmonic generation (SHG) without a cavity. When a long PPLN crystal is used in a squeezer, the beam propagation in the nonlinear medium does not follow the characteristics in thin crystals. Instead, it is operated under the long-crystal criteria, which the crystal length is multiple times longer than the Rayleigh range of the injected beam i n the crystals. Quasi

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.

Coarse-to-fine markerless gait analysis based on PCA and Gauss-Laguerre decomposition

NASA Astrophysics Data System (ADS)

Goffredo, Michela; Schmid, Maurizio; Conforto, Silvia; Carli, Marco; Neri, Alessandro; D'Alessio, Tommaso

2005-04-01

Human movement analysis is generally performed through the utilization of marker-based systems, which allow reconstructing, with high levels of accuracy, the trajectories of markers allocated on specific points of the human body. Marker based systems, however, show some drawbacks that can be overcome by the use of video systems applying markerless techniques. In this paper, a specifically designed computer vision technique for the detection and tracking of relevant body points is presented. It is based on the Gauss-Laguerre Decomposition, and a Principal Component Analysis Technique (PCA) is used to circumscribe the region of interest. Results obtained on both synthetic and experimental tests provide significant reduction of the computational costs, with no significant reduction of the tracking accuracy.

Dilaton field released under collision of dilatonic black holes with Gauss-Bonnet term

NASA Astrophysics Data System (ADS)

Gwak, Bogeun; Ro, Daeho

2017-08-01

We investigate the upper limit of the gravitational radiation released upon the collision of two dilatonic black holes by analyzing the Gauss-Bonnet term. Dilatonic black holes have a dilaton hair coupled with this term. Using the laws of thermodynamics, the upper limit of the radiation is obtained, which reflected the effects of the dilaton hair. The amount of radiation released is greater than that emitted by a Schwarzschild black hole due to the contribution from the dilaton hair. In the collision, most of the dilaton hair can be released through radiation, where the energy radiated by the dilaton hair is maximized when the horizon of one black hole is minimized for a fixed second black hole.

Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space

NASA Astrophysics Data System (ADS)

Wei, Shao-Wen; Liu, Yu-Xiao

2014-08-01

We study the triple points and phase diagrams in the extended phase space of the charged Gauss-Bonnet black holes in d-dimensional anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black holes. Employing the equation of state T=T(v,P), we demonstrate that the information of the phase transition and behavior of the Gibbs free energy are potential encoded in the T-v (T-rh) line with fixed pressure P. We get the phase diagrams for the charged Gauss-Bonnet black holes with different values of the charge Q and dimension d. The result shows that the small/large black hole phase transitions appear for any d, which is reminiscent of the liquid/gas transition of a Van der Waals type. Moreover, the interesting thermodynamic phenomena, i.e., the triple points and the small/intermediate/large black hole phase transitions are observed for d=6 and Q ∈(0.1705,0.1946).

Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule

NASA Astrophysics Data System (ADS)

Jin, Qinian; Wang, Wei

2018-03-01

The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.

Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis.

PubMed

Gutiérrez-Vega, Julio C; Rodríguez-Masegosa, Rodolfo; Chávez-Cerda, Sabino

2003-11-01

A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.

Detection of Interference Phase by Digital Computation of Quadrature Signals in Homodyne Laser Interferometry

PubMed Central

Rerucha, Simon; Buchta, Zdenek; Sarbort, Martin; Lazar, Josef; Cip, Ondrej

2012-01-01

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). PMID:23202038

Detection of interference phase by digital computation of quadrature signals in homodyne laser interferometry.

PubMed

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).

Effects of spatial curvature and anisotropy on the asymptotic regimes in Einstein-Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Pavluchenko, Sergey A.; Toporensky, Alexey

2018-05-01

In this paper we address two important issues which could affect reaching the exponential and Kasner asymptotes in Einstein-Gauss-Bonnet cosmologies—spatial curvature and anisotropy in both three- and extra-dimensional subspaces. In the first part of the paper we consider the cosmological evolution of spaces that are the product of two isotropic and spatially curved subspaces. It is demonstrated that the dynamics in D=2 (the number of extra dimensions) and D ≥ 3 is different. It was already known that for the Λ -term case there is a regime with "stabilization" of extra dimensions, where the expansion rate of the three-dimensional subspace as well as the scale factor (the "size") associated with extra dimensions reaches a constant value. This regime is achieved if the curvature of the extra dimensions is negative. We demonstrate that it takes place only if the number of extra dimensions is D ≥ 3. In the second part of the paper we study the influence of the initial anisotropy. Our study reveals that the transition from Gauss-Bonnet Kasner regime to anisotropic exponential expansion (with three expanding and contracting extra dimensions) is stable with respect to breaking the symmetry within both three- and extra-dimensional subspaces. However, the details of the dynamics in D=2 and D ≥ 3 are different. Combining the two described effects allows us to construct a scenario in D ≥ 3, where isotropization of outer and inner subspaces is reached dynamically from rather general anisotropic initial conditions.

Comparison of a 28 Channel-Receive Array Coil and Quadrature Volume Coil for Morphologic Imaging and T2 Mapping of Knee Cartilage at 7 Tesla

PubMed Central

Chang, Gregory; Wiggins, Graham C.; Xia, Ding; Lattanzi, Riccardo; Madelin, Guillaume; Raya, Jose G.; Finnerty, Matthew; Fujita, Hiroyuki; Recht, Michael P.; Regatte, Ravinder R.

2011-01-01

Purpose To compare a new birdcage-transmit, 28 channel-receive array (28 Ch) coil and a quadrature volume coil for 7 Tesla morphologic MRI and T2 mapping of knee cartilage. Methods The right knees of ten healthy subjects were imaged on a 7 Tesla whole body MR scanner using both coils. 3-dimensional fast low-angle shot (3D-FLASH) and multi-echo spin-echo (MESE) sequences were implemented. Cartilage signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), thickness, and T2 values were assessed. Results SNR/CNR was 17–400% greater for the 28 Ch compared to the quadrature coil (p≤0.005). Bland-Altman plots show mean differences between measurements of tibial/femoral cartilage thickness and T2 values obtained with each coil to be small (−0.002±0.009 cm/0.003±0.011 cm) and large (−6.8±6.7 ms/−8.2±9.7 ms), respectively. For the 28 Ch coil, when parallel imaging with acceleration factors (AF) 2, 3, and 4 was performed, SNR retained was: 62–69%, 51–55%, and 39–45%. Conclusion A 28 Ch knee coil provides increased SNR/CNR for 7T cartilage morphologic imaging and T2 mapping. Coils should be switched with caution during clinical studies because T2 values may differ. The greater SNR of the 28 Ch coil could be used to perform parallel imaging with AF2 and obtain similar SNR as the quadrature coil. PMID:22095723

Neutron star solutions with curvature induced scalarization in the extended Gauss-Bonnet scalar-tensor theories

NASA Astrophysics Data System (ADS)

Doneva, Daniela D.; Yazadjiev, Stoytcho S.

2018-04-01

In the present paper we study models of neutron stars in a class of extended scalar-tensor Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is exited only in the strong curvature regime. We show that in the framework of the ESTGB theories under consideration there exist new neutron star solutions which are formed via spontaneous scalarization of the general relativistic neutron stars. In contrast to the spontaneous scalarization in the standard scalar-tensor theories which is induced by the presence of matter, in our case the scalarization is induced by the spacetime curvature.

A SiGe Quadrature Pulse Modulator for Superconducting Qubit State Manipulation

NASA Astrophysics Data System (ADS)

Kwende, Randy; Bardin, Joseph

Manipulation of the quantum states of microwave superconducting qubits typically requires the generation of coherent modulated microwave pulses. While many off-the-shelf instruments are capable of generating such pulses, a more integrated approach is likely required if fault-tolerant quantum computing architectures are to be implemented. In this work, we present progress towards a pulse generator specifically designed to drive superconducing qubits. The device is implemented in a commercial silicon process and has been designed with energy-efficiency and scalability in mind. Pulse generation is carried out using a unique approach in which modulation is applied directly to the in-phase and quadrature components of a carrier signal in the 1-10 GHz frequency range through a unique digital-analog conversion process designed specifically for this application. The prototype pulse generator can be digitally programmed and supports sequencing of pulses with independent amplitude and phase waveforms. These amplitude and phase waveforms can be digitally programmed through a serial programming interface. Detailed performance of the pulse generator at room temperature and 4 K will be presented.

Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

2014-03-01

A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

A CMOS Self-Contained Quadrature Signal Generator for SoC Impedance Spectroscopy.

PubMed

Márquez, Alejandro; Pérez-Bailón, Jorge; Calvo, Belén; Medrano, Nicolás; Martínez, Pedro A

2018-04-30

This paper presents a low-power fully integrated quadrature signal generator for system-on-chip (SoC) impedance spectroscopy applications. It has been designed in a 0.18 μm-1.8 V CMOS technology as a self-contained oscillator, without the need for an external reference clock. The frequency can be digitally tuned from 10 to 345 kHz with 12-bit accuracy and a relative mean error below 1.7%, thus supporting a wide range of impedance sensing applications. The proposal is experimentally validated in two impedance spectrometry examples, achieving good magnitude and phase recovery results compared to the results obtained using a commercial LCR-meter. Besides the wide frequency tuning range, the proposed programmable oscillator features a total power consumption lower than 0.77 mW and an active area of 0.129 mm², thus constituting a highly suitable choice as stimulation module for instrument-on-a-chip devices.

GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma

PubMed Central

Lécz, Zs.; Konoplev, I. V.; Seryi, A.; Andreev, A.

2016-01-01

This paper proposes a novel and effective method for generating GigaGauss level, solenoidal quasi-static magnetic fields in under-dense plasma using screw-shaped high intensity laser pulses. This method produces large solenoidal fields that move with the driving laser pulse and are collinear with the accelerated electrons. This is in contrast with already known techniques which rely on interactions with over-dense or solid targets and generates radial or toroidal magnetic field localized at the stationary target. The solenoidal field is quasi-stationary in the reference frame of the laser pulse and can be used for guiding electron beams. It can also provide synchrotron radiation beam emittance cooling for laser-plasma accelerated electron and positron beams, opening up novel opportunities for designs of the light sources, free electron lasers, and high energy colliders based on laser plasma acceleration. PMID:27796327

GigaGauss solenoidal magnetic field inside bubbles excited in under-dense plasma

NASA Astrophysics Data System (ADS)

Lécz, Zs.; Konoplev, I. V.; Seryi, A.; Andreev, A.

2016-10-01

This paper proposes a novel and effective method for generating GigaGauss level, solenoidal quasi-static magnetic fields in under-dense plasma using screw-shaped high intensity laser pulses. This method produces large solenoidal fields that move with the driving laser pulse and are collinear with the accelerated electrons. This is in contrast with already known techniques which rely on interactions with over-dense or solid targets and generates radial or toroidal magnetic field localized at the stationary target. The solenoidal field is quasi-stationary in the reference frame of the laser pulse and can be used for guiding electron beams. It can also provide synchrotron radiation beam emittance cooling for laser-plasma accelerated electron and positron beams, opening up novel opportunities for designs of the light sources, free electron lasers, and high energy colliders based on laser plasma acceleration.

Wide and Narrow CMEs and Their Source Explosions Observed at the Spring 2003 SOHO-Sun-Ulysses Quadrature

NASA Technical Reports Server (NTRS)

Suess, Steven; Corti, G.; Poletto, G.; Sterling, A.; Moore, R.

2006-01-01

At the time of the spring 2003 Ulysses-SOHO-Sun quadrature, Ulysses was off the East limb of the Sun at 14.5 degrees north latitude and 4.91 AU. LASCO/C2 images show small transient events that originated from near the limb on May 25, 26 and 27 in the north-east quadrant, along with a large Coronal Mass Ejection (CME) that originated from an active region near disk center on May 26. Ulysses data bear clear signatures of the large CME, specifically including an enhanced abundance of highly ionized Fe. SOHO/UVCS spectra at 1.75 solar radii, near the radial direction to Ulysses, give no evidence of emission from high temperature lines, even for the large CME: instead, for the small events, occasional transient high emission in cool lines was observed, such as the CIII 977 Angstrom line usually absent at coronal levels. Each of these events lasted ca. 1 hour or less and never affected lines from ions forming above ca. 106K. Compact eruptions in Helium 304 Angstrom EIT images, related to the small UVCS transients, were observed at the limb of the Sun over the same period. At least one of these surge events produced a narrow CME observed in LASCO/C2. Most probably all these events are compact magnetic explosions (surges/jets, from around a small island of included polarity) which ejected cool material from lower levels. Ulysses data have been analyzed to find evidence of the cool, narrow CME events, but none or little was found. This puzzling scenario, where events seen by UVCS have no in situ counterparts and vice versa, can be partially explained once the region where the large CME originated is recognized as being at the center of the solar disk so that the CME material was actually much further from the Sun than the 1.7 Rsun height of the UVCS slit off the limb. Conversely, the narrow events may simply have missed Ulysses or been too brief for reliable signatures in composition and ionization state. A basic feature demonstrated by these observations is that large

Stress fields around two pores in an elastic body: exact quadrature domain solutions.

PubMed

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.

Ince-gauss based multiple intermodal phase-matched third-harmonic generations in a step-index silica optical fiber

NASA Astrophysics Data System (ADS)

Borne, Adrien; Katsura, Tomotaka; Félix, Corinne; Doppagne, Benjamin; Segonds, Patricia; Bencheikh, Kamel; Levenson, Juan Ariel; Boulanger, Benoit

2016-01-01

Several third-harmonic generation processes were performed in a single step-index germanium-doped silica optical fiber under intermodal phase-matching conditions. The nanosecond fundamental beam range between 1400 and 1600 nm. The transverse distributions of the energy were successfully modeled in the form of Ince-Gauss modes, pointing out some ellipticity of fiber core. From these experiments and theoretical calculations, we discuss the implementation of frequency degenerated triple photon generation that shares the same phase-matching condition as third-harmonic generation, which is its reverse process.

Transmittance and Tunneling Current through a Trapezoidal Barrier under Spin Polarization Consideration

NASA Astrophysics Data System (ADS)

Noor, F. A.; Nabila, E.; Mardianti, H.; Ariani, T. I.; Khairurrijal

2018-04-01

The transmittance and tunneling current in heterostructures under spin polarization consideration were studied by employing a zinc-blended structure for the heterostructures. An electron tunnels through a potential barrier by applying a bias voltage to the barrier, which is called the trapezoidal potential barrier. In order to study the transmittance, an Airy wave function approach was employed to find the transmittance. The obtained transmittance was then utilized to compute the tunneling current by using a Gauss quadrature method. It was shown that the transmittances were asymmetric with the incident angle of the electron. It was also shown that the tunneling currents increased as the bias voltage increased.

On a self-consistent representation of earth models, with an application to the computing of internal flattening

NASA Astrophysics Data System (ADS)

Denis, C.; Ibrahim, A.

Self-consistent parametric earth models are discussed in terms of a flexible numerical code. The density profile of each layer is represented as a polynomial, and figures of gravity, mass, mean density, hydrostatic pressure, and moment of inertia are derived. The polynomial representation also allows computation of the first order flattening of the internal strata of some models, using a Gauss-Legendre quadrature with a rapidly converging iteration technique. Agreement with measured geophysical data is obtained, and algorithm for estimation of the geometric flattening for any equidense surface identified by its fractional radius is developed. The program can also be applied in studies of planetary and stellar models.

MR imaging of the inner ear: comparison of a three-dimensional fast spin-echo sequence with use of a dedicated quadrature-surface coil with a gadolinium-enhanced spoiled gradient-recalled sequence.

PubMed

Naganawa, S; Ito, T; Fukatsu, H; Ishigaki, T; Nakashima, T; Ichinose, N; Kassai, Y; Miyazaki, M

1998-09-01

To prospectively evaluate the sensitivity and specificity of magnetic resonance (MR) imaging in the inner ear with a long echo train, three-dimensional (3D), asymmetric Fourier-transform, fast spin-echo (SE) sequence with use of a dedicated quadrature-surface phased-array coil to detect vestibular schwannoma in the cerebellopontine angle and the internal auditory canal. In 205 patients (410 ears) with ear symptoms, 1.5-T MR imaging was performed with unenhanced 3D asymmetric fast SE and gadolinium-enhanced 3D gradient-recalled (SPGR) sequences with use of a quadrature surface phased-array coil. The 3D asymmetric fast SE images were reviewed by two radiologists, with the gadolinium-enhanced 3D SPGR images used as the standard of reference. Nineteen lesions were detected in the 410 ears (diameter range, 2-30 mm; mean, 10.5 mm +/- 6.4 [standard deviation]; five lesions were smaller than 5 mm). With 3D asymmetric fast SE, sensitivity, specificity, and accuracy, respectively, were 100%, 99.5%, and 99.5% for observer 1 and 100%, 99.7%, and 99.8% for observer 2. The unenhanced 3D asymmetric fast SE sequence with a quadrature-surface phased-array coli allows the reliable detection of vestibular schwannoma in the cerebellopontine angle and internal auditory canal.

Holographic butterfly velocities in brane geometry and Einstein-Gauss-Bonnet gravity with matters

NASA Astrophysics Data System (ADS)

Huang, Wung-Hong

2018-03-01

In the first part of the paper we generalize the butterfly velocity formula to anisotropic spacetime. We apply the formula to evaluate the butterfly velocities in M-branes, D-branes, and strings backgrounds. We show that the butterfly velocities in M2-branes, M5-branes and the intersection M 2 ⊥ M 5 equal to those in fundamental strings, D4-branes and the intersection F 1 ⊥ D 4 backgrounds, respectively. These observations lead us to conjecture that the butterfly velocity is generally invariant under a double-dimensional reduction. In the second part of the paper, we study the butterfly velocity for Einstein-Gauss-Bonnet gravity with arbitrary matter fields. A general formula is obtained. We use this formula to compute the butterfly velocities in different backgrounds and discuss the associated properties.

A robust two-node, 13 moment quadrature method of moments for dilute particle flows including wall bouncing

NASA Astrophysics Data System (ADS)

Sun, Dan; Garmory, Andrew; Page, Gary J.

2017-02-01

For flows where the particle number density is low and the Stokes number is relatively high, as found when sand or ice is ingested into aircraft gas turbine engines, streams of particles can cross each other's path or bounce from a solid surface without being influenced by inter-particle collisions. The aim of this work is to develop an Eulerian method to simulate these types of flow. To this end, a two-node quadrature-based moment method using 13 moments is proposed. In the proposed algorithm thirteen moments of particle velocity, including cross-moments of second order, are used to determine the weights and abscissas of the two nodes and to set up the association between the velocity components in each node. Previous Quadrature Method of Moments (QMOM) algorithms either use more than two nodes, leading to increased computational expense, or are shown here to give incorrect results under some circumstances. This method gives the computational efficiency advantages of only needing two particle phase velocity fields whilst ensuring that a correct combination of weights and abscissas is returned for any arbitrary combination of particle trajectories without the need for any further assumptions. Particle crossing and wall bouncing with arbitrary combinations of angles are demonstrated using the method in a two-dimensional scheme. The ability of the scheme to include the presence of drag from a carrier phase is also demonstrated, as is bouncing off surfaces with inelastic collisions. The method is also applied to the Taylor-Green vortex flow test case and is found to give results superior to the existing two-node QMOM method and is in good agreement with results from Lagrangian modelling of this case.

3-D frequency-domain seismic wave modelling in heterogeneous, anisotropic media using a Gaussian quadrature grid approach

NASA Astrophysics Data System (ADS)

Zhou, Bing; Greenhalgh, S. A.

2011-01-01

We present an extension of the 3-D spectral element method (SEM), called the Gaussian quadrature grid (GQG) approach, to simulate in the frequency-domain seismic waves in 3-D heterogeneous anisotropic media involving a complex free-surface topography and/or sub-surface geometry. It differs from the conventional SEM in two ways. The first is the replacement of the hexahedral element mesh with 3-D Gaussian quadrature abscissae to directly sample the physical properties or model parameters. This gives a point-gridded model which more exactly and easily matches the free-surface topography and/or any sub-surface interfaces. It does not require that the topography be highly smooth, a condition required in the curved finite difference method and the spectral method. The second is the derivation of a complex-valued elastic tensor expression for the perfectly matched layer (PML) model parameters for a general anisotropic medium, whose imaginary parts are determined by the PML formulation rather than having to choose a specific class of viscoelastic material. Furthermore, the new formulation is much simpler than the time-domain-oriented PML implementation. The specified imaginary parts of the density and elastic moduli are valid for arbitrary anisotropic media. We give two numerical solutions in full-space homogeneous, isotropic and anisotropic media, respectively, and compare them with the analytical solutions, as well as show the excellent effectiveness of the PML model parameters. In addition, we perform numerical simulations for 3-D seismic waves in a heterogeneous, anisotropic model incorporating a free-surface ridge topography and validate the results against the 2.5-D modelling solution, and demonstrate the capability of the approach to handle realistic situations.

Design of a new low-phase-noise millimetre-wave quadrature voltage-controlled oscillator

NASA Astrophysics Data System (ADS)

Kashani, Zeinab; Nabavi, Abdolreza

2018-07-01

This paper presents a new circuit topology of millimetre-wave quadrature voltage-controlled oscillator (QVCO) using an improved Colpitts oscillator without tail bias. By employing an extra capacitance between the drain and source terminations of the transistors and optimising circuit values, a low-power and low-phase-noise (PN) oscillator is designed. For generating the output signals with 90° phase difference, a self-injection coupling network between two identical cores is used. The proposed QVCO dissipates no extra dc power for coupling, since there is no dc-path to ground for the coupled transistors and no extra noise is added to circuit. The best figure-of-merit is -188.5, the power consumption is 14.98-15.45 mW, in a standard 180-nm CMOS technology, for 58.2 GHz center frequency from 59.3 to 59.6 GHz. The PN is -104.86 dBc/Hz at 1-MHz offset.

Digital services using quadrature amplitude modulation (QAM) over CATV analog DWDM system

NASA Astrophysics Data System (ADS)

Yeh, JengRong; Selker, Mark D.; Trail, J.; Piehler, David; Levi, Israel

2000-04-01

Dense Wavelength Division Multiplexing (DWDM) has recently gained great popularity as it provides a cost effective way to increase the transmission capacity of the existing fiber cable plant. For a long time, Dense WDM was exclusively used for baseband digital applications, predominantly in terrestrial long haul networks and in some cases in metropolitan and enterprise networks. Recently, the performance of DWDM components and frequency-stabilized lasers has substantially improved while the costs have down significantly. This makes a variety of new optical network architectures economically viable. The first commercial 8- wavelength DWDM system designed for Hybrid Fiber Coax networks was reported in 1998. This type of DWDM system utilizes Sub-Carrier Multiplexing (SCM) of Quadrature Amplitude Modulated (QAM) signals to transport IP data digital video broadcast and Video on Demand on ITU grid lightwave carriers. The ability of DWDM to provide scalable transmission capacity in the optical layer with SCM granularity is now considered by many to be the most promising technology for future transport and distribution of broadband multimedia services.

Derivation of the Lorentz force law, the magnetic field concept and the Faraday Lenz and magnetic Gauss laws using an invariant formulation of the Lorentz transformation

NASA Astrophysics Data System (ADS)

Field, J. H.

2006-06-01

It is demonstrated how the right-hand sides of the Lorentz transformation equations may be written, in a Lorentz-invariant manner, as 4-vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. An important distinction between the physical meanings of the space time and energy momentum 4-vectors is pointed out. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field, in terms of spatial derivatives of the 4-vector potential, as well as the Faraday Lenz law and the Gauss law for magnetic fields. The connection between the Gauss law for the electric field and the electrodynamic Ampère law, due to the 4-vector character of the electromagnetic potential, is also pointed out.

Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

We construct an analytical approximation for the numerical black hole metric of P. Kanti et al. [Phys. Rev. D 54, 5049 (1996), 10.1103/PhysRevD.54.5049] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and a good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks, and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.

On stable exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

NASA Astrophysics Data System (ADS)

Ivashchuk, V. D.; Ernazarov, K. K.

2017-01-01

A (n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: ai ˜ exp (vit), i = 1, …, n, are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on (vi ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented.

Milne, a routine for the numerical solution of Milne's problem

NASA Astrophysics Data System (ADS)

Rawat, Ajay; Mohankumar, N.

2010-11-01

The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct. Program summaryProgram title: Milne Catalogue identifier: AEGS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_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.: 701 No. of bytes in distributed program, including test data, etc.: 6845 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC under Linux or Windows Operating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XP Classification: 4.11, 21.1, 21.2 Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature. Running time: The test included in the distribution takes a few seconds to run.

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

NASA Astrophysics Data System (ADS)

Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

2017-08-01

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels.

PubMed

Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

2017-08-01

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

Gauss Seidel-type methods for energy states of a multi-component Bose Einstein condensate

NASA Astrophysics Data System (ADS)

Chang, Shu-Ming; Lin, Wen-Wei; Shieh, Shih-Feng

2005-01-01

In this paper, we propose two iterative methods, a Jacobi-type iteration (JI) and a Gauss-Seidel-type iteration (GSI), for the computation of energy states of the time-independent vector Gross-Pitaevskii equation (VGPE) which describes a multi-component Bose-Einstein condensate (BEC). A discretization of the VGPE leads to a nonlinear algebraic eigenvalue problem (NAEP). We prove that the GSI method converges locally and linearly to a solution of the NAEP if and only if the associated minimized energy functional problem has a strictly local minimum. The GSI method can thus be used to compute ground states and positive bound states, as well as the corresponding energies of a multi-component BEC. Numerical experience shows that the GSI converges much faster than JI and converges globally within 10-20 steps.

Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term

NASA Astrophysics Data System (ADS)

de la Cruz-Dombriz, Álvaro; Farrugia, Gabriel; Levi Said, Jackson; Sáez-Chillón Gómez, Diego

2017-12-01

In the context of extended teleparallel gravity theories with a 3  +  1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological solutions. In particular when applied to a Friedmann-Lemaître-Robertson-Walker geometry in four-dimensional spacetime with standard fluids exclusively. We study different types of gravitational Lagrangians and reconstruct solutions provided by analytical expressions for either the cosmological scale factor or the Hubble parameter. We also show that it is possible to find Lagrangians of this type without a cosmological constant such that the behaviour of the ΛCDM model is precisely mimicked. The new Lagrangians may also lead to other phenomenological consequences opening up the possibility for new theories to compete directly with other extensions of General Relativity.

Fracture characterization by hybrid enumerative search and Gauss-Newton least-squares inversion methods

NASA Astrophysics Data System (ADS)

Alkharji, Mohammed N.

Most fracture characterization methods provide a general description of the fracture parameters as part of the reservoirs parameters; the fracture interaction and geometry within the reservoir is given less attention. T-Matrix and Linear Slip effective medium fracture models are implemented to invert the elastic tensor for the parameters and geometries of the fractures within the reservoir. The fracture inverse problem has an ill-posed, overdetermined, underconstrained rank-deficit system of equations. Least-squares inverse methods are used to solve the problem. A good starting initial model for the parameters is a key factor in the reliability of the inversion. Most methods assume that the starting parameters are close to the solution to avoid inaccurate local minimum solutions. The prior knowledge of the fracture parameters and their geometry is not available. We develop a hybrid, enumerative and Gauss-Newton, method that estimates the fracture parameters and geometry from the elastic tensor with no prior knowledge of the initial parameter values. The fracture parameters are separated into two groups. The first group contains the fracture parameters with no prior information, and the second group contains the parameters with known prior information. Different models are generated from the first group parameters by sampling the solution space over a predefined range of possible solutions for each parameter. Each model generated by the first group is fixed and used as a starting model to invert for the second group of parameters using the Gauss-Newton method. The least-squares residual between the observed elastic tensor and the estimated elastic tensor is calculated for each model. The model parameters that yield the least-squares residual corresponds to the correct fracture reservoir parameters and geometry. Two synthetic examples of fractured reservoirs with oil and gas saturations were inverted with no prior information about the fracture properties. The

Interpolation bias for the inverse compositional Gauss-Newton algorithm in digital image correlation

NASA Astrophysics Data System (ADS)

Su, Yong; Zhang, Qingchuan; Xu, Xiaohai; Gao, Zeren; Wu, Shangquan

2018-01-01

It is believed that the classic forward additive Newton-Raphson (FA-NR) algorithm and the recently introduced inverse compositional Gauss-Newton (IC-GN) algorithm give rise to roughly equal interpolation bias. Questioning the correctness of this statement, this paper presents a thorough analysis of interpolation bias for the IC-GN algorithm. A theoretical model is built to analytically characterize the dependence of interpolation bias upon speckle image, target image interpolation, and reference image gradient estimation. The interpolation biases of the FA-NR algorithm and the IC-GN algorithm can be significantly different, whose relative difference can exceed 80%. For the IC-GN algorithm, the gradient estimator can strongly affect the interpolation bias; the relative difference can reach 178%. Since the mean bias errors are insensitive to image noise, the theoretical model proposed remains valid in the presence of noise. To provide more implementation details, source codes are uploaded as a supplement.

All-optical simultaneous multichannel quadrature phase shift keying signal regeneration based on phase-sensitive amplification

NASA Astrophysics Data System (ADS)

Wang, Hongxiang; Wang, Qi; Bai, Lin; Ji, Yuefeng

2018-01-01

A scheme is proposed to realize the all-optical phase regeneration of four-channel quadrature phase shift keying (QPSK) signal based on phase-sensitive amplification. By utilizing conjugate pump and common pump in a highly nonlinear optical fiber, degenerate four-wave mixing process is observed, and QPSK signals are regenerated. The number of waves is reduced to decrease the cross talk caused by undesired nonlinear interaction during the coherent superposition process. In addition, to avoid the effect of overlapping frequency, frequency spans between pumps and signals are set to be nonintegral multiples. Optical signal-to-noise ratio improvement is validated by bit error rate measurements. Compared with single-channel regeneration, multichannel regeneration brings 0.4-dB OSNR penalty when the value of BER is 10-3, which shows the cross talk in regeneration process is negligible.

Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement.

PubMed

Nguyen, N; Milanfar, P; Golub, G

2001-01-01

In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized cross-validation method (GCV). We propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory, reducing the computational complexity of the GCV. Data-driven PSF and regularization parameter estimation experiments with synthetic and real image sequences are presented to demonstrate the effectiveness and robustness of our method.

Crystallization in Two Dimensions and a Discrete Gauss-Bonnet Theorem

NASA Astrophysics Data System (ADS)

De Luca, L.; Friesecke, G.

2018-02-01

We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (Heitmann and Radin in J Stat Phys 22(3):281-287, 1980), which concerns a system of N identical atoms in two dimensions interacting via the idealized pair potential V(r)=+∞ if r<1, -1 if r=1, 0 if r>1. This is done by endowing the bond graph of a general particle configuration with a suitable notion of discrete curvature, and appealing to a discrete Gauss-Bonnet theorem (Knill in Elem Math 67:1-7, 2012) which, as its continuous cousins, relates the sum/integral of the curvature to topological invariants. This leads to an exact geometric decomposition of the Heitmann-Radin energy into (i) a combinatorial bulk term, (ii) a combinatorial perimeter, (iii) a multiple of the Euler characteristic, and (iv) a natural topological energy contribution due to defects. An analogous exact geometric decomposition is also established for soft potentials such as the Lennard-Jones potential V(r)=r^{-6}-2r^{-12}, where two additional contributions arise, (v) elastic energy and (vi) energy due to non-bonded interactions.

Optical-wireless-optical full link for polarization multiplexing quadrature amplitude/phase modulation signal transmission.

PubMed

Li, Xinying; Yu, Jianjun; Chi, Nan; Zhang, Junwen

2013-11-15

We propose and experimentally demonstrate an optical wireless integration system at the Q-band, in which up to 40 Gb/s polarization multiplexing multilevel quadrature amplitude/phase modulation (PM-QAM) signal can be first transmitted over 20 km single-mode fiber-28 (SMF-28), then delivered over a 2 m 2 × 2 multiple-input multiple-output wireless link, and finally transmitted over another 20 km SMF-28. The PM-QAM modulated wireless millimeter-wave (mm-wave) signal at 40 GHz is generated based on the remote heterodyning technique, and demodulated by the radio-frequency transparent photonic technique based on homodyne coherent detection and baseband digital signal processing. The classic constant modulus algorithm equalization is used at the receiver to realize polarization demultiplexing of the PM-QAM signal. For the first time, to the best of our knowledge, we realize the conversion of the PM-QAM modulated wireless mm-wave signal to the optical signal as well as 20 km fiber transmission of the converted optical signal.

A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.

2008-05-15

We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive globalmore » information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.« less

Analysis of radial and longitudinal field of plasma wakefield generated by a Laguerre-Gauss laser pulse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Firouzjaei, Ali Shekari; Shokri, Babak

In the present paper, we study the wakes known as the donut wake which is generated by Laguerre-Gauss (LG) laser pulses. Effects of the special spatial profile of a LG pulse on the radial and longitudinal wakefields are presented via an analytical model in a weakly non-linear regime in two dimensions. Different aspects of the donut-shaped wakefields have been analyzed and compared with Gaussian-driven wakes. There is also some discussion about the accelerating-focusing phase of the donut wake. Variations of longitudinal and radial wakes with laser amplitude, pulse length, and pulse spot size have been presented and discussed. Finally, wemore » present the optimum pulse duration for such wakes.« less

Thermodynamic instability of topological black holes in Gauss-Bonnet gravity with a generalized electrodynamics

NASA Astrophysics Data System (ADS)

Hendi, S. H.; Panahiyan, S.

2014-12-01

Motivated by the string corrections on the gravity and electrodynamics sides, we consider a quadratic Maxwell invariant term as a correction of the Maxwell Lagrangian to obtain exact solutions of higher dimensional topological black holes in Gauss-Bonnet gravity. We first investigate the asymptotically flat solutions and obtain conserved and thermodynamic quantities which satisfy the first law of thermodynamics. We also analyze thermodynamic stability of the solutions by calculating the heat capacity and the Hessian matrix. Then, we focus on horizon-flat solutions with an anti-de Sitter (AdS) asymptote and produce a rotating spacetime with a suitable transformation. In addition, we calculate the conserved and thermodynamic quantities for asymptotically AdS black branes which satisfy the first law of thermodynamics. Finally, we perform thermodynamic instability criterion to investigate the effects of nonlinear electrodynamics in canonical and grand canonical ensembles.

Application of Gauss's law space-charge limited emission model in iterative particle tracking method

NASA Astrophysics Data System (ADS)

Altsybeyev, V. V.; Ponomarev, V. A.

2016-11-01

The particle tracking method with a so-called gun iteration for modeling the space charge is discussed in the following paper. We suggest to apply the emission model based on the Gauss's law for the calculation of the space charge limited current density distribution using considered method. Based on the presented emission model we have developed a numerical algorithm for this calculations. This approach allows us to perform accurate and low time consumpting numerical simulations for different vacuum sources with the curved emitting surfaces and also in the presence of additional physical effects such as bipolar flows and backscattered electrons. The results of the simulations of the cylindrical diode and diode with elliptical emitter with the use of axysimmetric coordinates are presented. The high efficiency and accuracy of the suggested approach are confirmed by the obtained results and comparisons with the analytical solutions.

Performance of Infinitely Wide Parabolic and Inclined Slider Bearings Lubricated with Couple Stress or Magnetic Fluids

NASA Astrophysics Data System (ADS)

Oladeinde, Mobolaji Humphrey; Akpobi, John Ajokpaoghene

2011-10-01

The hydrodynamic and magnetohydrodynamic (MHD) lubrication problem of infinitely wide inclined and parabolic slider bearings is solved numerically using the finite element method. The bearing configurations are discretized into three-node isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations are solved using Gauss quadrature to obtain a finite number of stiffness matrices. The global system of equations obtained from enforcing nodal continuity of pressure for the bearings are solved using the Gauss-Seidel iterative scheme with a convergence criterion of 10-10. Numerical computations reveal that, when compared for similar profile and couple stress parameters, greater pressure builds up in a parabolic slider compared to an inclined slider, indicating a greater wedge effect in the parabolic slider. The parabolic slider bearing is also shown to develop a greater load capacity when lubricated with magnetic fluids. The superior performance of parabolic slider bearing is more pronounced at greater Hartmann numbers for identical bearing structural parameters. It is also shown that when load carrying capacity is the yardstick for comparison, the parabolic slider bearings are superior to the inclined bearings when lubricated with couple stress or magnetic lubricants.

Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities

NASA Astrophysics Data System (ADS)

Peng, Jun-Jin

2014-11-01

An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge was recently proposed by Kim et al. They achieved this by introducing off-shell Noether currents and potentials. In this paper, we construct the crucial off-shell Noether current by the variation of the Bianchi identity for the expression of EOM, with the help of the property of Killing vector. Our Noether current, which contains an additional term that is just one half of the Lie derivative of a surface term with respect to the Killing vector, takes a different form in comparison with the one in their work. Then we employ the generalized formulation to calculate the quasi-local conserved charges for the most general charged spherically symmetric and the dyonic rotating black holes with AdS asymptotics in four-dimensional conformal Weyl gravity, as well as the charged spherically symmetric black holes in arbitrary dimensional Einstein-Gauss-Bonnet gravity coupled to Maxwell or nonlinear electrodynamics in AdS spacetime. Our results confirm those obtained through other methods in the literature.

Deflection of light by rotating regular black holes using the Gauss-Bonnet theorem

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Övgün, Ali; Saavedra, Joel; Vásquez, Yerko; González, P. A.

2018-06-01

In this paper, we study the weak gravitational lensing in the spacetime of rotating regular black hole geometries such as Ayon-Beato-García (ABG), Bardeen, and Hayward black holes. We calculate the deflection angle of light using the Gauss-Bonnet theorem (GBT) and show that the deflection of light can be viewed as a partially topological effect in which the deflection angle can be calculated by considering a domain outside of the light ray applied to the black hole optical geometries. Then, we demonstrate also the deflection angle via the geodesics formalism for these black holes to verify our results and explore the differences with the Kerr solution. These black holes have, in addition to the total mass and rotation parameter, different parameters of electric charge, magnetic charge, and deviation parameter. We find that the deflection of light has correction terms coming from these parameters, which generalizes the Kerr deflection angle.

Optimised collision avoidance for an ultra-close rendezvous with a failed satellite based on the Gauss pseudospectral method

NASA Astrophysics Data System (ADS)

Chu, Xiaoyu; Zhang, Jingrui; Lu, Shan; Zhang, Yao; Sun, Yue

2016-11-01

This paper presents a trajectory planning algorithm to optimise the collision avoidance of a chasing spacecraft operating in an ultra-close proximity to a failed satellite. The complex configuration and the tumbling motion of the failed satellite are considered. The two-spacecraft rendezvous dynamics are formulated based on the target body frame, and the collision avoidance constraints are detailed, particularly concerning the uncertainties. An optimisation solution of the approaching problem is generated using the Gauss pseudospectral method. A closed-loop control is used to track the optimised trajectory. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms.

Design and evaluation of a GaAs MMIC X-band active RC quadrature power divider

NASA Astrophysics Data System (ADS)

Henkus, J. C.

1991-03-01

The design and evaluation of a GaAs MMIC (Microwave Monolithic Integrated Circuit) X-band active RC Quadrature Power Divider (QPD) is addressed. This QPD can be used as part of a vector modulator. The chosen QPD topology consists of two active first order RC all pass networks and was converted into an MMIC design. The design is completely symmetrical except for two key resistors. On-wafer S parameter measurements were carried out; a special probe head configuration was composed in order to avoid measurement accuracy degradation associated with the reversal of the active output of the QPD. The measured nominal RF behavior of the chips complies with the simulated behavior to a very high degree. The optical, DC, and RF yield is very large (97, 83, and 74 percent respectively). A modification to Takashi's all pass network was proposed which offers gain/frequency slope control and compensation ability.

A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin

2018-01-01

In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.

Average symbol error rate for M-ary quadrature amplitude modulation in generalized atmospheric turbulence and misalignment errors

NASA Astrophysics Data System (ADS)

Sharma, Prabhat Kumar

2016-11-01

A framework is presented for the analysis of average symbol error rate (SER) for M-ary quadrature amplitude modulation in a free-space optical communication system. The standard probability density function (PDF)-based approach is extended to evaluate the average SER by representing the Q-function through its Meijer's G-function equivalent. Specifically, a converging power series expression for the average SER is derived considering the zero-boresight misalignment errors in the receiver side. The analysis presented here assumes a unified expression for the PDF of channel coefficient which incorporates the M-distributed atmospheric turbulence and Rayleigh-distributed radial displacement for the misalignment errors. The analytical results are compared with the results obtained using Q-function approximation. Further, the presented results are supported by the Monte Carlo simulations.

A Robust High-Performance GPS L1 Receiver with Single-stage Quadrature Redio-Frequency Circuit

NASA Astrophysics Data System (ADS)

Liu, Jianghua; Xu, Weilin; Wan, Qinq; Liu, Tianci

2018-03-01

A low power current reuse single-stage quadrature raido-frequency part (SQRF) is proposed for GPS L1 receiver in 180nm CMOS process. The proposed circuit consists of LNA, Mixer, QVCO, is called the QLMV cell. A two blocks stacked topology is adopted in this design. The parallel QVCO and mixer placed on the top forms the upper stacked block, and the LNA placed on the bottom forms the other stacked block. The two blocks share the current and achieve low power performance. To improve the stability, a float current source is proposed. The float current isolated the local oscillation signal and the input RF signal, which bring the whole circuit robust high-performance. The result shows conversion gain is 34 dB, noise figure is three dB, the phase noise is -110 dBc/Hz at 1MHz and IIP3 is -20 dBm. The proposed circuit dissipated 1.7mW with 1 V supply voltage.

Noise tolerance in optical waveguide circuits for recognition of optical 16 quadrature amplitude modulation codes

NASA Astrophysics Data System (ADS)

Inoshita, Kensuke; Hama, Yoshimitsu; Kishikawa, Hiroki; Goto, Nobuo

2016-12-01

In photonic label routers, various optical signal processing functions are required; these include optical label extraction, recognition of the label, optical switching and buffering controlled by signals based on the label information and network routing tables, and label rewriting. Among these functions, we focus on photonic label recognition. We have proposed two kinds of optical waveguide circuits to recognize 16 quadrature amplitude modulation codes, i.e., recognition from the minimum output port and from the maximum output port. The recognition function was theoretically analyzed and numerically simulated by finite-difference beam-propagation method. We discuss noise tolerance in the circuit and show numerically simulated results to evaluate bit-error-rate (BER) characteristics against optical signal-to-noise ratio (OSNR). The OSNR required to obtain a BER less than 1.0×10-3 for the symbol rate of 2.5 GBaud was 14.5 and 27.0 dB for recognition from the minimum and maximum output, respectively.

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

PubMed Central

Ettlinger, Andreas; Neuner, Hans; Burgess, Thomas

2018-01-01

The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning (“PDR”). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model (“GMM”), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model (“GHM”). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation. PMID:29385076

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors.

PubMed

Ettlinger, Andreas; Neuner, Hans; Burgess, Thomas

2018-01-31

The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning ("PDR"). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model ("GMM"), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model ("GHM"). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation.

Nonparaxial fractional Bessel and Bessel-Gauss auto-focusing light-sheet pincers and their higher-order spatial derivatives

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-05-01

Nonparaxial fractional electromagnetic Bessel and Bessel-Gauss auto-focusing light-sheet solutions and their spatial derivatives are synthesized stemming from the angular spectrum decomposition in plane waves. The propagation characteristics of these transverse electric-polarized light-sheets are analyzed by computing the radiated component of the incident electric field. Tight bending of the beam along curved trajectories and slit openings are observed, which could offer unique features and potential applications in the development of improved methods and devices in light-sheet tweezers for particle manipulation applications and dynamics in opto-fluidics, particle sizing and imaging to name a few examples. Moreover, computations of the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solutions.

Mutually unbiased phase states, phase uncertainties, and Gauss sums

NASA Astrophysics Data System (ADS)

Planat, M.; Rosu, H.

2005-10-01

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/sqrt{d}, with d the dimension of the finite Hilbert space, are becoming more and more studied for applications such as quantum tomography and cryptography, and in relation to entangled states and to the Heisenberg-Weil group of quantum optics. Complete sets of MUBs of cardinality d+1 have been derived for prime power dimensions d=pm using the tools of abstract algebra. Presumably, for non prime dimensions the cardinality is much less. Here we reinterpret MUBs as quantum phase states, i.e. as eigenvectors of Hermitian phase operators generalizing those introduced by Pegg and Barnett in 1989. We relate MUB states to additive characters of Galois fields (in odd characteristic p) and to Galois rings (in characteristic 2). Quantum Fourier transforms of the components in vectors of the bases define a more general class of MUBs with multiplicative characters and additive ones altogether. We investigate the complementary properties of the above phase operator with respect to the number operator. We also study the phase probability distribution and variance for general pure quantum electromagnetic states and find them to be related to the Gauss sums, which are sums over all elements of the field (or of the ring) of the product of multiplicative and additive characters. Finally, we relate the concepts of mutual unbiasedness and maximal entanglement. This allows to use well studied algebraic concepts as efficient tools in the study of entanglement and its information aspects.

Determination of projection effects of CMEs using quadrature observations with the two STEREO spacecraft

NASA Astrophysics Data System (ADS)

Bronarska, K.; Michalek, G.

2018-07-01

Since 1995 coronal mass ejections (CMEs) have been routinely observed thanks to the sensitive Large Angle and Spectrometric Coronagraphs (LASCO) on board the Solar and Heliospheric Observatory (SOHO) mission. Their observed characteristics are stored, among other, in the SOHO/LASCO catalog. These parameters are commonly used in scientific studies. Unfortunately, coronagraphic observations of CMEs are subject to projection effects. This makes it practically impossible to determine the true properties of CMEs and therefore makes it more difficult to forecast their geoeffectiveness. In this study, using quadrature observations with the two Solar Terrestrial Relations Observatory (STEREO) spacecrafts, we estimate the projection effect affecting velocity of CMEs included in the SOHO/LASCO catalog. It was demonstrated that this effect depends significantly on width and source location of CMEs. It can be very significant for narrow events and originating from the disk center. The effect diminishes with increasing width and absolute longitude of source location of CMEs. For very wide (width ⩾ 250°) or limb events (| longitude ⩾ 70°) projection effects completely disappears.

Sensitivity analysis of a coupled hydrodynamic-vegetation model using the effectively subsampled quadratures method

USGS Publications Warehouse

Kalra, Tarandeep S.; Aretxabaleta, Alfredo; Seshadri, Pranay; Ganju, Neil K.; Beudin, Alexis

2017-01-01

Coastal hydrodynamics can be greatly affected by the presence of submerged aquatic vegetation. The effect of vegetation has been incorporated into the Coupled-Ocean-Atmosphere-Wave-Sediment Transport (COAWST) Modeling System. The vegetation implementation includes the plant-induced three-dimensional drag, in-canopy wave-induced streaming, and the production of turbulent kinetic energy by the presence of vegetation. In this study, we evaluate the sensitivity of the flow and wave dynamics to vegetation parameters using Sobol' indices and a least squares polynomial approach referred to as Effective Quadratures method. This method reduces the number of simulations needed for evaluating Sobol' indices and provides a robust, practical, and efficient approach for the parameter sensitivity analysis. The evaluation of Sobol' indices shows that kinetic energy, turbulent kinetic energy, and water level changes are affected by plant density, height, and to a certain degree, diameter. Wave dissipation is mostly dependent on the variation in plant density. Performing sensitivity analyses for the vegetation module in COAWST provides guidance for future observational and modeling work to optimize efforts and reduce exploration of parameter space.

GPU-accelerated element-free reverse-time migration with Gauss points partition

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Jia, Xiaofeng; Qiang, Xiaodong

2018-06-01

An element-free method (EFM) has been demonstrated successfully in elasticity, heat conduction and fatigue crack growth problems. We present the theory of EFM and its numerical applications in seismic modelling and reverse time migration (RTM). Compared with the finite difference method and the finite element method, the EFM has unique advantages: (1) independence of grids in computation and (2) lower expense and more flexibility (because only the information of the nodes and the boundary of the concerned area is required). However, in EFM, due to improper computation and storage of some large sparse matrices, such as the mass matrix and the stiffness matrix, the method is difficult to apply to seismic modelling and RTM for a large velocity model. To solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition and utilise the graphics processing unit to improve the computational efficiency. We employ the compressed sparse row format to compress the intermediate large sparse matrices and attempt to simplify the operations by solving the linear equations with CULA solver. To improve the computation efficiency further, we introduce the concept of the lumped mass matrix. Numerical experiments indicate that the proposed method is accurate and more efficient than the regular EFM.

Average BER of subcarrier intensity modulated free space optical systems over the exponentiated Weibull fading channels.

PubMed

Wang, Ping; Zhang, Lu; Guo, Lixin; Huang, Feng; Shang, Tao; Wang, Ranran; Yang, Yintang

2014-08-25

The average bit error rate (BER) for binary phase-shift keying (BPSK) modulation in free-space optical (FSO) links over turbulence atmosphere modeled by the exponentiated Weibull (EW) distribution is investigated in detail. The effects of aperture averaging on the average BERs for BPSK modulation under weak-to-strong turbulence conditions are studied. The average BERs of EW distribution are compared with Lognormal (LN) and Gamma-Gamma (GG) distributions in weak and strong turbulence atmosphere, respectively. The outage probability is also obtained for different turbulence strengths and receiver aperture sizes. The analytical results deduced by the generalized Gauss-Laguerre quadrature rule are verified by the Monte Carlo simulation. This work is helpful for the design of receivers for FSO communication systems.

Star adaptation for two-algorithms used on serial computers

NASA Technical Reports Server (NTRS)

Howser, L. M.; Lambiotte, J. J., Jr.

1974-01-01

Two representative algorithms used on a serial computer and presently executed on the Control Data Corporation 6000 computer were adapted to execute efficiently on the Control Data STAR-100 computer. Gaussian elimination for the solution of simultaneous linear equations and the Gauss-Legendre quadrature formula for the approximation of an integral are the two algorithms discussed. A description is given of how the programs were adapted for STAR and why these adaptations were necessary to obtain an efficient STAR program. Some points to consider when adapting an algorithm for STAR are discussed. Program listings of the 6000 version coded in 6000 FORTRAN, the adapted STAR version coded in 6000 FORTRAN, and the STAR version coded in STAR FORTRAN are presented in the appendices.

On shifted Jacobi spectral method for high-order multi-point boundary value problems

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

2012-10-01

This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

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.

Subluminal group velocity and dispersion of Laguerre Gauss beams in free space.

PubMed

Bareza, Nestor D; Hermosa, Nathaniel

2016-05-27

That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein's postulate in special relativity. This has been a basic assumption in light's various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light's group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam's divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space.

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories

NASA Astrophysics Data System (ADS)

Doneva, Daniela D.; Yazadjiev, Stoytcho S.

2018-03-01

In the present Letter, we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black-hole solutions that are formed by spontaneous scalarization of the Schwarzschild black holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and a new branch of solutions with a nontrivial scalar field bifurcates from the Schwarzschild one. As a matter of fact, more than one branch with a nontrivial scalar field can bifurcate at different masses, but only the first one is supposed to be stable. This effect is quite similar to the spontaneous scalarization of neutron stars. In contrast to the standard spontaneous scalarization of neutron stars, which is induced by the presence of matter, in our case, the scalarization is induced by the curvature of the spacetime.

A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models

NASA Astrophysics Data System (ADS)

Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng

2012-09-01

Our goal in this paper is to improve the computational performance of the proximity algorithms for the L1/TV denoising model. This leads us to a new characterization of all solutions to the L1/TV model via fixed-point equations expressed in terms of the proximity operators. Based upon this observation we develop an algorithm for solving the model and establish its convergence. Furthermore, we demonstrate that the proposed algorithm can be accelerated through the use of the componentwise Gauss-Seidel iteration so that the CPU time consumed is significantly reduced. Numerical experiments using the proposed algorithm for impulsive noise removal are included, with a comparison to three recently developed algorithms. The numerical results show that while the proposed algorithm enjoys a high quality of the restored images, as the other three known algorithms do, it performs significantly better in terms of computational efficiency measured in the CPU time consumed.

Energy-dependent topological anti-de Sitter black holes in Gauss-Bonnet Born-Infeld gravity

NASA Astrophysics Data System (ADS)

Hendi, S. H.; Behnamifard, H.; Bahrami-Asl, B.

2018-03-01

Employing higher-curvature corrections to Einstein-Maxwell gravity has garnered a great deal of attention motivated by the high-energy regime in the quantum nature of black hole physics. In addition, one may employ gravity's rainbow to encode quantum gravity effects into black hole solutions. In this paper, we regard an energy-dependent static spacetime with various topologies and study its black hole solutions in the context of Gauss-Bonnet Born-Infeld (GB-BI) gravity. We study the thermodynamic properties and examine the first law of thermodynamics. Using a suitable local transformation, we endow the Ricci-flat black hole solutions with a global rotation and study the effects of rotation on thermodynamic quantities. We also investigate thermal stability in a canonical ensemble by calculating the heat capacity. We obtain the effects of various parameters on the horizon radius of stable black holes. Finally, we discuss a second-order phase transition in the extended phase space thermodynamics and investigate the critical behavior.

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories.

PubMed

Doneva, Daniela D; Yazadjiev, Stoytcho S

2018-03-30

In the present Letter, we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black-hole solutions that are formed by spontaneous scalarization of the Schwarzschild black holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and a new branch of solutions with a nontrivial scalar field bifurcates from the Schwarzschild one. As a matter of fact, more than one branch with a nontrivial scalar field can bifurcate at different masses, but only the first one is supposed to be stable. This effect is quite similar to the spontaneous scalarization of neutron stars. In contrast to the standard spontaneous scalarization of neutron stars, which is induced by the presence of matter, in our case, the scalarization is induced by the curvature of the spacetime.

Gauss-Seidel and Successive Overrelaxation Methods for Radiative Transfer with Partial Frequency Redistribution

NASA Astrophysics Data System (ADS)

Sampoorna, M.; Trujillo Bueno, J.

2010-04-01

The linearly polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest spectral lines requires solving an involved non-local thermodynamic equilibrium radiative transfer problem accounting for partial redistribution (PRD) effects. Fast radiative transfer methods for the numerical solution of PRD problems are also needed for a proper treatment of hydrogen lines when aiming at realistic time-dependent magnetohydrodynamic simulations of the solar chromosphere. Here we show how the two-level atom PRD problem with and without polarization can be solved accurately and efficiently via the application of highly convergent iterative schemes based on the Gauss-Seidel and successive overrelaxation (SOR) radiative transfer methods that had been previously developed for the complete redistribution case. Of particular interest is the Symmetric SOR method, which allows us to reach the fully converged solution with an order of magnitude of improvement in the total computational time with respect to the Jacobi-based local accelerated lambda iteration method.

Vectorial structures of linear-polarized Butterfly-Gauss vortex beams in the far zone

NASA Astrophysics Data System (ADS)

Cheng, Ke; Zhou, Yan; Lu, Gang; Yao, Na; Zhong, Xianqiong

2018-05-01

By introducing the Butterfly catastrophe to optics, the far-zone vectorial structures of Butterfly-Gauss beam with vortex and non-vortex are studied using the angular spectrum representation and stationary phase method. The influence of topological charge, linear-polarized angle, off-axis distance and scaling length on the far-zone vectorial structures, especially in the Poynting vector and angular momentum density of the corresponding beam is emphasized. The results show that the embedded optical vortex at source plane lead to special dark zones in the far zone, where the number of dark zone equals the absolute value of topological charge of optical vortex. Furthermore, the symmetry and direction of the special dark zones can be controlled by off-axis distance and scaling length, respectively. The linear-polarized angle adjusts only the Poynting vectors of TE and TM terms, but it does not affect those of whole beam. Finally, the vectorial expressions also indicate that the total angular momentum density is certainly zero owing to the far-zone stable structures rather than rotation behaviors.

Orbit and uncertainty propagation: a comparison of Gauss-Legendre-, Dormand-Prince-, and Chebyshev-Picard-based approaches

NASA Astrophysics Data System (ADS)

Aristoff, Jeffrey M.; Horwood, Joshua T.; Poore, Aubrey B.

2014-01-01

We present a new variable-step Gauss-Legendre implicit-Runge-Kutta-based approach for orbit and uncertainty propagation, VGL-IRK, which includes adaptive step-size error control and which collectively, rather than individually, propagates nearby sigma points or states. The performance of VGL-IRK is compared to a professional (variable-step) implementation of Dormand-Prince 8(7) (DP8) and to a fixed-step, optimally-tuned, implementation of modified Chebyshev-Picard iteration (MCPI). Both nearly-circular and highly-elliptic orbits are considered using high-fidelity gravity models and realistic integration tolerances. VGL-IRK is shown to be up to eleven times faster than DP8 and up to 45 times faster than MCPI (for the same accuracy), in a serial computing environment. Parallelization of VGL-IRK and MCPI is also discussed.

Accurate phase measurements for thick spherical objects using optical quadrature microscopy

NASA Astrophysics Data System (ADS)

Warger, William C., II; DiMarzio, Charles A.

2009-02-01

In vitro fertilization (IVF) procedures have resulted in the birth of over three million babies since 1978. Yet the live birth rate in the United States was only 34% in 2005, with 32% of the successful pregnancies resulting in multiple births. These multiple pregnancies were directly attributed to the transfer of multiple embryos to increase the probability that a single, healthy embryo was included. Current viability markers used for IVF, such as the cell number, symmetry, size, and fragmentation, are analyzed qualitatively with differential interference contrast (DIC) microscopy. However, this method is not ideal for quantitative measures beyond the 8-cell stage of development because the cells overlap and obstruct the view within and below the cluster of cells. We have developed the phase-subtraction cell-counting method that uses the combination of DIC and optical quadrature microscopy (OQM) to count the number of cells accurately in live mouse embryos beyond the 8-cell stage. We have also created a preliminary analysis to measure the cell symmetry, size, and fragmentation quantitatively by analyzing the relative dry mass from the OQM image in conjunction with the phase-subtraction count. In this paper, we will discuss the characterization of OQM with respect to measuring the phase accurately for spherical samples that are much larger than the depth of field. Once fully characterized and verified with human embryos, this methodology could provide the means for a more accurate method to score embryo viability.

High spatial resolution contrast-enhanced MR angiography of the supraaortic arteries using the quadrature body coil at 3.0T: a feasibility study.

PubMed

Willinek, Winfried A; Bayer, Thomas; Gieseke, Jürgen; von Falkenhausen, Marcus; Sommer, Torsten; Hoogeveen, Romhild; Wilhelm, Kai; Urbach, Horst; Schild, Hans H

2007-03-01

To examine whether the the increased signal-to-noise (S/N) available at 3.0T would permit the use of the quadrature body coil for high spatial resolution contrast-enhanced (CE) MR angiography (MRA), and whether the large FOV that was used in our routine 1.5T protocol would also be feasible at 3.0T. In a prospective study, 43 patients and five volunteers were examined on a clinical whole-body 3.0T MR unit (Intera, Philips Medical Systems, Best, The Netherlands) after institutional review board approval and informed consent. Three-dimensional CE MRA (T1 gradient echo-sequence with TR/TE = 5.7/1.93 msec.; acquisition time, 1:54 min.) using randomly segmented central k-space ordering (CENTRA) was acquired with the quadrature body coil, using over a FOV of 350 mm. A high-image matrix of 432x432 yielded a non-zero filled voxel size of 0.81 mm x 0.81 mm x 1.0 mm (0.66 mm(3)). For quantitative analysis, contrast ratios (CR) between vessels (S) and signal in surrounding tissue (ST) were calculated [(S-ST)/(S+ST)]. For qualitative analysis, image quality and presence of artifacts were rated by two radiologists in consensus on a five-point scale (1=excellent to 5=nondiagnostic). Digital subtraction angiography (DSA) served as the standard of reference in patients with vascular disease. In the five volunteers, 1.5T CE MRA using a phased array neurovascular coil was available for intraindividual comparison. 3.0T CE MRA was successfully performed in 48/48 subjects (100%). Mean CR+/- SD were 0.76 (139.30/182.42) and 0.87 (235.18/270.14) at 3.0T and 1.5T respectively . Mean image quality was 3.82+/-0.86. Intraindividual comparison between 1.5T and 3.0T CE MRA in the volunteers revealed no significant difference in image quality (4.2+/-0.74 vs 4.6+/-0.80; p>0.05). Vascular disease was correctly identified in 13/13 patients with DSA correlation. CE MRA of the supraaortic arteries is feasible at 3.0T using a large FOV of 350 mm. The signal gain at 3.0T enables high spatial resolution

Generation of highly pure Schrödinger's cat states and real-time quadrature measurements via optical filtering

NASA Astrophysics Data System (ADS)

Asavanant, Warit; Nakashima, Kota; Shiozawa, Yu; Yoshikawa, Jun-Ichi; Furusawa, Akira

2017-12-01

Until now, Schr\\"odinger's cat states are generated by subtracting single photons from the whole bandwidth of squeezed vacua. However, it was pointed out recently that the achievable purities are limited in such method (J. Yoshikawa, W. Asavanant, and A. Furusawa, arXiv:1707.08146 [quant-ph] (2017)). In this paper, we used our new photon subtraction method with a narrowband filtering cavity and generated a highly pure Schr\\"odinger's cat state with the value of $-0.184$ at the origin of the Wigner function. To our knowledge, this is the highest value ever reported without any loss corrections. The temporal mode also becomes exponentially rising in our method, which allows us to make a real-time quadrature measurement on Schr\\"odinger's cat states, and we obtained the value of $-0.162$ at the origin of the Wigner function.

Two-wavelength quadrature multipoint detection of partial discharge in power transformers using fiber Fabry-Perot acoustic sensors

NASA Astrophysics Data System (ADS)

Dong, Bo; Han, Ming; Wang, Anbo

2012-06-01

A reliable and low-cost two-wavelength quadrature interrogating method has been developed to demodulate optical signals from diaphragm-based Fabry-Perot interferometric fiber optic sensors for multipoint partial discharge detection in power transformers. Commercial available fused-silica parts (a wafer, a fiber ferrule, and a mating sleeve) and a cleaved optical single mode fiber were bonded together to form an extrinsic Fabry-Perot acoustic sensor. Two lasers with center wavelengths separated by a quarter of the period of sensor interference fringes were used to probe acousticwave- induced diaphragm vibration. A coarse wavelength-division multiplexing (CWDM) add/drop multiplexer was used to separate the reflected two wavelengths before two photo detectors. Optical couplers were used to distribute mixed laser light to each sensor-detector module for multiplexing purpose. Sensor structure, detection system design and experiment results are presented.

Relationship Between the Expansion Speed and Radial Speed of CMEs Confirmed Using Quadrature Observations from SOHO and STEREO

NASA Technical Reports Server (NTRS)

Gopalswamy, Nat; Makela, Pertti; Yashiro, Seiji

2011-01-01

It is difficult to measure the true speed of Earth-directed CMEs from a coronagraph along the Sun-Earth line because of the occulting disk. However, the expansion speed (the speed with which the CME appears to spread in the sky plane) can be measured by such coronagraph. In order to convert the expansion speed to radial speed (which is important for space weather applications) one can use empirical relationship between the two that assumes an average width for all CMEs. If we have the width information from quadrature observations, we can confirm the relationship between expansion and radial speeds derived by Gopalswamy et al. (2009, CEAB, 33, 115,2009). The STEREO spacecraft were in quadrature with SOHO (STEREO-A ahead of Earth by 87 and STEREO-B 94 behind Earth) on 2011 February 15, when a fast Earth-directed CME occurred. The CME was observed as a halo by the Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO. The sky-plane speed was measured by SOHO/LASCO as the expansion speed, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images measured the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (Vexp ) and radial speed (Vrad ) derived previously from geometrical considerations (Gopalswamy et al. 2009): Vrad = 1/2 (1 + cot w) Vexp, where w is the half width of the CME. STEREO-B images of the CME, we found that CME had a full width of 75 degrees, so w = 37.5 degrees. This gives the relation as Vrad = 1.15 Vexp. From LASCO observations, we measured Vexp = 897 km/s, so we get the radial speed as 1033 km/s. Direct measurement of radial speed from STEREO gives 945 km/s (STEREO-A) and 1057 km/s (STEREO-B). These numbers are different only by 2.3% and 8.5% (for STEREO-A and STEREO-B, respectively) from the computed value.

Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment

NASA Astrophysics Data System (ADS)

Crisnejo, Gabriel; Gallo, Emanuel

2018-06-01

We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with the same symmetries. The possibility of using the theorem follows from a correspondence between timelike curves followed by light rays in a plasma medium and spatial geodesics in an associated Riemannian optical metric. A similar correspondence follows for massive particles. For some examples and applications, we compute the deflection angle in weak gravitational fields for different plasma density profiles and gravitational fields.

On non-exponential cosmological solutions with two factor spaces of dimensions m and 1 in the Einstein-Gauss-Bonnet model with a Λ-term

NASA Astrophysics Data System (ADS)

Ernazarov, K. K.

2017-12-01

We consider a (m + 2)-dimensional Einstein-Gauss-Bonnet (EGB) model with the cosmological Λ-term. We restrict the metrics to be diagonal ones and find for certain Λ = Λ(m) class of cosmological solutions with non-exponential time dependence of two scale factors of dimensions m > 2 and 1. Any solution from this class describes an accelerated expansion of m-dimensional subspace and tends asymptotically to isotropic solution with exponential dependence of scale factors.

Modeling radiative transfer with the doubling and adding approach in a climate GCM setting

NASA Astrophysics Data System (ADS)

Lacis, A. A.

2017-12-01

The nonlinear dependence of multiply scattered radiation on particle size, optical depth, and solar zenith angle, makes accurate treatment of multiple scattering in the climate GCM setting problematic, due primarily to computational cost issues. In regard to the accurate methods of calculating multiple scattering that are available, their computational cost is far too prohibitive for climate GCM applications. Utilization of two-stream-type radiative transfer approximations may be computationally fast enough, but at the cost of reduced accuracy. We describe here a parameterization of the doubling/adding method that is being used in the GISS climate GCM, which is an adaptation of the doubling/adding formalism configured to operate with a look-up table utilizing a single gauss quadrature point with an extra-angle formulation. It is designed to closely reproduce the accuracy of full-angle doubling and adding for the multiple scattering effects of clouds and aerosols in a realistic atmosphere as a function of particle size, optical depth, and solar zenith angle. With an additional inverse look-up table, this single-gauss-point doubling/adding approach can be adapted to model fractional cloud cover for any GCM grid-box in the independent pixel approximation as a function of the fractional cloud particle sizes, optical depths, and solar zenith angle dependence.

Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Q.; Sprague, M. A.; Jonkman, J.

2014-01-01

This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context ofmore » LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.« less

Comparison of soft-input-soft-output detection methods for dual-polarized quadrature duobinary system

NASA Astrophysics Data System (ADS)

Chang, Chun; Huang, Benxiong; Xu, Zhengguang; Li, Bin; Zhao, Nan

2018-02-01

Three soft-input-soft-output (SISO) detection methods for dual-polarized quadrature duobinary (DP-QDB), including maximum-logarithmic-maximum-a-posteriori-probability-algorithm (Max-log-MAP)-based detection, soft-output-Viterbi-algorithm (SOVA)-based detection, and a proposed SISO detection, which can all be combined with SISO decoding, are presented. The three detection methods are investigated at 128 Gb/s in five-channel wavelength-division-multiplexing uncoded and low-density-parity-check (LDPC) coded DP-QDB systems by simulations. Max-log-MAP-based detection needs the returning-to-initial-states (RTIS) process despite having the best performance. When the LDPC code with a code rate of 0.83 is used, the detecting-and-decoding scheme with the SISO detection does not need RTIS and has better bit error rate (BER) performance than the scheme with SOVA-based detection. The former can reduce the optical signal-to-noise ratio (OSNR) requirement (at BER=10-5) by 2.56 dB relative to the latter. The application of the SISO iterative detection in LDPC-coded DP-QDB systems makes a good trade-off between requirements on transmission efficiency, OSNR requirement, and transmission distance, compared with the other two SISO methods.

Shear Recovery Accuracy in Weak-Lensing Analysis with the Elliptical Gauss-Laguerre Method

NASA Astrophysics Data System (ADS)

Nakajima, Reiko; Bernstein, Gary

2007-04-01

We implement the elliptical Gauss-Laguerre (EGL) galaxy-shape measurement method proposed by Bernstein & Jarvis and quantify the shear recovery accuracy in weak-lensing analysis. This method uses a deconvolution fitting scheme to remove the effects of the point-spread function (PSF). The test simulates >107 noisy galaxy images convolved with anisotropic PSFs and attempts to recover an input shear. The tests are designed to be immune to statistical (random) distributions of shapes, selection biases, and crowding, in order to test more rigorously the effects of detection significance (signal-to-noise ratio [S/N]), PSF, and galaxy resolution. The systematic error in shear recovery is divided into two classes, calibration (multiplicative) and additive, with the latter arising from PSF anisotropy. At S/N > 50, the deconvolution method measures the galaxy shape and input shear to ~1% multiplicative accuracy and suppresses >99% of the PSF anisotropy. These systematic errors increase to ~4% for the worst conditions, with poorly resolved galaxies at S/N simeq 20. The EGL weak-lensing analysis has the best demonstrated accuracy to date, sufficient for the next generation of weak-lensing surveys.

On temporal connectivity of PFC via Gauss-Markov modeling of fNIRS signals.

PubMed

Aydöre, Sergül; Mihçak, M Kivanç; Ciftçi, Koray; Akin, Ata

2010-03-01

Functional near-infrared spectroscopy (fNIRS) is an optical imaging method, which monitors the brain activation by measuring the successive changes in the concentration of oxy- and deoxyhemoglobin in real time. In this study, we present a method to investigate the functional connectivity of prefrontal cortex (PFC) Sby applying a Gauss-Markov model to fNIRS signals. The hemodynamic changes on PFC during the performance of cognitive paradigm are measured by fNIRS for 17 healthy adults. The color-word matching Stroop task is performed to activate 16 different regions of PFC. There are three different types of stimuli in this task, which can be listed as incongruent stimulus (IS), congruent stimulus (CS), and neutral stimulus (NS), respectively. We introduce a new measure, called "information transfer metric" (ITM) for each time sample. The behavior of ITMs during IS are significantly different from the ITMs during CS and NS, which is consistent with the outcome of the previous research, which concentrated on fNIRS signal analysis via color-word matching Stroop task. Our analysis shows that the functional connectivity of PFC is highly relevant with the cognitive load, i.e., functional connectivity increases with the increasing cognitive load.

Gauss-Seidel Iterative Method as a Real-Time Pile-Up Solver of Scintillation Pulses

NASA Astrophysics Data System (ADS)

Novak, Roman; Vencelj, Matja¿

2009-12-01

The pile-up rejection in nuclear spectroscopy has been confronted recently by several pile-up correction schemes that compensate for distortions of the signal and subsequent energy spectra artifacts as the counting rate increases. We study here a real-time capability of the event-by-event correction method, which at the core translates to solving many sets of linear equations. Tight time limits and constrained front-end electronics resources make well-known direct solvers inappropriate. We propose a novel approach based on the Gauss-Seidel iterative method, which turns out to be a stable and cost-efficient solution to improve spectroscopic resolution in the front-end electronics. We show the method convergence properties for a class of matrices that emerge in calorimetric processing of scintillation detector signals and demonstrate the ability of the method to support the relevant resolutions. The sole iteration-based error component can be brought below the sliding window induced errors in a reasonable number of iteration steps, thus allowing real-time operation. An area-efficient hardware implementation is proposed that fully utilizes the method's inherent parallelism.

Two dimensional fully nonlinear numerical wave tank based on the BEM

NASA Astrophysics Data System (ADS)

Sun, Zhe; Pang, Yongjie; Li, Hongwei

2012-12-01

The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.

Noise tolerance in wavelength-selective switching of optical differential quadrature-phase-shift-keying pulse train by collinear acousto-optic devices.

PubMed

Goto, Nobuo; Miyazaki, Yasumitsu

2014-06-01

Optical switching of high-bit-rate quadrature-phase-shift-keying (QPSK) pulse trains using collinear acousto-optic (AO) devices is theoretically discussed. Since the collinear AO devices have wavelength selectivity, the switched optical pulse trains suffer from distortion when the bandwidth of the pulse train is comparable to the pass bandwidth of the AO device. As the AO device, a sidelobe-suppressed device with a tapered surface-acoustic-wave (SAW) waveguide and a Butterworth-type filter device with a lossy SAW directional coupler are considered. Phase distortion of optical pulse trains at 40 to 100  Gsymbols/s in QPSK format is numerically analyzed. Bit-error-rate performance with additive Gaussian noise is also evaluated by the Monte Carlo method.

Long-time stability effects of quadrature and artificial viscosity on nodal discontinuous Galerkin methods for gas dynamics

NASA Astrophysics Data System (ADS)

Durant, Bradford; Hackl, Jason; Balachandar, Sivaramakrishnan

2017-11-01

Nodal discontinuous Galerkin schemes present an attractive approach to robust high-order solution of the equations of fluid mechanics, but remain accompanied by subtle challenges in their consistent stabilization. The effect of quadrature choices (full mass matrix vs spectral elements), over-integration to manage aliasing errors, and explicit artificial viscosity on the numerical solution of a steady homentropic vortex are assessed over a wide range of resolutions and polynomial orders using quadrilateral elements. In both stagnant and advected vortices in periodic and non-periodic domains the need arises for explicit stabilization beyond the numerical surface fluxes of discontinuous Galerkin spectral elements. Artificial viscosity via the entropy viscosity method is assessed as a stabilizing mechanism. It is shown that the regularity of the artificial viscosity field is essential to its use for long-time stabilization of small-scale features in nodal discontinuous Galerkin solutions of the Euler equations of gas dynamics. Supported by the Department of Energy Predictive Science Academic Alliance Program Contract DE-NA0002378.

An Investigation into the Application of Generalized Differential Quadrature Method to Bending Analysis of Composite Sandwich Plates

NASA Astrophysics Data System (ADS)

Ghassemi, Aazam; Yazdani, Mostafa; Hedayati, Mohamad

2017-12-01

In this work, based on the First Order Shear Deformation Theory (FSDT), an attempt is made to explore the applicability and accuracy of the Generalized Differential Quadrature Method (GDQM) for bending analysis of composite sandwich plates under static loading. Comparative studies of the bending behavior of composite sandwich plates are made between two types of boundary conditions for different cases. The effects of fiber orientation, ratio of thickness to length of the plate, the ratio of thickness of core to thickness of the face sheet are studied on the transverse displacement and moment resultants. As shown in this study, the role of the core thickness in deformation of these plates can be reversed by the stiffness of the core in comparison with sheets. The obtained graphs give very good results due to optimum design of sandwich plates. In Comparison with existing solutions, fast convergent rates and high accuracy results can be achieved by the GDQ method.

An attempt to determine the absolute geomagnetic field intensity in Southwestern Iceland during the Gauss-Matuyama reversal

NASA Astrophysics Data System (ADS)

Goguitchaichvili, Avto; Prévot, Michel; Thompson, John; Roberts, Neil

1999-08-01

We have measured the variation in the intensity of the geomagnetic field during the Gauss-Matuyama (N4-R3) polarity reversal by application of the Thelliers' method to specimens of lava flows from Hvalfjördur district in Western Iceland (Reynivallahals Mts.). Eleven lava flows all show very similar directions corresponding to an equatorial VGP (Plat=2.9°N, Plong=81.9°E, A95=4.2, K=119). Twenty-nine specimens from nine of the flows were pre-selected for palaeointensity determination on the basis that specimens from the same drill cores showed a single component of magnetisation upon thermal or AF demagnetisation, and possessed low magnetic viscosity and reversible susceptibility curves upon heating at 600-650°C. Observation that the directional data obtained in the course of the palaeointensity experiments occasionally showed substantial non-linearity indicates that a significant chemical remanent magnetization (CRM) can be acquired in the direction of the laboratory field during heating at T. For each double heating step we calculated the ratio of CRM( T) to the magnitude of the natural remanent magnetization (NRM( T)) in the direction of characteristic remanence (obtained independently from another specimen from the same core). When this ratio exceeded 15%, the paleointensity data was rejected. In addition, specimens for which the quality factor was less than 5 were rejected. Twelve reliable palaeointensity values were obtained from specimens representing five lava flows. The results confirm that the palaeointensity was substantially reduced during the N4-R3 reversal. The range of mean palaeointensity values obtained for the five flows is 8.8 to 20.5 and the overall mean is 14.8±4.6 μT. This corresponds to an equivalent VDM of 3.81±1.19 (10 22 A m 2). A comparison of all Thellier palaeointensity data from the R3 magnetozone in the Rayinivallahals Mts. area reveals a progressive although irregular increase in the palaeointensity between the Gauss

Truncated Painlevé expansion: Tanh-traveling wave solutions and reduction of sine-Poisson equation to a quadrature for stationary and nonstationary three-dimensional collisionless cold plasma

NASA Astrophysics Data System (ADS)

Ibrahim, R. S.; El-Kalaawy, O. H.

2006-10-01

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painlevé expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model.

Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-06-01

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

2013-01-01

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

The surface crack problem in an orthotropic plate under bending and tension

NASA Technical Reports Server (NTRS)

Wu, Bing-Hua; Erdogan, F.

1987-01-01

The elasticity problem for an infinite orthotropic flat plate containing a series of through and part through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three-dimensional material orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants were used. The effects of material orthotropy on the stress intensity factors was determined, the interaction between two asymmetrically arranged collinear cracks was investigated, and extensive numerical results regarding the stress intensity factors are provided. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium

NASA Astrophysics Data System (ADS)

Parand, Kourosh; Latifi, Sobhan; Delkhosh, Mehdi; Moayeri, Mohammad M.

2018-01-01

In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval [0, ∞). Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope, y'(0), is obtained as -1.191790649719421734122828603800159364 for η = 0.5. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids

NASA Astrophysics Data System (ADS)

Otero, Evelyn; Eliasson, Peter

2015-03-01

An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.

Dual-tone optical vector millimeter wave signal generated by frequency-nonupling the radio frequency 16-star quadrature-amplitude-modulation signal

NASA Astrophysics Data System (ADS)

Wu, Tonggen; Ma, Jianxin

2017-12-01

This paper proposes an original scheme to generate the photonic dual-tone optical millimeter wave (MMW) carrying the 16-star quadrature-amplitude-modulation (QAM) signal via an optical phase modulator (PM) and an interleaver with adaptive photonic frequency-nonupling without phase precoding. To enable the generated optical vector MMW signal to resist the power fading effect caused by the fiber chromatic dispersion, the modulated -5th- and +4th-order sidebands are selected from the output of the PM, which is driven by the precoding 16-star QAM signal. The modulation index of the PM is optimized to gain the maximum opto-electrical conversion efficiency. A radio over fiber link is built by simulation, and the simulated constellations and the bit error rate graph demonstrate that the frequency-nonupling 16-star QAM MMW signal has good transmission performance. The simulation results agree well with our theoretical results.

Generation and transmission of multilevel quadrature amplitude modulation formats using only one optical modulator: MATLAB Simulink simulation models

NASA Astrophysics Data System (ADS)

Binh, Le Nguyen

2009-04-01

A geometrical and phasor representation technique is presented to illustrate the modulation of the lightwave carrier to generate quadrature amplitude modulated (QAM) signals. The modulation of the amplitude and phase of the lightwave carrier is implemented using only one dual-drive Mach-Zehnder interferometric modulator (MZIM) with the assistance of phasor techniques. Any multilevel modulation scheme can be generated, but we illustrate specifically, the multilevel amplitude and differential phase shift keying (MADPSK) signals. The driving voltage levels are estimated for driving the traveling wave electrodes of the modulator. Phasor diagrams are extensively used to demonstrate the effectiveness of modulation schemes. MATLAB Simulink models are formed to generate the multilevel modulation formats, transmission, and detection in optically amplified fiber communication systems. Transmission performance is obtained for the multilevel optical signals and proven to be equivalent or better than those of binary level with equivalent bit rate. Further, the resilience to nonlinear effects is much higher for MADPSK of 50% and 33% pulse width as compared to non-return-to-zero (NRZ) pulse shaping.

Sensitivity analysis of a coupled hydrodynamic-vegetation model using the effectively subsampled quadratures method (ESQM v5.2)

NASA Astrophysics Data System (ADS)

Kalra, Tarandeep S.; Aretxabaleta, Alfredo; Seshadri, Pranay; Ganju, Neil K.; Beudin, Alexis

2017-12-01

Coastal hydrodynamics can be greatly affected by the presence of submerged aquatic vegetation. The effect of vegetation has been incorporated into the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modeling system. The vegetation implementation includes the plant-induced three-dimensional drag, in-canopy wave-induced streaming, and the production of turbulent kinetic energy by the presence of vegetation. In this study, we evaluate the sensitivity of the flow and wave dynamics to vegetation parameters using Sobol' indices and a least squares polynomial approach referred to as the Effective Quadratures method. This method reduces the number of simulations needed for evaluating Sobol' indices and provides a robust, practical, and efficient approach for the parameter sensitivity analysis. The evaluation of Sobol' indices shows that kinetic energy, turbulent kinetic energy, and water level changes are affected by plant stem density, height, and, to a lesser degree, diameter. Wave dissipation is mostly dependent on the variation in plant stem density. Performing sensitivity analyses for the vegetation module in COAWST provides guidance to optimize efforts and reduce exploration of parameter space for future observational and modeling work.

Behavior of Holographic Ricci Dark Energy in Scalar Gauss-Bonnet Gravity for Different Choices of the Scale Factor

NASA Astrophysics Data System (ADS)

Pasqua, Antonio; Chattopadhyay, Surajit; Khurshudyan, Martiros; Aly, Ayman A.

2014-09-01

In this paper, we studied the cosmological application of the interacting Ricci Dark Energy (RDE) model in the framework of the scalar Gauss-Bonnet modified gravity model. We studied the properties of the reconstructed potential , the Strong Energy Condition (SEC), the Weak Energy Condition (WEC) and the deceleration parameter q for three different models of scale factor, i.e. the emergent, the intermediate and the logamediate one. We obtained that , for the emergent scenario, has a decreasing behavior, while, for the logamediate scenario, the potential start with an increasing behavior then, for later times, it shows a slowly decreasing behavior. Finally, for the intermediate scenario, the potential has an initial increasing behavior, then for a time of t≈1.2, it starts to decrease. We also found that both SEC and WEC are violated for all the three scale factors considered. Finally, studying the plots of q, we derived that an accelerated universe can be achieved for the three models of scale factor considered.

Long-Term Quadrature Light Variability in Early Type Interacting Binary Systems

NASA Astrophysics Data System (ADS)

Peters, Geraldine J.; Wilson, R. E.; Vaccaro, T. R.

2014-01-01

Four years of Kepler observations have revealed a phenomenon in the light curves of short-period Algol-type eclipsing binaries that has never been reported from ground-based photometry. These systems display unequal brightness at their quadrature phases that numerically reverses over a time scale of about 100-400 days. We call these systems L/T (leading hemisphere/ trailing hemisphere) variables. Twenty-one such systems have so far been identified in the Kepler database and at least three classes of L/T behavior have been identified. The prototype is WX Draconis (A8V + K0IV, P=1.80 d) which shows L/ T light variations of 2-3%. The primary is a delta Scuti star with a dominant pulsation period of 41 m. The Kepler light curves are being analyzed with the 2013 version of the Wilson-Devinney (WD) program that includes major improvements in modeling star spots (i.e. spot motions due to drift and stellar rotation and spot growth and decay). Preliminary analysis of the WX Dra data suggests that the L/T variability can be fit with either an accretion hot spot on the primary (T = 2.3 T_phot) that jumps in longitude or a magnetic cool spotted region on the secondary. If the latter model is correct the dark region must occupy at least 20% of the surface of the facing hemisphere of the secondary if it is completely black, or a larger area if not completely black. In both hot and cool spot scenarios magnetic fields must play a role in the activity. Echelle spectra were recently secured with the KPNO 4-m telescope to determine the mass ratios of the L/T systems and their spectral types. This information will allow us to assess whether the hot or cool spot model explains the L/T activity. Progress toward this goal will be presented. Support from NASA grants NNX11AC78G and NNX12AE44G and USC’s Women in Science and Engineering (WiSE) program is greatly appreciated.

A mixed-effects regression model for longitudinal multivariate ordinal data.

PubMed

Liu, Li C; Hedeker, Donald

2006-03-01

A mixed-effects item response theory model that allows for three-level multivariate ordinal outcomes and accommodates multiple random subject effects is proposed for analysis of multivariate ordinal outcomes in longitudinal studies. This model allows for the estimation of different item factor loadings (item discrimination parameters) for the multiple outcomes. The covariates in the model do not have to follow the proportional odds assumption and can be at any level. Assuming either a probit or logistic response function, maximum marginal likelihood estimation is proposed utilizing multidimensional Gauss-Hermite quadrature for integration of the random effects. An iterative Fisher scoring solution, which provides standard errors for all model parameters, is used. An analysis of a longitudinal substance use data set, where four items of substance use behavior (cigarette use, alcohol use, marijuana use, and getting drunk or high) are repeatedly measured over time, is used to illustrate application of the proposed model.

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation.

PubMed

Zhang, Raoyang; Shan, Xiaowen; Chen, Hudong

2006-10-01

We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan [J. Fluid Mech. 550, 413 (2006)]. In addition to the higher-order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to third-order hydrodynamic moments. Numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number Kn can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsen's minimum and the asymptotic behavior of flow flux at large Kn.

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

The surface crack problem in an orthotropic plate under bending and tension

NASA Technical Reports Server (NTRS)

Wu, B. H.; Erdogan, F.

1986-01-01

The elasticity problem for an infinite orthotropic flat plate containing a series of through and part-through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three dimensional materials orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants has been used. The main purpose of this study is to determine the effect of material orthotropy on the stress intensity factors, to investigate the interaction between two asymmetrically arranged collinear cracks, and to provide extensive numerical results regarding the stress intensity factors. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.

15-digit accuracy calculations of Chandrasekhar's H-function for isotropic scattering by means of the double exponential formula

NASA Astrophysics Data System (ADS)

Kawabata, Kiyoshi

2016-12-01

This work shows that it is possible to calculate numerical values of the Chandrasekhar H-function for isotropic scattering at least with 15-digit accuracy by making use of the double exponential formula (DE-formula) of Takahashi and Mori (Publ. RIMS, Kyoto Univ. 9:721, 1974) instead of the Gauss-Legendre quadrature employed in the numerical scheme of Kawabata and Limaye (Astrophys. Space Sci. 332:365, 2011) and simultaneously taking a precautionary measure to minimize the effects due to loss of significant digits particularly in the cases of near-conservative scattering and/or errors involved in returned values of library functions supplied by compilers in use. The results of our calculations are presented for 18 selected values of single scattering albedo π0 and 22 values of an angular variable μ, the cosine of zenith angle θ specifying the direction of radiation incident on or emergent from semi-infinite media.

A Gauss-Seidel Iteration Scheme for Reference-Free 3-D Histological Image Reconstruction

PubMed Central

Daum, Volker; Steidl, Stefan; Maier, Andreas; Köstler, Harald; Hornegger, Joachim

2015-01-01

Three-dimensional (3-D) reconstruction of histological slice sequences offers great benefits in the investigation of different morphologies. It features very high-resolution which is still unmatched by in-vivo 3-D imaging modalities, and tissue staining further enhances visibility and contrast. One important step during reconstruction is the reversal of slice deformations introduced during histological slice preparation, a process also called image unwarping. Most methods use an external reference, or rely on conservative stopping criteria during the unwarping optimization to prevent straightening of naturally curved morphology. Our approach shows that the problem of unwarping is based on the superposition of low-frequency anatomy and high-frequency errors. We present an iterative scheme that transfers the ideas of the Gauss-Seidel method to image stacks to separate the anatomy from the deformation. In particular, the scheme is universally applicable without restriction to a specific unwarping method, and uses no external reference. The deformation artifacts are effectively reduced in the resulting histology volumes, while the natural curvature of the anatomy is preserved. The validity of our method is shown on synthetic data, simulated histology data using a CT data set and real histology data. In the case of the simulated histology where the ground truth was known, the mean Target Registration Error (TRE) between the unwarped and original volume could be reduced to less than 1 pixel on average after 6 iterations of our proposed method. PMID:25312918

Silicon photonic integrated circuit swept-source optical coherence tomography receiver with dual polarization, dual balanced, in-phase and quadrature detection.

PubMed

Wang, Zhao; Lee, Hsiang-Chieh; Vermeulen, Diedrik; Chen, Long; Nielsen, Torben; Park, Seo Yeon; Ghaemi, Allan; Swanson, Eric; Doerr, Chris; Fujimoto, James

2015-07-01

Optical coherence tomography (OCT) is a widely used three-dimensional (3D) optical imaging method with many biomedical and non-medical applications. Miniaturization, cost reduction, and increased functionality of OCT systems will be critical for future emerging clinical applications. We present a silicon photonic integrated circuit swept-source OCT (SS-OCT) coherent receiver with dual polarization, dual balanced, in-phase and quadrature (IQ) detection. We demonstrate multiple functional capabilities of IQ polarization resolved detection including: complex-conjugate suppressed full-range OCT, polarization diversity detection, and polarization-sensitive OCT. To our knowledge, this is the first demonstration of a silicon photonic integrated receiver for OCT. The integrated coherent receiver provides a miniaturized, low-cost solution for SS-OCT, and is also a key step towards a fully integrated high speed SS-OCT system with good performance and multi-functional capabilities. With further performance improvement and cost reduction, photonic integrated technology promises to greatly increase penetration of OCT systems in existing applications and enable new applications.

Silicon photonic integrated circuit swept-source optical coherence tomography receiver with dual polarization, dual balanced, in-phase and quadrature detection

PubMed Central

Wang, Zhao; Lee, Hsiang-Chieh; Vermeulen, Diedrik; Chen, Long; Nielsen, Torben; Park, Seo Yeon; Ghaemi, Allan; Swanson, Eric; Doerr, Chris; Fujimoto, James

2015-01-01

Optical coherence tomography (OCT) is a widely used three-dimensional (3D) optical imaging method with many biomedical and non-medical applications. Miniaturization, cost reduction, and increased functionality of OCT systems will be critical for future emerging clinical applications. We present a silicon photonic integrated circuit swept-source OCT (SS-OCT) coherent receiver with dual polarization, dual balanced, in-phase and quadrature (IQ) detection. We demonstrate multiple functional capabilities of IQ polarization resolved detection including: complex-conjugate suppressed full-range OCT, polarization diversity detection, and polarization-sensitive OCT. To our knowledge, this is the first demonstration of a silicon photonic integrated receiver for OCT. The integrated coherent receiver provides a miniaturized, low-cost solution for SS-OCT, and is also a key step towards a fully integrated high speed SS-OCT system with good performance and multi-functional capabilities. With further performance improvement and cost reduction, photonic integrated technology promises to greatly increase penetration of OCT systems in existing applications and enable new applications. PMID:26203382

Primordial spectra of slow-roll inflation at second-order with the Gauss-Bonnet correction

NASA Astrophysics Data System (ADS)

Wu, Qiang; Zhu, Tao; Wang, Anzhong

2018-05-01

The slow-roll inflation for a single scalar field that couples to the Gauss-Bonnet (GB) term represents an important higher-order curvature correction inspired by string theory. With the arrival of the era of precision cosmology, it is expected that the high-order corrections become more and more important. In this paper we study the observational predictions of the slow-roll inflation with the GB term by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble and GB coupling flow parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. In addition, by studying the theoretical predictions of the scalar spectral index and the tensor-to-scalar ratio with the Planck 2015 constraints in a model with power-law potential and GB coupling, we show that the second-order corrections are important in the future measurements. We expect that the understanding of the GB corrections in the primordial spectra and their constraints by forthcoming observational data will provide clues for the UV complete theory of quantum gravity, such as the string/M-theory.

Measurements of the temporal onset of mega-Gauss magnetic fields in a laser-driven solenoid

NASA Astrophysics Data System (ADS)

Goyon, Clement; Polllock, B. B.; Turnbull, D. T.; Hazi, A.; Ross, J. S.; Mariscal, D. A.; Patankar, S.; Williams, G. J.; Farmer, W. A.; Moody, J. D.; Fujioka, S.; Law, K. F. F.

2016-10-01

We report on experimental results obtained at Omega EP showing a nearly linear increase of the B-field up to about 2 mega-Gauss in 0.75 ns in a 1 mm3 region. The field is generated using 1 TW of 351 nm laser power ( 8*1015 W/cm2) incident on a laser-driven solenoid target. The coil target converts about 1% of the laser energy into the B-field measured both inside and outside the coil using proton deflectometry with a grid and Faraday rotation of probe beam through SiO2 glass. Proton data indicates a current rise up to hundreds of kA with a spatial distribution in the Au solenoid conductor evolving in time. These results give insight into the generating mechanism of the current between the plates and the time behavior of the field. These experiments are motivated by recent efforts to understand and utilize High Energy Density (HED) plasmas in the presence of external magnetic fields in areas of research from Astrophysics to Inertial Confinement Fusion. We will describe the experimental results and scale them to a NIF hohlraum size. This work was performed under the auspices of the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344.

0.125 mm(3) spatial resolution steady-state MR angiography of the thighs with a blood pool contrast agent using the quadrature body coil only at 1.5 Tesla.

PubMed

Boschewitz, Jack M; Hadizadeh, Dariusch R; Kukuk, Guido M; Meyer, Carsten; Wilhelm, Kai; Koscielny, Arne; Verrel, Frauke; Gieseke, Jürgen; Schild, Hans H; Willinek, Winfried A

2014-10-01

To implement and evaluate high spatial resolution three-dimensional MR contrast-enhanced angiography (3D-CEMRA) of the thighs using a blood pool contrast agent (BPCA) using the quadrature body coil only in patients with peripheral arterial occlusive disease (PAOD) in cases receiver coils cannot be used at 1.5 Tesla (T). Nineteen patients (mean age: 68.7 ± 11.2 years; range, 38-83 years) with known PAOD (Fontaine stages; III: 16, IV: 3) prospectively underwent 3D-CEMRA at 1.5T with a noninterpolated voxel size of 0.49 × 0.49 × 0.48 mm(3) . Digital subtraction angiography (DSA) was available for comparison in all patients. Two readers independently evaluated movement artifacts, overall image quality of 3D-CEMRA, and grade of stenosis as compared to DSA. SNR and CNR levels were quantified. The 3D-CEMRA was successfully completed in all patients. Patient movement artifacts that affected stenosis grading occurred in 3/38 thighs. Overall image quality was rated excellent in 15/38, good in 12/38, and diagnostic in 8/38 thighs. Stenosis grading matched with that in DSA in 35/38 thighs. High SNR and CNR were measured in all vessels. The 0.125 mm(3) spatial resolution 3D-CEMRA of the thighs with a BPCA is feasible using a quadrature body coil exclusively with excellent image quality despite long acquisition times. J. Magn. Reson. Imaging 2014;40:996-1001. © 2014 Wiley Periodicals, Inc. © 2014 Wiley Periodicals, Inc.

The generation of higher-order Laguerre-Gauss optical beams for high-precision interferometry.

PubMed

Carbone, Ludovico; Fulda, Paul; Bond, Charlotte; Brueckner, Frank; Brown, Daniel; Wang, Mengyao; Lodhia, Deepali; Palmer, Rebecca; Freise, Andreas

2013-08-12

Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light. We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry.

Small dark energy and stable vacuum from Dilaton-Gauss-Bonnet coupling in TMT

NASA Astrophysics Data System (ADS)

Guendelman, Eduardo I.; Nishino, Hitoshi; Rajpoot, Subhash

2017-04-01

In two measures theories (TMT), in addition to the Riemannian measure of integration, being the square root of the determinant of the metric, we introduce a metric-independent density Φ in four dimensions defined in terms of scalars \\varphi _a by Φ =\\varepsilon ^{μ ν ρ σ } \\varepsilon _{abcd} (partial _{μ }\\varphi _a)(partial _{ν }\\varphi _b) (partial _{ρ }\\varphi _c) (partial _{σ }\\varphi _d). With the help of a dilaton field φ we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton φ to the Gauss-Bonnet (GB) topological density {√{-g}} φ ( R_{μ ν ρ σ }^2 - 4 R_{μ ν }^2 + R^2 ) we obtain a theory that is scale invariant up to a total divergence. Integration of the \\varphi _a field equation leads to an integration constant that breaks the global scale symmetry. We discuss the stabilizing effects of the coupling of the dilaton to the GB-topological density on the vacua with a very small cosmological constant and the resolution of the `TMT Vacuum-Manifold Problem' which exists in the zero cosmological-constant vacuum limit. This problem generically arises from an effective potential that is a perfect square, and it gives rise to a vacuum manifold instead of a unique vacuum solution in the presence of many different scalars, like the dilaton, the Higgs, etc. In the non-zero cosmological-constant case this problem disappears. Furthermore, the GB coupling to the dilaton eliminates flat directions in the effective potential, and it totally lifts the vacuum-manifold degeneracy.

The Bassi Rebay 1 scheme is a special case of the Symmetric Interior Penalty formulation for discontinuous Galerkin discretisations with Gauss-Lobatto points

NASA Astrophysics Data System (ADS)

Manzanero, Juan; Rueda-Ramírez, Andrés M.; Rubio, Gonzalo; Ferrer, Esteban

2018-06-01

In the discontinuous Galerkin (DG) community, several formulations have been proposed to solve PDEs involving second-order spatial derivatives (e.g. elliptic problems). In this paper, we show that, when the discretisation is restricted to the usage of Gauss-Lobatto points, there are important similarities between two common choices: the Bassi-Rebay 1 (BR1) method, and the Symmetric Interior Penalty (SIP) formulation. This equivalence enables the extrapolation of properties from one scheme to the other: a sharper estimation of the minimum penalty parameter for the SIP stability (compared to the more general estimate proposed by Shahbazi [1]), more efficient implementations of the BR1 scheme, and the compactness of the BR1 method for straight quadrilateral and hexahedral meshes.

Quadrature-Quadrature Phase Shift Keying.

DTIC Science & Technology

1986-09-01

SECURITY CLASSIFICATION OF -IS PAfr All other editions are obsolete ’r- Ac P..N -N- %.. .. V . .. b . h S Debabrata Saha 1986 All Rights Reserved...1.2/T T~,pe of AISA Q -PSK AMSK 0 Y(IitIo ?6 orthogonal Four -level F, J." 𔃻 1i 1/ 2 H13.4 a H P6 E 44 3.5 Modulator Demodulator and Synchronization

A space-time lower-upper symmetric Gauss-Seidel scheme for the time-spectral method

NASA Astrophysics Data System (ADS)

Zhan, Lei; Xiong, Juntao; Liu, Feng

2016-05-01

The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge-Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower-upper symmetric Gauss-Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant-Friedrichs-Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.

Improvement of geomagnetic core field modeling with a priori information about Gauss coefficient correlations

NASA Astrophysics Data System (ADS)

Schachtschneider, R.; Rother, M.; Lesur, V.

2013-12-01

We introduce a method that enables us to account for existing correlations between Gauss coefficients in core field modelling. The information about the correlations are obtained from a highly accurate field model based on CHAMP data, e.g. the GRIMM-3 model. We compute the covariance matrices of the geomagnetic field, the secular variation, and acceleration up to degree 18 and use these in the regularization scheme of the core field inversion. For testing our method we followed two different approaches by applying it to two different synthetic satellite data sets. The first is a short data set with a time span of only three months. Here we test how the information about correlations help to obtain an accurate model when only very little information are available. The second data set is a large one covering several years. In this case, besides reducing the residuals in general, we focus on the improvement of the model near the boundaries of the data set where the accerelation is generally more difficult to handle. In both cases the obtained covariance matrices are included in the damping scheme of the regularization. That way information from scales that could otherwise not be resolved by the data can be extracted. We show that by using this technique we are able to improve the models of the field and the secular variation for both, the short and the long term data set, compared to approaches using more conventional regularization techniques.

A modified precise integration method for transient dynamic analysis in structural systems with multiple damping models

NASA Astrophysics Data System (ADS)

Ding, Zhe; Li, Li; Hu, Yujin

2018-01-01

Sophisticated engineering systems are usually assembled by subcomponents with significantly different levels of energy dissipation. Therefore, these damping systems often contain multiple damping models and lead to great difficulties in analyzing. This paper aims at developing a time integration method for structural systems with multiple damping models. The dynamical system is first represented by a generally damped model. Based on this, a new extended state-space method for the damped system is derived. A modified precise integration method with Gauss-Legendre quadrature is then proposed. The numerical stability and accuracy of the proposed integration method are discussed in detail. It is verified that the method is conditionally stable and has inherent algorithmic damping, period error and amplitude decay. Numerical examples are provided to assess the performance of the proposed method compared with other methods. It is demonstrated that the method is more accurate than other methods with rather good efficiency and the stable condition is easy to be satisfied in practice.

Relativistic semiempirical-core-potential calculations in Ca+,Sr+ , and Ba+ ions on Lagrange meshes

NASA Astrophysics Data System (ADS)

Filippin, Livio; Schiffmann, Sacha; Dohet-Eraly, Jérémy; Baye, Daniel; Godefroid, Michel

2018-01-01

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature to calculate matrix elements. Properties involving the low-lying metastable D 3 /2 ,5 /2 2 states of Ca+, Sr+, and Ba+ are studied, such as polarizabilities, one- and two-photon decay rates, and lifetimes. Good agreement is found with other theory and observation, which is promising for further applications in alkalilike systems.

Computing wave functions in multichannel collisions with non-local potentials using the R-matrix method

NASA Astrophysics Data System (ADS)

Bonitati, Joey; Slimmer, Ben; Li, Weichuan; Potel, Gregory; Nunes, Filomena

2017-09-01

The calculable form of the R-matrix method has been previously shown to be a useful tool in approximately solving the Schrodinger equation in nuclear scattering problems. We use this technique combined with the Gauss quadrature for the Lagrange-mesh method to efficiently solve for the wave functions of projectile nuclei in low energy collisions (1-100 MeV) involving an arbitrary number of channels. We include the local Woods-Saxon potential, the non-local potential of Perey and Buck, a Coulomb potential, and a coupling potential to computationally solve for the wave function of two nuclei at short distances. Object oriented programming is used to increase modularity, and parallel programming techniques are introduced to reduce computation time. We conclude that the R-matrix method is an effective method to predict the wave functions of nuclei in scattering problems involving both multiple channels and non-local potentials. Michigan State University iCER ACRES REU.

On the calculation of dynamic and heat loads on a three-dimensional body in a hypersonic flow

NASA Astrophysics Data System (ADS)

Bocharov, A. N.; Bityurin, V. A.; Evstigneev, N. M.; Fortov, V. E.; Golovin, N. N.; Petrovskiy, V. P.; Ryabkov, O. I.; Teplyakov, I. O.; Shustov, A. A.; Solomonov, Yu S.

2018-01-01

We consider a three-dimensional body in a hypersonic flow at zero angle of attack. Our aim is to estimate heat and aerodynamic loads on specific body elements. We are considering a previously developed code to solve coupled heat- and mass-transfer problem. The change of the surface shape is taken into account by formation of the iterative process for the wall material ablation. The solution is conducted on the multi-graphics-processing-unit (multi-GPU) cluster. Five Mach number points are considered, namely for M = 20-28. For each point we estimate body shape after surface ablation, heat loads on the surface and aerodynamic loads on the whole body and its elements. The latter is done using Gauss-type quadrature on the surface of the body. The comparison of the results for different Mach numbers is performed. We also estimate the efficiency of the Navier-Stokes code on multi-GPU and central processing unit architecture for the coupled heat and mass transfer problem.

Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alam, Aftab; Khan, S. N.; Wilson, Brian G.

2011-07-06

A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in ab initio electronic-structure calculations. We combine a weighted Voronoi tessellation with isoparametric integration via Gauss-Legendre quadratures to provide rapidly convergent VP integrals for a variety of integrands, including those with a Coulomb singularity. We showcase the capability of our approach by first applying it to an analytic charge-density model achieving machine-precision accuracy with expected convergence properties in milliseconds. For contrast, we compare our results to those using shape-functions and show our approach is greater than 10 5 times faster and 10more » 7 times more accurate. Furthermore, a weighted Voronoi tessellation also allows for a physics-based partitioning of space that guarantees convex, space-filling VP while reflecting accurate atomic size and site charges, as we show within KKR methods applied to Fe-Pd alloys.« less

Accurate computation of gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

We developed an accurate method to compute the gravitational field of a tesseroid. The method numerically integrates a surface integral representation of the gravitational potential of the tesseroid by conditionally splitting its line integration intervals and by using the double exponential quadrature rule. Then, it evaluates the gravitational acceleration vector and the gravity gradient tensor by numerically differentiating the numerically integrated potential. The numerical differentiation is conducted by appropriately switching the central and the single-sided second-order difference formulas with a suitable choice of the test argument displacement. If necessary, the new method is extended to the case of a general tesseroid with the variable density profile, the variable surface height functions, and/or the variable intervals in longitude or in latitude. The new method is capable of computing the gravitational field of the tesseroid independently on the location of the evaluation point, namely whether outside, near the surface of, on the surface of, or inside the tesseroid. The achievable precision is 14-15 digits for the potential, 9-11 digits for the acceleration vector, and 6-8 digits for the gradient tensor in the double precision environment. The correct digits are roughly doubled if employing the quadruple precision computation. The new method provides a reliable procedure to compute the topographic gravitational field, especially that near, on, and below the surface. Also, it could potentially serve as a sure reference to complement and elaborate the existing approaches using the Gauss-Legendre quadrature or other standard methods of numerical integration.

A LAGRANGIAN GAUSS-NEWTON-KRYLOV SOLVER FOR MASS- AND INTENSITY-PRESERVING DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Ruthotto, Lars

2017-01-01

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.

Basis set construction for molecular electronic structure theory: natural orbital and Gauss-Slater basis for smooth pseudopotentials.

PubMed

Petruzielo, F R; Toulouse, Julien; Umrigar, C J

2011-02-14

A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multiconfigurational self-consistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear diatomic molecule to produce a balanced basis set. Two general features that facilitate this basis construction are demonstrated. First, weak coupling exists between the optimal exponents of primitives with different angular momenta. Second, the optimal primitive exponents for a chosen system depend weakly on the particular level of theory employed for optimization. The explicit case considered here is a basis set appropriate for the Burkatzki-Filippi-Dolg pseudopotentials. Since these pseudopotentials are finite at nuclei and have a Coulomb tail, the recently proposed Gauss-Slater functions are the appropriate primitives. Double- and triple-zeta bases are developed for elements hydrogen through argon. These new bases offer significant gains over the corresponding Burkatzki-Filippi-Dolg bases at various levels of theory. Using a Gaussian expansion of the basis functions, these bases can be employed in any electronic structure method. Quantum Monte Carlo provides an added benefit: expansions are unnecessary since the integrals are evaluated numerically.

Quasi-Periodic Long-Term Quadrature Light Variability in Early Type Interacting Binary Systems

NASA Astrophysics Data System (ADS)

Peters, Geraldine Joan

2015-08-01

Four years of Kepler observations have revealed a class of Algol-type binaries in which the relative brightness of the quadrature light varies from > 1 to <1 on a time scale of about 100-400 days. The behavior pattern is quasi-periodic. We call these systems L/T (leading hemisphere/ trailing hemisphere) variables. Although L/T inequality in eclipsing binaries has been noted from ground-based photometry by several observers since the early 1950s, the regular or quasi-regular switching between maxima is new. Twenty L/T systems have so far been found in the Kepler database and at least three classes of L/T behavior have been identified. In this presentation I will give an update on the L/T phenomenon gleaned from the Kepler and K2 databases. The Kepler and K2 light curves are being analyzed with the 2015 version of the Wilson-Devinney (WD) program that includes major improvements in modeling star spots (i.e. spot motions due to drift and stellar rotation and spot growth and decay). The prototype L/T variable is WX Draconis (A8V + K0IV, P=1.80 d) which shows L/ T light variations of 2-3%. The primary is a delta Scuti star with a dominant pulsation period of 41 m. Preliminary analysis of the WX Dra data suggests that the L/T variability can be fit with either an accretion hot spot on the primary (T = 2.3 Tphot) that jumps in longitude or a magnetic cool spotted region on the secondary. If the latter model is correct the dark region must occupy at least 20% of the surface of the facing hemisphere of the secondary if it is completely black, or a larger area if not completely black. In both hot and cool spot scenarios magnetic fields must play a role in the activity. Support from NASA grants NNX11AC78G and NNX12AE44G and USC’s Women in Science and Engineering (WiSE) program is greatly appreciated.

Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl Teller Ginocchio potential wave functions

NASA Astrophysics Data System (ADS)

Michel, N.; Stoitsov, M. V.

2008-04-01

The fast computation of the Gauss hypergeometric function F12 with all its parameters complex is a difficult task. Although the F12 function verifies numerous analytical properties involving power series expansions whose implementation is apparently immediate, their use is thwarted by instabilities induced by cancellations between very large terms. Furthermore, small areas of the complex plane, in the vicinity of z=e, are inaccessible using F12 power series linear transformations. In order to solve these problems, a generalization of R.C. Forrey's transformation theory has been developed. The latter has been successful in treating the F12 function with real parameters. As in real case transformation theory, the large canceling terms occurring in F12 analytical formulas are rigorously dealt with, but by way of a new method, directly applicable to the complex plane. Taylor series expansions are employed to enter complex areas outside the domain of validity of power series analytical formulas. The proposed algorithm, however, becomes unstable in general when |a|, |b|, |c| are moderate or large. As a physical application, the calculation of the wave functions of the analytical Pöschl-Teller-Ginocchio potential involving F12 evaluations is considered. Program summaryProgram title: hyp_2F1, PTG_wf Catalogue identifier: AEAE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAE_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.: 6839 No. of bytes in distributed program, including test data, etc.: 63 334 Distribution format: tar.gz Programming language: C++, Fortran 90 Computer: Intel i686 Operating system: Linux, Windows Word size: 64 bits Classification: 4.7 Nature of problem: The Gauss hypergeometric function F12, with all its parameters complex, is uniquely

Ultrahigh-sensitive multimode interference-based fiber optic liquid-level sensor realized using illuminating zero-order Bessel-Gauss beam

NASA Astrophysics Data System (ADS)

Saha, Ardhendu; Datta, Arijit; Kaman, Surjit

2018-03-01

A proposal toward the enhancement in the sensitivity of a multimode interference-based fiber optic liquid-level sensor is explored analytically using a zero-order Bessel-Gauss (BG) beam as the input source. The sensor head consists of a suitable length of no-core fiber (NCF) sandwiched between two specialty high-order mode fibers. The coupling efficiency of various order modes inside the sensor structure is assessed using guided-mode propagation analysis and the performance of the proposed sensor has been benchmarked against the conventional sensor using a Gaussian beam. Furthermore, the study has been corroborated using a finite-difference beam propagation method in Lumerical's Mode Solutions software to investigate the propagation of the zero-order BG beam inside the sensor structure. Based on the simulation outcomes, the proposed scheme yields a maximum absolute sensitivity of up to 3.551 dB / mm and a sensing resolution of 2.816 × 10 - 3 mm through the choice of an appropriate length of NCF at an operating wavelength of 1.55 μm. Owing to this superior sensing performance, the reported sensing technology expedites an avenue to devise a high-performance fiber optic-level sensor that finds profound implication in different physical, biological, and chemical sensing purposes.

Light deflection and Gauss-Bonnet theorem: definition of total deflection angle and its applications

NASA Astrophysics Data System (ADS)

Arakida, Hideyoshi

2018-05-01

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild-de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ^4 on the optical reference geometry M^opt determined by the optical metric \\bar{g}_{ij}. On the basis of the definition of the total deflection angle α and the Gauss-Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry M^opt or the curved (r, φ ) subspace M^sub being a slice of constant time t and (2) the integral formula on the optical reference geometry M^opt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ ^4 and the line integral of the geodesic curvature κ _g along the curve C_{Γ}. As the curve C_{Γ}, we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r, φ ) subspace M^sub. We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild-de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein-Shapiro's formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild-de Sitter case, there appear order O(Lambda;m) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.

Gaussian Quadrature is an efficient method for the back-transformation in estimating the usual intake distribution when assessing dietary exposure.

PubMed

Dekkers, A L M; Slob, W

2012-10-01

In dietary exposure assessment, statistical methods exist for estimating the usual intake distribution from daily intake data. These methods transform the dietary intake data to normal observations, eliminate the within-person variance, and then back-transform the data to the original scale. We propose Gaussian Quadrature (GQ), a numerical integration method, as an efficient way of back-transformation. We compare GQ with six published methods. One method uses a log-transformation, while the other methods, including GQ, use a Box-Cox transformation. This study shows that, for various parameter choices, the methods with a Box-Cox transformation estimate the theoretical usual intake distributions quite well, although one method, a Taylor approximation, is less accurate. Two applications--on folate intake and fruit consumption--confirmed these results. In one extreme case, some methods, including GQ, could not be applied for low percentiles. We solved this problem by modifying GQ. One method is based on the assumption that the daily intakes are log-normally distributed. Even if this condition is not fulfilled, the log-transformation performs well as long as the within-individual variance is small compared to the mean. We conclude that the modified GQ is an efficient, fast and accurate method for estimating the usual intake distribution. Copyright © 2012 Elsevier Ltd. All rights reserved.

Chebyshev collocation spectral method for one-dimensional radiative heat transfer in linearly anisotropic-scattering cylindrical medium

NASA Astrophysics Data System (ADS)

Zhou, Rui-Rui; Li, Ben-Wen

2017-03-01

In this study, the Chebyshev collocation spectral method (CCSM) is developed to solve the radiative integro-differential transfer equation (RIDTE) for one-dimensional absorbing, emitting and linearly anisotropic-scattering cylindrical medium. The general form of quadrature formulas for Chebyshev collocation points is deduced. These formulas are proved to have the same accuracy as the Gauss-Legendre quadrature formula (GLQF) for the F-function (geometric function) in the RIDTE. The explicit expressions of the Lagrange basis polynomials and the differentiation matrices for Chebyshev collocation points are also given. These expressions are necessary for solving an integro-differential equation by the CCSM. Since the integrand in the RIDTE is continuous but non-smooth, it is treated by the segments integration method (SIM). The derivative terms in the RIDTE are carried out to improve the accuracy near the origin. In this way, a fourth order accuracy is achieved by the CCSM for the RIDTE, whereas it's only a second order one by the finite difference method (FDM). Several benchmark problems (BPs) with various combinations of optical thickness, medium temperature distribution, degree of anisotropy, and scattering albedo are solved. The results show that present CCSM is efficient to obtain high accurate results, especially for the optically thin medium. The solutions rounded to seven significant digits are given in tabular form, and show excellent agreement with the published data. Finally, the solutions of RIDTE are used as benchmarks for the solution of radiative integral transfer equations (RITEs) presented by Sutton and Chen (JQSRT 84 (2004) 65-103). A non-uniform grid refined near the wall is advised to improve the accuracy of RITEs solutions.

Multi-element stochastic spectral projection for high quantile estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ko, Jordan, E-mail: jordan.ko@mac.com; Garnier, Josselin

2013-06-15

We investigate quantile estimation by multi-element generalized Polynomial Chaos (gPC) metamodel where the exact numerical model is approximated by complementary metamodels in overlapping domains that mimic the model’s exact response. The gPC metamodel is constructed by the non-intrusive stochastic spectral projection approach and function evaluation on the gPC metamodel can be considered as essentially free. Thus, large number of Monte Carlo samples from the metamodel can be used to estimate α-quantile, for moderate values of α. As the gPC metamodel is an expansion about the means of the inputs, its accuracy may worsen away from these mean values where themore » extreme events may occur. By increasing the approximation accuracy of the metamodel, we may eventually improve accuracy of quantile estimation but it is very expensive. A multi-element approach is therefore proposed by combining a global metamodel in the standard normal space with supplementary local metamodels constructed in bounded domains about the design points corresponding to the extreme events. To improve the accuracy and to minimize the sampling cost, sparse-tensor and anisotropic-tensor quadratures are tested in addition to the full-tensor Gauss quadrature in the construction of local metamodels; different bounds of the gPC expansion are also examined. The global and local metamodels are combined in the multi-element gPC (MEgPC) approach and it is shown that MEgPC can be more accurate than Monte Carlo or importance sampling methods for high quantile estimations for input dimensions roughly below N=8, a limit that is very much case- and α-dependent.« less

A model for incomplete longitudinal multivariate ordinal data.

PubMed

Liu, Li C

2008-12-30

In studies where multiple outcome items are repeatedly measured over time, missing data often occur. A longitudinal item response theory model is proposed for analysis of multivariate ordinal outcomes that are repeatedly measured. Under the MAR assumption, this model accommodates missing data at any level (missing item at any time point and/or missing time point). It allows for multiple random subject effects and the estimation of item discrimination parameters for the multiple outcome items. The covariates in the model can be at any level. Assuming either a probit or logistic response function, maximum marginal likelihood estimation is described utilizing multidimensional Gauss-Hermite quadrature for integration of the random effects. An iterative Fisher-scoring solution, which provides standard errors for all model parameters, is used. A data set from a longitudinal prevention study is used to motivate the application of the proposed model. In this study, multiple ordinal items of health behavior are repeatedly measured over time. Because of a planned missing design, subjects answered only two-third of all items at a given point. Copyright 2008 John Wiley & Sons, Ltd.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

A simple and efficient shear-flexible plate bending element

NASA Technical Reports Server (NTRS)

Chaudhuri, Reaz A.

1987-01-01

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

A novel 2.5D finite difference scheme for simulations of resistivity logging in anisotropic media

NASA Astrophysics Data System (ADS)

Zeng, Shubin; Chen, Fangzhou; Li, Dawei; Chen, Ji; Chen, Jiefu

2018-03-01

The objective of this study is to develop a method to model 3D resistivity well logging problems in 2D formation with anisotropy, known as 2.5D modeling. The traditional 1D forward modeling extensively used in practice lacks the capability of modeling 2D formation. A 2.5D finite difference method (FDM) solving all the electric and magnetic field components simultaneously is proposed. Compared to other previous 2.5D FDM schemes, this method is more straightforward in modeling fully anisotropic media and easy to be implemented. Fourier transform is essential to this FDM scheme, and by employing Gauss-Legendre (GL) quadrature rule the computational time of this step can be greatly reduced. In the numerical examples, we first demonstrate the validity of the FDM scheme with GL rule by comparing with 1D forward modeling for layered anisotropic problems, and then we model a complicated 2D formation case and find that the proposed 2.5D FD scheme is much more efficient than 3D numerical methods.

Implementation of the infinite-range exterior complex scaling to the time-dependent complete-active-space self-consistent-field method

NASA Astrophysics Data System (ADS)

Orimo, Yuki; Sato, Takeshi; Scrinzi, Armin; Ishikawa, Kenichi L.

2018-02-01

We present a numerical implementation of the infinite-range exterior complex scaling [Scrinzi, Phys. Rev. A 81, 053845 (2010), 10.1103/PhysRevA.81.053845] as an efficient absorbing boundary to the time-dependent complete-active-space self-consistent field method [Sato, Ishikawa, Březinová, Lackner, Nagele, and Burgdörfer, Phys. Rev. A 94, 023405 (2016), 10.1103/PhysRevA.94.023405] for multielectron atoms subject to an intense laser pulse. We introduce Gauss-Laguerre-Radau quadrature points to construct discrete variable representation basis functions in the last radial finite element extending to infinity. This implementation is applied to strong-field ionization and high-harmonic generation in He, Be, and Ne atoms. It efficiently prevents unphysical reflection of photoelectron wave packets at the simulation boundary, enabling accurate simulations with substantially reduced computational cost, even under significant (≈50 % ) double ionization. For the case of a simulation of high-harmonic generation from Ne, for example, 80% cost reduction is achieved, compared to a mask-function absorption boundary.

Minimally doubled fermions and spontaneous chiral symmetry breaking

NASA Astrophysics Data System (ADS)

Osmanaj (Zeqirllari), Rudina; Hyka (Xhako), Dafina

2018-03-01

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks - Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss - Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

Computational techniques in gamma-ray skyshine analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

George, D.L.

1988-12-01

Two computer codes were developed to analyze gamma-ray skyshine, the scattering of gamma photons by air molecules. A review of previous gamma-ray skyshine studies discusses several Monte Carlo codes, programs using a single-scatter model, and the MicroSkyshine program for microcomputers. A benchmark gamma-ray skyshine experiment performed at Kansas State University is also described. A single-scatter numerical model was presented which traces photons from the source to their first scatter, then applies a buildup factor along a direct path from the scattering point to a detector. The FORTRAN code SKY, developed with this model before the present study, was modified tomore » use Gauss quadrature, recent photon attenuation data and a more accurate buildup approximation. The resulting code, SILOGP, computes response from a point photon source on the axis of a silo, with and without concrete shielding over the opening. Another program, WALLGP, was developed using the same model to compute response from a point gamma source behind a perfectly absorbing wall, with and without shielding overhead. 29 refs., 48 figs., 13 tabs.« less

Vortex Laser based on III-V semiconductor metasurface: direct generation of coherent Laguerre-Gauss modes carrying controlled orbital angular momentum

PubMed Central

Seghilani, Mohamed S.; Myara, Mikhael; Sellahi, Mohamed; Legratiet, Luc; Sagnes, Isabelle; Beaudoin, Grégoire; Lalanne, Philippe; Garnache, Arnaud

2016-01-01

The generation of a coherent state, supporting a large photon number, with controlled orbital-angular-momentum L = ħl (of charge l per photon) presents both fundamental and technological challenges: we demonstrate a surface-emitting laser, based on III-V semiconductor technology with an integrated metasurface, generating vortex-like coherent state in the Laguerre-Gauss basis. We use a first order phase perturbation to lift orbital degeneracy of wavefunctions, by introducing a weak anisotropy called here “orbital birefringence”, based on a dielectric metasurface. The azimuthal symmetry breakdown and non-linear laser dynamics create “orbital gain dichroism” allowing selecting vortex handedness. This coherent photonic device was characterized and studied, experimentally and theoretically. It exhibits a low divergence (<1°) diffraction limited beam, emitting 49 mW output power in the near-IR at λ ≃ 1 μm, a charge l = ±1, … ±4 (>50 dB vortex purity), and single frequency operation in a stable low noise regime (0.1% rms). Such high performance laser opens the path to widespread new photonic applications. PMID:27917885

Frequency-doubled microwave waveforms generation using a dual-polarization quadrature phase shift keying modulator driven by a single frequency radio frequency signal

NASA Astrophysics Data System (ADS)

Zhu, Zihang; Zhao, Shanghong; Li, Xuan; Qu, Kun; Lin, Tao

2018-01-01

A photonic approach to generate frequency-doubled microwave waveforms using an integrated dual-polarization quadrature phase shift keying (DP-QPSK) modulator driven by a sinusoidal radio frequency (RF) signal is proposed. By adjusting the dc bias points of the DP-QPSK modulator, the obtained second-order and six-order harmonics are in phase while the fourth-order harmonics are complementary when the orthogonal polarized outputs of the modulator are photodetected. After properly setting the modulation indices of the modulator, the amplitude of the second-order harmonic is 9 times of that of the six-order harmonic, indicating a frequency-doubled triangular waveform is generated. If a broadband 90° microwave phase shifter is attached after the photodetector (PD) to introduce a 90° phase shift, a frequency-doubled square waveform can be obtained after adjusting the amplitude of the second-order harmonic 3 times of that of the six-order harmonic. The proposal is first theoretically analyzed and then validated by simulation. Simulation results show that a 10 GHz triangular and square waveform sequences are successfully generated from a 5 GHz sinusoidal RF drive signal.

A memory efficient implementation scheme of Gauss error function in a Laguerre-Volterra network for neuroprosthetic devices

NASA Astrophysics Data System (ADS)

Li, Will X. Y.; Cui, Ke; Zhang, Wei

2017-04-01

Cognitive neural prosthesis is a manmade device which can be used to restore or compensate for lost human cognitive modalities. The generalized Laguerre-Volterra (GLV) network serves as a robust mathematical underpinning for the development of such prosthetic instrument. In this paper, a hardware implementation scheme of Gauss error function for the GLV network targeting reconfigurable platforms is reported. Numerical approximations are formulated which transform the computation of nonelementary function into combinational operations of elementary functions, and memory-intensive look-up table (LUT) based approaches can therefore be circumvented. The computational precision can be made adjustable with the utilization of an error compensation scheme, which is proposed based on the experimental observation of the mathematical characteristics of the error trajectory. The precision can be further customizable by exploiting the run-time characteristics of the reconfigurable system. Compared to the polynomial expansion based implementation scheme, the utilization of slice LUTs, occupied slices, and DSP48E1s on a Xilinx XC6VLX240T field-programmable gate array has decreased by 94.2%, 94.1%, and 90.0%, respectively. While compared to the look-up table based scheme, 1.0 ×1017 bits of storage can be spared under the maximum allowable error of 1.0 ×10-3 . The proposed implementation scheme can be employed in the study of large-scale neural ensemble activity and in the design and development of neural prosthetic device.

Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein-Gauss-Bonnet model with a Λ -term

NASA Astrophysics Data System (ADS)

Ivashchuk, V. D.; Kobtsev, A. A.

2018-02-01

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Λ is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned Λ , we find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H >0 and h, corresponding to factor spaces of dimensions 3 and l > 2, respectively and D = 1 + 3 + l. The fine-tuned Λ = Λ (x, l, α ) depends upon the ratio h/H = x, l and the ratio α = α _2/α _1 of two constants (α _2 and α _1) of the model. For fixed Λ , α and l > 2 the equation Λ (x,l,α ) = Λ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example l =3 is presented). For certain restrictions on x we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. A subclass of solutions with small enough variation of the effective gravitational constant G is considered. It is shown that all solutions from this subclass are stable.

Challenges in designing appropriate scaffolding to improve students' representational consistency: The case of a Gauss's law problem

NASA Astrophysics Data System (ADS)

Maries, Alexandru; Lin, Shih-Yin; Singh, Chandralekha

2017-12-01

Prior research suggests that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for a problem in electrostatics and the effect of increasing levels of scaffolding on students' representational consistency. Students in calculus-based introductory physics were given a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution in which they were asked to write a mathematical expression for the electric field in various regions and then plot the electric field. In study 1, we found that students had great difficulty in plotting the electric field as a function of the distance from the center of the sphere consistent with the mathematical expressions in various regions, and interviews with students suggested possible reasons which may account for this difficulty. Therefore, in study 2, we designed two scaffolding interventions with levels of support which built on each other (i.e., the second scaffolding level built on the first) in order to help students plot their expressions consistently and compared the performance of students provided with scaffolding with a comparison group which was not given any scaffolding support. Analysis of student performance with different levels of scaffolding reveals that scaffolding from an expert perspective beyond a certain level may sometimes hinder student performance and students may not even discern the relevance of the additional support. We provide possible interpretations for these findings based on in-depth, think-aloud student interviews.

Algorithmic-Reducibility = Renormalization-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') Replacing CRUTCHES!!!: Gauss Modular/Clock-Arithmetic Congruences = Signal X Noise PRODUCTS..

NASA Astrophysics Data System (ADS)

Siegel, J.; Siegel, Edward Carl-Ludwig

2011-03-01

Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!

Higher Order Thermal Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

Sorathiya, Shahajhan; Ansumali, Santosh

2013-03-01

Lattice Boltzmann method (LBM) modelling of thermal flows, compressible and micro flows requires an accurate velocity space discretization. The sub optimality of Gauss-Hermite quadrature in this regard is well known. Most of the thermal LBM in the past have suffered from instability due to lack of proper H-theorem and accuracy. Motivated from these issues, the present work develops along the two works and and imposes an eighth higher order moment to get correct thermal physics. We show that this can be done by adding just 6 more velocities to D3Q27 model and obtain a ``multi-speed on lattice thermal LBM'' with 33 velocities in 3D and calO (u4) and calO (T4) accurate fieq with a consistent H-theorem and inherent numerical stability. Simulations for Rayleigh-Bernard as well as velocity and temperature slip in micro flows matches with analytical results. Lid driven cavity set up for grid convergence is studied. Finally, a novel data structure is developed for HPC. The authors express their gratitude for computational resources and financial support provide by Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore, India.

Self-healing of Hermite-Gauss and Ince-Gauss beams

NASA Astrophysics Data System (ADS)

Aguirre-Olivas, Dilia; Mellado-Villaseñor, Gabriel; Arrizón, Victor; Chávez-Cerda, Sabino

2015-08-01

We analyze and demonstrate, numerically and experimentally, the self-healing effect in scaled propagation invariant beams, subject to opaque obstructions. The effect is quantitatively evaluated employing the Root Mean Square deviation and the similarity function.

Application of Gauss's theorem to quantify localized surface emissions from airborne measurements of wind and trace gases

DOE PAGES

Conley, Stephen; Faloona, Ian; Mehrotra, Shobhit; ...

2017-09-13

Airborne estimates of greenhouse gas emissions are becoming more prevalent with the advent of rapid commercial development of trace gas instrumentation featuring increased measurement accuracy, precision, and frequency, and the swelling interest in the verification of current emission inventories. Multiple airborne studies have indicated that emission inventories may underestimate some hydrocarbon emission sources in US oil- and gas-producing basins. Consequently, a proper assessment of the accuracy of these airborne methods is crucial to interpreting the meaning of such discrepancies. We present a new method of sampling surface sources of any trace gas for which fast and precise measurements can be mademore » and apply it to methane, ethane, and carbon dioxide on spatial scales of ~1000 m, where consecutive loops are flown around a targeted source region at multiple altitudes. Using Reynolds decomposition for the scalar concentrations, along with Gauss's theorem, we show that the method accurately accounts for the smaller-scale turbulent dispersion of the local plume, which is often ignored in other average mass balance methods. With the help of large eddy simulations (LES) we further show how the circling radius can be optimized for the micrometeorological conditions encountered during any flight. Furthermore, by sampling controlled releases of methane and ethane on the ground we can ascertain that the accuracy of the method, in appropriate meteorological conditions, is often better than 10 %, with limits of detection below 5 kg h -1 for both methane and ethane. Because of the FAA-mandated minimum flight safe altitude of 150 m, placement of the aircraft is critical to preventing a large portion of the emission plume from flowing underneath the lowest aircraft sampling altitude, which is generally the leading source of uncertainty in these measurements. Finally, we show how the accuracy of the method is strongly dependent on the number of sampling loops and

Application of Gauss's theorem to quantify localized surface emissions from airborne measurements of wind and trace gases

NASA Astrophysics Data System (ADS)

Conley, Stephen; Faloona, Ian; Mehrotra, Shobhit; Suard, Maxime; Lenschow, Donald H.; Sweeney, Colm; Herndon, Scott; Schwietzke, Stefan; Pétron, Gabrielle; Pifer, Justin; Kort, Eric A.; Schnell, Russell

2017-09-01

Airborne estimates of greenhouse gas emissions are becoming more prevalent with the advent of rapid commercial development of trace gas instrumentation featuring increased measurement accuracy, precision, and frequency, and the swelling interest in the verification of current emission inventories. Multiple airborne studies have indicated that emission inventories may underestimate some hydrocarbon emission sources in US oil- and gas-producing basins. Consequently, a proper assessment of the accuracy of these airborne methods is crucial to interpreting the meaning of such discrepancies. We present a new method of sampling surface sources of any trace gas for which fast and precise measurements can be made and apply it to methane, ethane, and carbon dioxide on spatial scales of ˜ 1000 m, where consecutive loops are flown around a targeted source region at multiple altitudes. Using Reynolds decomposition for the scalar concentrations, along with Gauss's theorem, we show that the method accurately accounts for the smaller-scale turbulent dispersion of the local plume, which is often ignored in other average mass balance methods. With the help of large eddy simulations (LES) we further show how the circling radius can be optimized for the micrometeorological conditions encountered during any flight. Furthermore, by sampling controlled releases of methane and ethane on the ground we can ascertain that the accuracy of the method, in appropriate meteorological conditions, is often better than 10 %, with limits of detection below 5 kg h-1 for both methane and ethane. Because of the FAA-mandated minimum flight safe altitude of 150 m, placement of the aircraft is critical to preventing a large portion of the emission plume from flowing underneath the lowest aircraft sampling altitude, which is generally the leading source of uncertainty in these measurements. Finally, we show how the accuracy of the method is strongly dependent on the number of sampling loops

Application of Gauss's theorem to quantify localized surface emissions from airborne measurements of wind and trace gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Conley, Stephen; Faloona, Ian; Mehrotra, Shobhit

Airborne estimates of greenhouse gas emissions are becoming more prevalent with the advent of rapid commercial development of trace gas instrumentation featuring increased measurement accuracy, precision, and frequency, and the swelling interest in the verification of current emission inventories. Multiple airborne studies have indicated that emission inventories may underestimate some hydrocarbon emission sources in US oil- and gas-producing basins. Consequently, a proper assessment of the accuracy of these airborne methods is crucial to interpreting the meaning of such discrepancies. We present a new method of sampling surface sources of any trace gas for which fast and precise measurements can be mademore » and apply it to methane, ethane, and carbon dioxide on spatial scales of ~1000 m, where consecutive loops are flown around a targeted source region at multiple altitudes. Using Reynolds decomposition for the scalar concentrations, along with Gauss's theorem, we show that the method accurately accounts for the smaller-scale turbulent dispersion of the local plume, which is often ignored in other average mass balance methods. With the help of large eddy simulations (LES) we further show how the circling radius can be optimized for the micrometeorological conditions encountered during any flight. Furthermore, by sampling controlled releases of methane and ethane on the ground we can ascertain that the accuracy of the method, in appropriate meteorological conditions, is often better than 10 %, with limits of detection below 5 kg h -1 for both methane and ethane. Because of the FAA-mandated minimum flight safe altitude of 150 m, placement of the aircraft is critical to preventing a large portion of the emission plume from flowing underneath the lowest aircraft sampling altitude, which is generally the leading source of uncertainty in these measurements. Finally, we show how the accuracy of the method is strongly dependent on the number of sampling loops and

Evaluation of Optimal Formulas for Gravitational Tensors up to Gravitational Curvatures of a Tesseroid

NASA Astrophysics Data System (ADS)

Deng, Xiao-Le; Shen, Wen-Bin

2018-01-01

The forward modeling of the topographic effects of the gravitational parameters in the gravity field is a fundamental topic in geodesy and geophysics. Since the gravitational effects, including for instance the gravitational potential (GP), the gravity vector (GV) and the gravity gradient tensor (GGT), of the topographic (or isostatic) mass reduction have been expanded by adding the gravitational curvatures (GC) in geoscience, it is crucial to find efficient numerical approaches to evaluate these effects. In this paper, the GC formulas of a tesseroid in Cartesian integral kernels are derived in 3D/2D forms. Three generally used numerical approaches for computing the topographic effects (e.g., GP, GV, GGT, GC) of a tesseroid are studied, including the Taylor Series Expansion (TSE), Gauss-Legendre Quadrature (GLQ) and Newton-Cotes Quadrature (NCQ) approaches. Numerical investigations show that the GC formulas in Cartesian integral kernels are more efficient if compared to the previously given GC formulas in spherical integral kernels: by exploiting the 3D TSE second-order formulas, the computational burden associated with the former is 46%, as an average, of that associated with the latter. The GLQ behaves better than the 3D/2D TSE and NCQ in terms of accuracy and computational time. In addition, the effects of a spherical shell's thickness and large-scale geocentric distance on the GP, GV, GGT and GC functionals have been studied with the 3D TSE second-order formulas as well. The relative approximation errors of the GC functionals are larger with the thicker spherical shell, which are the same as those of the GP, GV and GGT. Finally, the very-near-area problem and polar singularity problem have been considered by the numerical methods of the 3D TSE, GLQ and NCQ. The relative approximation errors of the GC components are larger than those of the GP, GV and GGT, especially at the very near area. Compared to the GC formulas in spherical integral kernels, these new GC

Reactive silica transport in fractured porous media: Analytical solutions for a system of parallel fractures

NASA Astrophysics Data System (ADS)

Yang, Jianwen

2012-04-01

A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

NASA Astrophysics Data System (ADS)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

Evaluation of FSK models for radiative heat transfer under oxyfuel conditions

NASA Astrophysics Data System (ADS)

Clements, Alastair G.; Porter, Rachael; Pranzitelli, Alessandro; Pourkashanian, Mohamed

2015-01-01

Oxyfuel is a promising technology for carbon capture and storage (CCS) applied to combustion processes. It would be highly advantageous in the deployment of CCS to be able to model and optimise oxyfuel combustion, however the increased concentrations of CO2 and H2O under oxyfuel conditions modify several fundamental processes of combustion, including radiative heat transfer. This study uses benchmark narrow band radiation models to evaluate the influence of assumptions in global full-spectrum k-distribution (FSK) models, and whether they are suitable for modelling radiation in computational fluid dynamics (CFD) calculations of oxyfuel combustion. The statistical narrow band (SNB) and correlated-k (CK) models are used to calculate benchmark data for the radiative source term and heat flux, which are then compared to the results calculated from FSK models. Both the full-spectrum correlated k (FSCK) and the full-spectrum scaled k (FSSK) models are applied using up-to-date spectral data. The results show that the FSCK and FSSK methods achieve good agreement in the test cases. The FSCK method using a five-point Gauss quadrature scheme is recommended for CFD calculations in oxyfuel conditions, however there are still potential inaccuracies in cases with very wide variations in the ratio between CO2 and H2O concentrations.

On the performance of dual-hop mixed RF/FSO wireless communication system in urban area over aggregated exponentiated Weibull fading channels with pointing errors

NASA Astrophysics Data System (ADS)

Wang, Yue; Wang, Ping; Liu, Xiaoxia; Cao, Tian

2018-03-01

The performance of decode-and-forward dual-hop mixed radio frequency / free-space optical system in urban area is studied. The RF link is modeled by the Nakagami-m distribution and the FSO link is described by the composite exponentiated Weibull (EW) fading channels with nonzero boresight pointing errors (NBPE). For comparison, the ABER results without pointing errors (PE) and those with zero boresight pointing errors (ZBPE) are also provided. The closed-form expression for the average bit error rate (ABER) in RF link is derived with the help of hypergeometric function, and that in FSO link is obtained by Meijer's G and generalized Gauss-Laguerre quadrature functions. Then, the end-to-end ABERs with binary phase shift keying modulation are achieved on the basis of the computed ABER results of RF and FSO links. The end-to-end ABER performance is further analyzed with different Nakagami-m parameters, turbulence strengths, receiver aperture sizes and boresight displacements. The result shows that with ZBPE and NBPE considered, FSO link suffers a severe ABER degradation and becomes the dominant limitation of the mixed RF/FSO system in urban area. However, aperture averaging can bring significant ABER improvement of this system. Monte Carlo simulation is provided to confirm the validity of the analytical ABER expressions.

Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems

DOE PAGES

Najm, Habib N.; Valorani, Mauro

2014-04-12

We explore the relation between the development of a non-negligible probability of negative states and the instability of numerical integration of the intrusive Galerkin ordinary differential equation system describing uncertain chemical ignition. To prevent this instability without resorting to either multi-element local polynomial chaos (PC) methods or increasing the order of the PC representation in time, we propose a procedure aimed at modifying the amplitude of the PC modes to bring the probability of negative state values below a user-defined threshold. This modification can be effectively described as a filtering procedure of the spectral PC coefficients, which is applied on-the-flymore » during the numerical integration when the current value of the probability of negative states exceeds the prescribed threshold. We demonstrate the filtering procedure using a simple model of an ignition process in a batch reactor. This is carried out by comparing different observables and error measures as obtained by non-intrusive Monte Carlo and Gauss-quadrature integration and the filtered intrusive procedure. Lastly, the filtering procedure has been shown to effectively stabilize divergent intrusive solutions, and also to improve the accuracy of stable intrusive solutions which are close to the stability limits.« less

Estimating overall exposure effects for the clustered and censored outcome using random effect Tobit regression models.

PubMed

Wang, Wei; Griswold, Michael E

2016-11-30

The random effect Tobit model is a regression model that accommodates both left- and/or right-censoring and within-cluster dependence of the outcome variable. Regression coefficients of random effect Tobit models have conditional interpretations on a constructed latent dependent variable and do not provide inference of overall exposure effects on the original outcome scale. Marginalized random effects model (MREM) permits likelihood-based estimation of marginal mean parameters for the clustered data. For random effect Tobit models, we extend the MREM to marginalize over both the random effects and the normal space and boundary components of the censored response to estimate overall exposure effects at population level. We also extend the 'Average Predicted Value' method to estimate the model-predicted marginal means for each person under different exposure status in a designated reference group by integrating over the random effects and then use the calculated difference to assess the overall exposure effect. The maximum likelihood estimation is proposed utilizing a quasi-Newton optimization algorithm with Gauss-Hermite quadrature to approximate the integration of the random effects. We use these methods to carefully analyze two real datasets. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

NASA Astrophysics Data System (ADS)

Rai, Prashant; Sargsyan, Khachik; Najm, Habib; Hermes, Matthew R.; Hirata, So

2017-09-01

A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss-Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm-1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

Magnetic potential, vector and gradient tensor fields of a tesseroid in a geocentric spherical coordinate system

NASA Astrophysics Data System (ADS)

Du, Jinsong; Chen, Chao; Lesur, Vincent; Lane, Richard; Wang, Huilin

2015-06-01

We examined the mathematical and computational aspects of the magnetic potential, vector and gradient tensor fields of a tesseroid in a geocentric spherical coordinate system (SCS). This work is relevant for 3-D modelling that is performed with lithospheric vertical scales and global, continent or large regional horizontal scales. The curvature of the Earth is significant at these scales and hence, a SCS is more appropriate than the usual Cartesian coordinate system (CCS). The 3-D arrays of spherical prisms (SP; `tesseroids') can be used to model the response of volumes with variable magnetic properties. Analytical solutions do not exist for these model elements and numerical or mixed numerical and analytical solutions must be employed. We compared various methods for calculating the response in terms of accuracy and computational efficiency. The methods were (1) the spherical coordinate magnetic dipole method (MD), (2) variants of the 3-D Gauss-Legendre quadrature integration method (3-D GLQI) with (i) different numbers of nodes in each of the three directions, and (ii) models where we subdivided each SP into a number of smaller tesseroid volume elements, (3) a procedure that we term revised Gauss-Legendre quadrature integration (3-D RGLQI) where the magnetization direction which is constant in a SCS is assumed to be constant in a CCS and equal to the direction at the geometric centre of each tesseroid, (4) the Taylor's series expansion method (TSE) and (5) the rectangular prism method (RP). In any realistic application, both the accuracy and the computational efficiency factors must be considered to determine the optimum approach to employ. In all instances, accuracy improves with increasing distance from the source. It is higher in the percentage terms for potential than the vector or tensor response. The tensor errors are the largest, but they decrease more quickly with distance from the source. In our comparisons of relative computational efficiency, we found

Numerical Grid Generation and Potential Airfoil Analysis and Design

DTIC Science & Technology

1988-01-01

Gauss- Seidel , SOR and ADI iterative methods e JACOBI METHOD In the Jacobi method each new value of a function is computed entirely from old values...preceding iteration and adding the inhomogeneous (boundary condition) term. * GAUSS- SEIDEL METHOD When we compute I in a Jacobi method, we have already...Gauss- Seidel method. Sufficient condition for p convergence of the Gauss- Seidel method is diagonal-dominance of [A].9W e SUCESSIVE OVER-RELAXATION (SOR

Vector-beam solutions of Maxwell's wave equation.

PubMed

Hall, D G

1996-01-01

The Hermite-Gauss and Laguerre-Gauss modes are well-known beam solutions of the scalar Helmholtz equation in the paraxial limit. As such, they describe linearly polarized fields or single Cartesian components of vector fields. The vector wave equation admits, in the paraxial limit, of a family of localized Bessel-Gauss beam solutions that can describe the entire transverse electric field. Two recently reported solutions are members of this family of vector Bessel-Gauss beam modes.

Precessional forcing of lacustrine sedimentation in the late Cenozoic Chemeron Basin, Central Kenya Rift, and calibration of the Gauss/Matuyama boundary

USGS Publications Warehouse

Deino, A.L.; Kingston, J.D.; Glen, J.M.; Edgar, R.K.; Hill, A.

2006-01-01

The fluviolacustrine sedimentary sequence of the Chemeron Formation exposed in the Barsemoi River drainage, Tugen Hills, Kenya, contains a package of five successive diatomite/fluvial cycles that record the periodic development of freshwater lakes within the axial portion of the Central Kenya Rift. The overwhelming abundance in the diatomite of planktonic species of the genera Aulacoseira and Stephanodiscus, and the virtual absence of benthic littoral diatoms and detrital material indicate areally extensive, deep lake systems. A paleomagnetic reversal stratigraphy has been determined and chronostratigraphic tie points established by 40Ar/39Ar dating of intercalated tuffs. The sequence spans the interval 3.1-2.35??Ma and bears a detailed record of the Gauss/Matuyama paleomagnetic transition. The 40Ar/39Ar age for this boundary of 2.589 ?? 0.003??Ma can be adjusted to concordance with the Astronomical Polarity Time Scale (APTS) on the basis of an independent calibration to 2.610??Ma, 29??kyr older than the previous APTS age. The diatomites recur at an orbital precessional interval of 23??kyr and are centered on a 400-kyr eccentricity maximum. It is concluded that these diatomite/fluvial cycles reflect a narrow interval of orbitally forced wet/dry climatic conditions that may be expressed regionally across East Africa. The timing of the lacustrine pulses relative to predicted insolation models favors origination of moisture from the northern Africa monsoon, rather than local circulation driven by direct equatorial insolation. This moisture event at 2.7-2.55??Ma, and later East African episodes at 1.9-1.7 and 1.1-0.9??Ma, are approximately coincident with major global climatic and oceanographic events. ?? 2006 Elsevier B.V. All rights reserved.

Computing the total atmospheric refraction for real-time optical imaging sensor simulation

NASA Astrophysics Data System (ADS)

Olson, Richard F.

2015-05-01

Fast and accurate computation of light path deviation due to atmospheric refraction is an important requirement for real-time simulation of optical imaging sensor systems. A large body of existing literature covers various methods for application of Snell's Law to the light path ray tracing problem. This paper provides a discussion of the adaptation to real time simulation of atmospheric refraction ray tracing techniques used in mid-1980's LOWTRAN releases. The refraction ray trace algorithm published in a LOWTRAN-6 technical report by Kneizys (et. al.) has been coded in MATLAB for development, and in C-language for simulation use. To this published algorithm we have added tuning parameters for variable path segment lengths, and extensions for Earth grazing and exoatmospheric "near Earth" ray paths. Model atmosphere properties used to exercise the refraction algorithm were obtained from tables published in another LOWTRAN-6 related report. The LOWTRAN-6 based refraction model is applicable to atmospheric propagation at wavelengths in the IR and visible bands of the electromagnetic spectrum. It has been used during the past two years by engineers at the U.S. Army Aviation and Missile Research, Development and Engineering Center (AMRDEC) in support of several advanced imaging sensor simulations. Recently, a faster (but sufficiently accurate) method using Gauss-Chebyshev Quadrature integration for evaluating the refraction integral was adopted.

A Preliminary Formation Flying Orbit Dynamics Analysis for Leonardo-BRDF

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Mailhe, Laurie M.

2001-01-01

Leonardo-BRDF is a new NASA mission concept proposed to allow the investigation of radiative transfer and its effect on the Earth's climate and atmospheric phenomenon. Enabled by the recent developments in small-satellite and formation flying technology, the mission is envisioned to be composed of an array of spacecraft in carefully designed orbits. The different perspectives provided by a distributed array of spacecraft offer a unique advantage to study the Earth's albedo. This paper presents the flight dynamics analysis performed in the context of the Leonardo-BRDF science requirements. First, the albedo integral is investigated and the effect of viewing geometry on science return is studied. The method used in this paper, based on Gauss quadrature, provides the optimal formation geometry to ensure that the value of the integral is accurately approximated. An orbit design approach is presented to achieve specific relative orbit geometries while simultaneously satisfying orbit dynamics constraints to reduce formation-keeping fuel expenditure. The relative geometry afforded by the design is discussed in terms of mission requirements. An optimal Lambert initialization scheme is presented with the required DeltaV to distribute all spacecraft from a common parking orbit into their appropriate orbits in the formation. Finally, formation-keeping strategies are developed and the associated DeltaV's are calculated to maintain the formation in the presence of perturbations.

Robust Bayesian Experimental Design for Conceptual Model Discrimination

NASA Astrophysics Data System (ADS)

Pham, H. V.; Tsai, F. T. C.

2015-12-01

A robust Bayesian optimal experimental design under uncertainty is presented to provide firm information for model discrimination, given the least number of pumping wells and observation wells. Firm information is the maximum information of a system can be guaranteed from an experimental design. The design is based on the Box-Hill expected entropy decrease (EED) before and after the experiment design and the Bayesian model averaging (BMA) framework. A max-min programming is introduced to choose the robust design that maximizes the minimal Box-Hill EED subject to that the highest expected posterior model probability satisfies a desired probability threshold. The EED is calculated by the Gauss-Hermite quadrature. The BMA method is used to predict future observations and to quantify future observation uncertainty arising from conceptual and parametric uncertainties in calculating EED. Monte Carlo approach is adopted to quantify the uncertainty in the posterior model probabilities. The optimal experimental design is tested by a synthetic 5-layer anisotropic confined aquifer. Nine conceptual groundwater models are constructed due to uncertain geological architecture and boundary condition. High-performance computing is used to enumerate all possible design solutions in order to identify the most plausible groundwater model. Results highlight the impacts of scedasticity in future observation data as well as uncertainty sources on potential pumping and observation locations.

Estimating multilevel logistic regression models when the number of clusters is low: a comparison of different statistical software procedures.

PubMed

Austin, Peter C

2010-04-22

Multilevel logistic regression models are increasingly being used to analyze clustered data in medical, public health, epidemiological, and educational research. Procedures for estimating the parameters of such models are available in many statistical software packages. There is currently little evidence on the minimum number of clusters necessary to reliably fit multilevel regression models. We conducted a Monte Carlo study to compare the performance of different statistical software procedures for estimating multilevel logistic regression models when the number of clusters was low. We examined procedures available in BUGS, HLM, R, SAS, and Stata. We found that there were qualitative differences in the performance of different software procedures for estimating multilevel logistic models when the number of clusters was low. Among the likelihood-based procedures, estimation methods based on adaptive Gauss-Hermite approximations to the likelihood (glmer in R and xtlogit in Stata) or adaptive Gaussian quadrature (Proc NLMIXED in SAS) tended to have superior performance for estimating variance components when the number of clusters was small, compared to software procedures based on penalized quasi-likelihood. However, only Bayesian estimation with BUGS allowed for accurate estimation of variance components when there were fewer than 10 clusters. For all statistical software procedures, estimation of variance components tended to be poor when there were only five subjects per cluster, regardless of the number of clusters.

Logistic Regression with Multiple Random Effects: A Simulation Study of Estimation Methods and Statistical Packages.

PubMed

Kim, Yoonsang; Choi, Young-Ku; Emery, Sherry

2013-08-01

Several statistical packages are capable of estimating generalized linear mixed models and these packages provide one or more of three estimation methods: penalized quasi-likelihood, Laplace, and Gauss-Hermite. Many studies have investigated these methods' performance for the mixed-effects logistic regression model. However, the authors focused on models with one or two random effects and assumed a simple covariance structure between them, which may not be realistic. When there are multiple correlated random effects in a model, the computation becomes intensive, and often an algorithm fails to converge. Moreover, in our analysis of smoking status and exposure to anti-tobacco advertisements, we have observed that when a model included multiple random effects, parameter estimates varied considerably from one statistical package to another even when using the same estimation method. This article presents a comprehensive review of the advantages and disadvantages of each estimation method. In addition, we compare the performances of the three methods across statistical packages via simulation, which involves two- and three-level logistic regression models with at least three correlated random effects. We apply our findings to a real dataset. Our results suggest that two packages-SAS GLIMMIX Laplace and SuperMix Gaussian quadrature-perform well in terms of accuracy, precision, convergence rates, and computing speed. We also discuss the strengths and weaknesses of the two packages in regard to sample sizes.

A Preliminary Formation Flying Orbit Dynamics Analysis for Leonardo-BRDF

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Mailhe, Laurie M.

2001-01-01

Leonardo-BRDF is a NASA mission concept proposed to allow the investigation of radiative transfer and its effect on the Earth's climate and atmospheric phenomenon. Enabled by the recent developments in small-satellite and formation flying technology, the mission is envisioned to be composed of an array of spacecraft in carefully designed orbits. The different perspectives provided by a distributed array of spacecraft offer a unique advantage to study the Earth's albedo. This paper presents the orbit dynamics analysis performed in the context of the Leonardo-BRDF science requirements. First, the albedo integral is investigated and the effect of viewing geometry on science return is studied. The method used in this paper, based on Gauss quadrature, provides the optimal formation geometry to ensure that the value of the integral is accurately approximated. An orbit design approach is presented to achieve specific relative orbit geometries while simultaneously satisfying orbit dynamics constraints to reduce formation-keeping fuel expenditure. The relative geometry afforded by the design is discussed in terms of mission requirements. An optimal two-burn initialization scheme is presented with the required delta-V to distribute all spacecraft from a common parking orbit into their appropriate orbits in the formation. Finally, formation-keeping strategies are developed and the associated delta-V's are calculated to maintain the formation in the presence of perturbations.

Flight Dynamics Analysis for Leonardo-BRDF

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Mailhe, Laurie; Bauer, Frank H. (Technical Monitor)

2000-01-01

Leonardo-BRDF (Bidirectional Reflectance Distribution Function) is a new NASA mission concept proposed to allow the investigation of radiative transfer and its effect on the Earth's climate and atmospheric phenomenon. Enabled by the recent developments in small-satellite and formation flying technology, the mission is envisioned to be composed of an array of spacecraft in carefully designed orbits. The different perspectives provided by a distributed array of spacecraft offer a unique advantage to study the Earth's albedo. This paper presents the flight dynamics analysis performed in the context of the Leonardo-BRDF science requirements. First, the albedo integral is investigated and the effect of viewing geometry on science return is studied. The method used in this paper, based on Gauss quadrature, provides the optimal formation geometry to ensure that the value of the integral is accurately approximated. An orbit design approach is presented to achieve specific relative orbit geometries while simultaneously satisfying orbit dynamics constraints to reduce formation-keeping fuel expenditure. The relative geometry afforded by the design is discussed in terms of mission requirements. An optimal Lambert initialization scheme is presented with the required Delta-V to distribute all spacecraft from a common parking orbit into their appropriate orbits in the formation. Finally, formation-keeping strategies are developed and the associated Delta-V's are calculated to maintain the formation in the presence of perturbations.

The Relationship Between the Expansion Speed and Radial Speed of CMEs Confirmed Using Quadrature Observations of the 2011 February 15 CME

NASA Astrophysics Data System (ADS)

Gopalswamy, N.; Makela, P.; Yashiro, S.; Davila, J. M.

2012-08-01

It is difficult to measure the true speed of Earth-directed CMEs from a coronagraph along the Sun-Earth line because of the occulting disk. However, the expansion speed (the speed with which the CME appears to spread in the sky plane) can be measured by such coronagraph. In order to convert the expansion speed to radial speed (which is important for space weather applications) one can use empirical relationship between the two that assumes an average width for all CMEs. If we have the width information from quadrature observations, we can confirm the relationship between expansion and radial speeds derived by Gopalswamy et al. (2009a). The STEREO spacecraft were in qudrature with SOHO (STEREO-A ahead of Earth by 87oand STEREO-B 94obehind Earth) on 2011 February 15, when a fast Earth-directed CME occurred. The CME was observed as a halo by the Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO. The sky-plane speed was measured by SOHO/LASCO as the expansion speed, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images measured the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (Vexp) and radial speed (Vrad) derived previously from geometrical considerations (Gopalswamy et al. 2009a): Vrad=1/2 (1 + cot w)Vexp, where w is the half width of the CME. STEREO-B images of the CME, we found that CME had a full width of 7 6o, so w=3 8o. This gives the relation as Vrad=1.1 4 Vexp. From LASCO observations, we measured Vexp=897 km/s, so we get the radial speed as 10 2 3 km/s. Direct measurement of radial speed yields 945 km/s (STEREO-A) and 105 8 km/s (STEREO-B). These numbers are different only by 7.6 % and 3.4 % (for STEREO-A and STEREO-B, respectively) from the computed value.

Studies on the Reduction of Intermodulation Generation in Communications Systems

DTIC Science & Technology

1980-07-07

AGENCY NAME & ADDRESS(ff dillfetmn from Controlling Office) IS. SECURITY CLASS. (of this report) Unclassified ISO . DECLASSIFICATION DOWNGRAD-ING SCHEDULE...FIELD 40GAUSS 120 GAUSS ISO GAUSS 340 GAUSS 1MG OSCILLOGRAMS OF 񓰨’ STAINLESS STEEL ADAPTER (SAMPLE A WITH EXTERNAL 2kHz AC MAGNETIC FIELD I PEAK...34P1 (,I P,2 -90- 7.07 GC; 0 V - iSo . .. _ 3D -100- AL(N23> ,-J/ -OLD/ / / OF-110 . O/ 070> V(HNS)// 2 -120 A(3080) , -i0.22 AL( NP) . / AG (H SI

Examination of Airborne FDEM System Attributes for UXO Mapping and Detection

DTIC Science & Technology

2009-11-01

quadrature output should only occur when there is a distortion in the transmitter waveform signal that correlates with the quadrature part of the...suggested that the S/N performance of the quadrature output of the two FDEM designs would be similar to the observed S/N of TEM systems, though...the semi-airborne configuration. We propose to extend the current SAIC codes to address this need, and to perform additional modeling using codes

Rows of optical vortices from elliptically perturbing a high-order beam

NASA Astrophysics Data System (ADS)

Dennis, Mark R.

2006-05-01

An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit-strength vortices is described. This behavior is studied in helical Ince-Gauss beams and astigmatic, generalized Hermite-Laguerre-Gauss beams, which are perturbations of Laguerre-Gauss beams. Approximations of these beams are derived for small perturbations, in which a neighborhood of the axis can be approximated by a polynomial in the complex plane: a Chebyshev polynomial for Ince-Gauss beams, and a Hermite polynomial for astigmatic beams.

Structural changes in the hot Algol OGLE-LMC-DPV-097 and its disc related to its long cycle

NASA Astrophysics Data System (ADS)

Garcés L, J.; Mennickent, R. E.; Djurašević, G.; Poleski, R.; Soszyński, I.

2018-06-01

Double Periodic Variables (DPVs) are hot Algols showing a long photometric cycle of uncertain origin. We report the discovery of changes in the orbital light curve of OGLE-LMC-DPV-097 which depend on the phase of its long photometric cycle. During the ascending branch of the long cycle the brightness at the first quadrature is larger than during the second quadrature, during the maximum of the long cycle the brightness is basically the same at both quadratures, during the descending branch the brightness at the second quadrature is larger than during the first quadrature, and during the minimum of the long cycle the secondary minimum disappears. We model the light curve at different phases of the long cycle and find that the data are consistent with changes in the properties of the accretion disc and two disc spots. The disc's size and temperature change with the long-cycle period. We find a smaller and hotter disc at minimum, and larger and cooler disc at maximum. The spot temperatures, locations, and angular sizes also show variability during the long cycle.

Numerical Computation of Subsonic Conical Diffuser Flows with Nonuniform Turbulent Inlet Conditions

DTIC Science & Technology

1977-09-01

Gauss - Seidel Point Iteration Method . . . . . . . . . . . . . . . 7.0 FACTORS AFFECTING THE RATE OF CONVERGENCE OF THE POINT...can be solved in several ways. For simplicity, a standard Gauss - Seidel iteration method is used to obtain the solution . The method updates the...FACTORS AFFECTING THE RATE OF CONVERGENCE OF THE POINT ITERATION ,ŘETHOD The advantage of using the Gauss - Seidel point iteration method to

Analytical evaluation of the combined influence of polarization mode dispersion and group velocity dispersion on the bit error rate performance of optical homodyne quadrature phase-shift keying systems

NASA Astrophysics Data System (ADS)

Taher, Kazi Abu; Majumder, Satya Prasad

2017-12-01

A theoretical approach is presented to evaluate the bit error rate (BER) performance of an optical fiber transmission system with quadrature phase-shift keying (QPSK) modulation under the combined influence of polarization mode dispersion (PMD) and group velocity dispersion (GVD) in a single-mode fiber (SMF). The analysis is carried out without and with polarization division multiplexed (PDM) transmission considering a coherent homodyne receiver. The probability density function (pdf) of the random phase fluctuations due to PMD and GVD at the output of the receiver is determined analytically, considering the pdf of differential group delay (DGD) to be Maxwellian distribution and that of GVD to be Gaussian approximation. The exact pdf of the phase fluctuation due to PMD and GVD is also evaluated from its moments using a Monte Carlo simulation technique. Average BER is evaluated by averaging the conditional BER over the pdf of the random phase fluctuation. The BER performance results are evaluated for different system parameters. It is found that PDM-QPSK coherent homodyne system suffers more power penalty than the homodyne QPSK system without PDM. A PDM-QPSK system suffers a penalty of 4.3 dB whereas power penalty of QPSK system is 3.0 dB at a BER of 10-9 for DGD of 0.8 Tb and GVD of 1700 ps/nm. Analytical results are compared with the experimental results reported earlier and found to have good conformity.

Bearings Only Tracking with Fusion from Heterogenous Passive Sensors: ESM/EO and Acoustic

DTIC Science & Technology

2017-02-01

consists of an unscented Kalman filter (UKF) to handle in-sequence ESM/EO measurements and an OOSM unscented Gauss-Helmert filter (OOSM-UGHF) to handle out...bearings-only tracking, target motion analysis, unscented Gauss-Helmert filter , out-of-sequence measurement. I. INTRODUCTION The commonly used passive...proposed an unscented Gauss-Helmert filter (UGHF) [22] [21] to solve this problem. The existing UGHF works with in-sequence measurements. Further

Circadian Rhythms in Plants, Insects and Mammals Exposed to ELF Magnetic and/or Electric Fields and Currents

DTIC Science & Technology

1975-08-28

favorable to the model. Parameter estimates from this fitting process, carried out in the nature of a "moving-average" throughout the cntilre serces of...34OWOLS Pl %%t4)1 uSSvMS~ USA NIWW 162-7-020 r,.6/WEfg 4/R:0 GAUSS.8:O.5 GAUSS.C:I.O GAUSS.D:2.0 GAtJ$ 360 :24 i ONCHRNHEC SCHOUL if .) 75.2 40.0 20

Performance Benchmark for a Prismatic Flow Solver

DTIC Science & Technology

2007-03-26

Gauss- Seidel (LU-SGS) implicit method is used for time integration to reduce the computational time. A one-equation turbulence model by Goldberg and...numerical flux computations. The Lower-Upper-Symmetric Gauss- Seidel (LU-SGS) implicit method [1] is used for time integration to reduce the...Sharov, D. and Nakahashi, K., “Reordering of Hybrid Unstructured Grids for Lower-Upper Symmetric Gauss- Seidel Computations,” AIAA Journal, Vol. 36

A Two-Dimensional Helmholtz Equation Solution for the Multiple Cavity Scattering Problem

DTIC Science & Technology

2013-02-01

obtained by using the block Gauss – Seidel iterative meth- od. To show the convergence of the iterative method, we define the error between two...models to the general multiple cavity setting. Numerical examples indicate that the convergence of the Gauss – Seidel iterative method depends on the...variational approach. A block Gauss – Seidel iterative method is introduced to solve the cou- pled system of the multiple cavity scattering problem, where

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dehghani, M.H.; Department of Physics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1; Perimeter Institute for Theoretical Physics, 35 Caroline Street North, Waterloo, Ontario

We investigate the existence of Taub-NUT (Newman-Unti-Tamburino) and Taub-bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in d dimensions. We find that for all nonextremal NUT solutions of Einstein gravity having no curvature singularity at r=N, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter {alpha} goes to zero. Furthermore there are no NUT solutions in Gauss-Bonnet gravity that yield nonextremal NUT solutions to Einstein gravity having a curvature singularity at r=N in the limit {alpha}{yields}0. Indeed, we have nonextreme NUT solutions in 2+2k dimensions withmore » nontrivial fibration only when the 2k-dimensional base space is chosen to be CP{sup 2k}. We also find that the Gauss-Bonnet gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a two-dimensional factor space of positive curvature. Indeed, when the base space has at most one positively curved two-dimensional space as one of its factor spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though there a curvature singularity exists at r=N. We also find that one can have bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces of zero or positive constant curvature. The only case for which one does not have bolt solutions is in the absence of a cosmological term with zero curvature base space.« less

Impact of inhalational exposure to ethanol fuel on the pharmacokinetics of verapamil, ibuprofen and fluoxetine as in vivo probe drugs for CYP3A, CYP2C and CYP2D in rats.

PubMed

Cardoso, Juciane Lauren Cavalcanti; Lanchote, Vera Lucia; Pereira, Maria Paula Marques; Capela, Jorge Manuel Vieira; de Moraes, Natália Valadares; Lepera, José Salvador

2015-10-01

Occupational toxicology and clinical pharmacology integration will be useful to understand potential exposure-drug interaction and to shape risk assessment strategies in order to improve occupational health. The aim of the present study was to evaluate the effect of exposure to ethanol fuel on in vivo activities of cytochrome P450 (CYP) isoenzymes CYP3A, CYP2C and CYP2D by the oral administration of the probe drugs verapamil, ibuprofen and fluoxetine. Male Wistar rats exposed to filtered air or to 2000 ppm ethanol in a nose-only inhalation chamber during (6 h/day, 5 days/week, 6 weeks) received single oral doses of 10 mg/kg verapamil or 25 mg/kg ibuprofen or 10 mg/kg fluoxetine. The enantiomers of verapamil, norverapamil, ibuprofen and fluoxetine in plasma were analyzed by LC-MS/MS. The area under the curve plasma concentration versus time extrapolated to infinity (AUC(0-∞)) was calculated using the Gauss-Laguerre quadrature. Inhalation exposure to ethanol reduces the AUC of both verapamil (approximately 2.7 fold) and norverapamil enantiomers (>2.5 fold), reduces the AUC(0-∞) of (+)-(S)-IBU (approximately 2 fold) and inhibits preferentially the metabolism of (-)-(R)-FLU. In conclusion, inhalation exposure of ethanol at a concentration of 2 TLV-STEL (6 h/day for 6 weeks) induces CYP3A and CYP2C but inhibits CYP2D in rats. Copyright © 2015 Elsevier Ltd. All rights reserved.

Numerical integration of discontinuous functions: moment fitting and smart octree

NASA Astrophysics Data System (ADS)

Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander

2017-11-01

A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.

Quantum frequency up-conversion of continuous variable entangled states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Wenyuan; Wang, Ning; Li, Zongyang

We demonstrate experimentally quantum frequency up-conversion of a continuous variable entangled optical field via sum-frequency-generation process. The two-color entangled state initially entangled at 806 and 1518 nm with an amplitude quadrature difference squeezing of 3.2 dB and phase quadrature sum squeezing of 3.1 dB is converted to a new entangled state at 530 and 1518 nm with the amplitude quadrature difference squeezing of 1.7 dB and phase quadrature sum squeezing of 1.8 dB. Our implementation enables the observation of entanglement between two light fields spanning approximately 1.5 octaves in optical frequency. The presented scheme is robust to the excess amplitude and phase noises of the pumpmore » field, making it a practical building block for quantum information processing and communication networks.« less

Large Deviations and Quasipotential for Finite State Mean Field Interacting Particle Systems

DTIC Science & Technology

2014-05-01

The conclusion then follows by applying Lemma 4.4.2. 132 119 4.4.1 Iterative solver: The widest neighborhood structure We employ Gauss - Seidel ...nearest neighborhood structure described in Section 4.4.2. We use Gauss - Seidel iterative method for our numerical experiments. The Gauss - Seidel ...x ∈ Bh, M x ∈ Sh\\Bh, where M ∈ (V,∞) is a very large number, so that the iteration (4.5.1) converges quickly. For simplicity, we restrict our

A Fast and Accurate Algorithm for l1 Minimization Problems in Compressive Sampling (Preprint)

DTIC Science & Technology

2013-01-22

However, updating uk+1 via the formulation of Step 2 in Algorithm 1 can be implemented through the use of the component-wise Gauss - Seidel iteration which...may accelerate the rate of convergence of the algorithm and therefore reduce the total CPU-time consumed. The efficiency of component-wise Gauss - Seidel ...Micchelli, L. Shen, and Y. Xu, A proximity algorithm accelerated by Gauss - Seidel iterations for L1/TV denoising models, Inverse Problems, 28 (2012), p

Generalizations of the Alternating Direction Method of Multipliers for Large-Scale and Distributed Optimization

DTIC Science & Technology

2014-05-01

exact one is solved later — as- signed as step 5 of Algorithm 2 — because at each iteration , the ADMM updates the variables in the Gauss - Seidel ...Jacobi ADMM (see Algo- rithm 5 below). Unlike the Gauss - Seidel ADMM, the Jacobi ADMM updates all the 70 blocks in parallel at every iteration : xk+1i...that extending ADMM straightforwardly from the classic Gauss - Seidel setting to the Jacobi setting, from two blocks to multiple blocks, will preserve

Proceedings of the Fourth Annual U.S. Army Conference on Applied Statistics, 21-23 October 1998.

DTIC Science & Technology

1999-11-01

1833) published a memoir Nouvelles mithodes pour la determination des cometes in which he introduced and named the method of least squares. In 1809...251,1972. 2. Sprott, D. A. "Gauss’s Contributions to Statistics." Historia Mathematica, vol. 5, pp. 183-203,1978. 3. Stigler, S. M. "An Attack on Gauss...Published by Legendre in 1820." Historia Mathematica. vol. 4, pp. 31-35, 1977. 4. Stigler, S. M. "Gauss and the Invention of Least Squares." The

Apparatus and method for enhancing tissue repair in mammals

NASA Technical Reports Server (NTRS)

Goodwin, Thomas J. (Inventor); Parker, Clayton R. (Inventor)

2009-01-01

An apparatus is introduced for the use of enhancing tissue repair in mammals. The apparatus includes a sleeve; an electrically conductive coil; a sleeve support; an electrical circuit configured to supply the coil with a square wave time varying electrical current sufficient to create approximately 0.05 gauss to 0.5 gauss. When in use, the sleeve of the apparatus is placed on a mammalian body part and the time varying electromagnetic force of from approximately 0.05 gauss to 0.5 gauss is generated on the mammalian body for an extended period of time so that the tissue is encouraged to be regenerated in the mammalian body part at a rate in excess of the normal tissue regeneration rate relative to regeneration without application of the time varying electromagnetic force.