Positive quadrature formulas III
NASA Astrophysics Data System (ADS)
Peherstorfer, Franz
2008-12-01
First we discuss briefly our former characterization theorem for positive interpolation quadrature formulas (abbreviated qf), provide an equivalent characterization in terms of Jacobi matrices, and give links and applications to other qf, in particular to Gauss-Kronrod quadratures and recent rediscoveries. Then for any polynomial t_n which generates a positive qf, a weight function (depending on n ) is given with respect to which t_n is orthogonal to mathbb{P}_{n-1} . With the help of this result an asymptotic representation of the quadrature weights is derived. In general the asymptotic behaviour is different from that of the Gaussian weights. Only under additional conditions do the quadrature weights satisfy the so-called circle law. Corresponding results are obtained for positive qf of Radau and Lobatto type.
Buchenauer, C.J.
1981-09-23
The quadrature phase angle phi (t) of a pair of quadrature signals S/sub 1/(t) and S/sub 2/(t) is digitally encoded on a real time basis by a quadrature digitizer for fractional phi (t) rotational excursions and by a quadrature up/down counter for full phi (t) rotations. The pair of quadrature signals are of the form S/sub 1/(t) = k(t) sin phi (t) and S/sub 2/(t) = k(t) cos phi (t) where k(t) is a signal common to both. The quadrature digitizer and the quadrature up/down counter may be used together or singularly as desired or required. Optionally, a digital-to-analog converter may follow the outputs of the quadrature digitizer and the quadrature up/down counter to provide an analog signal output of the quadrature phase angle phi (t).
Buchenauer, C. Jerald
1984-01-01
The quadrature phase angle .phi.(t) of a pair of quadrature signals S.sub.1 (t) and S.sub.2 (t) is digitally encoded on a real time basis by a quadrature digitizer for fractional .phi.(t) rotational excursions and by a quadrature up/down counter for full .phi.(t) rotations. The pair of quadrature signals are of the form S.sub.1 (t)=k(t) sin .phi.(t) and S.sub.2 (t)=k(t) cos .phi.(t) where k(t) is a signal common to both. The quadrature digitizer and the quadrature up/down counter may be used together or singularly as desired or required. Optionally, a digital-to-analog converter may follow the outputs of the quadrature digitizer and the quadrature up/down counter to provide an analog signal output of the quadrature phase angle .phi.(t).
Quadrature Mixer LO Leakage Suppression Through Quadrature DC Bias
BALDWIN, JESSE G; DUBBERT, DALE F.
2002-05-01
A new concept has been developed which allows direct-to-RF conversion of digitally synthesized waveforms. The concept named Quadrature Error Corrected Digital Waveform Synthesis (QECDWS) employs quadrature amplitude and phase predistortion to the complex waveform to reduce the undesirable quadrature image. Another undesirable product of QECDWS-based RF conversion is the Local Oscillator (LO) leakage through the quadrature upconverter (mixer). A common technique for reducing this LO leakage is to apply a quadrature bias to the mixer I and Q inputs. This report analyzes this technique through theory, lab measurement, and data analysis for a candidate quadrature mixer for Synthetic Aperture Radar (SAR) applications.
Quadrature wavelength scanning interferometry.
Moschetti, Giuseppe; Forbes, Alistair; Leach, Richard K; Jiang, Xiang; O'Connor, Daniel
2016-07-10
A novel method to double the measurement range of wavelength scanning interferometery (WSI) is described. In WSI the measured optical path difference (OPD) is affected by a sign ambiguity, that is, from an interference signal it is not possible to distinguish whether the OPD is positive or negative. The sign ambiguity can be resolved by measuring an interference signal in quadrature. A method to obtain a quadrature interference signal for WSI is described, and a theoretical analysis of the advantages is reported. Simulations of the advantages of the technique and of signal errors due to nonideal quadrature are discussed. The analysis and simulation are supported by experimental measurements to show the improved performances. PMID:27409307
NASA Astrophysics Data System (ADS)
Monien, H.
2010-04-01
Gaussian quadrature is a well-known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums has found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of Gaussian formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a kink singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has a very rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters.
Quadrature, Interpolation and Observability
NASA Technical Reports Server (NTRS)
Hodges, Lucille McDaniel
1997-01-01
Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method to certain non-polynomial functions as early as 1884. Conditions that guarantee the existence of quadrature formulas for certain collections of functions were studied by Tchebycheff, and his work was extended by others. Today, a class of functions which satisfies these conditions is called a Tchebycheff System. This thesis contains the definition of a Tchebycheff System, along with the theorems, proofs, and definitions necessary to guarantee the existence of quadrature formulas for such systems. Solutions of discretely observable linear control systems are of particular interest, and observability with respect to a given output function is defined. The output function is written as a linear combination of a collection of orthonormal functions. Orthonormal functions are defined, and their properties are discussed. The technique for evaluating the coefficients in the output function involves evaluating the definite integral of functions which can be shown to form a Tchebycheff system. Therefore, quadrature formulas for these integrals exist, and in many cases are known. The technique given is useful in cases where the method of direct calculation is unstable. The condition number of a matrix is defined and shown to be an indication of the the degree to which perturbations in data affect the accuracy of the solution. In special cases, the number of data points required for direct calculation is the same as the number required by the method presented in this thesis. But the method is shown to require more data points in other cases. A lower bound for the number of data points required is given.
Digital quadrature phase detection
Smith, J.A.; Johnson, J.A.
1992-05-26
A system for detecting the phase of a frequency or phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2[pi] when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2[pi] when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention. 6 figs.
Digital quadrature phase detection
Smith, James A.; Johnson, John A.
1992-01-01
A system for detecting the phase of a frequency of phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2.pi. when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2.pi. when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention.
Optimized quadrature surface coil designs
Kumar, Ananda; Bottomley, Paul A.
2008-01-01
Background Quadrature surface MRI/MRS detectors comprised of circular loop and figure-8 or butterfly-shaped coils offer improved signal-to-noise-ratios (SNR) compared to single surface coils, and reduced power and specific absorption rates (SAR) when used for MRI excitation. While the radius of the optimum loop coil for performing MRI at depth d in a sample is known, the optimum geometry for figure-8 and butterfly coils is not. Materials and methods The geometries of figure-8 and square butterfly detector coils that deliver the optimum SNR are determined numerically by the electromagnetic method of moments. Figure-8 and loop detectors are then combined to create SNR-optimized quadrature detectors whose theoretical and experimental SNR performance are compared with a novel quadrature detector comprised of a strip and a loop, and with two overlapped loops optimized for the same depth at 3 T. The quadrature detection efficiency and local SAR during transmission for the three quadrature configurations are analyzed and compared. Results The SNR-optimized figure-8 detector has loop radius r8 ∼ 0.6d, so r8/r0 ∼ 1.3 in an optimized quadrature detector at 3 T. The optimized butterfly coil has side length ∼ d and crossover angle of ≥ 150° at the center. Conclusions These new design rules for figure-8 and butterfly coils optimize their performance as linear and quadrature detectors. PMID:18057975
Length Scales in Bayesian Automatic Adaptive Quadrature
NASA Astrophysics Data System (ADS)
Adam, Gh.; Adam, S.
2016-02-01
Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1-16 (2012)] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule), mesoscopic (Simpson rule), and macroscopic (quadrature sums of high algebraic degrees of precision). Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived.
Quadrature formulas for Fourier coefficients
NASA Astrophysics Data System (ADS)
Bojanov, Borislav; Petrova, Guergana
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives.
Error Analysis of Quadrature Rules. Classroom Notes
ERIC Educational Resources Information Center
Glaister, P.
2004-01-01
Approaches to the determination of the error in numerical quadrature rules are discussed and compared. This article considers the problem of the determination of errors in numerical quadrature rules, taking Simpson's rule as the principal example. It suggests an approach based on truncation error analysis of numerical schemes for differential…
A generalized discrepancy and quadrature error bound
NASA Astrophysics Data System (ADS)
Hickernell, F. J.
1998-01-01
An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which depends only on the quadrature rule, is defined as a generalized discrepancy. The generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the L-p-star discrepancy and P-alpha that arises in the study of lattice rules.
Gaussian quadrature formulae for arbitrary positive measures.
Fernandes, Andrew D; Atchley, William R
2006-01-01
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218
Antenna-array, phase quadrature tracking system
NASA Technical Reports Server (NTRS)
Cubley, H. D.
1970-01-01
Phase relationship between input signals appearing on widely-spaced parallel connected antenna elements in array is automatically adjusted in phase quadrature tracking system. Compact and lightweight design permit use in wide variety of airborne communications networks.
Structured eigenvalue problems for rational gauss quadrature
NASA Astrophysics Data System (ADS)
Fasino, Dario; Gemignani, Luca
2007-08-01
The connection between Gauss quadrature rules and the algebraic eigenvalue problem for a Jacobi matrix was first exploited in the now classical paper by Golub and Welsch (Math. Comput. 23(106), 221?230, 1969). From then on many computational problems arising in the construction of (polynomial) Gauss quadrature formulas have been reduced to solving direct and inverse eigenvalue problems for symmetric tridiagonals. Over the last few years (rational) generalizations of the classical Gauss quadrature formulas have been studied, i.e., formulas integrating exactly in spaces of rational functions. This paper wants to illustrate that stable and efficient procedures based on structured numerical linear algebra techniques can also be devised for the solution of the eigenvalue problems arising in the field of rational Gauss quadrature.
Calculates Angular Quadrature Weights and Cosines.
1988-02-18
DSNQUAD calculates the angular quadrature weights and cosines for use in CCC-254/ANISN-ORNL. The subroutines in DSNQUAD were lifted from the XSDRN-PM code, which is supplied with the CCC-475/ SCALIAS-77 package.
Past and Future SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, Steven; Poletto, G.
2006-01-01
With the launch of SOHO, it again became possible to carry out quadrature observations. In comparison with earlier observations, the new capabilities of coronal spectroscopy with UVCS and in situ ionization state and composition with Ulysses/SWICS enabled new types of studies. Results from two studies serve as examples: (i) The acceleration profile of wind from small coronal holes. (ii) A high-coronal reconnecting current sheet as the source of high ionization state Fe in a CME at Ulysses. Generally quadrature observations last only for a few days, when Ulysses is within ca. 5 degrees of the limb. This means luck is required for the phenomenon of interest to lie along the radial direction to Ulysses. However, when Ulysses is at high southern latitude in winter 2007 and high northern latitude in winter 2008, there will be unusually favorable configurations for quadrature observations with SOHO and corresponding bracketing limb observations from STEREO A/B. Specifically, Ulysses will be within 5 degrees of the limb from December 2006 to May 2007 and within 10 degrees of the limb from December 2007 to May 2008. These long-lasting quadratures and bracketing STEREO A/B observations overcome the limitations inherent in the short observation intervals of typical quadratures. Furthermore, ionization and charge state measurements like those on Ulysses will also be made on STEREO and these will be essential for identification of CME ejecta - one of the prime objectives for STEREO.
Quadrature formulae for problems in mechanics
NASA Astrophysics Data System (ADS)
Milovanović, Gradimir V.; Igić, Tomislav; Tončev, Novica
2012-09-01
The fast progress in recent years in symbolic computation and variable-precision arithmetic provide a possibility for generating the recursion coefficients in the three-term recurrence relation for orthogonal polynomials with respect to several nonclassical weight functions, as well as the construction of the corresponding quadrature rules of Gaussian type. Such quadratures are very important in many applications in engineering (fracture mechanics, damage mechanics, etc.), as well as in other computational and applied sciences. The boundary element method (BEM), finite element method (FEM), methods for solving integral equations, etc. very often require the numerical evaluation of one dimensional or multiple integrals with singular or near singular integrands with a high precision. In this paper we give some improvements of quadrature rules of Gaussian type with logarithmic and/or algebraic singularities. A numerical examples is included.
Summation Paths in Clenshaw-Curtis Quadrature
NASA Astrophysics Data System (ADS)
Adam, S.; Adam, Gh.
2016-02-01
Two topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion of the integrand is to be done within a mathematical structure consisting of the union of coefficient families ordered into complete binary trees. Second, the scrutiny of the decay rates of the involved even and odd rank Chebyshev expansion coefficients with the increase of their rank labels enables the definition of Bayesian decision paths for the advancement to the numerical output.
Composite Gauss-Legendre Quadrature with Error Control
ERIC Educational Resources Information Center
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
Runge-Kutta based generalized convolution quadrature
NASA Astrophysics Data System (ADS)
Lopez-Fernandez, Maria; Sauter, Stefan
2016-06-01
We present the Runge-Kutta generalized convolution quadrature (gCQ) with variable time steps for the numerical solution of convolution equations for time and space-time problems. We present the main properties of the method and a convergence result.
Gauss-Laguerre interval quadrature rule
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Cvetkovic, Aleksandar S.
2005-10-01
In this paper we prove the existence and uniqueness of the Gaussian interval quadrature formula with respect to the generalized Laguerre weight function. An algorithm for numerical construction has also investigated and some suitable solutions are proposed. A few numerical examples are included.
Error Bounds for Quadrature Methods Involving Lower Order Derivatives
ERIC Educational Resources Information Center
Engelbrecht, Johann; Fedotov, Igor; Fedotova, Tanya; Harding, Ansie
2003-01-01
Quadrature methods for approximating the definite integral of a function f(t) over an interval [a,b] are in common use. Examples of such methods are the Newton-Cotes formulas (midpoint, trapezoidal and Simpson methods etc.) and the Gauss-Legendre quadrature rules, to name two types of quadrature. Error bounds for these approximations involve…
Uniform positive-weight quadratures for discrete ordinate transport calculations
Carew, J.F.; Zamonsky, G.
1999-02-01
Mechanical quadratures that allow systematic improvement and solution convergence are derived for application of the discrete ordinates method to the Boltzmann transport equation. the quadrature directions are arranged on n latitudinal levels, are uniformly distributed over the unit sphere, and have positive weights. Both a uniform and equal-weight quadrature set UE{sub n} and a uniform and Gauss-weight quadrature set UG{sub n} are derived. These quadratures have the advantage over the standard level-symmetric LQ{sub n} quadrature sets in that the weights are positive for all orders, and the solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased the points approach a uniform continuous distribution on the unit sphere and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased. Numerical calculations were performed to evaluate the application of the UE{sub n} quadrature set. Comparisons of the exact moments and those calculated using the UE{sub n} quadrature set demonstrate that the moment integrals are performed accurately except for distributions that are very sharply peaked along the direction of the polar axis. A series of DORT transport calculations of the >1-Mev neutron flux for a typical reactor core/pressure vessel geometry were also carried out. These calculations employed the UE{sub n} (n = 6, 10, 12, 18, and 24) quadratures and indicate that the UE{sub n} solutions have converged to within {approximately}0.5%. The UE{sub 24} solutions were also found to be more accurate than the calculations performed with the S{sub 16} level-symmetric quadratures.
Optically controlled quadrature coupler on silicon substrate
NASA Astrophysics Data System (ADS)
Bhadauria, Avanish; Sharma, Sonia; Sonania, Shikha; Akhtar, Jamil
2016-03-01
In this paper, we have proposed and studied an optically controlled quadrature coupler fabricated on silicon substrate. The optically controlled quadrature coupler can be realized by terminating its coupled or through ports by optically induced load. Simulation and experimental results show that by varying optical intensity, we can control the phase and amplitude of output RF signal and can realize optically controlled reflection type attenuator, reflection type phase-shifter and ultrafast switches. The new kind of proposed device can be useful for ultra-fast signal processing and modulation schemes in high speed communication especially in QPSK modulation. The optical control has several advantages over conventional techniques such as MEMS and other semiconductor switching, which have several inherent disadvantages and limitations like low response time, low power handling capacity, device parasitic and non-linearity.
Exponential fitting quadrature rule for functional equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Paternoster, B.; Santomauro, G.
2012-09-01
A Gaussian quadrature rule for periodic integrand function is presented. The weights and nodes depend on the frequency of the problem and they are constructed by following the exponential fitting theory. The composite rule based on this formula is derived. The analysis of the error is carried out and it proves that the exponentially fitted Gaussian rule is more accurate than the classical Gauss-Legendre rule when oscillatory functions are treated. Some numerical tests are presented.
Gauss Legendre Quadrature Formulae for Tetrahedra
NASA Astrophysics Data System (ADS)
Rathod, H. T.; Venkatesudu, B.; Nagaraja, K. V.
2005-09-01
In this paper we consider the Gauss Legendre quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)|0 = x, y, z = 1, x + y + z = 1} in the Cartesian three-dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (?, ?, ?) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2-cube: {(?, ?, ?)| - 1 = ?, ?,? = 1} in the (?, ?, ?) space. This overcomes the difficulties associated with the derivation of new weight co-efficients and sampling points. The effectiveness of the formulae is demonstrated by applying them to the integration of three nonpolynomial and three polynomial functions.
Positive interpolatory quadrature formulas and para-orthogonal polynomials
NASA Astrophysics Data System (ADS)
Bultheel, Adhemar; Daruis, Leyla; Gonzalez-Vera, Pablo
2005-07-01
We establish a relation between quadrature formulas on the interval [-1,1] that approximate integrals of the form and Szego quadrature formulas on the unit circle that approximate integrals of the form . The functions [mu](x) and [omega]([theta]) are assumed to be weight functions on [-1,1] and [-[pi],[pi
Correlated quadratures of resonance fluorescence and the generalized uncertainty relation
NASA Technical Reports Server (NTRS)
Arnoldus, Henk F.; George, Thomas F.; Gross, Rolf W. F.
1994-01-01
Resonance fluorescence from a two-state atom has been predicted to exhibit quadrature squeezing below the Heisenberg uncertainty limit, provided that the optical parameters (Rabi frequency, detuning, laser linewidth, etc.) are chosen carefully. When the correlation between two quadratures of the radiation field does not vanish, however, the Heisenberg limit for quantum fluctuations might be an unrealistic lower bound. A generalized uncertainty relation, due to Schroedinger, takes into account the possible correlation between the quadrature components of the radiation, and it suggests a modified definition of squeezing. We show that the coherence between the two levels of a laser-driven atom is responsible for the correlation between the quadrature components of the emitted fluorescence, and that the Schrodinger uncertainty limit increases monotonically with the coherence. On the other hand, the fluctuations in the quadrature field diminish with an increasing coherence, and can disappear completely when the coherence reaches 1/2, provided that certain phase relations hold.
Two-frequency-dependent Gauss quadrature rules
NASA Astrophysics Data System (ADS)
Kim, Kyung Joong
2005-02-01
We construct two-frequency-dependent Gauss quadrature rules which can be applied for approximating the integration of the product of two oscillatory functions with different frequencies [beta]1 and [beta]2 of the forms,yi(x)=fi,1(x) cos([beta]ix)+fi,2(x) sin([beta]ix), i=1,2,where the functions fi,j(x) are smooth. A regularization procedure is presented to avoid the singularity of the Jacobian matrix of nonlinear system of equations which is induced as one frequency approaches the other frequency. We provide numerical results to compare the accuracy of the classical Gauss rule and one- and two-frequency-dependent rules.
The May 1997 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Suess, Steven T.; Poletto, G.; Romoli, M.; Neugebauer, M.; Goldstein, B. E.; Simnett, G.
2000-01-01
We present results from the May 1997 SOHO-Ulysses quadrature, near sunspot minimum. Ulysses was at 5.1 AU, 100 north of the solar equator, and off the east limb. It was, by chance, also at the very northern edge of the streamer belt. Nevertheless, SWOOPS detected only slow, relatively smooth wind and there was no direct evidence of fast wind from the northern polar coronal hole or of mixing with fast wind. LASCO images show that the streamer belt at 10 N was narrow and sharp at the beginning and end of the two week observation interval, but broadened in the middle. A corresponding change in density, but not flow speed, occurred at Ulysses. Coronal densities derived from UVCS show that physical parameters in the lower corona are closely related to those in the solar wind, both over quiet intervals and in transient events on the limb. One small transient observed by both LASCO and UVCS is analyzed in detail.
Power flow control using quadrature boosters
NASA Astrophysics Data System (ADS)
Sadanandan, Sandeep N.
A power system that can be controlled within security constraints would be an advantage to power planners and real-time operators. Controlling flows can lessen reliability issues such as thermal limit violations, power stability problems, and/or voltage stability conditions. Control of flows can also mitigate market issues by reducing congestion on some lines and rerouting power to less loaded lines or onto preferable paths. In the traditional control of power flows, phase shifters are often used. More advanced methods include using Flexible AC Transmission System (FACTS) Controllers. Some examples include Thyristor Controlled Series Capacitors, Synchronous Series Static Compensators, and Unified Power Flow Controllers. Quadrature Boosters (QBs) have similar structures to phase-shifters, but allow for higher voltage magnitude during real power flow control. In comparison with other FACTS controllers QBs are not as complex and not as expensive. The present study proposes to use QBs to control power flows on a power system. With the inclusion of QBs, real power flows can be controlled to desired scheduled values. In this thesis, the linearized power flow equations used for power flow analysis were modified for the control problem. This included modifying the Jacobian matrix, the power error vector, and calculating the voltage injected by the quadrature booster for the scheduled real power flow. Two scenarios were examined using the proposed power flow control method. First, the power flow in a line in a 5-bus system was modified with a QB using the method developed in this thesis. Simulation was carried out using Matlab. Second, the method was applied to a 30-bus system and then to a 118-bus system using several QBs. In all the cases, the calculated values of the QB voltages led to desired power flows in the designated line.
Algorithm 699 - A new representation of Patterson's quadrature formulae
NASA Technical Reports Server (NTRS)
Krogh, Fred T.; Van Snyder, W.
1991-01-01
A method is presented to reduce the number of coefficients necessary to represent Patterson's quadrature formulae. It also reduces the amount of storage necessary for storing function values, and produces slightly smaller error in evaluating the formulae.
Experimental study of quadrature spring rate at tuned dry gyro
NASA Astrophysics Data System (ADS)
Hayakawa, Yoshiaki; Murayama, Naoshi
A survey result on the mechanism of quadrature spring rate occurring at the tuned dry gyro is given. It is noted that the quadrature spring rate is a damping torque. This damping torque is similar to the spring reaction torque generated by the flexure displacement angles and drives the gyro rotor back to a balanced position. In order to investigate the mechanism of damping occurring at the gyro rotor, the relation between surrounding gas pressure and damping factor under gyro nonoperating was measured. Furthermore, the drag torque acting on the gyro rotor was measured by the back EMF method at different surrounding gas pressure. As a result of these testings, it was found out that the quadrature spring rate was generated by gas movement of the flexure around and drag forces due to bearing loss and windage loss, and the mechanism and magnitude of each damping torque which are contributor to the quadrature spring rate were extracted separately.
Squeezing quadrature rotation in the acoustic band via optomechanics
NASA Astrophysics Data System (ADS)
Guccione, Giovanni; Slatyer, Harry J.; Carvalho, André R. R.; Buchler, Ben C.; Lam, Ping Koy
2016-03-01
We examine the use of optomechanically generated squeezing to obtain a sensitivity enhancement for interferometers in the gravitational-wave band. The intrinsic dispersion characteristics of optomechanical squeezing around the mechanical frequency are able to produce squeezing at different quadratures over the spectrum, a feature required by gravitational-wave interferometers to beat the standard quantum limit over an extended frequency range. Under realistic assumptions we show that the amount of available squeezing and the intrinsic quadrature rotation may provide, compared to similar amounts of fixed-quadrature squeezing, a detection advantage. A significant challenge for this scheme, however, is the amount of excess noise that is generated in the unsqueezed quadrature at frequencies near the mechanical resonance.
Optical encryption system using quadrature multiplexing
NASA Astrophysics Data System (ADS)
Islam, Mohammed Nazrul; Alam, Mohammad S.
2006-08-01
Optical security systems have attracted much research interest recently for information security and fraud deterrent applications. A number of encryption techniques have been proposed in the literature, which includes double random-phase encryption, polarization encoding, encryption and verification using a multiplexed minimum average correlation energy phase-encrypted filter. Most of these reports employ a pseudo-random code for each information to be encrypted, where it requires individual storage capacity or transmission channel for further processing of each information. The objective of this paper is to develop an optical encryption system employing quadrature multiplexing to enhance the storage/transmission capacity of the system. Two information signals are encrypted using the same code but employing two orthogonal functions and then they are multiplexed together in the same domain. As the orthogonal functions have zero cross-correlation between them, so the encrypted information are expected to be unaffected by each other. Each encryption and multiplexing process can accommodate two information signals for a single code and a single storage cell or transmission channel. The same process can be performed in multiple steps to increase the multiplexing capability of the system. For decryption purpose, the composite encoded signal is correlated using the appropriate code and the appropriate function. The proposed technique has been found to work excellent in computer simulation with binary as well as gray level images. It has also been verified that the encrypted images remain secure, because no unwanted reproduction is possible without having the appropriate code and function.
Two integrator loop quadrature oscillators: A review
Soliman, Ahmed M.
2012-01-01
A review of the two integrator loop oscillator circuits providing two quadrature sinusoidal output voltages is given. All the circuits considered employ the minimum number of capacitors namely two except one circuit which uses three capacitors. The circuits considered are classified to four different classes. The first class includes floating capacitors and floating resistors and the active building blocks realizing these circuits are the Op Amp or the OTRA. The second class employs grounded capacitors and includes floating resistors and the active building blocks realizing these circuits are the DCVC or the unity gain cells or the CFOA. The third class employs grounded capacitors and grounded resistors and the active building blocks realizing these circuits are the CCII. The fourth class employs grounded capacitors and no resistors and the active building blocks realizing these circuits are the TA. Transformation methods showing the generation of different classes from each other is given in details and this is one of the main objectives of this paper. PMID:25685396
Orthogonal rational functions and quadrature on an interval
NASA Astrophysics Data System (ADS)
van Deun, J.; Bultheel, A.
2003-04-01
Rational functions with real poles and poles in the complex lower half-plane, orthogonal on the real line, are well known. Quadrature formulas similar to the Gauss formulas for orthogonal polynomials have been studied. We generalize to the case of arbitrary complex poles and study orthogonality on a finite interval. The zeros of the orthogonal rational functions are shown to satisfy a quadratic eigenvalue problem. In the case of real poles, these zeros are used as nodes in the quadrature formulas.
An exponentially fitted quadrature rule over unbounded intervals
NASA Astrophysics Data System (ADS)
Conte, D.; Paternoster, B.; Santomauro, G.
2012-09-01
A new class of quadrature formulae for the computation of integrals over unbounded intervals with oscillating integrand is illustrated. Such formulae are a generalization of the gaussian quadrature formulae by exploiting the Exponential Fitting theory. The coefficients depend on the frequency of oscillation, in order to improve the accuracy of the solution. The construction of the methods with 1, 2 and 3 nodes is described, together with the comparison of the order of accuracy with respect to classical formulae.
Quadrature mixture LO suppression via DSW DAC noise dither
Dubbert, Dale F.; Dudley, Peter A.
2007-08-21
A Quadrature Error Corrected Digital Waveform Synthesizer (QECDWS) employs frequency dependent phase error corrections to, in effect, pre-distort the phase characteristic of the chirp to compensate for the frequency dependent phase nonlinearity of the RF and microwave subsystem. In addition, the QECDWS can employ frequency dependent correction vectors to the quadrature amplitude and phase of the synthesized output. The quadrature corrections cancel the radars' quadrature upconverter (mixer) errors to null the unwanted spectral image. A result is the direct generation of an RF waveform, which has a theoretical chirp bandwidth equal to the QECDWS clock frequency (1 to 1.2 GHz) with the high Spurious Free Dynamic Range (SFDR) necessary for high dynamic range radar systems such as SAR. To correct for the problematic upconverter local oscillator (LO) leakage, precision DC offsets can be applied over the chirped pulse using a pseudo-random noise dither. The present dither technique can effectively produce a quadrature DC bias which has the precision required to adequately suppress the LO leakage. A calibration technique can be employed to calculate both the quadrature correction vectors and the LO-nulling DC offsets using the radar built-in test capability.
Gaussian quadrature inference for continuous-variable quantum key distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, L.; Imre, S.
2016-05-01
We propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We demonstrate the results through the adaptive multicarrier quadrature division (AMQD) scheme. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of GQI. We prove the secret key rate formulas for a multiple access multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) scheme. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario.
The Fall 2000 and Fall 2001 SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.
2000-01-01
SOHO-Ulysses quadrature occurs when the SOHO-Sun-Ulysses included angle is 90 degrees. It is only at such times that the same plasma leaving the Sun in the direction of Ulysses can first be remotely analyzed with SOHO instruments and then later be sampled in situ by Ulysses instruments. The quadratures in December 2000 and 2001 are of special significance because Ulysses will be near the south and north heliographic poles, respectively, and the solar cycle will be near sunspot maximum. Quadrature geometry is sometimes confusing and observations are influenced by solar rotation. The Fall 2000 and 2001 quadratures are more complex than usual because Ulysses is not in a true polar orbit and the orbital speed of Ulysses about the Sun is becoming comparable to the speed of SOHO about the Sun. In 2000 Ulysses will always be slightly behind the pole but will appear to hang over the pole for over two months because it is moving around the Sun in the same direction as SOHO. In 20001, Ulysses will be slightly in front of the pole so that its footpoint will be directly observable. Detailed plots will be shown of the relative positions of SOHO and Ulysses will their relative positions. In neither case is true quadrature actually achieved, but this works to the observers advantage in 2001.
The Fall 2000 and Fall 2001 SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.; Rose, M. Franklin (Technical Monitor)
2001-01-01
SOHO-Ulysses quadrature occurs when the SOHO-Sun-Ulysses included angle is 90 degrees. It is only at such times that the same plasma leaving the Sun in the direction of Ulysses can first be remotely analyzed with SOHO instruments and then later be sampled in situ by Ulysses instruments. The quadratures in December 2000 and 2001 are of special significance because Ulysses will be near the south and north heliographic poles, respectively, and the solar cycle will be near sunspot maximum. Quadrature geometry is sometimes confusing and observations are influenced by solar rotation. The Fall 2000 and 2001 quadratures are more complex than usual because Ulysses is not in a true polar orbit and the orbital speed of Ulysses about the Sun is becoming comparable to the speed of SOHO about the Sun. In 2000 Ulysses will always be slightly behind the pole but will appear to hang over the pole for over two months because it is moving around the Sun in the same direction as SOHO. In 2001 Ulysses will be slightly in front of the pole so that its footpoint will be directly observable. Detailed plots will be shown of the relative positions of SOHO and Ulysses will their relative positions. In neither case is true quadrature actually achieved, but this works to the observers advantage in 2001.
Gauss Quadratures - the Keystone of Lattice Boltzmann Models
NASA Astrophysics Data System (ADS)
Piaud, Benjamin; Blanco, Stéphane; Fournier, Richard; Ambruş, Victor Eugen; Sofonea, Victor
2014-01-01
In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss-Hermite quadrature. The second one is the SLB(N;K,L,M) family, derived by using the spherical coordinate system and the Gauss-Laguerre, as well as the Gauss-Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.
Discrete Ordinate Quadrature Selection for Reactor-based Eigenvalue Problems
Jarrell, Joshua J; Evans, Thomas M; Davidson, Gregory G
2013-01-01
In this paper we analyze the effect of various quadrature sets on the eigenvalues of several reactor-based problems, including a two-dimensional (2D) fuel pin, a 2D lattice of fuel pins, and a three-dimensional (3D) reactor core problem. While many quadrature sets have been applied to neutral particle discrete ordinate transport calculations, the Level Symmetric (LS) and the Gauss-Chebyshev product (GC) sets are the most widely used in production-level reactor simulations. Other quadrature sets, such as Quadruple Range (QR) sets, have been shown to be more accurate in shielding applications. In this paper, we compare the LS, GC, QR, and the recently developed linear-discontinuous finite element (LDFE) sets, as well as give a brief overview of other proposed quadrature sets. We show that, for a given number of angles, the QR sets are more accurate than the LS and GC in all types of reactor problems analyzed (2D and 3D). We also show that the LDFE sets are more accurate than the LS and GC sets for these problems. We conclude that, for problems where tens to hundreds of quadrature points (directions) per octant are appropriate, QR sets should regularly be used because they have similar integration properties as the LS and GC sets, have no noticeable impact on the speed of convergence of the solution when compared with other quadrature sets, and yield more accurate results. We note that, for very high-order scattering problems, the QR sets exactly integrate fewer angular flux moments over the unit sphere than the GC sets. The effects of those inexact integrations have yet to be analyzed. We also note that the LDFE sets only exactly integrate the zeroth and first angular flux moments. Pin power comparisons and analyses are not included in this paper and are left for future work.
Error estimates for Gaussian quadratures of analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2009-12-01
For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points ±1 and the sum of semi-axes [varrho]>1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.
The development of accurate and efficient methods of numerical quadrature
NASA Technical Reports Server (NTRS)
Feagin, T.
1973-01-01
Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.
An Algorithm to Evaluate Imbalances of Quadrature Mixers
NASA Astrophysics Data System (ADS)
Asami, Koji; Arai, Michiaki
It is essential, as bandwidths of wireless communications get wider, to evaluate the imbalances among quadrature mixer ports, in terms of carrier phase offset, IQ gain imbalance, and IQ skew. Because it is time consuming to separate skew, gain imbalance and carrier phase offset evaluation during test is often performed using a composite value, without separation of the imbalance factors. This paper describes an algorithm for enabling separation among quadrature mixer gain imbalance, carrier phase offset, and skew. Since the test time is reduced by the proposed method, it can be applied during high volume production testing.
Trapezoidal rule quadrature algorithms for MIMD distributed memory computers
Lyness, J.N.; Plowman, S.E.
1994-08-01
An approach to multi-dimensional quadrature, designed to exploit parallel architectures, is described. This involves transforming the integral in such a way that an accurate result is given by the trapezoidal rule; and by evaluating the resulting sum in a manner which may be efficiently implemented on parallel architectures. This approach is to be implemented in the Liverpool NAG transputer library.
From Lobatto Quadrature to the Euler Constant "e"
ERIC Educational Resources Information Center
Khattri, Sanjay Kumar
2010-01-01
Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…
Wave-Based Inversion & Imaging for the Optical Quadrature Microscope
Lehman, S K
2005-10-27
The Center for Subsurface Sensing & Imaging System's (CenSSIS) Optical Quadrature Microscope (OQM) is a narrow band visible light microscope capable of measuring both amplitude and phase of a scattered field. We develop a diffraction tomography, that is, wave-based, scattered field inversion and imaging algorithm, for reconstructing the refractive index of the scattering object.
Gaussian rational quadrature formulas for ill-scaled integrands
NASA Astrophysics Data System (ADS)
Illán González, J. R.
2009-12-01
A flexible treatment of Gaussian quadrature formulas based on rational functions is given to evaluate the integral , when f is meromorphic in a neighborhood V of the interval I and W(x) is an ill-scaled weight function. Some numerical tests illustrate the power of this approach in comparison with Gautschi's method.
Archimedes Quadrature of the Parabola: A Mechanical View
ERIC Educational Resources Information Center
Oster, Thomas J.
2006-01-01
In his famous quadrature of the parabola, Archimedes found the area of the region bounded by a parabola and a chord. His method was to fill the region with infinitely many triangles each of whose area he could calculate. In his solution, he stated, without proof, three preliminary propositions about parabolas that were known in his time, but are…
Applying Quadrature Rules with Multiple Nodes to Solving Integral Equations
Hashemiparast, S. M.; Avazpour, L.
2008-09-01
There are many procedures for the numerical solution of Fredholm integral equations. The main idea in these procedures is accuracy of the solution. In this paper, we use Gaussian quadrature with multiple nodes to improve the solution of these integral equations. The application of this method is illustrated via some examples, the related tables are given at the end.
Extraction of quadrature phase information from multiple pulse NMR signals
NASA Technical Reports Server (NTRS)
Rhim, W.-K.; Burum, D. P.; Vaughan, R. W.
1976-01-01
A multiple pulse sequence (8-pulse sequence) used for high-resolution solid state NMR is analyzed with regard to the information available from each of the four wide sampling windows. It is demonstrated that full quadrature phase information can be obtained using only a single phase detector and that, for the commonly encountered situation where the spectral width is much less than the folding frequency, the signals from the various windows can be combined easily using standard complex Fourier transform software. An improvement in the signal-to-noise ratio equal to the square root of 3 is obtained over either standard single or quadrature phase detection schemes. Procedures for correcting spectral distortions are presented.
On a quadrature formula of Gori and Micchelli
NASA Astrophysics Data System (ADS)
Yang, Shijun
2005-04-01
Sparked by Bojanov (J. Comput. Appl. Math. 70 (1996) 349), we provide an alternate approach to quadrature formulas based on the zeros of the Chebyshev polynomial of the first kind for any weight function w introduced and studied in Gori and Micchelli (Math. Comp. 65 (1996) 1567), thereby improving on their observations. Upon expansion of the divided differences, we obtain explicit expressions for the corresponding Cotes coefficients in Gauss-Turan quadrature formulas for and I(fTn;w) for a Gori-Micchelli weight function. It is also interesting to mention what has been neglected for about 30 years by the literature is that, as a consequence of expansion of the divided differences in the special case when , the solution of the famous Turan's Problem 26 raised in 1980 was in fact implied by a result of Micchelli and Rivlin (IBM J. Res. Develop. 16 (1972) 372) in 1972. Some concluding comments are made in the final section.
Accurate Computation of Gaussian Quadrature for Tension Powers
NASA Astrophysics Data System (ADS)
Singer, Saša
2007-09-01
We consider Gaussian quadrature formulæ which exactly integrate a system of tension powers 1,x,x2,…,xn-3, sinh(px), cosh(px), on a given interval [a,b], where n⩾4 is an even integer and p>0 is a given tension parameter. In some applications it is essential that p can be changed dynamically, and we need an efficient "on-demand" algorithm that calculates the nodes and weights of Gaussian quadrature formulas for many different values of p, which are not known in advance. It is an interesting numerical challenge to achieve the required full machine precision accuracy in such an algorithm, for all possible values of p. By exploiting various analytic and numerical techniques, we show that this can be done efficiently for all reasonably low values of n that are of any practical importance.
Quadrature formulae for classes of functions of low smoothness
Nursultanov, E D; Tleukhanova, N T
2003-10-31
For Sobolev and Korobov spaces of functions of several variables a quadrature formula with explicitly defined coefficients and nodes is constructed. This formula is precise for trigonometric polynomials with harmonics from the corresponding step hyperbolic cross. The error of the quadrature formula in the classes W{sup {alpha}}{sub p}[0,1]{sup n}, E{sup {alpha}}[0,1]{sup n} is o((ln M){sup {beta}}/M{sup {alpha}}), where M is the number of nodes and {beta} is a parameter depending on the class. The problem of the approximate calculation of multiple integrals for functions in W{sup {alpha}}{sub p}[0,1]{sup n} is considered in the case when this class does not lie in the space of continuous functions, that is, for {alpha}{<=}1/p.
Efficient quadrature multichannel processor algorithms for MCD applications
NASA Astrophysics Data System (ADS)
Corden, I. R.; Carrasco, R. A.
1992-06-01
The forthcoming third generation of satellites incorporating multichannel demodulator (MCD) processors, and the needs apparent within aviation systems, induce the requirement for efficient band processing algorithms with specific regard to the quadrature processing arrangement. This paper presents a coherent z-domain formulation of the pertinent digital transmultiplexer algorithms for the on-board processing (OBP) scenario, with a view to establishig a set of desirable algorithmic properties suitable for the preferred complex oriented quadrature processing algorithms. Stemming from the principles set forth, an ensemble of new algorithms based upon mixes of Hilbert transforming and real transform algorithms is presented, wherein the established concepts relating to the telephone network transmultiplexer algorithms are able to be exploited in certain cases. Further, the computational load of one of the methods is lower than that of a known prominent OBP related technique. The computational necessities of the various algorithms are laid down for comparative purposes in addition to the mathematical descriptions.
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.
Some new applications of truncated Gauss-Laguerre quadrature formulas
NASA Astrophysics Data System (ADS)
Mastroianni, G.; Monegato, G.
2008-12-01
We show how truncated Gauss-Laguerre quadrature formulas can be used to produce accurate approximations and high rates of convergence, also when they are applied to integrand functions having only an algebraic type decay to zero at infinity. The approach presented in the paper is proposed for the computation of integrals and for the construction of Nyström type interpolants for some second kind integral equations.
Solar Wind Characteristics from SOHO-Sun-Ulysses Quadrature Observations
NASA Technical Reports Server (NTRS)
Poletto, Giannina; Suess, Steve T.; Six, N. Frank (Technical Monitor)
2002-01-01
Over the past few years, we have been running SOHO (Solar and Heliospheric Observatory)-Sun-Ulysses quadrature campaigns, aimed at comparing the plasma properties at coronal altitudes with plasma properties at interplanetary distances. Coronal plasma has been observed by SOHO experiments: mainly, we used LASCO (Large Angle and Spectrometric Coronagraph Experiment) data to understand the overall coronal configuration at the time of quadratures and analyzed SUMER (Solar Ultraviolet Measurements of Emitted Radiation), CDS (Coronal Diagnostic Spectrometer) and UVCS (Ultraviolet Coronagraph Spectrometer) data to derive its physical characteristics. At interplanetary distances, SWICS (Solar Wind Ion Composition Spectrometer) and SWOOPS (Solar Wind Observation over the Poles of the Sun) aboard Ulysses provided us with interplanetary plasma data. Here we report on results from some of the campaigns. We notice that, depending on the geometry of the quadrature, i.e. on whether the radial to Ulysses traverses the corona at high or low latitudes, we are able to study different kinds of solar wind. In particular, a comparison between low-latitude and high-latitude wind, allowed us to provide evidence for differences in the acceleration of polar, fast plasma and equatorial, slow plasma: the latter occurring at higher levels and through a more extended region than fast wind. These properties are shared by both the proton and heavy ions outflows. Quadrature observations may provide useful information also on coronal vs. in situ elemental composition. To this end, we analyzed spectra taken in the corona, at altitudes ranging between approx. 1.02 and 2.2 solar radii, and derived the abundances of a number of ions, including oxygen and iron. Values of the O/Fe ratio, at coronal levels, have been compared with measurements of this ratio made by SWICS at interplanetary distances. Our results are compared with previous findings and predictions from modeling efforts.
Statistical Quadrature Evolution for Continuous-Variable Quantum Key Distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, Laszlo; Imre, Sandor
2016-05-01
We propose a statistical quadrature evolution (SQE) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The SQE framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. We define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of our method. We prove the secret key rate formulas for a multiple access multicarrier CVQKD. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario. This work was partially supported by the GOP-1.1.1-11-2012-0092 project sponsored by the EU and European Structural Fund, by the Hungarian Scientific Research Fund - OTKA K-112125, and by the COST Action MP1006.
Discrete ordinates with new quadrature sets and modified source conditions
Ganguly, K.; Allen, E.J., Victory, H.D. Jr. )
1989-01-01
A major shortcoming of the discrete ordinates method with the Gauss-Legendre quadrature set is that when the number of secondaries per primary c and the order of approximation N are not too large, all the (N + 1)v (the flux being of the form exp({minus}x/v)) lie in ({minus}1,1). It is known, however, that the largest v{sub j} corresponding to the asymptotic flux is greater than unity. The Legendre polynomial used for obtaining the quadrature set is orthogonal with respect to weight unity in the range ({minus}1,1). However, the Case and Zweifel eigenfunctions derived from the exact solution of one-speed transport theory are orthogonal with respect to a complicated weight function w({mu}) and {mu} in the half-range and full-range cases, respectively. In this paper, the authors have used a set of orthogonal polynomials with respect to w ({mu}) to develop quadrature sets to be used in the discrete ordinates calculation.
Fast evaluation of quadrature formulae on the sphere
NASA Astrophysics Data System (ADS)
Keiner, Jens; Potts, Daniel
2008-03-01
Recently, a fast approximate algorithm for the evaluation of expansions in terms of standard mathrm{L}^2left(mathbb{S}^2right) -orthonormal spherical harmonics at arbitrary nodes on the sphere mathbb{S}^2 has been proposed in [S. Kunis and D. Potts. Fast spherical Fourier algorithms. JE Comput. Appl. Math., 161:75-98, 2003]. The aim of this paper is to develop a new fast algorithm for the adjoint problem which can be used to compute expansion coefficients from sampled data by means of quadrature rules. We give a formulation in matrix-vector notation and an explicit factorisation of the spherical Fourier matrix based on the former algorithm. Starting from this, we obtain the corresponding factorisation of the adjoint spherical Fourier matrix and are able to describe the associated algorithm for the adjoint transformation which can be employed to evaluate quadrature rules for arbitrary weights and nodes on the sphere. We provide results of numerical tests showing the stability of the obtained algorithm using as examples classical Gauss-Legendre and Clenshaw-Curtis quadrature rules as well as the HEALPix pixelation scheme and an equidistribution.
Testing the Empirical Shock Arrival Model Using Quadrature Observations
NASA Technical Reports Server (NTRS)
Gopalswamy, N.; Makela, P.; Xie, H.; Yashiro, S.
2013-01-01
The empirical shock arrival (ESA) model was developed based on quadrature data from Helios (in situ) and P-78 (remote sensing) to predict the Sun-Earth travel time of coronal mass ejections (CMEs). The ESA model requires earthward CME speed as input, which is not directly measurable from coronagraphs along the Sun-Earth line. The Solar Terrestrial Relations Observatory (STEREO) and the Solar and Heliospheric Observatory (SOHO) were in quadrature during 20102012, so the speeds of Earth-directed CMEs were observed with minimal projection effects. We identified a set of 20 full halo CMEs in the field of view of SOHO that were also observed in quadrature by STEREO. We used the earthward speed from STEREO measurements as input to the ESA model and compared the resulting travel times with the observed ones from L1 monitors. We find that the model predicts the CME travel time within about 7.3 h, which is similar to the predictions by the ENLIL model. We also find that CME-CME and CME-coronal hole interaction can lead to large deviations from model predictions.
An Application of the Quadrature-Free Discontinuous Galerkin Method
NASA Technical Reports Server (NTRS)
Lockard, David P.; Atkins, Harold L.
2000-01-01
The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.
Advanced quadratures and periodic boundary conditions in parallel 3D S{sub n} transport
Manalo, K.; Yi, C.; Huang, M.; Sjoden, G.
2013-07-01
Significant updates in numerical quadratures have warranted investigation with 3D Sn discrete ordinates transport. We show new applications of quadrature departing from level symmetric (S{sub 2}o). investigating 3 recently developed quadratures: Even-Odd (EO), Linear-Discontinuous Finite Element - Surface Area (LDFE-SA), and the non-symmetric Icosahedral Quadrature (IC). We discuss implementation changes to 3D Sn codes (applied to Hybrid MOC-Sn TITAN and 3D parallel PENTRAN) that can be performed to accommodate Icosahedral Quadrature, as this quadrature is not 90-degree rotation invariant. In particular, as demonstrated using PENTRAN, the properties of Icosahedral Quadrature are suitable for trivial application using periodic BCs versus that of reflective BCs. In addition to implementing periodic BCs for 3D Sn PENTRAN, we implemented a technique termed 'angular re-sweep' which properly conditions periodic BCs for outer eigenvalue iterative loop convergence. As demonstrated by two simple transport problems (3-group fixed source and 3-group reflected/periodic eigenvalue pin cell), we remark that all of the quadratures we investigated are generally superior to level symmetric quadrature, with Icosahedral Quadrature performing the most efficiently for problems tested. (authors)
Quadrature rules with multiple nodes for evaluating integrals with strong singularities
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.
2006-05-01
We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.
Chen, Hua-Pin
2014-01-01
The electronically tunable quadrature oscillator using a single multiple-output current controlled current differencing transconductance amplifier (MO-CCCDTA) and grounded passive components is presented. The proposed configuration uses a single MO-CCCDTA, two grounded capacitors and one grounded resistor. Two high-output impedance quadrature current signals and two quadrature voltage signals with 90° phase difference. The oscillation condition and oscillation frequency of the proposed quadrature oscillator are independently controllable. The use of only grounded passive components makes the proposed circuit ideal for integrated circuit implementation. PMID:25121124
Parametric generation of quadrature squeezing of mirrors in cavity optomechanics
Liao, Jie-Qiao; Law, C. K.
2011-03-15
We propose a method to generate quadrature-squeezed states of a moving mirror in a Fabry-Perot cavity. This is achieved by exploiting the fact that when the cavity is driven by an external field with a large detuning, the moving mirror behaves as a parametric oscillator. We show that parametric resonance can be reached approximately by modulating the driving field amplitude at a frequency matching the frequency shift of the mirror. The parametric resonance leads to an efficient generation of squeezing, which is limited by the thermal noise of the environment.
Experimental demonstration of microring quadrature phase-shift keying modulators.
Dong, Po; Xie, Chongjin; Chen, Long; Fontaine, Nicolas K; Chen, Young-kai
2012-04-01
Advanced optical modulation formats are a key technology to increase the capacity of optical communication networks. Mach-Zehnder modulators are typically used to generate various modulation formats. Here, we report the first experimental demonstration of quadrature phase-shift keying (QPSK) modulation using compact microring modulators. Generation of 20 Gb/s QPSK signals is demonstrated with 30 μm radius silicon ring modulators with drive voltages of ~6 V. These compact QPSK modulators may be used in miniature optical transponders for high-capacity optical data links. PMID:22466187
Noise-cancelling quadrature magnetic position, speed and direction sensor
Preston, Mark A.; King, Robert D.
1996-01-01
An array of three magnetic sensors in a single package is employed with a single bias magnet for sensing shaft position, speed and direction of a motor in a high magnetic noise environment. Two of the three magnetic sensors are situated in an anti-phase relationship (i.e., 180.degree. out-of-phase) with respect to the relationship between the other of the two sensors and magnetically salient target, and the third magnetic sensor is situated between the anti-phase sensors. The result is quadrature sensing with noise immunity for accurate relative position, speed and direction measurements.
The Nature of the Nodes, Weights and Degree of Precision in Gaussian Quadrature Rules
ERIC Educational Resources Information Center
Prentice, J. S. C.
2011-01-01
We present a comprehensive proof of the theorem that relates the weights and nodes of a Gaussian quadrature rule to its degree of precision. This level of detail is often absent in modern texts on numerical analysis. We show that the degree of precision is maximal, and that the approximation error in Gaussian quadrature is minimal, in a…
Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM.
Sorokina, Mariia; Sygletos, Stylianos; Ellis, Andrew; Turitsyn, Sergei
2015-07-01
We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats). PMID:26125381
A Family of Exponential Fitting Direct Quadrature Methods for Volterra Integral Equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Ferro, M.; Ixaru, L. Gr.; Paternoster, B.
2010-09-01
A new class of direct quadrature methods for the solution of Volterra Integral Equations with periodic solution is illustrated. Such methods are based on an exponential fitting gaussian quadrature formula, whose coefficients depend on the problem parameters, in order to better reproduce the behavior the analytical solution. The construction of the methods is described, together with the analysis of the order of accuracy.
General n-dimensional quadrature transform and its application to interferogram demodulation.
Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis
2003-05-01
Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward. PMID:12747439
Quadrature phase interferometer for high resolution force spectroscopy
NASA Astrophysics Data System (ADS)
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A.; Bellon, Ludovic
2013-09-01
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5 × 10^{-15} m/sqrtHz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.
Quadrature phase interferometer for high resolution force spectroscopy
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A.; Bellon, Ludovic
2013-09-15
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5×10{sup −15} m/√(Hz)), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.
Weighted discrete least-squares polynomial approximation using randomized quadratures
NASA Astrophysics Data System (ADS)
Zhou, Tao; Narayan, Akil; Xiu, Dongbin
2015-10-01
We discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation. The problem stems from uncertainty quantification (UQ), where the independent variables of the functions are random variables with specified probability measure. We propose to construct the least squares approximation on points randomly and uniformly sampled from tensor product Gaussian quadrature points. We analyze the stability properties of this method and prove that the method is asymptotically stable, provided that the number of points scales linearly (up to a logarithmic factor) with the cardinality of the polynomial space. Specific results in both bounded and unbounded domains are obtained, along with a convergence result for Chebyshev measure. Numerical examples are provided to verify the theoretical results.
Quadrature phase interferometer for high resolution force spectroscopy.
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A; Bellon, Ludovic
2013-09-01
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5×10(-15) m/√Hz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm. PMID:24089852
Double-Referential Holography and Spatial Quadrature Amplitude Modulation
NASA Astrophysics Data System (ADS)
Zukeran, Keisuke; Okamoto, Atsushi; Takabayashi, Masanori; Shibukawa, Atsushi; Sato, Kunihiro; Tomita, Akihisa
2013-09-01
We proposed a double-referential holography (DRH) that allows phase-detection without external additional beams. In the DRH, phantom beams, prepared in the same optical path as signal beams and preliminary multiplexed in a recording medium along with the signal, are used to produce interference fringes on an imager for converting a phase into an intensity distribution. The DRH enables stable and high-accuracy phase detection independent of the fluctuations and vibrations of the optical system owing to medium shift and temperature variation. Besides, the collinear arrangement of the signal and phantom beams leads to the compactness of the optical data storage system. We conducted an experiment using binary phase modulation signals for verifying the DRH operation. In addition, 38-level spatial quadrature amplitude modulation signals were successfully reproduced with the DRH by numerical simulation. Furthermore, we verified that the distributed phase-shifting method moderates the dynamic range consumption for the exposure of phantom beams.
Terahertz single-shot quadrature phase-shifting interferometry.
Földesy, Péter
2012-10-01
A single-shot quadrature phase-shifting interferometry architecture is presented that is applicable to antenna coupled detector technologies. The method is based on orthogonally polarized object and reference beams and on linear and circular polarization sensitive antennas in space-division multiplexing. The technique can be adapted to two-, three-, and four-step and Gabor holography recordings. It is also demonstrated that the space-division multiplexing does not necessarily cause sparse sampling. A sub-THz detector array is presented containing multiple on-chip antennas and FET plasma wave detectors implemented in a 90 nm complementary metal-oxide semiconductor technology. As an example, two-step phase-shifting reconstruction results are given at 360 GHz. PMID:23027273
Quadrature squeezed photons from a two-level system.
Schulte, Carsten H H; Hansom, Jack; Jones, Alex E; Matthiesen, Clemens; Le Gall, Claire; Atatüre, Mete
2015-09-10
Resonance fluorescence arises from the interaction of an optical field with a two-level system, and has played a fundamental role in the development of quantum optics and its applications. Despite its conceptual simplicity, it entails a wide range of intriguing phenomena, such as the Mollow-triplet emission spectrum, photon antibunching and coherent photon emission. One fundamental aspect of resonance fluorescence--squeezing in the form of reduced quantum fluctuations in the single photon stream from an atom in free space--was predicted more than 30 years ago. However, the requirement to operate in the weak excitation regime, together with the combination of modest oscillator strength of atoms and low collection efficiencies, has continued to necessitate stringent experimental conditions for the observation of squeezing with atoms. Attempts to circumvent these issues had to sacrifice antibunching, owing to either stimulated forward scattering from atomic ensembles or multi-photon transitions inside optical cavities. Here, we use an artificial atom with a large optical dipole enabling 100-fold improvement of the photon detection rate over the natural atom counterpart and reach the necessary conditions for the observation of quadrature squeezing in single resonance-fluorescence photons. By implementing phase-dependent homodyne intensity-correlation detection, we demonstrate that the electric field quadrature variance of resonance fluorescence is three per cent below the fundamental limit set by vacuum fluctuations, while the photon statistics remain antibunched. The presence of squeezing and antibunching simultaneously is a fully non-classical outcome of the wave-particle duality of photons. PMID:26322581
Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature
NASA Technical Reports Server (NTRS)
Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)
2000-01-01
This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.
Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation
NASA Technical Reports Server (NTRS)
Mcreynolds, S. R.
1975-01-01
A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.
NASA Technical Reports Server (NTRS)
Desmarais, R. N.
1975-01-01
Computer programs for computing Gaussian quadrature abscissas and weights are described. For the classical case the programs use Laguerre iteration to compute abscissas as zeros of orthogonal polynomials. The polynomials are evaluated from known recursion coefficients. The nonclassical case is handled similarly except that the recursion coefficients are computed by numerical integration. A sample problem, with input and output, is presented to illustrate the use of the programs. It computes the quadrature abscissas and weights associated with the weight function over the interval (0,1) for quadrature orders from 16 to 96 in increments of 8.
NASA Astrophysics Data System (ADS)
Knizhnerman, Leonid
2010-01-01
Stability of passing from Gaussian quadrature data to the Lanczos recurrence coefficients is considered. Special attention is paid to estimates explicitly expressed in terms of quadrature data and not having weights in denominators. It has been shown that the recent approach, exploiting integral representation of Hankel determinants, implies quantitative improvement of D. Laurie's constructive estimate. It has also been demonstrated that a particular implementation on the Hankel determinant approach gives an estimate being unimprovable up to a coefficient; the corresponding example involves quadrature data with a small but not too small weight. It follows that polynomial increase of a general case upper bound in terms of the dimension is unavoidable.
NASA Astrophysics Data System (ADS)
Bauman, Brian J.; Xiao, Hong
2010-08-01
Forbes introduced the usage of Gaussian quadratures in optical design for circular pupils and fields, and for a specific visible wavelength band. In this paper, Gaussian quadrature methods of selecting rays in ray-tracing are derived for noncircular pupil shapes, such as obscured and vignetted apertures. In addition, these methods are generalized for square fields, and for integrating performance over arbitrary wavelength bands. Integration over wavelength is aided by the use of a novel chromatic coordinate. These quadratures achieve low calculations with fewer rays (by orders of magnitude) than uniform sampling schemes.
Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature
Brito, K. D.; Sprague, M. A.
2012-10-01
Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for a given model size or total computation time.
NASA Astrophysics Data System (ADS)
Evans, W. A. B.; Torre, A.
2012-11-01
The paper focusses on the advantages of using high-order Gauss-Legendre quadratures for the precise evaluation of integrals with both smooth and rapidly changing integrands. Aspects of their precision are analysed in the light of Gauss' error formula. Some "test examples" are considered and evaluated in multiple precision to ≈ 200 significant decimal digits with David Bailey's multiprecision package to eliminate truncation/rounding errors. The increase of precision on doubling the number of subintervals is analysed, the relevant quadrature attribute being the precision increment. In order to exemplify the advantages that high-order quadrature afford, the technique is then used to evaluate several plots of the Rayleigh-Sommerfeld diffraction integral for axi-symmetric source fields defined on a planar aperture. A comparison of the high-order quadrature method against various FFT-based methods is finally given.
Cui, Junning; He, Zhangqiang; Jiu, Yuanwei; Tan, Jiubin; Sun, Tao
2016-09-01
The demand for minimal cyclic nonlinearity error in laser interferometry is increasing as a result of advanced scientific research projects. Research shows that the quadrature phase error is the main effect that introduces cyclic nonlinearity error, and polarization-mixing cross talk during beam splitting is the main error source that causes the quadrature phase error. In this paper, a new homodyne quadrature laser interferometer configuration based on nonpolarization beam splitting and balanced interference between two circularly polarized laser beams is proposed. Theoretical modeling indicates that the polarization-mixing cross talk is elaborately avoided through nonpolarizing and Wollaston beam splitting, with a minimum number of quadrature phase error sources involved. Experimental results show that the cyclic nonlinearity error of the interferometer is up to 0.6 nm (peak-to-valley value) without any correction and can be further suppressed to 0.2 nm with a simple gain and offset correction method. PMID:27607285
Information entropy of Gegenbauer polynomials and Gaussian quadrature
NASA Astrophysics Data System (ADS)
Sánchez-Ruiz, Jorge
2003-05-01
In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.
Modeling of optical quadrature microscopy for imaging mouse embryos
NASA Astrophysics Data System (ADS)
Warger, William C., II; DiMarzio, Charles A.
2008-02-01
Optical quadrature microscopy (OQM) has been shown to provide the optical path difference through a mouse embryo, and has led to a novel method to count the total number of cells further into development than current non-toxic imaging techniques used in the clinic. The cell counting method has the potential to provide an additional quantitative viability marker for blastocyst transfer during in vitro fertilization. OQM uses a 633 nm laser within a modified Mach-Zehnder interferometer configuration to measure the amplitude and phase of the signal beam that travels through the embryo. Four cameras preceded by multiple beamsplitters record the four interferograms that are used within a reconstruction algorithm to produce an image of the complex electric field amplitude. Here we present a model for the electric field through the primary optical components in the imaging configuration and the reconstruction algorithm to calculate the signal to noise ratio when imaging mouse embryos. The model includes magnitude and phase errors in the individual reference and sample paths, fixed pattern noise, and noise within the laser and detectors. This analysis provides the foundation for determining the imaging limitations of OQM and the basis to optimize the cell counting method in order to introduce additional quantitative viability markers.
Modulator-free quadrature amplitude modulation signal synthesis
NASA Astrophysics Data System (ADS)
Liu, Zhixin; Kakande, Joseph; Kelly, Brian; O'Carroll, John; Phelan, Richard; Richardson, David J.; Slavík, Radan
2014-12-01
The ability to generate high-speed on-off-keyed telecommunication signals by directly modulating a semiconductor laser’s drive current was one of the most exciting prospective applications of the nascent field of laser technology throughout the 1960s. Three decades of progress led to the commercialization of 2.5 Gbit s-1-per-channel submarine fibre optic systems that drove the growth of the internet as a global phenomenon. However, the detrimental frequency chirp associated with direct modulation forced industry to use external electro-optic modulators to deliver the next generation of on-off-keyed 10 Gbit s-1 systems and is absolutely prohibitive for today’s (>)100 Gbit s-1 coherent systems, which use complex modulation formats (for example, quadrature amplitude modulation). Here we use optical injection locking of directly modulated semiconductor lasers to generate complex modulation format signals showing distinct advantages over current and other currently researched solutions.
Electronically Tunable Differential Integrator: Linear Voltage Controlled Quadrature Oscillator
Nandi, Rabindranath; Pattanayak, Sandhya; Das, Sagarika
2015-01-01
A new electronically tunable differential integrator (ETDI) and its extension to voltage controlled quadrature oscillator (VCQO) design with linear tuning law are proposed; the active building block is a composite current feedback amplifier with recent multiplication mode current conveyor (MMCC) element. Recently utilization of two different kinds of active devices to form a composite building block is being considered since it yields a superior functional element suitable for improved quality circuit design. The integrator time constant (τ) and the oscillation frequency (ωo) are tunable by the control voltage (V) of the MMCC block. Analysis indicates negligible phase error (θe) for the integrator and low active ωo-sensitivity relative to the device parasitic capacitances. Satisfactory experimental verifications on electronic tunability of some wave shaping applications by the integrator and a double-integrator feedback loop (DIFL) based sinusoid oscillator with linear fo variation range of 60 KHz~1.8 MHz at low THD of 2.1% are verified by both simulation and hardware tests. PMID:27347537
Modulator-free quadrature amplitude modulation signal synthesis
Liu, Zhixin; Kakande, Joseph; Kelly, Brian; O’Carroll, John; Phelan, Richard; Richardson, David J.; Slavík, Radan
2014-01-01
The ability to generate high-speed on–off-keyed telecommunication signals by directly modulating a semiconductor laser’s drive current was one of the most exciting prospective applications of the nascent field of laser technology throughout the 1960s. Three decades of progress led to the commercialization of 2.5 Gbit s−1-per-channel submarine fibre optic systems that drove the growth of the internet as a global phenomenon. However, the detrimental frequency chirp associated with direct modulation forced industry to use external electro-optic modulators to deliver the next generation of on–off-keyed 10 Gbit s−1 systems and is absolutely prohibitive for today’s (>)100 Gbit s−1 coherent systems, which use complex modulation formats (for example, quadrature amplitude modulation). Here we use optical injection locking of directly modulated semiconductor lasers to generate complex modulation format signals showing distinct advantages over current and other currently researched solutions. PMID:25523757
Quantitative phase imaging using grating-based quadrature phase interferometer
NASA Astrophysics Data System (ADS)
Wu, Jigang; Yaqoob, Zahid; Heng, Xin; Cui, Xiquan; Yang, Changhuei
2007-02-01
In this paper, we report the use of holographic gratings, which act as the free-space equivalent of the 3x3 fiber-optic coupler, to perform full field phase imaging. By recording two harmonically-related gratings in the same holographic plate, we are able to obtain nontrivial phase shift between different output ports of the gratings-based Mach-Zehnder interferometer. The phase difference can be adjusted by changing the relative phase of the recording beams when recording the hologram. We have built a Mach-Zehnder interferometer using harmonically-related holographic gratings with 600 and 1200 lines/mm spacing. Two CCD cameras at the output ports of the gratings-based Mach-Zehnder interferometer are used to record the full-field quadrature interferograms, which are subsequently processed to reconstruct the phase image. The imaging system has ~12X magnification with ~420μmx315μm field-of-view. To demonstrate the capability of our system, we have successfully performed phase imaging of a pure phase object and a paramecium caudatum.
Radiation transport modeling using extended quadrature method of moments
NASA Astrophysics Data System (ADS)
Vikas, V.; Hauck, C. D.; Wang, Z. J.; Fox, R. O.
2013-08-01
The radiative transfer equation describes the propagation of radiation through a material medium. While it provides a highly accurate description of the radiation field, the large phase space on which the equation is defined makes it numerically challenging. As a consequence, significant effort has gone into the development of accurate approximation methods. Recently, an extended quadrature method of moments (EQMOM) has been developed to solve univariate population balance equations, which also have a large phase space and thus face similar computational challenges. The distinct advantage of the EQMOM approach over other moment methods is that it generates moment equations that are consistent with a positive phase space density and has a moment inversion algorithm that is fast and efficient. The goal of the current paper is to present the EQMOM method in the context of radiation transport, to discuss advantages and disadvantages, and to demonstrate its performance on a set of standard one-dimensional benchmark problems that encompass optically thin, thick, and transition regimes. Special attention is given in the implementation to the issue of realizability—that is, consistency with a positive phase space density. Numerical results in one dimension are promising and lay the foundation for extending the same framework to multiple dimensions.
Electronically Tunable Differential Integrator: Linear Voltage Controlled Quadrature Oscillator.
Nandi, Rabindranath; Pattanayak, Sandhya; Venkateswaran, Palaniandavar; Das, Sagarika
2015-01-01
A new electronically tunable differential integrator (ETDI) and its extension to voltage controlled quadrature oscillator (VCQO) design with linear tuning law are proposed; the active building block is a composite current feedback amplifier with recent multiplication mode current conveyor (MMCC) element. Recently utilization of two different kinds of active devices to form a composite building block is being considered since it yields a superior functional element suitable for improved quality circuit design. The integrator time constant (τ) and the oscillation frequency (ω o ) are tunable by the control voltage (V) of the MMCC block. Analysis indicates negligible phase error (θ e ) for the integrator and low active ω o -sensitivity relative to the device parasitic capacitances. Satisfactory experimental verifications on electronic tunability of some wave shaping applications by the integrator and a double-integrator feedback loop (DIFL) based sinusoid oscillator with linear f o variation range of 60 KHz~1.8 MHz at low THD of 2.1% are verified by both simulation and hardware tests. PMID:27347537
A fast method of numerical quadrature for p-version finite element matrices
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1993-01-01
A new technique of numerical quadrature especially suited for p-version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.
Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods
Cao, Huiliang; Li, Hongsheng; Kou, Zhiwei; Shi, Yunbo; Tang, Jun; Ma, Zongmin; Shen, Chong; Liu, Jun
2016-01-01
This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses’ quadrature errors are different, and the quadrature correction system should be arranged independently. The process leading to quadrature error is proposed, and the Charge Injecting Correction (CIC), Quadrature Force Correction (QFC) and Coupling Stiffness Correction (CSC) methods are introduced. The correction objects of these three methods are the quadrature error signal, force and the coupling stiffness, respectively. The three methods are investigated through control theory analysis, model simulation and circuit experiments, and the results support the theoretical analysis. The bias stability results based on CIC, QFC and CSC are 48 °/h, 9.9 °/h and 3.7 °/h, respectively, and this value is 38 °/h before quadrature error correction. The CSC method is proved to be the better method for quadrature correction, and it improves the Angle Random Walking (ARW) value, increasing it from 0.66 °/√h to 0.21 °/√h. The CSC system general test results show that it works well across the full temperature range, and the bias stabilities of the six groups’ output data are 3.8 °/h, 3.6 °/h, 3.4 °/h, 3.1 °/h, 3.0 °/h and 4.2 °/h, respectively, which proves the system has excellent repeatability. PMID:26751455
Directional dual-tree complex wavelet packet transforms for processing quadrature signals.
Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin
2016-03-01
Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals. PMID:25388779
Extended Gaussian quadratures for functions with an end-point singularity of logarithmic type
NASA Astrophysics Data System (ADS)
Pachucki, K.; Puchalski, M.; Yerokhin, V. A.
2014-11-01
The extended Gaussian quadrature rules are shown to be an efficient tool for numerical integration of wide class of functions with singularities of logarithmic type. The quadratures are exact for the functions pol1n-1(x)+lnx pol2n-1(x), where pol1n-1(x) and pol2n-1(x) are two arbitrary polynomials of degree n-1 and n is the order of the quadrature formula. We present an implementation of numerical algorithm that calculates the nodes and the weights of the quadrature formulas, provide a Fortran code for numerical integration, and test the performance of different kinds of Gaussian quadratures for functions with logarithmic singularities. Catalogue identifier: AETP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2535 No. of bytes in distributed program, including test data, etc.: 39 963 Distribution format: tar.gz Programming language: Mathematica, Fortran. Computer: PCs or higher performance computers. Operating system: Linux, Windows, MacOS. RAM: Kilobytes. Classification: 4.11. Nature of problem: Quadrature formulas for numerical integration, effective for a wide class of functions with end-point singularities of logarithmic type. Solution method: The method of solution is based on the algorithm developed in Ref. [1] with some modifications. Running time: Milliseconds to minutes. J. Ma, V. Rokhlin, S. Wandzura, Generalized Gaussian quadrature rules for systems of arbitrary functions, Soc. Indust. Appl. Math. J. Numer. Anal. 33 (3) (1996) 971-996.
NASA Astrophysics Data System (ADS)
Čársky, Petr
2010-09-01
The UGU term was used as a model of the UGT term, and its evaluation by numerical quadrature was examined systematically with a training set of eight molecules. Minimum numbers of points have been determined for radial Gauss-Legendre and angular Lebedev quadratures that preserve the accuracy needed for practical applications. These quadratures are recommended for efficient calculation of electron scattering by polyatomic molecules.
The generation of arbitrary order, non-classical, Gauss-type quadrature for transport applications
Spence, Peter J.
2015-09-01
A method is presented, based upon the Stieltjes method (1884), for the determination of non-classical Gauss-type quadrature rules, and the associated sets of abscissae and weights. The method is then used to generate a number of quadrature sets, to arbitrary order, which are primarily aimed at deterministic transport calculations. The quadrature rules and sets detailed include arbitrary order reproductions of those presented by Abu-Shumays in [4,8] (known as the QR sets, but labelled QRA here), in addition to a number of new rules and associated sets; these are generated in a similar way, and we label them the QRS quadrature sets. The method presented here shifts the inherent difficulty (encountered by Abu-Shumays) associated with solving the non-linear moment equations, particular to the required quadrature rule, to one of the determination of non-classical weight functions and the subsequent calculation of various associated inner products. Once a quadrature rule has been written in a standard form, with an associated weight function having been identified, the calculation of the required inner products is achieved using specific variable transformations, in addition to the use of rapid, highly accurate quadrature suited to this purpose. The associated non-classical Gauss quadrature sets can then be determined, and this can be done to any order very rapidly. In this paper, instead of listing weights and abscissae for the different quadrature sets detailed (of which there are a number), the MATLAB code written to generate them is included as Appendix D. The accuracy and efficacy (in a transport setting) of the quadrature sets presented is not tested in this paper (although the accuracy of the QRA quadrature sets has been studied in [12,13]), but comparisons to tabulated results listed in [8] are made. When comparisons are made with one of the azimuthal QRA sets detailed in [8], the inherent difficulty in the method of generation, used there, becomes apparent
Schuyler, Adam D; Maciejewski, Mark W; Stern, Alan S; Hoch, Jeffrey C
2015-01-01
Nonuniform sampling (NUS) in multidimensional NMR permits the exploration of higher dimensional experiments and longer evolution times than the Nyquist Theorem practically allows for uniformly sampled experiments. However, the spectra of NUS data include sampling-induced artifacts and may be subject to distortions imposed by sparse data reconstruction techniques, issues not encountered with the discrete Fourier transform (DFT) applied to uniformly sampled data. The characterization of these NUS-induced artifacts allows for more informed sample schedule design and improved spectral quality. The DFT–Convolution Theorem, via the point-spread function (PSF) for a given sampling scheme, provides a useful framework for exploring the nature of NUS sampling artifacts. In this work, we analyze the PSFs for a set of specially constructed NUS schemes to quantify the interplay between randomization and dimensionality for reducing artifacts relative to uniformly undersampled controls. In particular, we find a synergistic relationship between the indirect time dimensions and the “quadrature phase dimension” (i.e. the hypercomplex components collected for quadrature detection). The quadrature phase dimension provides additional degrees of freedom that enable partial-component NUS (collecting a subset of quadrature components) to further reduce sampling-induced aliases relative to traditional full-component NUS (collecting all quadrature components). The efficacy of artifact reduction is exponentially related to the dimensionality of the sample space. Our results quantify the utility of partial-component NUS as an additional means for introducing decoherence into sampling schemes and reducing sampling artifacts in high dimensional experiments. PMID:25899289
Design and Application of Quadrature Compensation Patterns in Bulk Silicon Micro-Gyroscopes
Ni, Yunfang; Li, Hongsheng; Huang, Libin
2014-01-01
This paper focuses on the detailed design issues of a peculiar quadrature reduction method named system stiffness matrix diagonalization, whose key technology is the design and application of quadrature compensation patterns. For bulk silicon micro-gyroscopes, a complete design and application case was presented. The compensation principle was described first. In the mechanical design, four types of basic structure units were presented to obtain the basic compensation function. A novel layout design was proposed to eliminate the additional disturbing static forces and torques. Parameter optimization was carried out to maximize the available compensation capability in a limited layout area. Two types of voltage loading methods were presented. Their influences on the sense mode dynamics were analyzed. The proposed design was applied on a dual-mass silicon micro-gyroscope developed in our laboratory. The theoretical compensation capability of a quadrature equivalent angular rate no more than 412 °/s was designed. In experiments, an actual quadrature equivalent angular rate of 357 °/s was compensated successfully. The actual compensation voltages were a little larger than the theoretical ones. The correctness of the design and the theoretical analyses was verified. They can be commonly used in planar linear vibratory silicon micro-gyroscopes for quadrature compensation purpose. PMID:25356646
On the Computation of High Order Rys Quadrature Weights and Nodes
NASA Technical Reports Server (NTRS)
Schwenke, David W.
2014-01-01
Since its introduction in 1976, the Rys Quadrature method has proven a very attractive method for evaluating electron repulsion integrals for calculations using Gaussian type orbitals. Since then, there have been considerable refinements of the method, but at it's core, Gaussian weights and nodes are used to exactly evaluate using a numerical approach to the transform integral. One of the powers of the Rys Quadrature method is the relative ease in evaluating integrals involving functions of high angular momentum. In this work we report on the complete resolution of these numerical difficulties, and we have easily computed accurate quadrature weights and nodes up to order 101. All calculations were carried out using 128-bit precision.
Řeháček, Jaroslav; Teo, Yong Siah; Hradil, Zdeněk; Wallentowitz, Sascha
2015-01-01
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterodyne detection can often lead to the latter giving more accurate estimates. This observation is also partly a manifestation of a fundamental relationship between the respective data uncertainties for the two schemes. In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection. PMID:26195198
Quadrature rules for finite element approximations of 1D nonlocal problems
NASA Astrophysics Data System (ADS)
Zhang, Xiaoping; Gunzburger, Max; Ju, Lili
2016-04-01
It is well known that calculations of the entries of the stiffness matrix in the finite element approximations of nonlocal diffusion and mechanics models are often very time-consuming due to the double integration process over the domain and the singularities of the nonlocal kernel functions. In this paper, we propose some effective and accurate quadrature rules for computing these double integrals for one-dimensional nonlocal problems; in particular, for problems with highly singular kernels, the corresponding inner integrals can be first evaluated exactly in our method, and the outer one then will be approximated by some popular quadrature rules. With these quadrature rules, the assembly of the stiffness matrix in the finite element method for the nonlocal problems becomes similar to that for the classical partial differential equations and is thus quite efficient.
Phase measurement device using inphase and quadrature components for phase estimation
NASA Technical Reports Server (NTRS)
Halverson, Peter G. (Inventor); Ware, Brent (Inventor); Shaddock, Daniel A. (Inventor); Spero, Robert E. (Inventor)
2009-01-01
A phasemeter for estimating the phase of a signal. For multi-tone signals, multiple phase estimates may be provided. An embodiment includes components operating in the digital domain, where a sampled input signal is multiplied by cosine and sine terms to provide estimates of the inphase and quadrature components. The quadrature component provides an error signal that is provided to a feedback loop, the feedback loop providing a model phase that tends to track the phase of a tone in the input signal. The cosine and sine terms are generated from the model phase. The inphase and quadrature components are used to form a residual phase, which is added to the model phase to provide an estimate of the phase of the input signal. Other embodiments are described and claimed.
Low-Latitude Solar Wind During the Fall 1998 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Poletto, G.; Suess, S. T.; Biesecker, D. A.; Esser, R.; Gloeckler, G.; Ko, Y.-K.; Zurbuchen, T. H.
2002-01-01
Solar and Heliospheric Observatory (SOH0)-Ulysses quadratures occur when the SOHO-Sun-Ulysses-included angle is 90 deg. These offer the opportunity to directly compare properties of plasma parcels, observed by SOHO [Dorningo et al.] in the low corona, with properties of the same parcels measured, in due time, in situ, by Ulysses [ Wenzel et al]. We refer the reader to Suess et al. for an extended discussion of SOHO-Ulysses quadrature geometry. Here it suffices to recall that there are two quadratures per year, as SOHO makes its one-year revolution around the Sun. This, because SOHO is at the L1 Lagrangian point, in essentially the same place as the Earth, while Ulysses is in a near-polar -5-year solar orbit with a perihelion of 1.34 AU and aphelion of 5.4 AU.
Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David
2013-05-21
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes. PMID:23697409
NASA Astrophysics Data System (ADS)
Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David
2013-05-01
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.
Cao, Yuan; Chan, Erwin H W; Wang, Xudong; Feng, Xinhuan; Guan, Bai-ou
2015-10-15
A photonic microwave quadrature filter is presented. It has a very simple structure, very low phase imbalance, and high signal-to-noise ratio performance. Experimental results are presented that demonstrate a photonic microwave quadrature filter with a 3 dB operating frequency range of 10.5-26.5 GHz, an amplitude and phase imbalance of less than ±0.3 dB and ±0.15°, and a signal-to-noise ratio of more than 121 dB in a 1 Hz noise bandwidth. PMID:26469589
Microwave photonic quadrature filter based on an all-optical programmable Hilbert transformer.
Huang, Thomas X H; Yi, Xiaoke; Minasian, Robert A
2011-11-15
A microwave photonic quadrature filter, new to our knowledge, based on an all-optical Hilbert transformer is presented. It is based on mapping of a Hilbert transform transfer function between the optical and electrical domains, using a programmable Fourier-domain optical processor and high-speed photodiodes. The technique enables the realization of an extremely wide operating bandwidth, tunable programmable bandwidth, and a highly precise amplitude and phase response. Experimental results demonstrate a microwave quadrature filter from 10 to 20 GHz, which achieves an amplitude imbalance of less than ±0.23 dB and a phase imbalance of less than ±0.5°. PMID:22089590
On the remainder term of Gauss-Radau quadratures for analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2008-09-01
For analytic functions the remainder term of Gauss-Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ±1 and a sum of semi-axes [varrho]>1 for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209-226] is proved.
Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity
NASA Astrophysics Data System (ADS)
Bultheel, Adhemar; Daruis, Leyla; González-Vera, Pablo
2009-09-01
In this paper we investigate the Szego-Radau and Szego-Lobatto quadrature formulas on the unit circle. These are (n+m)-point formulas for which m nodes are fixed in advance, with m=1 and m=2 respectively, and which have a maximal domain of validity in the space of Laurent polynomials. This means that the free parameters (free nodes and positive weights) are chosen such that the quadrature formula is exact for all powers zj, -p<=j<=p, with p=p(n,m) as large as possible.
An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures
NASA Astrophysics Data System (ADS)
Calabrò, F.; Corbo Esposito, A.
2009-07-01
This work is devoted to the study of quadrature rules for integration with respect to (w.r.t.) general probability measures with known moments. Automatic calculation of the Clenshaw-Curtis rules is considered and analyzed. It is shown that it is possible to construct these rules in a stable manner for quadrature w.r.t. balanced measures. In order to make a comparison Gauss rules and their stable implementation for integration w.r.t. balanced measures are recalled. Convergence rates are tested in the case of binomial measures.
NASA Astrophysics Data System (ADS)
Amin, Najam Muhammad; Zhigong, Wang; Zhiqun, Li
2015-05-01
A down-conversion in-phase/quadrature (I/Q) mixer employing a folded-type topology, integrated with a passive differential quadrature all-pass filter (D-QAF), in order to realize the final down-conversion stage of a 60 GHz receiver architecture is presented in this work. Instead of employing conventional quadrature generation techniques such as a polyphase filter or a frequency divider for the local oscillator (LO) of the mixer, a passive D-QAF structure is employed. Fabricated in a 65 nm CMOS process, the mixer exhibits a voltage gain of 7-8 dB in an intermediate frequency (IF) band ranging from 10 MHz-1.75 GHz. A fixed LO frequency of 12 GHz is used to down-convert a radio frequency (RF) band of 10.25-13.75 GHz. The mixer displays a third order input referred intercept point (IIP3) ranging from -8.75 to -7.37 dBm for a fixed IF frequency of 10 MHz and a minimum single-sideband noise figure (SSB-NF) of 11.3 dB. The mixer draws a current of 6 mA from a 1.2 V supply voltage dissipating a power of 7.2 mW. Project supported by the National High Technology Research and Development Program of China (No. 2011AA010200).
Oder, J.M.
1997-12-01
Several new quadrature sets for use in the discrete ordinates method of solving the Boltzmann neutral particle transport equation are derived. These symmetric quadratures extend the traditional symmetric quadratures by allowing ordinates perpendicular to one or two of the coordinate axes. Comparable accuracy with fewer required ordinates is obtained. Quadratures up to seventh order are presented. The validity and efficiency of the quadratures is then tested and compared with the Sn level symmetric quadratures relative to a Monte Carlo benchmark solution. The criteria for comparison include current through the surface, scalar flux at the surface, volume average scalar flux, and time required for convergence. Appreciable computational cost was saved when used in an unstructured tetrahedral cell code using highly accurate characteristic methods. However, no appreciable savings in computation time was found using the new quadratures compared with traditional Sn methods on a regular Cartesian mesh using the standard diamond difference method. These quadratures are recommended for use in three-dimensional calculations on an unstructured mesh.
Numerical Quadrature and Operator Splitting in Finite Element Methods for Cardiac Electrophysiology
Krishnamoorthi, Shankarjee; Sarkar, Mainak; Klug, William S.
2015-01-01
SUMMARY We examine carefully the numerical accuracy and computational efficiency of alternative formulations of the finite-element solution procedure for the mono-domain equations of cardiac electrophysiology (EP), focusing on the interaction of spatial quadrature implementations with operator splitting, examining both nodal and Gauss quadrature methods, and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of “lumped” approximations of consistent capacitance and mass matrices. Most generally we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state-variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally we illustrate some of the physiological consequences of discretization error in EP simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce non-uniform meshes having a large distribution of element sizes. PMID:23873868
NASA Astrophysics Data System (ADS)
Warger, William C., II; Newmark, Judith A.; Zhao, Bing; Warner, Carol M.; DiMarzio, Charles A.
2006-02-01
Present imaging techniques used in in vitro fertilization (IVF) clinics are unable to produce accurate cell counts in developing embryos past the eight-cell stage. We have developed a method that has produced accurate cell counts in live mouse embryos ranging from 13-25 cells by combining Differential Interference Contrast (DIC) and Optical Quadrature Microscopy. Optical Quadrature Microscopy is an interferometric imaging modality that measures the amplitude and phase of the signal beam that travels through the embryo. The phase is transformed into an image of optical path length difference, which is used to determine the maximum optical path length deviation of a single cell. DIC microscopy gives distinct cell boundaries for cells within the focal plane when other cells do not lie in the path to the objective. Fitting an ellipse to the boundary of a single cell in the DIC image and combining it with the maximum optical path length deviation of a single cell creates an ellipsoidal model cell of optical path length deviation. Subtracting the model cell from the Optical Quadrature image will either show the optical path length deviation of the culture medium or reveal another cell underneath. Once all the boundaries are used in the DIC image, the subtracted Optical Quadrature image is analyzed to determine the cell boundaries of the remaining cells. The final cell count is produced when no more cells can be subtracted. We have produced exact cell counts on 5 samples, which have been validated by Epi-Fluorescence images of Hoechst stained nuclei.
A Simple Approximation for the Symbol Error Rate of Triangular Quadrature Amplitude Modulation
NASA Astrophysics Data System (ADS)
Duy, Tran Trung; Kong, Hyung Yun
In this paper, we consider the error performance of the regular triangular quadrature amplitude modulation (TQAM). In particular, using an accurate exponential bound of the complementary error function, we derive a simple approximation for the average symbol error rate (SER) of TQAM over Additive White Gaussian Noise (AWGN) and fading channels. The accuracy of our approach is verified by some simulation results.
Serbes, G; Aydin, N
2011-01-01
Dual-tree complex wavelet transform (DTCWT), which is a shift invariant transform with limited redundancy, is an improved version of discrete wavelet transform. Complex quadrature signals are dual channel signals obtained from the systems employing quadrature demodulation. An example of such signals is quadrature Doppler signal obtained from blood flow analysis systems. Prior to processing Doppler signals using the DTCWT, directional flow signals must be obtained and then two separate DTCWT applied, increasing the computational complexity. In this study, in order to decrease computational complexity, a symmetrical modified DTCWT algorithm is proposed (SMDTCWT). A comparison between the new transform and the symmetrical phasing-filter technique is presented. Additionally denoising performance of SMDTCWT is compared with the DWT and the DTCWT using simulated signals. The results show that the proposed method gives the same output as the symmetrical phasing-filter method, the computational complexity for processing quadrature signals using DTCWT is greatly reduced and finally the SMDTCWT based denoising outperforms conventional DWT with same computational complexity. PMID:22255416
Saturation dependence of the quadrature conductivity of oil-bearing sands
NASA Astrophysics Data System (ADS)
Schmutz, M.; Blondel, A.; Revil, A.
2012-02-01
We have investigated the complex conductivity of oil-bearing sands with six distinct oil types including sunflower oil, silicone oil, gum rosin, paraffin, engine oil, and an industrial oil of complex composition. In all these experiments, the oil was the non-wetting phase. The in-phase (real) conductivity follows a power law relationship with the saturation (also known as the second Archie's law) but with a saturation exponent n raging from 1.1 to 3.1. In most experiments, the quadrature conductivity follows also a power law relationship with the water saturation but with a power law exponent p can be either positive or negative. For some samples, the quadrature conductivity first increases with saturation and then decreases indicating that two processes compete in controlling the quadrature conductivity. One is related to the insulating nature of the oil phase and a second could be associated with the surface area of the oil / water interface. The quadrature conductivity seems to be influenced not only by the value of the saturation exponent n (according to the Vinegar and Waxman model, p = n - 1), but also by the surface area between the oil phase and the water phase especially for very water-repellent oil having a fractal oil-water interface.
A multivariate quadrature based moment method for LES based modeling of supersonic combustion
NASA Astrophysics Data System (ADS)
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2012-07-01
The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.
NUMERICAL APPROXIMATION OF SEMI-INTEGRALS AND SEMIDERIVATIVES BY PRODUCT QUADRATURE RULES
This paper is concerned with the numerical calculation of the semi-integral and semiderivative of a function f, whose values f (xj) are known on a discrete set of abscissas 0 = x(1) < x(2) < ... < x(n). A family of product quadrature rules is developed to approximate the semi-int...
Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
1997-01-01
This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.
Pang, Yong; Yu, Baiying; Vigneron, Daniel B; Zhang, Xiaoliang
2014-02-01
Quadrature coils are often desired in MR applications because they can improve MR sensitivity and also reduce excitation power. In this work, we propose, for the first time, a quadrature array design strategy for parallel transmission at 298 MHz using single-feed circularly polarized (CP) patch antenna technique. Each array element is a nearly square ring microstrip antenna and is fed at a point on the diagonal of the antenna to generate quadrature magnetic fields. Compared with conventional quadrature coils, the single-feed structure is much simple and compact, making the quadrature coil array design practical. Numerical simulations demonstrate that the decoupling between elements is better than -35 dB for all the elements and the RF fields are homogeneous with deep penetration and quadrature behavior in the area of interest. Bloch equation simulation is also performed to simulate the excitation procedure by using an 8-element quadrature planar patch array to demonstrate its feasibility in parallel transmission at the ultrahigh field of 7 Tesla. PMID:24649430
Pang, Yong; Yu, Baiying; Vigneron, Daniel B.
2014-01-01
Quadrature coils are often desired in MR applications because they can improve MR sensitivity and also reduce excitation power. In this work, we propose, for the first time, a quadrature array design strategy for parallel transmission at 298 MHz using single-feed circularly polarized (CP) patch antenna technique. Each array element is a nearly square ring microstrip antenna and is fed at a point on the diagonal of the antenna to generate quadrature magnetic fields. Compared with conventional quadrature coils, the single-feed structure is much simple and compact, making the quadrature coil array design practical. Numerical simulations demonstrate that the decoupling between elements is better than –35 dB for all the elements and the RF fields are homogeneous with deep penetration and quadrature behavior in the area of interest. Bloch equation simulation is also performed to simulate the excitation procedure by using an 8-element quadrature planar patch array to demonstrate its feasibility in parallel transmission at the ultrahigh field of 7 Tesla. PMID:24649430
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.
NASA Astrophysics Data System (ADS)
Gabriel, C.; Aiello, A.; Berg-Johansen, S.; Marquardt, Ch.; Leuchs, G.
2012-07-01
Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [C. Gabriel et al., Phys. Rev. Lett. 106, 060502 (2011)]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, -1.2 dB ± 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations are, depending on the measurement scheme.
A PWM quadrature-booster phase shifter for ac power transmission
Lopes, L.A.C.; Joos, G.; Ooi, B.T.
1997-01-01
The conventional structures used for phase shifters employ quadrature voltage injection controlled by means of on-load tap changers that require considerable maintenance. Line-commutated thyristor structures have been proposed to replace tap changers, but problems related to filter requirements or the number of switches have limited their utilization. This paper proposes a pulse width modulation (PWM) quadrature-booster phase shifter based on a force-commutated ac controller. It offers features such as fast dynamic response, continuous variation of the phase angle with low harmonic injection, and it requires a simple power structure and can be controlled by adjusting the duty cycle of the switches. The operating principles of the proposed phase shifter are analyzed and their feasibility is demonstrated through digital simulation and experimental implementation.
Solution of stochastic media transport problems using a numerical quadrature-based method
Pautz, S. D.; Franke, B. C.; Prinja, A. K.; Olson, A. J.
2013-07-01
We present a new conceptual framework for analyzing transport problems in random media. We decompose such problems into stratified subproblems according to the number of material pseudo-interfaces within realizations. For a given subproblem we assign pseudo-interface locations in each realization according to product quadrature rules, which allows us to deterministically generate a fixed number of realizations. Quadrature integration of the solutions of these realizations thus approximately solves each subproblem; the weighted superposition of solutions of the subproblems approximately solves the general stochastic media transport problem. We revisit some benchmark problems to determine the accuracy and efficiency of this approach in comparison to randomly generated realizations. We find that this method is very accurate and fast when the number of pseudo-interfaces in a problem is generally low, but that these advantages quickly degrade as the number of pseudo-interfaces increases. (authors)
NASA Astrophysics Data System (ADS)
Pierré, J.-E.; Passieux, J.-C.; Périé, J.-N.; Bugarin, F.; Robert, L.
2016-02-01
Like subset-based methods, the very first finite element versions of digital image correlation were closely related to the regular structure of images, as they were based on regular quadrilateral elements corresponding to an integer number of pixels. The use of unstructured meshes, to exploit the full potential of FE-DIC in structural mechanics, is now widespread. Most of the time, the formulation, the quadrature and the definition of the region of interest still rely on the pixels grid. In this paper, a formulation in the physical coordinate system and not in the image frame is proposed for 2D digital image correlation. In addition to a more precise definition of the region of interest, it allows the use of a more accurate quadrature rule. It is also shown that lens distortions can be successfully taken into account directly with such a formalism.
Adams, M.L. ); Wareing, T.A. )
1993-01-01
We study diffusion-synthetic acceleration (DSA) for within-group scattering iterations in discrete ordinates calculations. We consider analytic (not spatially discretized) equations in Cartesian coordinates with linearly anisotropic scattering. We place no restrictions on the discrete ordinates quadrature set. We assume an infinite homogeneous medium. Our main results are as follows: 1. DSA is unstable in two dimensions (2D) and three dimensions (3D), given forward-peaked scattering. It can be stabilized by taking extra transport sweeps each iteration. 2. Standard DSA is unstable, given any quadrature set that does not correctly integrate linear functions of angle. 3. Relative to one dimension (ID), DSA's performance is degraded in 2D and 3D.
A note on the bounds of the error of Gauss-Turan-type quadratures
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.
2007-03-01
This note is concerned with estimates for the remainder term of the Gauss-Turan quadrature formula,where is the Gori-Michelli weight function, with Un-1(t) denoting the (n-1)th degree Chebyshev polynomial of the second kind, and f is a function analytic in the interior of and continuous on the boundary of an ellipse with foci at the points +/-1 and sum of semiaxes [varrho]>1. The present paper generalizes the results in [G.V. Milovanovic, M.M. Spalevic, Bounds of the error of Gauss-Turan-type quadratures, J. Comput. Appl. Math. 178 (2005) 333-346], which is concerned with the same problem when s=1.
NASA Astrophysics Data System (ADS)
Zhen, Shenglai; Chen, Bo; Yuan, Liang; Li, Min; Liang, Jing; Yu, Benli
2010-03-01
In-phase and quadrature-phase (I/Q) signals often need to be formed in the laser interferometric vibration measurement technique. To avoid the disadvantages of traditional I/Q signals forming methods such as effect of piezoelectric ceramic (PZT) for generating high frequency carrier, or optical configuration with complicated structure, a novel interferometric vibration measurement sensor with quadrature detection is proposed. The sensor utilizes simple optical configuration which contains 1/8 wave plate to generate two I/Q signals, then the signals were processed by arctangent algorithm which is compiled by Labview software through data acquisition card. Theoretical analysis and experimental Lissajous figures synthesis prove the phase orthogonality of the two signals. The experimental results indicate that the system can measure the vibration displacement accurately.
An accurate quadrature technique for the contact boundary in 3D finite element computations
NASA Astrophysics Data System (ADS)
Duong, Thang X.; Sauer, Roger A.
2015-01-01
This paper presents a new numerical integration technique for 3D contact finite element implementations, focusing on a remedy for the inaccurate integration due to discontinuities at the boundary of contact surfaces. The method is based on the adaptive refinement of the integration domain along the boundary of the contact surface, and is accordingly denoted RBQ for refined boundary quadrature. It can be used for common element types of any order, e.g. Lagrange, NURBS, or T-Spline elements. In terms of both computational speed and accuracy, RBQ exhibits great advantages over a naive increase of the number of quadrature points. Also, the RBQ method is shown to remain accurate for large deformations. Furthermore, since the sharp boundary of the contact surface is determined, it can be used for various purposes like the accurate post-processing of the contact pressure. Several examples are presented to illustrate the new technique.
Quadrature algorithms to the luminosity distance with a time-dependent dark energy model
Yue, Nan-Nan; Liu, De-Zi; Pei, Xiao-Xing; Zhang, Tong-Jie; Yang, Zhi-Liang; Zhu, Fang-Fang E-mail: bingzi@mail.bnu.edu.cn E-mail: fiona-90@live.cn E-mail: zlyang@bnu.edu.cn
2011-11-01
In our previous work [1], we have proposed two methods for computing the luminosity distance d{sub L}{sup Λ} in ΛCDM model. In this paper, two effective quadrature algorithms, known as Romberg Integration and composite Gaussian Quadrature, are presented to calculate the luminosity distance d{sub L}{sup CPL} in the Chevallier-Polarski-Linder parametrization(CPL) model. By comparing both the efficiency and accuracy of the two algorithms, we find that the second is more promising. Moreover, we develop another strategy adapted for approximating d{sub L}{sup Λ} in flat ΛCDM universe. To some extent, our methods can make contributions to the recent numerical stimulation for the investigation of dark energy cosmology.
New Adaptive Method for IQ Imbalance Compensation of Quadrature Modulators in Predistortion Systems
NASA Astrophysics Data System (ADS)
Zareian, Hassan; Vakili, Vahid Tabataba
2009-12-01
Imperfections in quadrature modulators (QMs), such as inphase and quadrature (IQ) imbalance, can severely impact the performance of power amplifier (PA) linearization systems, in particular in adaptive digital predistorters (PDs). In this paper, we first analyze the effect of IQ imbalance on the performance of a memory orthogonal polynomials predistorter (MOP PD), and then we propose a new adaptive algorithm to estimate and compensate the unknown IQ imbalance in QM. Unlike previous compensation techniques, the proposed method was capable of online IQ imbalance compensation with faster convergence, and no special calibration or training signals were needed. The effectiveness of the proposed IQ imbalance compensator was validated by simulations. The results clearly show the performance of the MOP PD to be enhanced significantly by adding the proposed IQ imbalance compensator.
Analysis of V-cycle multigrid algorithms for forms defined by numerical quadrature
Bramble, J.H. . Dept. of Mathematics); Goldstein, C.I.; Pasciak, J.E. . Applied Mathematics Dept.)
1994-05-01
The authors describe and analyze certain V-cycle multigrid algorithms with forms defined by numerical quadrature applied to the approximation of symmetric second-order elliptic boundary value problems. This approach can be used for the efficient solution of finite element systems resulting from numerical quadrature as well as systems arising from finite difference discretizations. The results are based on a regularity free theory and hence apply to meshes with local grid refinement as well as the quasi-uniform case. It is shown that uniform (independent of the number of levels) convergence rates often hold for appropriately defined V-cycle algorithms with as few as one smoothing per grid. These results hold even on applications without full elliptic regularity, e.g., a domain in R[sup 2] with a crack.
Quadrature conductivity: A quantitative indicator of bacterial abundance in porous media
Chi Zhang; Andre Revil; Yoshiko Fujita; Junko Munakata-Marr; George Redden
2014-09-01
ABSTRACT The abundance and growth stages of bacteria in subsurface porous media affect the concentrations and distributions of charged species within the solid-solution interfaces. Therefore, spectral induced polarization (SIP) measurements can be used to monitor changes in bacterial biomass and growth stage. Our goal was to gain a better understanding of the SIP response of bacteria present in a porous material. Bacterial cell surfaces possess an electric double layer and therefore become polarized in an electric field. We performed SIP measurements over the frequency range of 0.1–1 kHz on cell suspensions alone and cell suspensions mixed with sand at four pore water conductivities. We used Zymomonas mobilis at four different cell densities (in- cluding the background). The quadrature conductivity spectra exhibited two peaks, one around 0.05–0.10 Hz and the other around 1–10 Hz. Because SIP measurements on bacterial suspensions are typically made at frequencies greater than 1 Hz, these peaks have not been previously reported. In the bac-terial suspensions in growth medium, the quadrature conduc-tivity at peak I was linearly proportional to the density of the bacteria. For the case of the suspensions mixed with sands, we observed that peak II presented a smaller increase in the quadrature conductivity with the cell density. A comparison of the experiments with and without sand grains illustrated the effect of the porous medium on the overall quadrature con- ductivity response (decrease in the amplitude and shift of the peaks to the lower frequencies). Our results indicate that for a given porous medium, time-lapse SIP has potential for mon- itoring changes in bacterial abundance within porous media.
Rational Gauss-Chebyshev quadrature formulas for complex poles outside [-1,1
NASA Astrophysics Data System (ADS)
Deckers, Karl; van Deun, Joris; Bultheel, Adhemar
2008-06-01
In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [-1,1] to arbitrary complex poles outside [-1,1] . The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside [-1,1] .
Variable transformations and Gauss-Legendre quadrature for integrals with endpoint singularities
NASA Astrophysics Data System (ADS)
Sidi, Avram
2009-09-01
Gauss-Legendre quadrature formulas have excellent convergence properties when applied to integrals int^1_0f(x) dx with fin C^infty[0,1] . However, their performance deteriorates when the integrands f(x) are in C^infty(0,1) but are singular at x=0 and/or x=1 . One way of improving the performance of Gauss-Legendre quadrature in such cases is by combining it with a suitable variable transformation such that the transformed integrand has weaker singularities than those of f(x) . Thus, if x=psi(t) is a variable transformation that maps [0,1] onto itself, we apply Gauss-Legendre quadrature to the transformed integral int^1_{0}f(psi(t))psi'(t) dt , whose singularities at t=0 and/or t=1 are weaker than those of f(x) at x=0 and/or x=1 . In this work, we first define a new class of variable transformations we denote widetilde{mathcal{S}}_{p,q} , where p and q are two positive parameters that characterize it. We also give a simple and easily computable representative of this class. Next, by invoking some recent results by the author concerning asymptotic expansions of Gauss-Legendre quadrature approximations as the number of abscissas tends to infinity, we present a thorough study of convergence of the combined approximation procedure, with variable transformations from widetilde{mathcal{S}}_{p,q} . We show how optimal results can be obtained by adjusting the parameters p and q of the variable transformation in an appropriate fashion. We also give numerical examples that confirm the theoretical results.
Schrenk, Bernhard; Dris, Stefanos; Bakopoulos, Paraskevas; Lazarou, Ioannis; Voigt, Karsten; Zimmermann, Lars; Avramopoulos, Hercules
2012-08-01
Optical quadrature amplitude modulation (QAM) is experimentally demonstrated with a low-complexity modulator based on a semiconductor optical amplifier and electroabsorption modulator. Flexible amplitude/phase format transmission is achieved. The applicability of octary QAM for coherent optical access networks with sustainable 3 Gb/s per-user bandwidth is investigated for a long reach of 100 km, and its compatibility with a potentially high split is verified. PMID:22859139
Hayward, Thomas J; Oba, Roger M
2013-07-01
Numerical methods are presented for approximating the probability density functions (pdf's) of acoustic fields and receiver-array responses induced by a given joint pdf of a set of acoustic environmental parameters. An approximation to the characteristic function of the random acoustic field (the inverse Fourier transform of the field pdf) is first obtained either by construction of the empirical characteristic function (ECF) from a random sample of the acoustic parameters, or by application of generalized Gaussian quadrature to approximate the integral defining the characteristic function. The Fourier transform is then applied to obtain an approximation of the pdf by a continuous function of the field variables. Application of both the ECF and generalized Gaussian quadrature is demonstrated in an example of a shallow-water ocean waveguide with two-dimensional uncertainty of sound speed and attenuation coefficient in the ocean bottom. Both approximations lead to a smoother estimate of the field pdf than that provided by a histogram, with generalized Gaussian quadrature providing a smoother estimate at the tails of the pdf. Potential applications to acoustic system performance quantification and to nonparametric acoustic signal processing are discussed. PMID:23862782
A Gaussian quadrature method for total energy analysis in electronic state calculations
NASA Astrophysics Data System (ADS)
Fukushima, Kimichika
This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.
Wu, S.H.; Wu, C.Y.; Hsu, P.
1996-12-31
This work considers radiative heat transfer in a three-dimensional, rectangular, scattering medium exposed to diffuse radiation. Applying the quadrature method with singularity subtraction to the exact integral equations in terms of the moments of intensity can generate highly accurate solutions, and so the method is adopted in this work. The example solutions provided are for radiative equilibrium in homogeneous absorbing-emitting media, and for radiative transfer in nonhomogeneous absorbing-scattering (isotropic and linearly anisotropic) media with non-reflecting surfaces. To validate the solutions, the present results are compared with the solutions obtained by the YIX method and other methods.
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
NASA Technical Reports Server (NTRS)
Campbell, Joel
2008-01-01
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
Mathews, K.A.; Brennan, C.R.
1995-12-31
The exponential characteristic method is one of a family of nonlinear spatial quadratures which are positive and at least second order accurate. The authors initially developed the method in slab geometry, where it gave accurate results for deep penetration problems using coarse meshes. Characteristic methods are restricted to Cartesian geometries, so they next tested it with rectangular cells, where it was again a strong performer. Here the authors extend the method to unstructured grids of arbitrarily shaped and oriented triangles and report on its performance.
Optimization of quadrature signal processing for laser interferometers for demanding applications
NASA Astrophysics Data System (ADS)
PodŻorny, Tomasz; Budzyń, Grzegorz; Tkaczyk, Jakub
2016-06-01
Presented paper performs an analysis of quadrature signal processing algorithms for high demanding laser interferometry applications. Careful signal processing is required to minimize nonlinearities which come from optical path and components' imperfections, and reduce overall instrumental error. Paper focuses on algebraic fits, because implementation for real time systems was a main requirement. The most demanding applications are stationary measurements where the position slightly fluctuates in the range below one fringe period. Therefore, analysis was performed for samples that were spread along a few milliradians of a full circle.
Nodal systems with maximal domain of exactness for Gaussian quadrature formulas
NASA Astrophysics Data System (ADS)
Berriochoa, E.; Cachafeiro, A.
2008-03-01
The aim of this work is to study quadrature formulas for measures on the complex plane. The novelty of our contribution is to consider the exactness on subspaces of polynomials on the variables z and . Using this approach we characterize, in a unified way, the classical nodal systems for measures on the real line and the nodal systems for measures on the unit circle, which are based on para-orthogonal polynomials. We also characterize the nodal systems on the unit circle, which are not based on para-orthogonal polynomials (only for the case of nodal systems with 1 or 2 points).
Extremal states for photon number and quadratures as gauges for nonclassicality
NASA Astrophysics Data System (ADS)
Hradil, Z.; Řeháček, J.; de la Hoz, P.; Leuchs, G.; Sánchez-Soto, L. L.
2015-04-01
Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertainty relation, as well as a couple of weaker inequalities obtained by relaxing some restrictions of the problem. We also find the intelligent states saturating that relation and complete their characterization by considering extra constraints on the second-order moments of the variables involved. Using these moments, we construct performance measures tailored to diagnose photon-added and Schrödinger-cat-like states, among others.
On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands
NASA Astrophysics Data System (ADS)
Cruz-Barroso, Ruymán; González-Vera, Pablo; Njåstad, Olav
2007-04-01
In this paper, quadrature formulas with an arbitrary number of nodes and exactly integrating trigonometric polynomials up to degree as high as possible are constructed in order to approximate 2?-periodic weighted integralsE For this purpose, certain bi-orthogonal systems of trigonometric functions are introduced and their most relevant properties studied. Some illustrative numerical examples are also given. The paper completes the results previously given by Szeg? in Magy Tud Akad Mat Kut Intez K?zl 8:255?273, 1963 and by some of the authors in Annales Mathematicae et Informaticae 32:5?44, 2005.
Automatic IQ Imbalance Compensation Technique for Quadrature Modulator by Single-Tone Testing
NASA Astrophysics Data System (ADS)
Kim, Minseok; Konishi, Yohei; Takada, Jun-Ichi; Gao, Boxin
This letter proposes an automatic IQ imbalance compensation technique for quadrature modulators by means of spectrum measurement of RF signal using a spectrum analyzer. The analyzer feeds back only magnitude information of the frequency spectrum of the signal. To realize IQ imbalance compensation, the conventional method of steepest descent is modified; the descent direction is empirically determined and a variable step-size is introduced for accelerating convergence. The experimental results for a four-channel transmitter operating at 11GHz are presented for verification.
Vibration analysis of shear deformable circular arches by the differential quadrature method
NASA Astrophysics Data System (ADS)
Kang, K.; Bert, C. W.; Striz, A. G.
1995-06-01
The differential quadrature method is applied in the computation of the eigenvalues of the equations of motion governing in-plane and out-of-plane vibration of circular arches, based on the Bresse-Timoshenko beam theory in which both rotatory inertia and shear deformation are taken into account. Fundamental frequencies are calculated for arches of rectangular and circular cross sections under clamped-clamped end conditions and the results are compared with numerical solutions by another method. The present method gives good accuracy with only a limited number of grid points.
Application of Quadrature Methods for Re-Weighting in Lattice QCD
Abdou Abdel-Rehim, William Detmold, Kostas Orginos
2011-12-01
Re-weighting is a useful tool that has been employed in Lattice QCD in different contexts including, tuning the strange quark mass, approaching the light quark mass regime, and simulating electromagnetic fields on top of QCD gauge configurations. In case of re-weighting the sea quark mass, the re-weighting factor is given by the ratio of the determinants of two Dirac operators D{sub a} and D{sub b}. A popular approach for computing this ratio is to use a pseudofermion representation of the determinant of the composite operator {Omega} = D{sub a}(D{sub b}{sup {dagger}}D{sub b}){sup -1} D{sub a}{sup {dagger}}. Here, we study using quadrature methods together with noise vectors to compute the ratio of determinants. We show that, with quadrature methods each determinant can be computed separately using the operators {Omega}{sub a} = D{sub a}{sup {dagger}}D{sub a} and {Omega}{sub b} = D{sub b}{sup {dagger}} D{sub b}. We also discuss using bootstrap re-sampling to remove the bias from the determinant estimator.
First CFOA-based explicit-current-output quadrature sinusoidal oscillators using grounded capacitors
NASA Astrophysics Data System (ADS)
Lahiri, Abhirup; Jaikla, Winai; Siripruchyanun, Montree
2013-02-01
To date, no current-feedback operational amplifier (CFOA)-based sinusoidal oscillator has been reported which provides all the following features simultaneously: (i) current-mode quadrature sinusoidal oscillator providing two explicit-current-outputs (ECOs) from high output impedance terminals, (ii) employing no more than three CFOA ICs and six passive components, which include two grounded capacitors, (iii) offers independent tuning of the condition of oscillation (CO) via a resistor and (iv) provides tunability of the ratio of amplitudes of the generated quadrature ECOs via a separate resistor. To the best of authors' knowledge, this article reports first CFOA-based QOs in current-mode (i.e. providing two ECO signals). Experimental results using AD844 CFOA ICs from Analog Devices have been included to verify the workability of the proposed oscillator circuits. An example automatic gain control (AGC) loop to regulate the oscillation amplitude and control the THD has also been used and verified using SPICE simulations using the AD844 macro-model.
Shilyagin, P A; Gelikonov, G V; Gelikonov, V M; Moiseev, A A; Terpelov, D A
2014-07-31
We have thoroughly investigated the method of simultaneous reception of spectral components with the achromatised quadrature phase shift between two portions of a reference wave, designed for the effective suppression of the 'mirror' artefact in the resulting image obtained by means of spectral domain optical coherence tomography (SD OCT). We have developed and experimentally tested a phase-shifting element consisting of a beam divider, which splits the reference optical beam into the two beams, and of delay lines being individual for each beam, which create a mutual phase difference of π/2 in the double pass of the reference beam. The phase shift achromatism over a wide spectral range is achieved by using in the delay lines the individual elements with different dispersion characteristics. The ranges of admissible adjustment parameters of the achromatised delay line are estimated for exact and inexact conformity of the geometric characteristics of its components to those calculated. A possibility of simultaneous recording of the close-to-quadrature spectral components with a single linear photodetector element is experimentally confirmed. The suppression of the artefact mirror peak in the OCT-signal by an additional 9 dB relative to the level of its suppression is experimentally achieved when the air delay line is used. Two-dimensional images of the surface positioned at an angle to the axis of the probe beam are obtained with the correction of the 'mirror' artefact while maintaining the dynamic range of the image. (laser biophotonics)
Selcuk, N.; Kayakol, N.
1996-11-01
Effects of order of approximation (S{sub 2} and S{sub 4}), angular quadrature (S{sub n} and S{sub n}{prime}) and spatial differencing (diamond and variable-weight) schemes, on the predictive accuracy of discrete ordinates method were investigated by predicting the distributions of radiative flux density and source term of a rectangular enclosure problem and comparing the results with exact solutions produced previously. The enclosure problem is based on data reported earlier on a large-scale experimental furnace with steep temperature gradients. It is a black-walled enclosure containing an absorbing-emitting medium of constant properties. Comparisons show that better agreement is obtained in radiative energy source terms than in flux densities and that the order of approximation plays a more significant role than angular quadrature and spatial differencing schemes in the accuracy of predicted radiative flux densities and radiative energy source terms. Only slight improvements are obtained when S{sub n} and variable-weight differencing schemes are employed.
Mathews, K.; Sjoden, G.; Minor, B. )
1994-09-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in slab geometry is derived and compared with current methods. It is similar to the linear characteristic (or, in slab geometry, the linear nodal) quadrature but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx), whose parameters are root-solved to match the known (from the previous iteration) average and first moment of the source over the cell. Like the linear adaptive method, the exponential characteristic method is positive and nonlinear but more accurate and more readily extended to other cell shapes. The nonlinearity has not interfered with convergence. The authors introduce the exponential moment functions,'' a generalization of the functions used by Walters in the linear nodal method, and use them to avoid numerical ill-conditioning. The method exhibits O([Delta]x[sup 4]) truncation error on fine enough meshes; the error is insensitive to mesh size for coarse meshes. In a shielding problem, it is accurate to 10% using 16-mfp-thick cells; conventional methods err by 8 to 15 orders of magnitude. The exponential characteristic method is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems.
Maximum of the modulus of kernels in Gauss-Turan quadratures
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2008-06-01
We study the kernels K_{n,s}(z) in the remainder terms R_{n,s}(f) of the Gauss-Turan quadrature formulae for analytic functions on elliptical contours with foci at pm 1 , when the weight omega is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel \\vert K_{n,s}(z)\\vert attains its maximum on the real axis (positive real semi-axis) for each ngeq n_0, n_0Dn_0(rho,s) . It was stated as a conjecture in [Mathematics of Computation 72 (2003), 1855-1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes n in the corresponding Gauss-Turan quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each ngeq n_0, n_0Dn_0(rho,s) . Numerical examples are included. Retrieve articles in all Journals with MSC (1991): [41]41A55, [42]65D30, [43]65D32
Methods to Prescribe Particle Motion to Minimize Quadrature Error in Meshfree Methods
NASA Astrophysics Data System (ADS)
Templeton, Jeremy; Erickson, Lindsay; Morris, Karla; Poliakoff, David
2015-11-01
Meshfree methods are an attractive approach for simulating material systems undergoing large-scale deformation, such as spray break up, free surface flows, and droplets. Particles, which can be easily moved, are used as nodes and/or quadrature points rather than a relying on a fixed mesh. Most methods move particles according to the local fluid velocity that allows for the convection terms in the Navier-Stokes equations to be easily accounted for. However, this is a trade-off against numerical accuracy as the flow can often move particles to configurations with high quadrature error, and artificial compressibility is often required to prevent particles from forming undesirable regions of high and low concentrations. In this work, we consider the other side of the trade-off: moving particles based on reducing numerical error. Methods derived from molecular dynamics show that particles can be moved to minimize a surrogate for the solution error, resulting in substantially more accurate simulations at a fixed cost. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
A dual-band quadrature VCO with gain proportional to oscillation frequency
NASA Astrophysics Data System (ADS)
Wenrui, Zhu; Haigang, Yang; Tongqiang, Gao; Hui, Zhang
2013-08-01
This paper presents a novel dual-band quadrature voltage controlled oscillator (VCO) with the gain proportional to the oscillation frequency. Frequency synthesizers with this VCO can reduce the bandwidth fluctuation over all the frequency ranges without compensation or calibration. Besides the original switched capacitor array, an extra switched varactor array is adopted for the implementation of the proposed VCO. The tuning technique of changing the values of the capacitor and varactor at the same ratio is also derived. For verification purposes, a 2.5 G/3.5 G dual-band quadrature VCO is fabricated in a 0.13 μm CMOS process for WiMAX applications. Measurement results show that the VCO gain is closely proportional to the oscillation frequency with ±16% variation over the entire frequency range. The phase noise is -138.15 dBc/Hz at 10 MHz from the 2.5 GHz carrier and -137.44 dBc/Hz at 10 MHz from the 3.5 GHz carrier.
A multivariate quadrature based approach for LES based supersonic combustion modeling
NASA Astrophysics Data System (ADS)
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2010-11-01
The direct quadrature method of moments (DQMOM) was developed to solve high-dimensional probability density function (PDF) equations that arise in the description of turbulent combustion. This method is particularly useful in shock-containing supersonic internal flows such as those encountered in scramjet engines. In the DQMOM approach, the PDF is described in terms of a finite number of weighted delta functions whose weights and locations in composition space are obtained by solving specific transport equations. Since this approach is fully Eulerian in nature, it is advantageous compared to conventional Lagrangian methods used for solving the PDF transport equation. However, implementation of this formulation in the context of the large eddy simulation (LES) methodology leads to large numerical errors. For instance, the high-resolution numerical schemes used in LES lead to non-realizable and diffusive evolution of the DQMOM equations. Here, we propose a novel semi-discrete quadrature method of moments (SeQMOM) that overcomes this problem. A decoupling procedure is used to extend this method to multivariate PDF descriptions. The numerical implementation in LES as well as validation exercises will be presented.
Low-Latitude Solar Wind During the Fall 1998 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Poletto, G.; Suess, Steven T.; Biesecker, D.; Esser, R.; Gloeckler, G.; Zurbuchen, T.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
The Fall 1998 SOlar-Heliospheric Observatory (SOHO) - Ulysses quadrature occurred when Ulysses was at 5.2 AU, 17.4 deg South of the equator, and off the West line of the Sun. SOHO coronal observations, at heliocentric distances of a few solar radii, showed that the line through the solar center and Ulysses crossed, over the first days of observations, a dark, weakly emitting area and through the northern edge of a streamer complex during the second half of the quadrature campaign. Ulysses in situ observations showed this transition to correspond to a decrease from higher speed wind typical of coronal hole flow to low speed wind. Physical parameters (density, temperature, flow speed) of the low latitude coronal plasma sampled over the campaign are determined using constraints from what is the same plasma measured later in situ and simulating the intensities of the Hydrogen Lyman-alpha and OVI 1032 and 1037 Angstrom lines, measured by the Ultra Violet Coronagraph Spectrometer (UVCS) on SOHO. The densities, temperatures and outflow speed are compared with the same characteristic flow parameters for high-latitude fast wind streams and typical slow solar wind.
A quadrature based method of moments for nonlinear Fokker-Planck equations
NASA Astrophysics Data System (ADS)
Otten, Dustin L.; Vedula, Prakash
2011-09-01
Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.
Suppressing the mechanical quadrature error of a quartz double-H gyroscope through laser trimming
NASA Astrophysics Data System (ADS)
Zhao, Ke; Feng, Li-Hui; Wang, Qian-Qian; Liu, Ming-Zhi; Wang, Ben-Guo; Cui, Fang; Sun, Yu-Nan
2013-11-01
In this paper, we introduce a z-axis quartz gyroscope using a double-H tuning fork, which has a high sensitivity. However, it also causes a large mechanical quadrature error. The laser trimming method is used to suppress this error at quartz level. The trimming law is obtained through the finite element method (FEM). A femtosecond laser processing system is used to trim the gold balancing masses on the beams, and experimental results are basically consistent with the simulated ones. The mechanical quadrature error is suppressed by 96%, from 26.3° s-1 to 1.1° s-1. Nonlinearity changes from 1.48% to 0.30%, angular random walk (ARW) is reduced from 2.19° h-1/2 to 1.42° h-1/2, and bias instability is improved by a factor of 7.7, from 197.6° h-1 to 25.4° h-1.
Patsourakos, Spiros; Vourlidas, Angelos E-mail: vourlidas@nrl.navy.mil
2009-08-01
The nature of coronal mass ejection (CME)-associated low corona propagating disturbances, 'extreme ultraviolet (EUV) waves', has been controversial since their discovery by EIT on SOHO. The low-cadence, single-viewpoint EUV images and the lack of simultaneous inner corona white-light observations have hindered the resolution of the debate on whether they are true waves or just projections of the expanding CME. The operation of the twin EUV imagers and inner corona coronagraphs aboard STEREO has improved the situation dramatically. During early 2009, the STEREO Ahead (STA) and Behind (STB) spacecrafts observed the Sun in quadrature having a {approx}90 deg. angular separation. An EUV wave and CME erupted from active region 11012, on February 13, when the region was exactly at the limb for STA and hence at disk center for STB. The STEREO observations capture the development of a CME and its accompanying EUV wave not only with high cadence but also in quadrature. The resulting unprecedented data set allowed us to separate the CME structures from the EUV wave signatures and to determine without doubt the true nature of the wave. It is a fast-mode MHD wave after all.
Performance of a Coded Non-Square Quadrature Amplitude Modulation Scheme over Fading Channels
NASA Astrophysics Data System (ADS)
Li, L.; Divsalar, D.; Dolinar, S.
2004-02-01
It is shown that a non-square (NS) 2^(2n+1)-ary quadrature amplitude modulation (QAM) can be decomposed into a single-parity-check (SPC) block encoder and a memoryless modulator with independent in-phase (I) and quadrature (Q) symbol mapping. When NS-2^(2n+1)-QAM is concatenated with a forward-error-correcting (FEC) code, iterative demodulation and decoding of the FEC code and the inherent SPC code of NS-2^(2n+1)-QAM exploits the modulation's inherent memory and its independent I- and Q-channel mapping and demapping. The capacity and the bit-/symbol-error-rate (BER/SER) performance of coded and uncoded NS-2^(2n+1)-QAM systems are given for both additive white Gaussian noise (AWGN) channels and Rayleigh fading channels and are compared to those of other conventional 2^(2n+1)-ary systems. Simulation results show that, with iterative demodulation and decoding, coded NS-8QAM outperforms three conventional 8-ary systems by at least 0.65 dB on AWGN channels and by at least 0.57 dB on Rayleigh fading channels at BER = 10^(-5), when the FEC code is a concatenation of (15,11) Hamming codes with rate-1 accumulator codes, while coded NS-32QAM outperforms standard 32QAM by about 0.45 dB on AWGN channels and by about 0.27 dB on Rayleigh fading channels.
NASA Astrophysics Data System (ADS)
Hasegawa, Takemitsu; Hibino, Susumu; Hosoda, Yohsuke; Ninomiya, Ichizo
2007-08-01
An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162?170, 1980) of adaptive type based on the Newton?Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207?217, 1991; ACM Trans. Math. Softw. 17:218?232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner?s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229?259. Academic, Orlando, FL, 1971).
NASA Astrophysics Data System (ADS)
Ogawa, Hisashi; Ohdan, Hideaki; Miyata, Kazunori; Taguchi, Masahiro; Makino, Kenzo; Yonezawa, Hidehiro; Yoshikawa, Jun-ichi; Furusawa, Akira
2016-06-01
Real-time controls based on quantum measurements are powerful tools for various quantum protocols. However, their experimental realization has been limited by mode mismatch between the temporal mode of quadrature measurement and that heralded by photon detection. Here, we demonstrate real-time quadrature measurement of a single-photon wave packet induced by photon detection by utilizing continuous temporal-mode matching between homodyne detection and an exponentially rising temporal mode. Single photons in exponentially rising modes are also expected to be useful resources for interactions with other quantum systems.
Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals
Quine, Richard W.; Rinard, George A.; Eaton, Sandra S.; Eaton, Gareth R.
2014-01-01
The use of multiple synchronized outputs from an AWG provides the opportunity to perform EPR experiments differently than by conventional EPR. We report a method for reconstructing the quadrature EPR spectrum from periodic signals that are generated with sinusoidal magnetic field modulation such as continuous wave (CW), multiharmonic, or rapid scan experiments. The signal is down-converted to an intermediate frequency (IF) that is less than the field scan or field modulation frequency and then digitized in a single channel. This method permits use of a high-pass analog filter before digitization to remove the strong non-EPR signal at the IF, that might otherwise overwhelm the digitizer. The IF is the difference between two synchronized X-band outputs from a Tektronix AWG 70002A arbitrary waveform generator (AWG), one of which is for excitation and the other is the reference for down-conversion. To permit signal averaging, timing was selected to give an exact integer number of full cycles for each frequency. In the experiments reported here the IF was 5 kHz and the scan frequency was 40 kHz. To produce sinusoidal rapid scans with a scan frequency eight times IF, a third synchronized output generated a square wave that was converted to a sine wave. The timing of the data acquisition with a Bruker SpecJet II was synchronized by an external clock signal from the AWG. The baseband quadrature signal in the frequency domain was reconstructed. This approach has the advantages that (i) the non-EPR response at the carrier frequency is eliminated, (ii) both real and imaginary EPR signals are reconstructed from a single physical channel to produce an ideal quadrature signal, and (iii) signal bandwidth does not increase relative to baseband detection. Spectra were obtained by deconvolution of the reconstructed signals for solid BDPA (1,3-bisdiphenylene-2-phenylallyl) in air, 0.2 mM trityl OX63 in water, 15N perdeuterated tempone, and a nitroxide with a 0.5 G partially
Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals.
Tseitlin, Mark; Yu, Zhelin; Quine, Richard W; Rinard, George A; Eaton, Sandra S; Eaton, Gareth R
2014-10-30
The use of multiple synchronized outputs from an arbitrary waveform generator (AWG) provides the opportunity to perform EPR experiments differently than by conventional EPR. We report a method for reconstructing the quadrature EPR spectrum from periodic signals that are generated with sinusoidal magnetic field modulation such as continuous wave (CW), multiharmonic, or rapid scan experiments. The signal is down-converted to an intermediate frequency (IF) that is less than the field scan or field modulation frequency and then digitized in a single channel. This method permits use of a high-pass analog filter before digitization to remove the strong non-EPR signal at the IF, that might otherwise overwhelm the digitizer. The IF is the difference between two synchronized X-band outputs from a Tektronix AWG 70002A, one of which is for excitation and the other is the reference for down-conversion. To permit signal averaging, timing was selected to give an exact integer number of full cycles for each frequency. In the experiments reported here the IF was 5kHz and the scan frequency was 40kHz. To produce sinusoidal rapid scans with a scan frequency eight times IF, a third synchronized output generated a square wave that was converted to a sine wave. The timing of the data acquisition with a Bruker SpecJet II was synchronized by an external clock signal from the AWG. The baseband quadrature signal in the frequency domain was reconstructed. This approach has the advantages that (i) the non-EPR response at the carrier frequency is eliminated, (ii) both real and imaginary EPR signals are reconstructed from a single physical channel to produce an ideal quadrature signal, and (iii) signal bandwidth does not increase relative to baseband detection. Spectra were obtained by deconvolution of the reconstructed signals for solid BDPA (1,3-bisdiphenylene-2-phenylallyl) in air, 0.2mM trityl OX63 in water, (15)N perdeuterated tempone, and a nitroxide with a 0.5G partially-resolved proton
Fast wavelength-scanning interferometry technique with derivative detection of quadrature signals
NASA Astrophysics Data System (ADS)
Číp, O.; Mikel, B.; Lazar, J.
2006-04-01
We present a laser interferometer where a narrow-line width tuneable VCSEL laser (Vertical-Cavity Surface-Emitting Laser) working at 760 nm is used. For the detection of an absolute distance, we have used a fast wavelength-scanning interferometry technique. In the first part of the work we introduce the absolute laser interferometer as a demonstrator for research of a digital detection of quadrature signals (X-cos and Y-sin). This interferometer uses polarized beams and magnitude division of interference fringes. The wavelength of VCSEL laser is swept with the mode-hop free tuning range more than 1.2 nm, by means of the amplitude modulation of the injection current. At the same time, the operating temperature of the VCSEL is stabilized with a fast digital temperature controller. We control the wavelength value and whole tuning process of the laser with the frequency lock to selected modes of an external Fabry-Perot etalon. Except the frequency lock, the Fabry-Perot mode spectrum identifies wavelength-tuning interval of VCSEL during each sweep. A digital signal processor (DSP) is heart of the control and detection system. It samples intensity signal from Fabry- Perot etalon and X-Y quadrature signals from the detection unit of the interferometer. After 1 nm sweep of the VCSEL wavelength, we obtain a number of passed interference fringes and the number of passed Fabry-Perot resonance modes, at the same time. On basis of these measured quantities we are able to calculate the instantaneous value of the optical path length difference between the measuring and reference arm of the demonstrational interferometer. The other part of the work is oriented to research and experimental testing of the digital detection of quadrature signals (X-cos and Y-sin) processed only on basis of one intensity signal (X-axis) that is produced by a simple photo-detector. On basis of traditional inversion function arctan(Y/X) we are able to determine instantaneous phase between interference
Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals
NASA Astrophysics Data System (ADS)
Tseitlin, Mark; Yu, Zhelin; Quine, Richard W.; Rinard, George A.; Eaton, Sandra S.; Eaton, Gareth R.
2014-12-01
The use of multiple synchronized outputs from an arbitrary waveform generator (AWG) provides the opportunity to perform EPR experiments differently than by conventional EPR. We report a method for reconstructing the quadrature EPR spectrum from periodic signals that are generated with sinusoidal magnetic field modulation such as continuous wave (CW), multiharmonic, or rapid scan experiments. The signal is down-converted to an intermediate frequency (IF) that is less than the field scan or field modulation frequency and then digitized in a single channel. This method permits use of a high-pass analog filter before digitization to remove the strong non-EPR signal at the IF, that might otherwise overwhelm the digitizer. The IF is the difference between two synchronized X-band outputs from a Tektronix AWG 70002A, one of which is for excitation and the other is the reference for down-conversion. To permit signal averaging, timing was selected to give an exact integer number of full cycles for each frequency. In the experiments reported here the IF was 5 kHz and the scan frequency was 40 kHz. To produce sinusoidal rapid scans with a scan frequency eight times IF, a third synchronized output generated a square wave that was converted to a sine wave. The timing of the data acquisition with a Bruker SpecJet II was synchronized by an external clock signal from the AWG. The baseband quadrature signal in the frequency domain was reconstructed. This approach has the advantages that (i) the non-EPR response at the carrier frequency is eliminated, (ii) both real and imaginary EPR signals are reconstructed from a single physical channel to produce an ideal quadrature signal, and (iii) signal bandwidth does not increase relative to baseband detection. Spectra were obtained by deconvolution of the reconstructed signals for solid BDPA (1,3-bisdiphenylene-2-phenylallyl) in air, 0.2 mM trityl OX63 in water, 15N perdeuterated tempone, and a nitroxide with a 0.5 G partially
Fürstenau, N; Schmidt, M; Bock, W J; Urbanczyk, W
1998-02-01
We describe the combination of a polarimetric pressure sensor with a two-wavelength passive quadrature demodulation system allowing for dynamic pressure sensing in the 10-MPa range with unambiguous fringe counting. Furthermore, continuous phase measurement with the arctan method applied to the quadrature interference signals after automatic offset subtraction is demonstrated for the first time, to our knowledge. A single low-coherent superluminescent diode is used as a light source, and a polarizing beam splitter in combination with two adjustable interference filters of slightly different central wavelengths serves for the creation of the quadrature signals. Results of initial experiments with 60-ms pressure relaxation-time constants with the fringe-counting technique demonstrate the performance that was predicted theoretically. The measured pressure sensitivity exhibits excellent agreement with the previous research of Bock and Urbanczyk [IEEE Trans. Instrum. Meas. 44, 694-697 (1995)] using a polarimetric readout. The fringe-contrast variation and the measurement range obtained experimentally show the fiber dispersion to influence dephasing (deviation from quadrature) and visibility decrease significantly with increasing pressure. PMID:18268638
Harris, R.; Wang, Z.; Liu, Y.
2007-11-19
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.
NASA Astrophysics Data System (ADS)
Harris, Rob; Wang, Z. J.; Liu, Yen
2008-01-01
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation.
Sorgenfrei, B L; Edelstein, W A
1996-07-01
Using separate preamplifiers for the two outputs of a quadrature receive coil (and then combining the preamplifier outputs in a quadrature hybrid) provides a better signal-to-noise ratio (SNR) than is obtained by directly combining the quadrature outputs in a hybrid followed by a single preamplifier. The advantage of the two-preamplifier configuration increases when the body coil impedance changes and is no longer matched to 50 ohms. Using 0.4 dB noise figure preamplifiers, theory predicts 1.53, 0.42, 0, 0.42, and 1.53 dB SNR advantage of the two-preamplifier configuration over the one-preamplifier arrangement at body coil impedances of 12.5, 25, 50, 100, and 200 ohms, respectively. Experimental hot/cold resistor noise figure measurements indicate 2.86, 0.65, 0.36, 0.83, and 1.40 dB noise figure advantage for the two preamplifier configuration relative to the one-preamplifier configuration at those impedances. Empirical gains larger than theoretically calculated are attributable to insertion losses of various circuit elements, such as the quadrature hybrid, for the one-preamplifier configuration. PMID:8795028
NASA Astrophysics Data System (ADS)
Shizgal, Bernie D.
2016-08-01
Nonclassical quadratures based on a new set of half-range polynomials, Tn(x) , orthogonal with respect to w(x) =e - x - b /√{ x } for x ∈ [ 0 , ∞) are employed in the efficient calculation of the nuclear fusion reaction rate coefficients from cross section data. The parameter b = B /√{kB T } in the weight function is temperature dependent and B is the Gamow factor. The polynomials Tn(x) satisfy a three term recurrence relation defined by two sets of recurrence coefficients, αn and βn. These recurrence coefficients define in turn the tridiagonal Jacobi matrix whose eigenvalues are the quadrature points and the weights are calculated from the first components of the eigenfunctions. For nonresonant nuclear reactions for which the astrophysical function can be expressed as a lower order polynomial in the relative energy, the convergence of the thermal average of the reactive cross section with this nonclassical quadrature is extremely rapid requiring in many cases 2-4 quadrature points. The results are compared with other libraries of nuclear reaction rate coefficient data reported in the literature.
Khaleghi, Salman; Chitgarha, Mohammad Reza; Yilmaz, Omer F; Tur, Moshe; Haney, Michael W; Langrock, Carsten; Fejer, Martin M; Willner, Alan E
2013-05-15
We experimentally demonstrate a reconfigurable optical converter/encoder for quadrature amplitude modulated (QAM) signals. The system utilizes nonlinear wavelength multicasting, conversion-dispersion delays, and simultaneous nonlinear multiplexing and sampling. We show baud rate tunability (31 and 20 Gbaud) and reconfigurable conversions from lower-order QAM signals to higher-order QAM signals (e.g., 64-QAM). PMID:23938882
Spherical-earth gravity and magnetic anomaly modeling by Gauss-Legendre quadrature integration
NASA Technical Reports Server (NTRS)
Von Frese, R. R. B.; Hinze, W. J.; Braile, L. W.; Luca, A. J.
1981-01-01
Gauss-Legendre quadrature integration is used to calculate the anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical earth. The procedure involves representation of the anomalous source as a distribution of equivalent point gravity poles or point magnetic dipoles. The distribution of equivalent point sources is determined directly from the volume limits of the anomalous body. The variable limits of integration for an arbitrarily shaped body are obtained from interpolations performed on a set of body points which approximate the body's surface envelope. The versatility of the method is shown by its ability to treat physical property variations within the source volume as well as variable magnetic fields over the source and observation surface. Examples are provided which illustrate the capabilities of the technique, including a preliminary modeling of potential field signatures for the Mississippi embayment crustal structure at 450 km.
Stochastic path integral approach to continuous quadrature measurement of a single fluorescing qubit
NASA Astrophysics Data System (ADS)
Jordan, Andrew N.; Chantasri, Areeya; Huard, Benjamin
I will present a theory of continuous quantum measurement for a superconducting qubit undergoing fluorescent energy relaxation. The fluorescence of the qubit is detected via a phase-preserving heterodyne measurement, giving the cavity mode quadrature signals as two continuous qubit readout results. By using the stochastic path integral approach to the measurement physics, we obtain the most likely fluorescence paths between chosen boundary conditions on the state, and compute approximate correlation functions between all stochastic variables via diagrammatic perturbation theory. Of particular interest are most-likely paths describing increasing energy during the florescence. Comparison to Monte Carlo numerical simulation and experiment will be discussed. This work was supported by US Army Research Office Grants No. W911NF-09-0-01417 and No. W911NF-15-1-0496, by NSF Grant DMR-1506081, by John Templeton Foundation Grant ID 58558, and by the DPSTT Project Thailand.
NASA Astrophysics Data System (ADS)
Ezz-Eldien, S. S.
2016-07-01
This manuscript presents a new numerical approach to approximate the solution of a class of fractional variational problems. The presented approach is consisting of using the shifted Legendre orthonormal polynomials as basis functions of the operational matrix of fractional derivatives (described in the Caputo sense) and that of fractional integrals (described in the sense of Riemann-Liouville) with the help of the Legendre-Gauss quadrature formula together with the Lagrange multipliers method for converting such fractional variational problems into easier problems that consist of solving an algebraic system in the unknown coefficients. The convergence of the proposed method is analyzed. Finally, in order to demonstrate the accuracy of the present method, some test problems are introduced with their approximate solutions and comparisons with other numerical approaches.
Real-space quadrature: A convenient, efficient representation for multipole expansions
NASA Astrophysics Data System (ADS)
Rogers, David M.
2015-02-01
Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem—completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson's operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation.
NASA Technical Reports Server (NTRS)
Dobson, Chris C.; Jones, Jonathan E.; Chavers, Greg
2003-01-01
A polychromatic microwave quadrature interferometer has been characterized using several laboratory plasmas. Reflections between the transmitter and the receiver have been observed, and the effects of including reflection terms in the data reduction equation have been examined. An error analysis which includes the reflections, modulation of the scene beam amplitude by the plasma, and simultaneous measurements at two frequencies has been applied to the empirical database, and the results are summarized. For reflection amplitudes around 1096, the reflection terms were found to reduce the calculated error bars for electron density measurements by about a factor of 2. The impact of amplitude modulation is also quantified. In the complete analysis, the mean error bar for high- density measurements is 7.596, and the mean phase shift error for low-density measurements is 1.2". .
Stress fields around two pores in an elastic body: exact quadrature domain solutions
Crowdy, Darren
2015-01-01
Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky–Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores. PMID:26339198
Kienreich, I. W.; Temmer, M.; Veronig, A. M. E-mail: mat@igam.uni-graz.a
2009-10-01
We present the first observations of a global coronal wave ('EIT wave') from the two STEREO satellites in quadrature. The wave's initiation site was at the disk center in STEREO-B and precisely on the limb in STEREO-A. These unprecedented observations from the STEREO Extreme Ultraviolet Imaging (EUVI) instruments enable us to gain insight into the wave's kinematics, initiation, and three-dimensional structure. The wave propagates globally over the whole solar hemisphere visible to STEREO-B with a constant velocity of {approx}263 +- 16 km s{sup -1}. From the two STEREO observations, we derive a height of the wave in the range of {approx}80-100 Mm. Comparison of the wave kinematics with the early phase of the erupting coronal mass ejection (CME) structure indicates that the wave is initiated by the CME lateral expansion, and then propagates freely with a velocity close to the fast magnetosonic speed in the quiet solar corona.
All-atomic generation and noise-quadrature filtering of squeezed vacuum in hot Rb vapor
NASA Astrophysics Data System (ADS)
Horrom, Travis; Romanov, Gleb; Novikova, Irina; Mikhailov, Eugeniy E.
2013-01-01
With our all-atomic squeezing and filtering setup, we demonstrate control over the noise amplitudes and manipulation of the frequency-dependent squeezing angle of a squeezed vacuum quantum state by passing it through an atomic medium with electromagnetically induced transparency (EIT). We generate low sideband frequency squeezed vacuum using the polarization self-rotation effect in a hot Rb vapor cell, and direct it through a second atomic vapor subject to EIT conditions. We use the frequency-dependent absorption of the EIT window to demonstrate an example of squeeze amplitude attenuation and squeeze angle rotation of the quantum noise quadratures of the squeezed probe. These studies have implications for quantum memory and storage as well as gravitational wave interferometric detectors.
Minor, B.; Mathews, K.
1995-07-01
The exponential characteristic (EC) spatial quadrature for discrete ordinates neutral particle transport previously introduced in slab geometry is extended here to x-y geometry with rectangular cells. The method is derived and compared with current methods. It is similar to the linear characteristic (LC) quadrature (a linear-linear moments method) but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx + cy), whose parameters are rootsolved to match the known (from the previous iteration) spatial average and first moments of the source over the cell. Similarly, EC assumes exponential distributions of flux along cell edges through which particles enter the cell, with parameters chosen to match the average and first moments of flux, as passed from the adjacent, upstream cells (or as determined by boundary conditions). Like the linear adaptive (LA) method, EC is positive and nonlinear. It is more accurate than LA and does not require subdivision of cells. The nonlinearity has not interfered with convergence. The exponential moment functions, which were introduced with the slab geometry method, are extended to arbitrary dimensions (numbers of arguments) and used to avoid numerical ill conditioning. As in slab geometry, the method approaches O({Delta}x{sup 4}) global truncation error on fine-enough meshes, while the error is insensitive to mesh size for coarse meshes. Performance of the method is compared with that of the step characteristic, LC, linear nodal, step adaptive, and LA schemes. The EC method is a strong performer with scattering ratios ranging from 0 to 0.9 (the range tested), particularly so for lower scattering ratios. As in slab geometry, EC is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems.
NASA Astrophysics Data System (ADS)
Gorbachev, D. V.; Ivanov, V. I.
2015-08-01
Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles.
NASA Technical Reports Server (NTRS)
Clark, William A. (Inventor); Juneau, Thor N. (Inventor); Lemkin, Mark A. (Inventor); Roessig, Allen W. (Inventor)
2001-01-01
A microfabricated vibratory rate gyroscope to measure rotation includes two proof-masses mounted in a suspension system anchored to a substrate. The suspension has two principal modes of compliance, one of which is driven into oscillation. The driven oscillation combined with rotation of the substrate about an axis perpendicular to the substrate results in Coriolis acceleration along the other mode of compliance, the sense-mode. The sense-mode is designed to respond to Coriolis accelerationwhile suppressing the response to translational acceleration. This is accomplished using one or more rigid levers connecting the two proof-masses. The lever allows the proof-masses to move in opposite directions in response to Coriolis acceleration. The invention includes a means for canceling errors, termed quadrature error, due to imperfections in implementation of the sensor. Quadrature-error cancellation utilizes electrostatic forces to cancel out undesired sense-axis motion in phase with drive-mode position.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Rashidi, Mohammad Mehdi
2016-04-01
In this paper, we propose a modified cubic B-spline differential quadrature method (MCB-DQM) to solve three-dimensional (3D) coupled viscous Burger equation with appropriate initial and boundary conditions. In this method, modified cubic B-spline is treated as a basis function in the differential quadrature method (DQM) to compute the weighting coefficients. In this way, the Burger equation is reduced into a system of ordinary differential equations. An optimal strong stability-preserving Runge-Kutta (SSP-RK) method is employed to solve the resulting system of ordinary differential equations. In order to illustrate the accuracy and efficiency of the proposed method, a numerical problem is considered. From the numerical experiment, it is found that the computed result is in good agreement with the exact solution. Stability analysis of the method is also carried out using the matrix stability analysis method and found to be unconditionally stable.
NASA Technical Reports Server (NTRS)
Caves, C. M.; Schumaker, B. L.
1985-01-01
A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).
Error analysis in some Gauss-Turan-Radau and Gauss-Turan-Lobatto quadratures for analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.
2004-03-01
We consider the generalized Gauss-Turan quadrature formulae of Radau and Lobatto type for approximating . The aim of this paper is to analyze the remainder term in the case when f is an analytic function in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses (cf. SIAM J. Numer. Anal. 80 (1983) 1170). Sufficient conditions on the convergence for some of such quadratures, associated with the generalized Chebyshev weight functions, are found. Using some ideas from Hunter (BIT 35 (1995) 64) we obtain new estimates of the remainder term, which are very exact. Some numerical results and illustrations are shown.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Kumar, Jai
2014-11-01
In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.
2007-01-01
During quadrature, plasma seen on the limb of the Sun, along the radi al direction to Ulysses, by SOHO or STEREO can be sampled in situ as lt later passes Ulysses. A figure shows a coronagraph image, the rad ial towards Ulysses at 58 deg. S. and the SOHO/UVCS slit positions d uring one set of observations. A CME subsequently occurred and passed Ulysses (at 3/4 AU) 15 days later.
NASA Astrophysics Data System (ADS)
El-Orany, Faisal A. A.
2006-12-01
For the multiphoton intensity-dependent Jaynes Cummings model (JCM) described by a two-level atom interacting with a radiation field, we prove that there is a relationship between the atomic inversion and the quadrature squeezing. We give the required condition to obtain best information from this relation. Also we show that this relation is only sensitive to large values of the detuning parameter. Furthermore, we discuss briefly such relation for the off-resonance standard JCM.
NASA Astrophysics Data System (ADS)
Warger, William C., II; Newmark, Judith A.; Chang, ChihChing; Brooks, Dana H.; Warner, Carol M.; DiMarzio, Charles A.
2005-03-01
The Multifunctional Staring Mode Microscope was developed to permit three modes of imaging for cell counting in mouse embryos: Optical Quadrature, Differential Interference Contrast (DIC), and Fluorescence Imaging. The Optical Quadrature Microscope, consisting of a modified Mach-Zender Interferometer, uses a 632.8 nm laser to measure the amplitude and phase of the signal beam that travels through the embryo. Four cameras, preceded by multiple beamsplitters, are used to read the four interferograms, which are then combined to produce an image of the complex electric field amplitude. The phase of the complex amplitude is then unwrapped using a 2-D phase unwrap algorithm and images of optical path length are produced. To combine the additional modes of DIC and Fluorescence Imaging with the Optical Quadrature Microscope, a 632.8 nm narrow bandpass beamsplitter was placed at the output of the microscope. This allows the laser light to continue through the Mach-Zender while all other wavelengths are reflected at 90 degrees to another camera. This was effective in combining the three modes as the fluorescence wavelength for the Hoechst stain is well below the bandpass window of the beamsplitter. Both live and fixed samples have been successfully imaged in all three modes. Accuracy in cell counting was achieved by using the DIC image for detecting cell boundaries and the Optical Quadrature image for phase mapping to determine where cells overlap. The final results were verified by Hoechst fluorescence imaging to count the individual nuclei. Algorithms are currently being refined so larger cell counts can be done more efficiently.
A Homodyne Quadrature Laser Interferometer for Micro-Asperity Deformation Analysis
PogaČnik, Aljaž; Požar, Tomaž; Kalin, Mitjan; Možina, Janez
2013-01-01
We report on the successful realization of a contactless, non-perturbing, displacement-measuring system for characterizing the surface roughness of polymer materials used in tribological applications. A single, time-dependent, scalar value, dubbed the collective micro-asperity deformation, is extracted from the normal-displacement measurements of normally loaded polymer samples. The displacement measurements with a sub-nanometer resolution are obtained with a homodyne quadrature laser interferometer. The measured collective micro-asperity deformation is critical for a determination of the real contact area and thus for the realistic contact conditions in tribological applications. The designed measuring system senses both the bulk creep as well as the micro-asperity creep occurring at the roughness peaks. The final results of our experimental measurements are three time-dependent values of the collective micro-asperity deformation for the three selected surface roughnesses. These values can be directly compared to theoretical deformation curves, which can be derived using existing real-contact-area models. PMID:23296328
Generation of fast neturon spectra using an adaptive Gauss-Kronrod Quadrature algorithm
NASA Astrophysics Data System (ADS)
Triplett, Brian Scott
A lattice physics calculation is often the first step in analyzing a nuclear reactor. This calculation condenses regions of the reactor into average parameters (i.e., group constants) that can be used in coarser full-core, time-dependent calculations. This work presents a high-fidelity deterministic method for calculating the neutron energy spectrum in an infinite medium. The spectrum resulting from this calculation can be used to generate accurate group constants. This method includes a numerical algorithm based on Gauss-Kronrod Quadrature to determine the neutron transfer source to a given energy while controlling numerical error. This algorithm was implemented in a pointwise transport solver program called Pointwise Fast Spectrum Generator (PWFSG). PWFSG was benchmarked against the Monte Carlo program MCNP and another pointwise spectrum generation program, CENTRM, for a set of fast reactor infinite medium example cases. PWFSG showed good agreement with MCNP, yielding coefficients of determination above 98% for all example cases. In addition, PWFSG had 6 to 8 times lower flux estimation error than CENTRM in the cases examined. With run-times comparable to CENTRM, PWFSG represents a robust set of methods for generation of fast neutron spectra with increased accuracy without increased computational cost.
Recursive, in-place algorithm for the hexagonal orthogonal oriented quadrature image pyramid
NASA Technical Reports Server (NTRS)
Watson, Andrew B.
1989-01-01
Pyramid image transforms have proven useful in image coding and pattern recognition. The hexagonal orthogonal oriented quadrature image pyramid (HOP), transforms an image into a set of orthogonal, oriented, odd and even bandpass subimages. It operates on a hexagonal input lattice and employs seven kernels, each of which occupies a neighborhood consisting of a point and a hexagon of six nearest neighbors. The kernels consist of one lowpass and six bandpass kernels that are orthogonal, self-similar, and localized in space, spatial frequency, orientation, and phase. The kernels are first applied to the image samples to create the first level of the pyramid, then to the lowpass coefficients to create the next level. The resulting pyramid is a compact, efficient image code. Here, a recursive, in-place algorithm for computation of the HOP transform is described. The transform may be regarded as a depth-first traversal of a tree structure. It is shown that the algorithm requires a number of operations that is on the order of the number of pixels.
Accurate phase measurements for thick spherical objects using optical quadrature microscopy
NASA Astrophysics Data System (ADS)
Warger, William C., II; DiMarzio, Charles A.
2009-02-01
In vitro fertilization (IVF) procedures have resulted in the birth of over three million babies since 1978. Yet the live birth rate in the United States was only 34% in 2005, with 32% of the successful pregnancies resulting in multiple births. These multiple pregnancies were directly attributed to the transfer of multiple embryos to increase the probability that a single, healthy embryo was included. Current viability markers used for IVF, such as the cell number, symmetry, size, and fragmentation, are analyzed qualitatively with differential interference contrast (DIC) microscopy. However, this method is not ideal for quantitative measures beyond the 8-cell stage of development because the cells overlap and obstruct the view within and below the cluster of cells. We have developed the phase-subtraction cell-counting method that uses the combination of DIC and optical quadrature microscopy (OQM) to count the number of cells accurately in live mouse embryos beyond the 8-cell stage. We have also created a preliminary analysis to measure the cell symmetry, size, and fragmentation quantitatively by analyzing the relative dry mass from the OQM image in conjunction with the phase-subtraction count. In this paper, we will discuss the characterization of OQM with respect to measuring the phase accurately for spherical samples that are much larger than the depth of field. Once fully characterized and verified with human embryos, this methodology could provide the means for a more accurate method to score embryo viability.
Genovese, Luigi; Deutsch, Thierry
2015-12-21
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in density functional theory (DFT) is given by the external potential or the pseudo-potential describing the interaction between ions and electrons. The accuracy of the collocation method used is therefore very important for the reliability of subsequent treatments like self-consistent field solutions of the electronic structure problems. By construction, the collocation method introduces numerical artifacts typical of real-space treatments, like the so-called egg-box error, which may spoil the numerical stability of the description when the real-space grid is too coarse. As the external potential is an input of the problem, even a highly precise computational treatment cannot cope this inconvenience. We present in this paper a new quadrature scheme that is able to exactly preserve the moments of a given analytic function even for large grid spacings, while reconciling with the traditional collocation method when the grid spacing is small enough. In the context of real-space electronic structure calculations, we show that this method improves considerably the stability of the results for large grid spacings, opening up the path towards reliable low-accuracy DFT calculations with a reduced number of degrees of freedom. PMID:26372293
Real-space quadrature: A convenient, efficient representation for multipole expansions
Rogers, David M.
2015-02-21
Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem—completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson’s operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation.
Algorithm for the Time-Propagation of the Radial Diffusion Equation Based on a Gaussian Quadrature
Gillespie, Dirk
2015-01-01
The numerical integration of the time-dependent spherically-symmetric radial diffusion equation from a point source is considered. The flux through the source can vary in time, possibly stochastically based on the concentration produced by the source itself. Fick’s one-dimensional diffusion equation is integrated over a time interval by considering a source term and a propagation term. The source term adds new particles during the time interval, while the propagation term diffuses the concentration profile of the previous time step. The integral in the propagation term is evaluated numerically using a combination of a new diffusion-specific Gaussian quadrature and interpolation on a diffusion-specific grid. This attempts to balance accuracy with the least number of points for both integration and interpolation. The theory can also be extended to include a simple reaction-diffusion equation in the limit of high buffer concentrations. The method is unconditionally stable. In fact, not only does it converge for any time step Δt, the method offers one advantage over other methods because Δt can be arbitrarily large; it is solely defined by the timescale on which the flux source turns on and off. PMID:26208111
Real-space quadrature: a convenient, efficient representation for multipole expansions.
Rogers, David M
2015-02-21
Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem-completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson's operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation. PMID:25701996
Digital services using quadrature amplitude modulation (QAM) over CATV analog DWDM system
NASA Astrophysics Data System (ADS)
Yeh, JengRong; Selker, Mark D.; Trail, J.; Piehler, David; Levi, Israel
2000-04-01
Dense Wavelength Division Multiplexing (DWDM) has recently gained great popularity as it provides a cost effective way to increase the transmission capacity of the existing fiber cable plant. For a long time, Dense WDM was exclusively used for baseband digital applications, predominantly in terrestrial long haul networks and in some cases in metropolitan and enterprise networks. Recently, the performance of DWDM components and frequency-stabilized lasers has substantially improved while the costs have down significantly. This makes a variety of new optical network architectures economically viable. The first commercial 8- wavelength DWDM system designed for Hybrid Fiber Coax networks was reported in 1998. This type of DWDM system utilizes Sub-Carrier Multiplexing (SCM) of Quadrature Amplitude Modulated (QAM) signals to transport IP data digital video broadcast and Video on Demand on ITU grid lightwave carriers. The ability of DWDM to provide scalable transmission capacity in the optical layer with SCM granularity is now considered by many to be the most promising technology for future transport and distribution of broadband multimedia services.
Direct Quadrature Method of Moments for LES-based Modeling of Supersonic Combustion
NASA Astrophysics Data System (ADS)
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2009-11-01
The LES/transported probability density function (PDF) model has been successfully used for predictive modeling of turbulent combustion in low-speed flows. The PDF approach evolves the joint-distribution of the gas-phase thermochemical composition and is ideally suited for supersonic flows, where conserved-scalar approaches are not valid due to the compressible nature of the flow. In low-speed flows, the high-dimensionality of the PDF transport equation is handled through the use of Monte-Carlo based stochastic methods. However, the presence of shocks and large density and pressure gradients pose significant challenges in the use of these stochastic methods for high-speed flows. In this work, we propose a direct quadrature method of moments (DQMOM) approach, which is a fully Eulerian method for solving the PDF transport equation. Here, the subfilter PDF is discretized in terms of a finite number of delta functions, each characterized by a weight and an abscissa. Eulerian transport equations for these quantities are similar in structure to scalar transport equations and can be solved using finite-volume/finite difference approaches. Here, the accuracy of the DQMOM approach and the numerical implementation of this method using shock-capturing schemes are discussed.
NASA Astrophysics Data System (ADS)
Jamaly, Seyed Mohammad; Hasan Saidi, Mohammad; Ghafourian, Akbar
2007-11-01
In this study, due to the weaknesses of the models with Lagrangian approaches, an attempt has been made to model the spray flow with Eulerian approach. In this regard, the quadrature-based moment closure model for the spray equation, the so-called DQMOM, is applied. This method overcomes the shortcoming of other Eulerian methods while it is in good agreement with the Lagrangian methods. After that, the model has been developed to be able to deal with the evaporating droplets. Moreover, the feasibility of applying non-linear external forces, such as drag forces, and evaporation laws for the droplets are considered and implemented. The required order for the equations in this method has been studied thoroughly as well. Finally, the solution procedure for accurate computations of multi dimension problems is presented. In general, the proposed modified DQMOM method can consider and solve all kinds of spray flows with any desirable dimension for the problem. Here, assuming one-way coupling situation with the gas-phase in an axial engine, the spray phase equations are solved by the proposed method to account for evaporating droplets. Results are compared with the methods with Lagrangian approach and the computational costs and accuracies of the methods are compared as well.
Quadrature Method of Moments for the Simulation of Turbulent Reacting Flows
NASA Astrophysics Data System (ADS)
Raman, Venkatramanan; Pitsch, Heinz; Fox, Rodney
2003-11-01
Computational schemes for turbulent reacting flow systems typically solve the species transport equations using a grid-based Eulerian technique. Such schemes inherently do not contain information about the sub-grid scalar PDF required for the computation of the non-linear reaction source terms and sub-grid scalar dissipation. Though a transport equation for the scalar PDF can be formulated, the high-dimensional equation has to be solved using a computationally expensive particle-based Lagrangian scheme. To overcome this difficulty, the Direct Quadrature Method of Moments (DQMOM) is used to approximate the joint composition PDF by a set of delta functions. The delta-functions are characterized by their location and size, both of which are obtained by solving Eulerian transport equations. Using a N-peak description, N species-moments can be forced to be accurate. The Direct QMOM model is extended to LES schemes and comparisons are made with transported-PDF simulations for both reacting and non-reacting mixing layer setup. Re-formulation of the DQMOM equation leads to conditional multi-environment method that can be used for describing combustion systems that exhibit extinction.
Bottom-series coupled quadrature VCO using the inductive gate voltage boosting technique
NASA Astrophysics Data System (ADS)
Jang, Sheng-Lyang; Chou, Li-Te
2013-09-01
This article presents a new low-voltage bottom-series coupled quadrature voltage-controlled oscillator (QVCO), which consists of two n-core cross-coupled VCOs with the bottom-series coupling transistors. The low-voltage operation is obtained via an inductive gate voltage boosting technique. The proposed CMOS QVCO has been implemented with the TSMC 0.18 µm CMOS technology and the die area is 0.897 × 0.767 mm2. At the supply voltage of 0.7 V, the total power consumption is 1.5 mW. The free-running frequency of the QVCO is tuneable from 3.77 to 4.12 GHz as the tuning voltage is varied from 0.0 to 0.7 V. The measured phase noise at 1 MHz frequency offset is -123.35 dBc/Hz at the oscillation frequency of 4.12 GHz and the figure of merit of the proposed QVCO is -193.5 dBc/Hz.
Low Voltage Low Power Quadrature LC Oscillator Based on Back-gate Superharmonic Capacitive Coupling
NASA Astrophysics Data System (ADS)
Ma, Minglin; Li, Zhijun
2013-09-01
This work introduces a new low voltage low power superharmonic capacitive coupling quadrature LC oscillator (QLCO) made by coupling two identical cross-connected LC oscillators without tail transistor. In each of the core oscillators, the back-gate nodes of the cross-coupled NMOS pair and PMOS pair, acting as common mode nodes, have been connected directly. Then the core oscillators are coupled together via capacitive coupling of the PMOS common mode node in one of the core oscillators to the NMOS common mode node in the other core oscillator, and vice versa. Only capacitors are used for coupling of the two core oscillators and therefore no extra noise sources are imposed on the circuit. Operation of the proposed QLCO was investigated with simulation using a commercial 0.18 µm RF CMOS technology: it shows a power dissipation of 5.2 mW from a 0.6 V supply voltage. Since the proposed core oscillator has Complementary NMOS and PMOS cross coupled pairs, and capacitive coupling method will not introduce extra phase noise, so this circuit can operate with a low phase noise as low as -126.8 dBc/Hz at 1 MHz offset from center oscillation frequency of 2.4 GHz, as confirmed with simulation.
Hu, Wei; Zhao, Zhangyan; Wang, Yunfeng; Zhang, Haiying; Lin, Fujiang
2014-03-01
The designed sensor enables accurate reconstruction of chest-wall movement caused by cardiopulmonary activities, and the algorithm enables estimation of respiration, heartbeat rate, and some indicators of heart rate variability (HRV). In particular, quadrature receiver and arctangent demodulation with calibration are introduced for high linearity representation of chest displacement; 24-bit ADCs with oversampling are adopted for radar baseband acquisition to achieve a high signal resolution; continuous-wavelet filter and ensemble empirical mode decomposition (EEMD) based algorithm are applied for cardio/pulmonary signal recovery and separation so that accurate beat-to-beat interval can be acquired in time domain for HRV analysis. In addition, the wireless sensor is realized and integrated on a printed circuit board compactly. The developed sensor system is successfully tested on both simulated target and human subjects. In simulated target experiments, the baseband signal-to-noise ratio (SNR) is 73.27 dB, high enough for heartbeat detection. The demodulated signal has 0.35% mean squared error, indicating high demodulation linearity. In human subject experiments, the relative error of extracted beat-to-beat intervals ranges from 2.53% to 4.83% compared with electrocardiography (ECG) R-R peak intervals. The sensor provides an accurate analysis for heart rate with the accuracy of 100% for p = 2% and higher than 97% for p = 1%. PMID:24235293
NASA Technical Reports Server (NTRS)
Cao, Chang-Qi
1996-01-01
The amplitude and transverse quadrature component squeezing of coherent light in high Q cavity by injection of atoms of two-photon transition are studied. The Golubev-Sokolov master equation and generating function approach are utilized to derive the exact variances of photon number and of transverse quadrature component as function of t. The correlation functions and power spectrums of photon number noise and of output photon current noise are also investigated.
The 2011 February 15 Coronal Mass Ejection: Reconciling SOHO and STEREO Observations in Quadrature
NASA Technical Reports Server (NTRS)
Gopalswamy, Natchimuthuk
2011-01-01
The Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO observed a fast halo coronal mass ejection on 2011 February 15. The STEREO spacecraft were in quadrature with SOHO (STEREO-A ahead of Earth by 87 degrees and STEREO-B 94 degrees behind Earth), enabling CME measurement using the three spacecraft. The sky-plane speed measured by SOHO/LASCO is closely related to the expansion speed of the CME, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images measured the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (V(sub exp) ) and radial speed (V(sub rad)) derived previously from geometrical considerations (Gopalswamy et al. 2009): = V(sub rad) = 1/2 (1 + cot w) V(sub exp), where w is the half width of the CME. We can also measure the Earthward speed of the CME directly from the STEREO measurements. The travel time to Earth predicted from the Earthward speed using the Empirical Shock Arrival model is approximately 12 hours shorter than the actual travel time obtained from in situ measurements at Ll. The primary reason for this discrepancy seems to be the interaction with the two preceding CMEs that slowed down the CME in question. The CME interaction is also confirmed from the radio enhancement observed by Wind/WAVES and STEREO WAVES experiments.
A quadrature demodulation method based on tracking the ultrasound echo frequency.
Feng, Naizhang; Zhang, Jianqiu; Wang, Weiqi
2006-12-22
The ultrasound echo attenuation depends on frequency, propagating depth and tissue characteristics. Thus, the attenuation dependent on frequency results in a larger attenuation of high frequencies than lower when the wave propagates through the tissue. As a result, the central frequency of the echo generates the increasing downshift with the increasing of depth. In the traditional I/Q demodulation method, it is assumed that the central frequency of the echo is the same as the transmitting frequency and unchanged all time. The assumption directly causes that the acquired I/Q signals are not perfect baseband ones but biased due to the echo attenuation. In addition, the unreasonable assumption will keep the echo from getting better signal-to-noise ratio. A quadrature demodulation method based on tracking the ultrasound echo frequency is proposed in this paper. The method consists of the traditional I/Q demodulator, the frequency tracking module, the phase compensation module and the dynamic filtering module. The outputs of I/Q demodulator are biased. Autocorrelation technique is utilized in the frequency tracking unit to estimate the frequency bias according to the outputs of I/Q demodulator. The estimated bias feeds to the phase compensation unit which can eliminate the frequency bias by simple trigonometric function transform. The compensated signals feed to the dynamic filter and are further processed. The bandwidth of the dynamic filter decreases with the increasing of the depth, which makes the echo acquire better SNR in different depth. The efficiency of the proposed method is testified by both simulations and experiments. PMID:16860363
Niebauer, T M; Constantino, A; Billson, R; Hankla, A; Nelson, P G
2015-06-20
A corner-cube retroreflector has the property that the optical path length for a reflected laser beam is insensitive to rotations about a mathematical point called its optical center (OC). This property is exploited in ballistic absolute gravity meters in which a proof mass containing a corner-cube retroreflector is dropped in a vacuum, and its position is accurately determined with a laser interferometer. In order to avoid vertical position errors when the proof mass rotates during free fall, it is important to collocate its center of mass (COM) with the OC of the retroreflector. This is commonly done using a mechanical scale-based balancing procedure, which has limited accuracy due to the difficulty in finding the exact position of the COM and the OC. This paper describes a novel way to achieve the collocation by incorporating the proof mass into a pendulum and using a quadrature interferometer to interrogate its apparent translation in its twist mode. The mismatch between the COM and OC generates a signal in a quiet part of the spectrum where no mechanical resonance exists. This allows us to tune the position of the COM relative to the OC to an accuracy of about 1 μm in all three axes. This provides a way to directly demonstrate that a rotation of the proof mass by several degrees causes an apparent translation in the direction of the laser beam of less than 1 nm. This technique allows an order of magnitude improvement over traditional methods of balancing. PMID:26193025
NASA Technical Reports Server (NTRS)
Sidi, Avram; Pennline, James A.
1999-01-01
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
NASA Technical Reports Server (NTRS)
Sidi, Avram; Pennline, James A.
1999-01-01
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
SOHO-Ulysses Coordinated Studies During the Two Extended Quadratures and the Alignment of 2007-2008
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.
2007-01-01
During SOHO-Sun-Ulysses quadratures the geometry of the configuration makes it possible to sample "in situ" the plasma parcels that are remotely observed in the corona. Although the quadrature position occurs at a well defined instant in time, we typically take data while Ulysses is within +/- 5 degrees of the limb, with the understanding that plasma sampled by Ulysses over this time interval can all be traced to its source in the corona. The relative positions of SOHO and Ulysses in winter 2007 (19 Dec 2006-28 May 2007) are unusual: the SOHO-Sun-Ulysses included angle is always between 85 and 95 degrees - the quadrature lasts for 5 months! This provides an opportunity for extended observations of specific observing objectives. In addition, in summer 2007, Ulysses (at 1.34 AU) is in near-radial alignment with Earth/ACE/Wind and SOHO, allowing us to analyze radial gradients and propagation in the solar wind and inner heliosphere. Our own quadrature campaigns rely heavily on LASCO and UVCS coronal observations: LASCO giving the overall context above 2 solar radii while the UVCS spectrograph acquired data from - 1.5 to, typically, 4-5 solar radii. In the past, coronal parameters have been derived from data acquired by these two experiments and compared with "in situ" data of Ulysses' SWOOPS and SWICS. Data from other experiments like EIT, CDS, SUMER, Sac Peak Fe XIV maps, magnetic field maps from the Wilcox solar magnetograph, MLSO, from MDI, and from the Ulysses magnetograph experiment have been, and will be, used to complement LASCO/UVCS/SWOOPS and SWICS data. We anticipate that observations by ACE/WIND/STEREO/Hinode and other missions will be relevant as well. During the IHY campaigns, Ulysses will be 52-80 degrees south in winter 2007, near sunspot minimum. Hence, our own scientific objective will be to sample high speed wind or regions of transition between slow and fast wind. This might be a very interesting situation - not met in previous quadratures - allowing
Complete gravity field of an ellipsoidal prism by Gauss-Legendre quadrature
NASA Astrophysics Data System (ADS)
Roussel, C.; Verdun, J.; Cali, J.; Masson, F.
2015-12-01
The increasing availability of geophysical models of the Earth's lithosphere and mantle has generated renewed interest in computation of theoretical gravity effects at global and regional scales. At the same time, the increasing availability of gravity gradient anomalies derived from satellite measurements, such as those provided by GOCE satellite, requires mathematical methods that directly model the gravity gradient anomalies in the same reference frame as GOCE gravity gradients. Our main purpose is to interpret these anomalies in terms of source and density distribution. Numerical integration methods for calculating gravity gradient values are generally based on a mass discretization obtained by decomposing the Earth's layers into a finite number of elementary solid bodies. In order to take into account the curvature of the Earth, spherical prisms or `tesseroids' have been established unequivocally as accurate computation tools for determining the gravitational effects of large-scale structures. The question which then arises from, is whether gravity calculation methods using spherical prisms remain valid when factoring in the ellipticity of the Earth. In the paper, we outline a comprehensive method to numerically compute the complete gravity field with the help of the Gauss-Legendre quadrature involving ellipsoidal shaped prisms. The assessment of this new method is conducted by comparison between the gravity gradient values of simple sources obtained by means of numerical and analytical calculations, respectively. A comparison of the gravity gradients obtained from PREM and LITHO1.0 models using spherical- and ellipsoidal-prism-based methods is also presented. Numerical results indicate that the error on gravity gradients, caused by the use of the spherical prism instead of its ellipsoidal counterpart to describe an ellipsoidally shaped Earth, is useful for a joint analysis with those deduced from GOCE satellite measurements. Provided that a suitable scaling
Quasi-Periodic Long-Term Quadrature Light Variability in Early Type Interacting Binary Systems
NASA Astrophysics Data System (ADS)
Peters, Geraldine Joan
2015-08-01
Four years of Kepler observations have revealed a class of Algol-type binaries in which the relative brightness of the quadrature light varies from > 1 to <1 on a time scale of about 100-400 days. The behavior pattern is quasi-periodic. We call these systems L/T (leading hemisphere/ trailing hemisphere) variables. Although L/T inequality in eclipsing binaries has been noted from ground-based photometry by several observers since the early 1950s, the regular or quasi-regular switching between maxima is new. Twenty L/T systems have so far been found in the Kepler database and at least three classes of L/T behavior have been identified. In this presentation I will give an update on the L/T phenomenon gleaned from the Kepler and K2 databases. The Kepler and K2 light curves are being analyzed with the 2015 version of the Wilson-Devinney (WD) program that includes major improvements in modeling star spots (i.e. spot motions due to drift and stellar rotation and spot growth and decay). The prototype L/T variable is WX Draconis (A8V + K0IV, P=1.80 d) which shows L/ T light variations of 2-3%. The primary is a delta Scuti star with a dominant pulsation period of 41 m. Preliminary analysis of the WX Dra data suggests that the L/T variability can be fit with either an accretion hot spot on the primary (T = 2.3 Tphot) that jumps in longitude or a magnetic cool spotted region on the secondary. If the latter model is correct the dark region must occupy at least 20% of the surface of the facing hemisphere of the secondary if it is completely black, or a larger area if not completely black. In both hot and cool spot scenarios magnetic fields must play a role in the activity. Support from NASA grants NNX11AC78G and NNX12AE44G and USC’s Women in Science and Engineering (WiSE) program is greatly appreciated.
Large eddy simulations of coal jet flame ignition using the direct quadrature method of moments
NASA Astrophysics Data System (ADS)
Pedel, Julien
The Direct Quadrature Method of Moments (DQMOM) was implemented in the Large Eddy Simulation (LES) tool ARCHES to model coal particles. LES coupled with DQMOM was first applied to nonreacting particle-laden turbulent jets. Simulation results were compared to experimental data and accurately modeled a wide range of particle behaviors, such as particle jet waviness, spreading, break up, particle clustering and segregation, in different configurations. Simulations also accurately predicted the mean axial velocity along the centerline for both the gas phase and the solid phase, thus demonstrating the validity of the approach to model particles in turbulent flows. LES was then applied to the prediction of pulverized coal flame ignition. The stability of an oxy-coal flame as a function of changing primary gas composition (CO2 and O2) was first investigated. Flame stability was measured using optical measurements of the flame standoff distance in a 40 kW pilot facility. Large Eddy Simulations (LES) of the facility provided valuable insight into the experimentally observed data and the importance of factors such as heterogeneous reactions, radiation or wall temperature. The effects of three parameters on the flame stand-off distance were studied and simulation predictions were compared to experimental data using the data collaboration method. An additional validation study of the ARCHES LES tool was then performed on an air-fired pulverized coal jet flame ignited by a preheated gas flow. The simulation results were compared qualitatively and quantitatively to experimental observations for different inlet stoichiometric ratios. LES simulations were able to capture the various combustion regimes observed during flame ignition and to accurately model the flame stand-off distance sensitivity to the stoichiometric ratio. Gas temperature and coal burnout predictions were also examined and showed good agreement with experimental data. Overall, this research shows that high
NASA Astrophysics Data System (ADS)
Chang, Chun; Huang, Benxiong; Xu, Zhengguang; Li, Bin
2015-12-01
A partial-response-pulse-shaped 16-ary quadrature amplitude modulation (16QAM) format called quadrature duoquaternary (QDQ) modulation, which can achieve higher spectral efficiency than Nyquist-pulse-shaped 16QAM and realize super-Nyquist wavelength-division-multiplexing (WDM) transmission, is proposed. The dual-polarized QDQ (DP-QDQ) modulation principle and coherent reception based on digital signal processing (DSP) are presented. The performance of the DP-QDQ scheme is investigated in 32-GBaud super-Nyquist-WDM systems by simulation. The simulation results show that DP-QDQ has only a 1.3 dB optical-signal-to-noise-ratio (OSNR) penalty for the 28-GHz-spaced 5-channel super-Nyquist-WDM case relative to the single-channel case. Compared with Nyquist-pulse-shaped 16QAM, DP-QDQ not only has a higher spectral efficiency, but also a lower sensitivity to sampling time error and a better dispersion tolerance. The 28-GHz-spaced 5-channel super-Nyquist-WDM DP-QDQ system can successfully implement 1520-km transmission at the forward-error-correction (FEC) bit-error-rate (BER) requirements.
Sjoden, G.E.
1992-03-01
A new discrete ordinates spatial quadrature scheme is presented for solving neutral particle transport problems. This new scheme, called the exponential characteristic method, is developed here in slab geometry with isotropic scattering. This method uses a characteristic integration of the Boltzmann transport equation with an exponential function as the assumed from of the source distribution, continuous across each spatial cell. The exponential source function is constructed to globally conserve zeroth and first spatial source moments and is non-negative. Characteristic integration ensures non-negative fluxes and flux moments. Numerical testing indicates that convergence of the exponential characteristic scheme is fourth order in the limit of vanishingly thin cells. Highly accurate solutions to optically thick problems can result using this scheme with very coarse meshes. Comparing accuracy and computational cost with existing spatial quadrature schemes (diamond difference, linear discontinuous, linear characteristic, linear adaptive, etc.), the exponential characteristic scheme typically performed best. This scheme is expected to be expandable to two dimensions in a straight forward manner. Due to the high accuracies achievable using coarse meshes, this scheme may allow researchers to obtain solutions to transport problems once thought too large or too difficult to be adequately solved conventional computer systems.
NASA Astrophysics Data System (ADS)
Kiani, Maryam; Pourtakdoust, Seid H.
2014-12-01
A novel algorithm is presented in this study for estimation of spacecraft's attitudes and angular rates from vector observations. In this regard, a new cubature-quadrature particle filter (CQPF) is initially developed that uses the Square-Root Cubature-Quadrature Kalman Filter (SR-CQKF) to generate the importance proposal distribution. The developed CQPF scheme avoids the basic limitation of particle filter (PF) with regards to counting the new measurements. Subsequently, CQPF is enhanced to adjust the sample size at every time step utilizing the idea of confidence intervals, thus improving the efficiency and accuracy of the newly proposed adaptive CQPF (ACQPF). In addition, application of the q-method for filter initialization has intensified the computation burden as well. The current study also applies ACQPF to the problem of attitude estimation of a low Earth orbit (LEO) satellite. For this purpose, the undertaken satellite is equipped with a three-axis magnetometer (TAM) as well as a sun sensor pack that provide noisy geomagnetic field data and Sun direction measurements, respectively. The results and performance of the proposed filter are investigated and compared with those of the extended Kalman filter (EKF) and the standard particle filter (PF) utilizing a Monte Carlo simulation. The comparison demonstrates the viability and the accuracy of the proposed nonlinear estimator.
Yue, Yang; Zhang, Bo; Wang, Qiang; Lofland, Rob; O'Neil, Jason; Anderson, Jon
2016-03-21
Dual-polarization quadrature amplitude modulation (DP-QAM) is one of the feasible paths towards 100-Gb/s, 400-Gb/s and 1-Tb/s optical fiber communications systems. For DP-QAM transmitter, the time mismatch between the in-phase and quadrature (IQ) or x-polarized and y-polarized (XY) tributary channels is known as the IQ or XY skew. Large uncompensated IQ or XY skew can significantly degrade the optical fiber communications system performance. Sometimes, time-interleaved return-to-zero (RZ) DP signal is preferred with lower nonlinear polarization scattering induced penalty. In this work, detection and alignment of DP-QAM transmitter IQ and XY skews using reconfigurable interference is experimentally demonstrated. For IQ skew detection, a total dynamic range of 26.4 dB is achieved with ~1-dB power change for 0.5-ps skew from well alignment. For XY skew detection, it shows 23.2-dB dynamic range, and ~1.5-dB power change is achieved for 1-ps XY skew. Fast detection algorithm for arbitrary skew is also proposed and experimentally verified. The scheme is compatible with different modulation formats, flexible data sequences, and variable waveforms. PMID:27136859
Li, Ye; Yu, Baiying; Pang, Yong; Vigneron, Daniel B; Zhang, Xiaoliang
2013-01-01
The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR) in magnetic resonance (MR) imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM) technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM) and the differential mode (DM) of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays. PMID:24265823
Li, Ye; Yu, Baiying; Pang, Yong; Vigneron, Daniel B.; Zhang, Xiaoliang
2013-01-01
The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR) in magnetic resonance (MR) imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM) technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM) and the differential mode (DM) of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays. PMID:24265823
Application of a quadrature-based moments method to the modeling of volcanic plumes
NASA Astrophysics Data System (ADS)
de'Michieli Vitturi, Mattia; Barsotti, Sara; Neri, Augusto
2014-05-01
(namely the moments) are then derived and their transport equations formulated. For this work we extended, by adopting the method of moments, the Eulerian steady-state volcanic plume model presented in Barsotti et al. (2008). Differently from the original works where pyroclastic particles were partitioned in a finite number of classes with different size and properties, the new model is able to consider a continuous size distribution function of pyroclasts, f(D), representing the particles (for unit volume) with diameter between D and D+dD. Accordingly, transport equations for the moments of the ash particles size distribution are derived and the equations of the plume are expressed in terms of the moments. Here we present the new multiphase model formulation based on the implementation of the quadrature method of moments together with its advantages and drawbacks with respect to previous approaches. Results of a sensitivity analysis of the model with respect to the parameters of the continuous distribution describing the grain sizes at the vent (lognormal or beta distributions) are also shown and discussed. Barsotti, S., Neri, A., and Scire, J.: The VOL-CALPUFF model for atmospheric ash dispersal: 1. Approach and physical formulation, Journal of Geophysical Research, 113, 2008.
NASA Astrophysics Data System (ADS)
Harris, Robert Evan
2008-10-01
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and nonlinear advection equations, and the Euler equations. The new quadrature-free approach is then extended to handle local adaptive hp-refinement (grid and order refinement). Efficient edge-based adaptation utilizing a binary tree search algorithm is employed. Several different adaptation criteria which focus computational effort near high gradient regions are presented. Both h- and p-refinements are presented in a general framework where it is possible to perform either or both on any grid cell at any time. Several well-known inviscid flow test cases, subjected to various levels of adaptation, are utilized to demonstrate the effectiveness of the method. An analysis of the accuracy and stability properties of the spectral volume (SV) method is then presented. The current work seeks to address the issue of stability, as well as polynomial quality, in the design of SV partitions. A new approach is presented, which efficiently locates stable partitions by means of constrained minimization. Once stable partitions are located, a
NASA Technical Reports Server (NTRS)
Suess, Steven; Corti, G.; Poletto, G.; Sterling, A.; Moore, R.
2006-01-01
At the time of the spring 2003 Ulysses-SOHO-Sun quadrature, Ulysses was off the East limb of the Sun at 14.5 degrees north latitude and 4.91 AU. LASCO/C2 images show small transient events that originated from near the limb on May 25, 26 and 27 in the north-east quadrant, along with a large Coronal Mass Ejection (CME) that originated from an active region near disk center on May 26. Ulysses data bear clear signatures of the large CME, specifically including an enhanced abundance of highly ionized Fe. SOHO/UVCS spectra at 1.75 solar radii, near the radial direction to Ulysses, give no evidence of emission from high temperature lines, even for the large CME: instead, for the small events, occasional transient high emission in cool lines was observed, such as the CIII 977 Angstrom line usually absent at coronal levels. Each of these events lasted ca. 1 hour or less and never affected lines from ions forming above ca. 106K. Compact eruptions in Helium 304 Angstrom EIT images, related to the small UVCS transients, were observed at the limb of the Sun over the same period. At least one of these surge events produced a narrow CME observed in LASCO/C2. Most probably all these events are compact magnetic explosions (surges/jets, from around a small island of included polarity) which ejected cool material from lower levels. Ulysses data have been analyzed to find evidence of the cool, narrow CME events, but none or little was found. This puzzling scenario, where events seen by UVCS have no in situ counterparts and vice versa, can be partially explained once the region where the large CME originated is recognized as being at the center of the solar disk so that the CME material was actually much further from the Sun than the 1.7 Rsun height of the UVCS slit off the limb. Conversely, the narrow events may simply have missed Ulysses or been too brief for reliable signatures in composition and ionization state. A basic feature demonstrated by these observations is that large
NASA Astrophysics Data System (ADS)
de Basabe, Jonás D.
2011-08-01
Zhou & Greenhalgh have recently presented an application of the Gaussian quadrature grid to seismic modelling in which the authors propose a meshing scheme that partitions the domain independently of the discontinuities in the media parameters. This comment aims to clarify the implications that this strategy has on the accuracy.
NASA Astrophysics Data System (ADS)
Mao, Youxin; Flueraru, Costel; Chang, Shoude; Popescu, Dan P.; Sowa, Michael G.
2011-05-01
A performance analysis of signal to noise ratio for an optical coherence tomography system with quadrature detection and a semiconductor optical amplifier in the sample arm is discussed. The results are compared and discussed in relation to a conventional OCT system (without optical amplification). An increase of the signal to noise ratio up to 14 dB at a depth of 0.5 mm is obtained compared to the system without the optical amplifier. Overall, an improvement was demonstrated for signal coming from deeper regions within the samples. Arterial plaque from a myocardial infarction-prone Watanabe heritable hyperlipidemic (WHHLMI) rabbit is visualized and characterized using this system. Improvement of signal to noise ratio increases the penetration depth possible for OCT images, from 1 mm to 2 mm within the vessel wall of an artery. Preliminary results show that vulnerable plaque with fibrous cap, macrophage accumulations and calcification in the arterial tissue are measurable with this OCT system.
Minor, B.M.
1993-09-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport with rectangular cells is developed. Numerical problems arising in the derivation required the development of exponential moment functions. These functions are used to remove indeterminant forms which can cause catastrophic cancellations. The EC method is positive and nonlinear. It conserves particles and satisfies first moment balance. Comparisons of the EC method's performance to other methods in optically thin and thick spatial cells were performed. For optically thin cells, the EC method was shown to converge to the correct answer, with third order truncation error in the thin cell limit. In deep penetration problems, the EC method attained its highest computational efficiencies compared to the other methods. For all the deep penetration problems examined, the number of spatial cells required by the EC method to attain a desired accuracy was less than the other methods.... Mathematics functions, Nuclear radiation, Nuclear engineering, Radiation attenuation, Radiation shielding, Transport theory, Radiation transport.
NASA Technical Reports Server (NTRS)
Watson, J. S.; Mistretta, G. D.; Bonavito, N. L.
1975-01-01
A quadrature algorithm is presented which employs analytical expressions for the variations of satellite orbital elements caused by air drag. The Hamiltonian is formally preserved and the Jacobi constants of the motion are advanced with time through the variational equations. The atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabulated data at all altitudes and simultaneously reduces the variational equations to definite integrals with closed form evaluations, whose limits are in terms of the eccentric anomaly. Results are given for two intense air drag satellites and indicate that the satellite ephemerides produced by this method in conjunction with the Vinti program are of very high accuracy.
NASA Astrophysics Data System (ADS)
Ghasemi, Seiyed E.; Hatami, M.; Hatami, J.; Sahebi, S. A. R.; Ganji, D. D.
2016-02-01
In this paper, flow analysis for a non-Newtonian third grade blood in coronary and femoral arteries is simulated numerically. Blood is considered as the third grade non-Newtonian fluid under periodic body acceleration motion and pulsatile pressure gradient. Differential Quadrature Method (DQM) and Crank Nicholson Method (CNM) are used to solve the Partial Differential Equation (PDE) governing equation by which a good agreement between them was observed in the results. The influences of some physical parameters such as amplitude, lead angle and body acceleration frequency on non-dimensional velocity and profiles are considered. For instance, the results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, ϕ, make higher velocity profiles in the center line of both arteries.
Quadrature Rotating-Frame Gradient Fields for Ultra-Low FieldNuclear Magnetic Resonance and Imaging
Bouchard, Louis-Serge
2005-12-30
Magnetic resonance imaging (MRI) in very low fields isfundamentally limited by untruncated concomitant gradients which causesevere distortions in image acquisition and volume selection if thegradient fields are strong compared to the static field. In this paper,it is shown that gradient fields oscillating in quadrature can be usedfor spatial encoding in low fields and provide substantial improvementsover conventional encoding methods using static gradients. In particular,cases where the gradient field is comparable to or higher than theexternal field, Gmax/B0>1, are examined. It is shown thatundistorted slice selection and image encoding is possible because ofsmaller geometric phase errors introduced during cyclic motions of theHamiltonian. In the low field limit (Gmax/B_0 ->infinity) sliceselection is achieved with a combination of soft pulse segments and acoherent train of hard pulses to average out concomitant fields over thefast scale of the rf Hamiltonian.
NASA Astrophysics Data System (ADS)
Greenhalgh, Stewart; Zhou, Bing; Maurer, Hansruedi
2010-05-01
We have developed a modified version of the spectral element method (SEM), called the Gaussian Quadrature Grid (GQG) approach, for frequency domain 3D seismic modelling in arbitrary heterogeneous, anisotropic media. The model may incorporate an arbitrary free-surface topography and irregular subsurface interfaces. Unlike the SEM ,it does not require a powerful mesh generator such as the Delauney Triangular or TetGen. Rather, the GQG approach replaces the element mesh with Gaussian quadrature abscissae to directly sample the physical properties of the model parameters and compute the weighted residual or variational integral. This renders the model discretisation simple and easily matched to the model topography, as well as direct control of the model paramterisation for subsequent inversion. In addition, it offers high accuracy in numerical modelling provided that an appropriate density of the Gaussian quadrature abscissae is employed. The second innovation of the GQG is the incorporation of a new implementation of perfectly matched layers to suppress artificial reflections from the domain margins. We employ PML model parameters (specified complex valued density and elastic moduli) rather than explicitly solving the governing wave equation with a complex co-ordinate system as in conventional approaches. Such an implementation is simple, general, effective and easily extendable to any class of anisotropy and other numerical modelling methods. The accuracy of the GQG approach is controlled by the number of Gaussian quadrature points per minimum wavelength, the so-called sampling density. The optimal sampling density should be the one which enables high definition of geological characteristics and high precision of the variational integral evaluation and spatial differentiation. Our experiments show that satisfactory results can be obtained using sampling densities of 5 points per minimum wavelength. Efficiency of the GQG approach mainly depends on the linear
NASA Technical Reports Server (NTRS)
Smith, A. C.; Yang, H.
1989-01-01
The quadrature phase detection technique was used to simultaneously monitor the phase and amplitude of a toneburst signal normally reflected from an adhesively bonded steel-to-rubber interface. The measured phase was found to show a positive shift for all bonded samples with respect to the disbonded state - the phase shift being larger for samples with weaker bonds, as manifested by smaller values of applied tensile loads at failure. A model calculation, which incorporates the concept of interfacial strength into the usual problem of wave propagation in multilayered media, was used to deduce a bond-quality parameter from an experimentally measured phase shift. This bond-quality parameter was found to be correlated with the tensile strength of the adhesive bonds at failure loads.
NASA Astrophysics Data System (ADS)
Fakir, Md. Moslemuddin; Khatun, Sabira; Jusoh, Abdul Wahab; Ramli, Mohammad Fadzli; Muhamad, Wan Zuki Azman Wan
2015-05-01
Finite Element Method (FEM) and Differential Quadrature Method (DQM) are two very important numerical solution techniques to solve engineering and physical science problems. Usually elements are sub-divided uniformly in FEM (conventional FEM, CFEM) to obtain temperature distribution behavior in a fin with extra computational complexity to obtain a fair solution with required accuracy. In this paper an algorithm to enhance the FEM (named EFEM) is presented by considering non-uniform sub-elements and applied successfully to investigate one dimensional heat distribution phenomenon in an insulated-tip thin rectangular fin. The obtained results are compared with CFEM, efficient DQM (EDQM, with non-uniform mesh generation) and exact solution. EFEM results exhibits more accuracy than CFEM and EDQM and agree very well with exact solution showing its potentiality.
NASA Astrophysics Data System (ADS)
Fox, R. O.; Laurent, F.; Massot, M.
2008-03-01
The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v,u;x,t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. [F. Laurent, M. Massot, P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, J. Comput. Phys. 194 (2004) 505-543]. The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox [D.L. Marchisio, R.O. Fox, Solution of population balance equations using the direct quadrature method of moments, J. Aerosol Sci. 36 (2005) 43-73] to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to focus on the difficulties associated with treating size-dependent coalescence and to avoid numerical uncertainty issues associated with two-way coupling, only one-way coupling between the droplets and a given gas velocity field is considered. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver. The third key point of the study is a detailed description of the limitations associated with each method, thus giving criteria for
NASA Astrophysics Data System (ADS)
Longoni, Gianluca
In the nuclear science and engineering field, radiation transport calculations play a key-role in the design and optimization of nuclear devices. The linear Boltzmann equation describes the angular, energy and spatial variations of the particle or radiation distribution. The discrete ordinates method (S N) is the most widely used technique for solving the linear Boltzmann equation. However, for realistic problems, the memory and computing time require the use of supercomputers. This research is devoted to the development of new formulations for the SN method, especially for highly angular dependent problems, in parallel environments. The present research work addresses two main issues affecting the accuracy and performance of SN transport theory methods: quadrature sets and acceleration techniques. New advanced quadrature techniques which allow for large numbers of angles with a capability for local angular refinement have been developed. These techniques have been integrated into the 3-D SN PENTRAN (Parallel Environment Neutral-particle TRANsport) code and applied to highly angular dependent problems, such as CT-Scan devices, that are widely used to obtain detailed 3-D images for industrial/medical applications. In addition, the accurate simulation of core physics and shielding problems with strong heterogeneities and transport effects requires the numerical solution of the transport equation. In general, the convergence rate of the solution methods for the transport equation is reduced for large problems with optically thick regions and scattering ratios approaching unity. To remedy this situation, new acceleration algorithms based on the Even-Parity Simplified SN (EP-SSN) method have been developed. A new stand-alone code system, PENSSn (Parallel Environment Neutral-particle Simplified SN), has been developed based on the EP-SSN method. The code is designed for parallel computing environments with spatial, angular and hybrid (spatial/angular) domain
NASA Technical Reports Server (NTRS)
Gopalswamy, Nat; Makela, Pertti; Yashiro, Seiji
2011-01-01
It is difficult to measure the true speed of Earth-directed CMEs from a coronagraph along the Sun-Earth line because of the occulting disk. However, the expansion speed (the speed with which the CME appears to spread in the sky plane) can be measured by such coronagraph. In order to convert the expansion speed to radial speed (which is important for space weather applications) one can use empirical relationship between the two that assumes an average width for all CMEs. If we have the width information from quadrature observations, we can confirm the relationship between expansion and radial speeds derived by Gopalswamy et al. (2009, CEAB, 33, 115,2009). The STEREO spacecraft were in quadrature with SOHO (STEREO-A ahead of Earth by 87 and STEREO-B 94 behind Earth) on 2011 February 15, when a fast Earth-directed CME occurred. The CME was observed as a halo by the Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO. The sky-plane speed was measured by SOHO/LASCO as the expansion speed, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images measured the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (Vexp ) and radial speed (Vrad ) derived previously from geometrical considerations (Gopalswamy et al. 2009): Vrad = 1/2 (1 + cot w) Vexp, where w is the half width of the CME. STEREO-B images of the CME, we found that CME had a full width of 75 degrees, so w = 37.5 degrees. This gives the relation as Vrad = 1.15 Vexp. From LASCO observations, we measured Vexp = 897 km/s, so we get the radial speed as 1033 km/s. Direct measurement of radial speed from STEREO gives 945 km/s (STEREO-A) and 1057 km/s (STEREO-B). These numbers are different only by 2.3% and 8.5% (for STEREO-A and STEREO-B, respectively) from the computed value.
Lo, Joseph; Shizgal, Bernie D
2006-11-21
Spectral methods based on nonclassical polynomials and Fourier basis functions or sinc interpolation techniques are compared for several eigenvalue problems for the Fokker-Planck and Schrodinger equations. A very rapid spectral convergence of the eigenvalues versus the number of quadrature points is obtained with the quadrature discretization method (QDM) and the appropriate choice of the weight function. The QDM is a pseudospectral method and the rate of convergence is compared with the sinc method reported by Wei [J. Chem. Phys., 110, 8930 (1999)]. In general, sinc methods based on Fourier basis functions with a uniform grid provide a much slower convergence. The paper considers Fokker-Planck equations (and analogous Schrodinger equations) for the thermalization of electrons in atomic moderators and for a quartic potential employed to model chemical reactions. The solution of the Schrodinger equation for the vibrational states of I2 with a Morse potential is also considered. PMID:17129090
NASA Technical Reports Server (NTRS)
Wang, C.-W.; Stark, W.
2005-01-01
This article considers a quaternary direct-sequence code-division multiple-access (DS-CDMA) communication system with asymmetric quadrature phase-shift-keying (AQPSK) modulation for unequal error protection (UEP) capability. Both time synchronous and asynchronous cases are investigated. An expression for the probability distribution of the multiple-access interference is derived. The exact bit-error performance and the approximate performance using a Gaussian approximation and random signature sequences are evaluated by extending the techniques used for uniform quadrature phase-shift-keying (QPSK) and binary phase-shift-keying (BPSK) DS-CDMA systems. Finally, a general system model with unequal user power and the near-far problem is considered and analyzed. The results show that, for a system with UEP capability, the less protected data bits are more sensitive to the near-far effect that occurs in a multiple-access environment than are the more protected bits.
NASA Technical Reports Server (NTRS)
Kifle, Muli; Vanderaar, Mark
1994-01-01
Union bounds and Monte Carlo simulation Bit-Error-Rate (BER) performance results are presented for various 32-ary and 64-ary Quadrature Amplitude Modulation (QAM) schemes. Filtered and unfiltered modulation formats are compared for the best packing arrangement in peak power limited systems. It is verified that circular constellations which populate as many symbols as possible at the peak magnitude offer the best performance. For example: a 32-ary QAM scheme based on concentric circles offers about 1.05 dB better peak power improvement at a BER of 10(exp -6) over the scheme optimized for average power using triangular symbol packing. This peak power improvement increases to 1.25 dB for comparable 64-ary QAM schemes. This work serves as a precursor to determine the feasibility of a combined modem/codec that can accommodate Broadband Integrated Services Digital Network (B-ISDN) at a rate of 155.52 Mbps through typical transponder bandwidths of 36 MHz and 54 MHz.
Cui, Yan; He, Yuxi; Wang, Pingshan
2014-01-01
A highly tunable and sensitive radio-frequency (RF) sensor is presented for the measurement of aqueous-solution dielectric properties. Two quadrature hybrids are utilized to achieve destructive interference that eliminates the probing signals at both measurement ports. As a result, weak signals of material-under-test (MUT) are elevated for high sensitivity detections at different frequencies. The sensor is demonstrated through measuring 2-propanol-water solution permittivity at 0.01 mole fraction concentration level from ~4 GHz to ~12 GHz. De-ionized water and methanol-water solution are used to calibrate the sensor for quantitative MUT analysis through our proposed model. Micro-meter coplanar waveguides (CPW) are fabricated as RF sensing electrodes. A polydimethylsiloxane (PDMS) microfluidic channel is employed to introduce 250 nL liquid, of which ~1 nL is effectively the MUT. The permittivity and the relaxation time of 2-propanol-water solution are obtained. Compared with our power divider based sensors, the differential reflection coefficients in this work provide additional information that complements the transmission coefficient methods. PMID:25197266
NASA Astrophysics Data System (ADS)
Kimachi, Akira; Ando, Shigeru; Doi, Motonori; Nishi, Shogo
2011-12-01
We propose a three-phase spectral matching imager (3PSMI) to realize a novel spectral matching method called quadrature spectral matching (QSM) in real time. The 3PSMI is comprised of the correlation image sensor (CIS) and wavelength-swept monochromatic illumination (WSMI) to perform QSM at each pixel on the CIS at a video frame rate. QSM consists of spectral correlation between an ac component of an object spectrum and an orthonormal pair of reference spectra, being equivalent to projecting the ac object spectrum onto a two-dimensional subspace spanned by the reference spectra. Similarity of the ac object spectrum to the reference spectra is evaluated in terms of the azimuth angle of the projection, independently of the norm of the ac object spectrum as well as spatial intensity distribution of the WSMI. A programable spectral light source is employed to implement the WSMI so that the spectral characteristics of the WSMI and CIS cancel each other and thus do not affect QSM on the 3PSMI. Experimental results confirm that the developed 3PSMI system can distinguish objects with smaller difference in spectral reflectance in real time than RGB imaging with off-the-shelf cameras.
NASA Astrophysics Data System (ADS)
El-Orany, Faisal A. A.
2005-11-01
In this paper we consider a system consisting of a two-level atom in an excited state interacting with two modes of a radiation field prepared initially in l-photon coherent states. This system is described by a two-mode multiphoton (i.e., k1,k2) Jaynes-Cummings model (JCM). For this system we investigate the occurrence of the revival-collapse phenomenon (RCP) in the evolution of the single-mode, two-mode, sum and difference quadrature squeezing. We show that there is a class of states for which all these types of squeezing exhibit RCP similar to that involved in the corresponding atomic inversion. Also we show numerically that the single-mode squeezing of the first mode for (k1,k2) = (3,1) provides RCP similar to that of the atomic inversion of the case (k1,k2) = (1,1); however, sum and difference squeezing give partial information on that case. Moreover, we show that single-mode, two-mode and sum squeezing for the case (k1,k2) = (2,2) provides information on the atomic inversion of the single-mode two-photon JCM. We derive the rescaled squeezing factors giving accurate information on the atomic inversion for all cases. The consequences of these results are that the homodyne and heterodyne detectors can be used to detect the RCP for the two-mode JCM.
NASA Astrophysics Data System (ADS)
Vikas, V.; Wang, Z. J.; Fox, R. O.
2013-09-01
Population balance equations with advection and diffusion terms can be solved using quadrature-based moment methods. Recently, high-order realizable finite-volume schemes with appropriate realizability criteria have been derived for the advection term. However, hitherto no work has been reported with respect to realizability problems for the diffusion term. The current work focuses on developing high-order realizable finite-volume schemes for diffusion. The pitfalls of existing finite-volume schemes for the diffusion term based on the reconstruction of moments are discussed, and it is shown that realizability can be guaranteed only with the 2nd-order scheme and that the realizability criterion for the 2nd-order scheme is the same as the stability criterion. However, realizability of moments cannot be guaranteed when higher-order moment-based reconstruction schemes are used. To overcome this problem, realizable high-order finite-volume schemes based on the reconstruction of weights and abscissas are proposed and suitable realizability criteria are derived. The realizable schemes can achieve higher than 2nd-order accuracy for problems with smoothly varying abscissas. In the worst-case scenario of highly nonlinear abscissas, the realizable schemes are 2nd-order accurate but have lower error magnitudes compared to existing schemes. The results obtained using the realizable high-order schemes are shown to be consistent with those obtained using the 2nd-order moment-based reconstruction scheme.
Sainath, Kamalesh; Teixeira, Fernando L
2014-05-01
We discuss the application of complex-plane Gauss-Laguerre quadrature (CGLQ) to efficiently evaluate two-dimensional Fourier integrals arising as the solution to electromagnetic fields radiated by elementary dipole antennas embedded within planar-layered media exhibiting arbitrary material parameters. More specifically, we apply CGLQ to the long-standing problem of rapidly and efficiently evaluating the semi-infinite length "tails" of the Fourier integral path while simultaneously and robustly guaranteeing absolute, exponential convergence of the field solution despite diversity in the doubly anisotropic layer parameters, source type (i.e., electric or equivalent magnetic dipole), source orientation, observed field type (magnetic or electric), (nonzero) frequency, and (nonzero) source-observer separation geometry. The proposed algorithm exhibits robustness despite unique challenges arising for the fast evaluation of such two-dimensional integrals. Herein we develop the mathematical treatment to rigorously evaluate the tail integrals using CGLQ, as well as discuss and address the specific issues posed to the CGLQ method when anisotropic, layered media are present. To empirically demonstrate the CGLQ algorithm's computational efficiency, versatility, and accuracy, we perform a convergence analysis along with two case studies related to modeling of electromagnetic resistivity tools employed in geophysical prospection of layered, anisotropic Earth media and validating the ability of isoimpedance substrates to enhance the radiation performance of planar antennas placed in close proximity to metallic ground planes. PMID:25353911
NASA Astrophysics Data System (ADS)
Smith, Elwyn; Wada, Naoya; Chujo, Wataru; Sampson, David D.
2002-06-01
High-power ultra-broadband sources such as a supercontinuum are very attractive in optical coherence tomography (OCT) and optical coherence-domain reflectometry (OCDR) due to their very high resolution potential. However, the large and extensive coherence-function sidelobes typical of such sources preclude their use in conventional OCDR and OCT systems. In addition, device or sample dispersion over such broad bandwidths may also significantly limit the achievable performance. Here we describe a novel experiment using a supercontinuum source with a static Michelson interferometer to perform OCDR at 1.55micrometers . Quadrature spectral detection is used to maximize the scanning range and to allow direct compensation for both the undesirable spectral shape of the source and for the dispersion in the system. Such a non-scanning-interferometer approach is an interesting possible alternative for very broadband, ultra-high resolution OCT systems. We demonstrate that an otherwise obscured small reflection next to a large reflection can be revealed by appropriately weighting the data to reshape the supercontinuum spectrum and compensate for dispersion. Significant reduction of the supercontinuum coherence function sidelobes is achieved, and a resolution in air of 7micrometers (FWHM) is obtained, or less than 5micrometers in media of refractive index 1.45.
0.8-5.2GHz Broad-Band SiGe-MMIC Quadrature Mixer for Software Defined Radio Receiver
NASA Astrophysics Data System (ADS)
Murakami, Keishi; Suematsu, Noriharu; Tsutsumi, Koji; Kanazawa, Gakushi; Sekine, Tomotsugu; Kubo, Hiroshi; Isota, Yoji
For the next generation wireless terminals used in the software defined radio (SDR), multi-band / multi-mode transceivers and their MMIC are required which cover the wide RF frequency range from several hundreds MHz up to several GHz. In this paper, 0.8-5.2GHz broad-band SiGe-MMIC quadrature mixer (Q-MIX) for multi-band / multi-mode direct conversion receiver has been developed. By using a static type frequency divider as a 90 degrees local (LO) power divider, measured error vector magnitude (EVM) of less than 3.1% can be achieved in the cases of 0.8/2.1GHz W-CDMA and 5.2GHz wireless Local Area Network (LAN) (IEEE 802.11a) reception. This Q-MIX also shows broad-band characteristic for base-band signal and is applicable for 4G cellular. By using fabricated Q-MIX, a multi-band / multi-mode (1.9GHz (3rd generation cellular (W-CDMA)) / 5.2GHz (4th generation cellular (Multi-Carrier (MC)-CDMA))) receiver has been developed and it has firstly demonstrated the successful reception of motion picture via W-CDMA and MC-CDMA.
NASA Astrophysics Data System (ADS)
Hort, R. D.; Revil, A.; Munakata-Marr, J.; Mao, D.
2015-07-01
Electrical resistivity measurements can potentially be used to remotely monitor fate and transport of ionic oxidants such as permanganate (MnO4-) during in situ chemical oxidation (ISCO) of contaminants like trichloroethene (TCE). Time-lapse two-dimensional bulk conductivity and induced polarization surveys conducted during a sand tank ISCO simulation demonstrated that MnO4- plume movement could be monitored in a qualitative manner using bulk conductivity tomograms, although chargeability was below sensitivity limits. We also examined changes to in-phase and quadrature electrical conductivity resulting from ion injection, MnO2 and Cl- production, and pH change during TCE and humate oxidation by MnO4- in homogeneous aqueous solutions and saturated porous media samples. Data from the homogeneous samples demonstrated that inversion of the sand tank resistivity data using a common Tikhonov regularization approach was insufficient to recover an accurate conductivity distribution within the tank. While changes to in-phase conductivity could be successfully modeled, quadrature conductivity values could not be directly related to TCE oxidation product or MnO4- concentrations at frequencies consistent with field induced polarization surveys, limiting the utility of quadrature conductivity for monitoring ISCO.
NASA Astrophysics Data System (ADS)
Tornabene, Francesco; Viola, Erasmo; Inman, Daniel J.
2009-12-01
This paper focuses on the dynamic behavior of functionally graded conical, cylindrical shells and annular plates. The last two structures are obtained as special cases of the conical shell formulation. The first-order shear deformation theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is developed within the theory of linear elasticity, when materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. Two different power-law distributions are considered for the ceramic volume fraction. The homogeneous isotropic material is inferred as a special case of functionally graded materials (FGM). The governing equations of motion, expressed as functions of five kinematic parameters, are discretized by means of the generalized differential quadrature (GDQ) method. The discretization of the system leads to a standard linear eigenvalue problem, where two independent variables are involved without using the Fourier modal expansion methodology. For the homogeneous isotropic special case, numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. Different typologies of non-uniform grid point distributions are considered. Finally, for the functionally graded material case numerical results illustrate the influence of the power-law exponent and of the power-law distribution choice on the mechanical behavior of shell structures.
Dai, Y.; Ding, M. D.; Chen, P. F.; Zhang, J.
2012-11-01
We report quadrature observations of an extreme-ultraviolet (EUV) wave event on 2011 January 27 obtained by the Extreme Ultraviolet Imager on board the Solar Terrestrial Relations Observatory, and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. Two components are revealed in the EUV wave event. A primary front is launched with an initial speed of {approx}440 km s{sup -1}. It appears that significant emission enhancement occurs in the hotter channel while deep emission reduction occurs in the cooler channel. When the primary front encounters a large coronal loop system and slows down, a secondary, much fainter, front emanates from the primary front with a relatively higher starting speed of {approx}550 km s{sup -1}. Afterward, the two fronts propagate independently with increasing separation. The primary front finally stops at a magnetic separatrix, while the secondary front travels farther until it fades out. In addition, upon the arrival of the secondary front, transverse oscillations of a prominence are triggered. We suggest that the two components are of different natures. The primary front belongs to a non-wave coronal mass ejection (CME) component, which can be reasonably explained with the field-line stretching model. The multi-temperature behavior may be caused by considerable heating due to nonlinear adiabatic compression on the CME frontal loop. As for the secondary front, it is most likely a linear fast-mode magnetohydrodynamic wave that propagates through a medium of the typical coronal temperature. X-ray and radio data provide us with complementary evidence in support of the above scenario.
Ibrahim, R. S.; El-Kalaawy, O. H.
2006-10-15
The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model.
NASA Astrophysics Data System (ADS)
Wang, Yanyi; Li, Xinying; Yu, Jianjun
2016-01-01
We numerically and experimentally investigate high-speed quadrature phase shift keying (QPSK) vector signal generation based on a single Mach-Zehnder intensity modulator employing a precoding technique. We experimentally demonstrate 16-Gbaud QPSK vector signal generation at 16-GHz carrier adopting optical carrier suppression with precoding technique, and it is the highest baud rate generated by this technology. The 16-Gbaud QPSK modulated vector signal is delivered over a 20-km large effective area fiber or 2-km single-mode fiber with a bit-error-rate less than the hard-decision forward-error-correction threshold of 3.8×10-3.
Ishimura, Shota; Kikuchi, Kazuro
2015-03-01
We apply the eight-state trellis-coded modulation (TCM) using signal constellations of four-dimensional M-ary quadrature-amplitude modulation (4D-MQAM) to optical communication systems for the first time to our knowledge. In the TCM scheme, the free distance of the trellis diagram is equal to the minimum distance between constellation points in partitioned subsets, which enlarges the coding gain effectively. In fact, its asymptotic power efficiency is 3-dB larger than that of the set-partitioned 4D-MQAM (SP-4D-MQAM) format, while their spectral efficiencies are the same. Such theoretical predictions are confirmed through computer simulations on eight-state TCM with constellations of 4D-4QAM (i.e., 4D quadrature phase-shift keying: 4D-QPSK) and 4D-16QAM. In particular, eight-state TCM with 4D-QPSK constellations is practically important because of its simple encoder structure, relatively low computational cost, and high coding gain against dual-polarization QPSK (DP-QPSK) and SP-4D-QPSK. Through measurements of its bit-error rate (BER) performance, we confirm that the coding gain against DP-QPSK is about 3 dB at BER=10(-3). PMID:25836886
Kropf, Pascal; Shmuel, Amir
2016-07-01
Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested
Goto, Nobuo; Miyazaki, Yasumitsu
2014-06-01
Optical switching of high-bit-rate quadrature-phase-shift-keying (QPSK) pulse trains using collinear acousto-optic (AO) devices is theoretically discussed. Since the collinear AO devices have wavelength selectivity, the switched optical pulse trains suffer from distortion when the bandwidth of the pulse train is comparable to the pass bandwidth of the AO device. As the AO device, a sidelobe-suppressed device with a tapered surface-acoustic-wave (SAW) waveguide and a Butterworth-type filter device with a lossy SAW directional coupler are considered. Phase distortion of optical pulse trains at 40 to 100 Gsymbols/s in QPSK format is numerically analyzed. Bit-error-rate performance with additive Gaussian noise is also evaluated by the Monte Carlo method. PMID:24922411
NASA Astrophysics Data System (ADS)
Kamimura, Tatsuya; Lee, Sang-yeop; Tanoi, Satoru; Ito, Hiroyuki; Ishihara, Noboru; Masu, Kazuya
2012-04-01
A low power-supply voltage and high-frequency quadrature voltage-controlled oscillator (QVCO) using a combination of capacitor coupling and transformer feedback techniques is presented. The capacitor coupling technique can boost the transconductance of the LC-VCO core and coupling transconductance of QVCO at high frequency. Also, this technique can improve the quality factor of the QVCO at high frequency with low power-supply voltage, compared with the conventional QVCO. In addition, the capacitor coupling QVCO with transformer feedback can improve the quality factor of QVCO. Using this topology, the QVCO is able to operate at over 10 GHz with lower power-supply voltage. Implemented in the 90 nm complementary metal oxide semiconductor (CMOS) process, the proposed QVCO measures 1-MHz-offset phase noise of -94 dBc/Hz at 13 GHz while consuming 0.68 mW from a 0.1 V power-supply.
NASA Astrophysics Data System (ADS)
Wang, Jin; Cao, Yongsheng; Chen, Fushen
2015-01-01
We present the performance analysis of a spectral amplitude code labeled system with 100 Gb/s polarization division multiplexed (PDM) differential quadrature phase shift keying payload in simulation. Direct detection is chosen to demodulate the PDM payload by applying a polarization tracker, while 4-bits of the 156 Mb/s spectral amplitude code label is coherently detected with a scheme of frequency-swept coherent detection. We optimize the payload laser linewidth as well as the frequency spacing between the payload and label. For back-to-back system and 96 km transmission, label eye opening factors are 0.95 and 0.94, respectively, while payload optical signal-to-noise ratios are 20.6 dB and 22.0 dB, and the payload received optical powers are -15.0 dBm and -14.5 dBm for a bit error rate value of 10-9. The results show that both the payload and label have good transmission performances after long-haul transmission in a standard single mode fiber and dispersion compensating fiber, and the payload could be well demodulated after 288 km transmission.
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
NASA Astrophysics Data System (ADS)
Rexer, Moritz; Hirt, Christian
2015-11-01
In geodesy and geophysics, spherical harmonic techniques are popular for modelling topography and potential fields with ever-increasing spatial resolution. For ultra-high-degree spherical harmonic modelling, i.e. degree 10,000 or more, classical algorithms need to be extended to avoid under- or overflow problems associated with the computation of associated Legendre functions (ALFs). In this work, two quadrature algorithms—the Gauss-Legendre (GL) quadrature and the quadrature following Driscoll/Healy (DH)—and their implementation for the purpose of ultra-high (surface) spherical harmonic analysis of spheroid functions are reviewed and modified for application to ultra-high degree. We extend the implementation of the algorithms in the SHTOOLS software package (v2.8) by (1) the X-number (or Extended Range Arithmetic) method for accurate computation of ALFs and (2) OpenMP directives enabling parallel processing within the analysis. Our modifications are shown to achieve feasible computation times and a very high precision: a degree-21,600 band-limited (=frequency limited) spheroid topographic function may be harmonically analysed with a maximum space-domain error of 3 × 10^{-5} and 5 × 10^{-5} m in 6 and 17 h using 14 CPUs for the GL and for the DH quadrature, respectively. While not being inferior in terms of precision, the GL quadrature outperforms the DH algorithm in terms of computation time. In the second part of the paper, we apply the modified quadrature algorithm to represent for—the first time—gridded topography models for Earth, Moon and Mars as ultra-high-degree series expansions comprising more than 2 billion coefficients. For the Earth's topography, we achieve a resolution of harmonic degree 43,200 (equivalent to 500 m in the space domain), for the Moon of degree 46,080 (equivalent to 120 m) and Mars to degree 23,040 (equivalent to 460 m). For the quality of the representation of the topographic functions in spherical harmonics, we use the
NASA Astrophysics Data System (ADS)
Aoki, T.; Saitou, D.; Fujimoto, K.; Fujihashi, C.; Shimakawa, K.; Koughia, K.; Kasap, S. O.
2010-11-01
Wideband quadrature frequency resolved spectroscopy (QFRS) of photoluminescence (PL) lifetime distributions from 2 ns to 160 s is shown to be very effective in elucidating the characteristic features of radiative transitions of Er3+ ions in GeGaSe and GeGaS chalcogenides glasses (ChGs). Undoped GeGaSe ChGs show triple-peak lifetime distributions of which two short-lifetimes are associated with singlet-triplet excitons and longest-lifetime, ~20 s, with radiative tunnelling (RT) of distant-pairs (DPs). Er-doped GeGaSe and GeGaS ChGs exhibit a double-peak lifetime distribution, consisting of a peak at ~3.3 and ~5.3 ms, respectively, a characteristic of the Er3+ luminescence centre and another peak at ~20 s, similar to that of undoped GeGaSe ChGs. It is shown that the QFRS can separate and analyse two mixed radiative transitions of Nd3+ ions, 4F3/2V4I15/2 and 4F5/2,2H9/2V4I15/2 in GaLaS ChGs. From the QFRS results we can experimentally extract the branching ratio βJ and lifetime τ approx 77 (μs for 4 lasing transitions 4F3/2→4IJ(J = 9/2, 11/2, 13/2, 15/2) of Nd3+ ions in GaLaS ChGs, in particular, the weakest transition 4F3/2→4I15/2.
NASA Astrophysics Data System (ADS)
Tornabene, Francesco; Liverani, Alfredo; Caligiana, Gianni
2012-10-01
The Generalized Differential Quadrature (GDQ) method is applied to study the dynamic behavior of anisotropic doubly-curved shells and panels of revolution with a free-form meridian. The First-order Shear Deformation Theory (FSDT) is used to analyze the above mentioned moderately thick structural elements. In order to include the effect of the initial curvature in the evaluation of the stress resultants three different approaches, specifically Qatu approach, Toorani-Lakis approach and Reissner-Mindlin approach, are considered and compared. An improvement of the Classical Reissner-Mindlin Theory (CRMT) using a different kinematical model is considered. By so doing a generalization of the theory of anisotropic doubly-curved shells and panels of revolution is proposed. Four different anisotropic shell theories, namely General First-order Shear Deformation Theory by Qatu (GFSDTQ), General First-order Shear Deformation Theory by Toorani-Lakis (GFSDTTL), General First-order Shear Deformation Theory by Reissner-Mindlin (GFSDTRM) and Classical Reissner-Mindlin Theory (CRMT), are compared in order to show the differences and the accuracy of these theories. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. Simple Rational Bézier curves are used to define the meridian curve of the revolution structures. Results are obtained taking the meridian and circumferential coordinates into account, without using the Fourier modal expansion methodology. Furthermore, GDQ results are compared with those obtained by using commercial programs such as Abaqus, Ansys, Nastran, Straus and Pro/Mechanica. Very good agreement is observed.
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.
Li, Xinying; Yu, Jianjun
2016-07-01
We propose a novel and simple 2×2 multiple-input multiple-output (MIMO) optical-wireless integration system, in which optical independent-sideband modulation enabled by an in-phase/quadrature (I/Q) modulator, instead of optical polarization multiplexing, is used to assist the simultaneous generation of two wireless millimeter-wave (mm-wave) signals. Software-based digital signal processing is used to generate the driving signal for the I/Q modulator, the output of which is two independent single-sideband optical vector signals located at two sides of a large central optical carrier. Based on our proposed 2×2 MIMO optical-wireless integration system, we experimentally demonstrate the simultaneous generation and 2×2 MIMO wireless delivery of two independent 40-GHz quadrature-phase-shift-keying (QPSK) wireless mm-wave signals. Each 40-GHz QPSK wireless mm-wave signal can carry up to 4-Gbaud transmitter data with a bit-error ratio less than the hard-decision forward-error-correction threshold of 3.8×10^{-3}. PMID:27367121
NASA Astrophysics Data System (ADS)
Thomas, D. C.; Scott, M. A.; Evans, J. A.; Tew, K.; Evans, E. J.
2015-02-01
We introduce B\\'{e}zier projection as an element-based local projection methodology for B-splines, NURBS, and T-splines. This new approach relies on the concept of B\\'{e}zier extraction and an associated operation introduced here, spline reconstruction, enabling the use of B\\'{e}zier projection in standard finite element codes. B\\'{e}zier projection exhibits provably optimal convergence and yields projections that are virtually indistinguishable from global $L^2$ projection. B\\'{e}zier projection is used to develop a unified framework for spline operations including cell subdivision and merging, degree elevation and reduction, basis roughening and smoothing, and spline reparameterization. In fact, B\\'{e}zier projection provides a \\emph{quadrature-free} approach to refinement and coarsening of splines. In this sense, B\\'{e}zier projection provides the fundamental building block for $hpkr$-adaptivity in isogeometric analysis.
Song, Manli; Chen, Jyh-Horng; Chen, Ji; Lin, In-Tsang
2015-01-01
This study attempts to compare the signal-to-noise ratio (SNR) of the 40 mm High-Temperature Superconducting (HTS) surface resonator at 77 K and the 35 mm commercial quadrature (QD) surface resonator at 300 K in a 3 Tesla (T) MRI imager. To aquire images for the comparison, we implemented a phantom experiment using the 40 mm diameter Bi2Sr2Ca2Cu3Ox (Bi-2223) HTS surface resonator, the 35 mm commercial QD surface resonator and the 40 mm professionally-made copper surface resonator. The HTS surface resonator at 77 K provided a 1.43-fold SNR gain over the QD surface resonator at 300 K and provided a 3.84-fold SNR gain over the professionally-made copper surface resonator at 300 K on phantom images. The results agree with the predictions, and the difference between the predicted SNR gains and measured SNR gains is 1%. Although the geometry of the HTS surface resonator is different from the QD surface resonator, its SNR is still higher. The results demonstrate that a higher image quality can be obtained with the HTS surface resonator at 77 K. With the HTS surface resonator, the SNR can be improved, suggesting that the HTS surface resonator is a potentially helpful diagnostic tool for MRI imaging in various applications. PMID:25812124
Numerical quadrature for slab geometry transport algorithms
Hennart, J.P.; Valle, E. del
1995-12-31
In recent papers, a generalized nodal finite element formalism has been presented for virtually all known linear finite difference approximations to the discrete ordinates equations in slab geometry. For a particular angular directions {mu}, the neutron flux {Phi} is approximated by a piecewise function Oh, which over each space interval can be polynomial or quasipolynomial. Here we shall restrict ourselves to the polynomial case. Over each space interval, {Phi} is a polynomial of degree k, interpolating parameters given by in the continuous and discontinuous cases, respectively. The angular flux at the left and right ends and the k`th Legendre moment of {Phi} over the cell considered are represented as.
Sequential quadrature measurements for plasma diagnostics
NASA Astrophysics Data System (ADS)
Martin-Hidalgo, Julio
The study of the ionosphere has been very important due to its effects on terrestrial and satellite communications. This thesis presents an introduction of the ionosphere effects, its modeling and measurement methods that have been used along the history. The Sweeping Impedance Probe (SIP) has proven over the years to be a reliable method based on the radio frequency (RF) behavior of the plasma. A new SIP architecture is presented based on the latest techniques available, using a Vector Network Analyzer (VNA) detection and employing dynamic correction of errors with Correlated Double Sampling (CDS) and a reference channel. The design will be detailed showing the component selection based on their performance parameters. In this sense, several analyses have been made to ensure that the sweep rate and accuracy requirements can be met. The testing and calibration methodology is developed to further increase the final accuracy of the instrument. Lastly, the main conclusions of the project are summarized and new and exciting lines of work are presented for what is expected to be the next generation of SIP instruments.
NASA Astrophysics Data System (ADS)
Yeh, Chien-Hung; Chen, Hsing-Yu; Chow, Chi-Wai; Wu, Yu-Fu
2012-01-01
We use a commercially available 1.2 GHz bandwidth reflective semiconductor optical amplifier (RSOA)--based optical network unit (ONU) to achieve 10-gbits/s upstream traffic for an optical orthogonal frequency division multiplexing (OFDM) long-reach passive optical network (LR-PON). This is the first time the 64--quadrature amplitude modulation (QAM) OFDM format has been applied to RSOA-ONU to achieve a 75 km fiber transmission length. In the proposed LR-PON, the upstream power penalty of 5.2 dB at the bit error rate of 3.8×10-3 is measured by using a 64-QAM OFDM modulation after the 75 km fiber transmission without dispersion compensation.
A Novel Sample Based Quadrature Phase Shift Keying Demodulator
Ali, Sawal Hamid Md
2014-01-01
This paper presents a new practical QPSK receiver that uses digitized samples of incoming QPSK analog signal to determine the phase of the QPSK symbol. The proposed technique is more robust to phase noise and consumes up to 89.6% less power for signal detection in demodulation operation. On the contrary, the conventional QPSK demodulation process where it uses coherent detection technique requires the exact incoming signal frequency; thus, any variation in the frequency of the local oscillator or incoming signal will cause phase noise. A software simulation of the proposed design was successfully carried out using MATLAB Simulink software platform. In the conventional system, at least 10 dB signal to noise ratio (SNR) is required to achieve the bit error rate (BER) of 10−6, whereas, in the proposed technique, the same BER value can be achieved with only 5 dB SNR. Since some of the power consuming elements such as voltage control oscillator (VCO), mixer, and low pass filter (LPF) are no longer needed, the proposed QPSK demodulator will consume almost 68.8% to 99.6% less operational power compared to conventional QPSK demodulator. PMID:25197687
Radio frequency path characterization for wide band quadrature amplitude modulation
Bracht, R.
1998-12-31
Remote, high speed, high explosive wave front monitoring requires very high bandwidth telemetry to allow transmission of diagnostic data before the explosion destroys the sensor system itself. The main motivation for this study is that no known existing implementation of this sort has been applied to realistic weapons environments. These facts have prompted the research and gathering of data that can be used to extrapolate towards finding the best modulation method for this application. In addition to research of similar existing analysis and testing operations, data was recently captured from a Joint Test Assembly (JTA) Air Launched Cruise Missile (ALCM) flight.
Phase-sensitive frequency conversion of quadrature modulated signals.
Webb, R P; Power, M; Manning, R J
2013-05-20
Two mechanisms that can make frequency conversion based on nonlinear mixing dependent on the phase of the input signal are identified. A novel phase-to-polarization converter that converts the orthogonal phase components of an input signal to two orthogonally polarized outputs is proposed. The operation of this scheme and a previously reported scheme at an increased symbol rate are simulated with semiconductor optical amplifiers (SOAs) as the nonlinear devices. Experimental results demonstrate the effectiveness of SOAs for nonlinear mixing over a wide range of wavelengths and difference frequencies and confirm the accuracy of the numerical model. PMID:23736490
Fidelity between Gaussian mixed states with quantum state quadrature variances
NASA Astrophysics Data System (ADS)
Hai-Long, Zhang; Chun, Zhou; Jian-Hong, Shi; Wan-Su, Bao
2016-04-01
In this paper, from the original definition of fidelity in a pure state, we first give a well-defined expansion fidelity between two Gaussian mixed states. It is related to the variances of output and input states in quantum information processing. It is convenient to quantify the quantum teleportation (quantum clone) experiment since the variances of the input (output) state are measurable. Furthermore, we also give a conclusion that the fidelity of a pure input state is smaller than the fidelity of a mixed input state in the same quantum information processing. Project supported by the National Basic Research Program of China (Grant No. 2013CB338002) and the Foundation of Science and Technology on Information Assurance Laboratory (Grant No. KJ-14-001).
Atomic-position resolution by quadrature-field measurement
NASA Astrophysics Data System (ADS)
Storey, Pippa; Collett, Matthew; Walls, Daniel
1993-01-01
An atom passing through a standing light field imparts a position-dependent phase shift to the field. By making a phase-sensitive measurement of the field, it is possible to resolve the atom's position to much less than the wavelength of the light. The field measurement results in the creation of virtual slits, and diffraction and interference phenomena may be observed. The phase measurements give welcher Weg information and enable ``quantum-eraser'' experiments to be realized.
Quadrature Moments Method for the Simulation of Turbulent Reactive Flows
NASA Technical Reports Server (NTRS)
Raman, Venkatramanan; Pitsch, Heinz; Fox, Rodney O.
2003-01-01
A sub-filter model for reactive flows, namely the DQMOM model, was formulated for Large Eddy Simulation (LES) using the filtered mass density function. Transport equations required to determine the location and size of the delta-peaks were then formulated for a 2-peak decomposition of the FDF. The DQMOM scheme was implemented in an existing structured-grid LES solver. Simulations of scalar shear layer using an experimental configuration showed that the first and second moments of both reactive and inert scalars are in good agreement with a conventional Lagrangian scheme that evolves the same FDF. Comparisons with LES simulations performed using laminar chemistry assumption for the reactive scalar show that the new method provides vast improvements at minimal computational cost. Currently, the DQMOM model is being implemented for use with the progress variable/mixture fraction model of Pierce. Comparisons with experimental results and LES simulations using a single-environment for the progress-variable are planned. Future studies will aim at understanding the effect of increase in environments on predictions.
Zrelli, K; Barilero, T; Cavatore, E; Berthoumieux, H; Le Saux, T; Croquette, V; Lemarchand, A; Gosse, C; Jullien, L
2011-04-01
Biological samples exhibit huge molecular diversity over large concentration ranges. Titrating a given compound in such mixtures is often difficult, and innovative strategies emphasizing selectivity are thus demanded. To overcome limitations inherent to thermodynamics, we here present a generic technique where discrimination relies on the dynamics of interaction between the target of interest and a probe introduced in excess. Considering an ensemble of two-state exchanging reactants submitted to temperature modulation, we first demonstrate that the amplitude of the out-of-phase concentration oscillations is maximum for every compound involved in a reaction whose equilibrium constant is equal to unity and whose relaxation time is equal to the inverse of the excitation angular frequency. Taking advantage of this feature, we next devise a highly specific detection protocol and validate it using a microfabricated resistive heater and an epifluorescence microscope, as well as labeled oligonucleotides to model species displaying various dynamic properties. As expected, quantification of a sought for strand is obtained even if interfering reagents are present in similar amounts. Moreover, our approach does not require any separation and is compatible with imaging. It could then benefit some of the numerous binding assays performed every day in life sciences. PMID:21355619
Advances in Disentangling Age, Cohort, and Time Effects: No Quadrature of the Circle, but a Help
ERIC Educational Resources Information Center
Masche, J. Gowert; van Dulmen, Manfred H. M.
2004-01-01
Based on Schaie's (1965) general developmental model, various data-driven and theory-based approaches to the exploration and disentangling of age, cohort, and time effects on human behavior have emerged. This paper presents and discusses an advancement of data-driven interpretations that stresses parsimony when interpreting the results of…
Quadrature amplitude modulation (QAM) using binary-driven coupling-modulated rings
NASA Astrophysics Data System (ADS)
Karimelahi, Samira; Sheikholeslami, Ali
2016-05-01
We propose and fully analyze a compact structure for DAC-free pure optical QAM modulation. The proposed structure is the first ring resonator-based DAC-free QAM modulator reported in the literature, to the best of our knowledge. The device consists of two segmented add-drop Mach Zehnder interferometer-assisted ring modulators (MZIARM) in an IQ configuration. The proposed architecture is investigated based on the parameters from SOI technology where various key design considerations are discussed. We have included the loss in the MZI arms in our analysis of phase and amplitude modulation using MZIARM for the first time and show that the imbalanced loss results in a phase error. The output level linearity is also studied for both QAM-16 and QAM-64 not only based on optimizing RF segment lengths but also by optimizing the number of segments. In QAM-16, linearity among levels is achievable with two segments while in QAM-64 an additional segment may be required.
Pulsed laser interferometry with sub-picometer resolution using quadrature detection.
Shao, Lei; Gorman, Jason J
2016-07-25
Femtosecond pulsed laser interferometry has important applications in measuring picometer-level displacements on sub-nanosecond time scales. In this paper, we experimentally examine its achievable displacement resolution, as well as the relationship between the laser's optical spectrum and the interferometer's effective wavelength. The resulting broadband displacement noise and noise floor of the pulsed laser Michelson interferometer are equivalent to that achieved with a stabilized continuous wave HeNe laser, where values of 1.01 nm RMS and 27.75 fm/√Hz have been demonstrated. It is also shown that a single effective wavelength can accurately describe the fringes of the pulsed laser interferometer but the effective wavelength value can only be determined from the optical spectrum under certain conditions. These results will be used for time-resolved displacement metrology with picosecond temporal resolution in the future. PMID:27464192
NASA Astrophysics Data System (ADS)
von Nessi, G. T.; Hole, M. J.; The MAST Team
2014-11-01
We present recent results and technical breakthroughs for the Bayesian inference of tokamak equilibria using force-balance as a prior constraint. Issues surrounding model parameter representation and posterior analysis are discussed and addressed. These points motivate the recent advancements embodied in the Bayesian Equilibrium Analysis and Simulation Tool (BEAST) software being presently utilized to study equilibria on the Mega-Ampere Spherical Tokamak (MAST) experiment in the UK (von Nessi et al 2012 J. Phys. A 46 185501). State-of-the-art results of using BEAST to study MAST equilibria are reviewed, with recent code advancements being systematically presented though out the manuscript.
Single-shot full-field OCT based on four quadrature phase-stepped interferometer
NASA Astrophysics Data System (ADS)
Hrebesh, Molly Subhash; Watanabe, Yuuki; Dabu, Razvan; Sato, Manabu
2008-02-01
We demonstrate a compact single-shot full-field optical coherence tomography (OCT) system for obtaining real-time high-resolution depth resolved en-face OCT images from weakly scattering specimens. The experimental setup is based on a Linnik type polarization Michelson interferometer and a four-channel compact polarization phase stepper optics. The four-channel phase-stepper optics comprise of a dual channel beam splitter, a Wollaston prism and a pair of wave plate for simultaneously capturing four quadratually phase-stepped images on a single CCD. The interferometer is illuminated using a SLD source with a central wavelength of 842 nm and a bandwidth of 16.2 nm, yielding an axial resolution of 19.8 μm. Using a 10 × (0.25-NA) microscope objective and a CCD camera with 400 × 400 pixels, the system covers an area of 225 μm × 225 μm with a transverse resolution of 4.4 μm. The en-face OCT images of an onion is measured with an exposure time of 7ms and a frame rate of 28 fps.
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.
NASA Astrophysics Data System (ADS)
Yang, Ping; Feng, Xue-Wen; Liang, Wen-Jun; Wu, Kai-Su
2015-02-01
It is the main aim of this paper to investigate the numerical solutions of the inverse black body radiation problems. The inverse black body radiation problem is ill-posed. Using Gaussian-Laguerre integral formula which is a higher accuracy numerical integration formula with less node numbers to approximate the integral item of black body radiation equation, the black radiation equation is converted into a group of lower dimension algebraic equations. To solve the lower dimension algebraic equation, it only needs to use common Tikhonov regularization methods. The regularization parameter is chosen by using L-curve. Our method reduces the complexity of the algorithm, so the operability of our method is enhanced. Numerical results show that our algorithm is simple and effective, and has better calculation accuracy at the same time.
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.
Dieringer, Matthias Alexander; Els, Antje; Waiczies, Helmar; Waiczies, Sonia; Schulz-Menger, Jeanette; Niendorf, Thoralf
2012-01-01
Cardiac morphology and function assessment by magnetic resonance imaging is of increasing interest for a variety of mouse models in pre-clinical cardiac research, such as myocardial infarction models or myocardial injury/remodeling in genetically or pharmacologically induced hypertension. Signal-to-noise ratio (SNR) constraints, however, limit image quality and blood myocardium delineation, which crucially depend on high spatial resolution. Significant gains in SNR with a cryogenically cooled RF probe have been shown for mouse brain MRI, yet the potential of applying cryogenic RF coils for cardiac MR (CMR) in mice is, as of yet, untapped. This study examines the feasibility and potential benefits of CMR in mice employing a 400 MHz cryogenic RF surface coil, compared with a conventional mouse heart coil array operating at room temperature. The cryogenic RF coil affords SNR gains of 3.0 to 5.0 versus the conventional approach and hence enables an enhanced spatial resolution. This markedly improved image quality – by better deliniation of myocardial borders and enhanced depiction of papillary muscles and trabeculae – and facilitated a more accurate cardiac chamber quantification, due to reduced intraobserver variability. In summary the use of a cryogenically cooled RF probe represents a valuable means of enhancing the capabilities of CMR of mice. PMID:22870323
A Novel Quadrature Signal Estimation Method for a Planar Capacitive Incremental Displacement Sensor
NASA Astrophysics Data System (ADS)
Yu, Jian-Ping; Wang, Wen; Li, Xin; Zhou, Zhao-Zhong
2016-06-01
This paper presents a novel phase-shift arctangent (PSA) interpolation method to improve the measurement accuracy of a planar capacitive incremental displacement sensor. Signals of planar capacitive micro-sensors acquire waveform errors, including sensitivity differences and phase-shift errors, because of static errors and dynamic disturbances. In the proposed PSA scheme, such errors are removed completely by loading a particular arctangent function. Moreover, measuring efficiency of the proposed planar capacitive sensors is improved by combining coarse measurement and fine estimation. Experiments show unanimous results to model-based fitting. When electrode length is four times the gap distance, applying the PSA interpolation method decreases waveform errors from more than 4 % to 1.72 %.
NASA Astrophysics Data System (ADS)
Lambers, James V.
2016-06-01
The stiffness of systems of ODEs that arise from spatial discretization of PDEs causes difficulties for both explicit and implicit time-stepping methods. Krylov Subspace Spectral (KSS) methods present a balance between the efficiency of explicit methods and the stability of implicit methods by computing each Fourier coefficient from an individualized approximation of the solution operator of the PDE. While KSS methods are explicit methods that exhibit a high order of accuracy and stability similar to that of implicit methods, their efficiency needs to be improved. Here, a detailed asymptotic study is performed in order to rapidly estimate all nodes, thus drastically reducing computational expense without sacrificing accuracy. Extension to PDEs on a disk, through expansions built on Legendre polynomials, is also discussed. Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff nonlinear systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this talk, it is proposed to modify EPI methods by using KSS methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. Numerical experiments demonstrate that this modification causes the number of Krylov projection steps to become bounded independently of the grid size, thus dramatically improving efficiency and scalability. It is also demonstrated that the convergence of Krylov projection can be significantly accelerated, without noticeable loss of accuracy, through filtering techniques, thus improving performance and scalability even further.
Armas-Pérez, Julio C; Hernández-Ortiz, Juan P; de Pablo, Juan J
2015-12-28
A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. The validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions. PMID:26723642
NASA Astrophysics Data System (ADS)
Armas-Pérez, Julio C.; Hernández-Ortiz, Juan P.; de Pablo, Juan J.
2015-12-01
A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. The validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions.
Zou Yu; Kavousanakis, Michail E.; Kevrekidis, Ioannis G.; Fox, Rodney O.
2010-07-20
The study of particle coagulation and sintering processes is important in a variety of research studies ranging from cell fusion and dust motion to aerosol formation applications. These processes are traditionally simulated using either Monte-Carlo methods or integro-differential equations for particle number density functions. In this paper, we present a computational technique for cases where we believe that accurate closed evolution equations for a finite number of moments of the density function exist in principle, but are not explicitly available. The so-called equation-free computational framework is then employed to numerically obtain the solution of these unavailable closed moment equations by exploiting (through intelligent design of computational experiments) the corresponding fine-scale (here, Monte-Carlo) simulation. We illustrate the use of this method by accelerating the computation of evolving moments of uni- and bivariate particle coagulation and sintering through short simulation bursts of a constant-number Monte-Carlo scheme.
Hasan, Mehedi; Hall, Trevor
2015-11-01
A photonic integrated circuit architecture for implementing frequency upconversion is proposed. The circuit consists of a 1×2 splitter and 2×1 combiner interconnected by two stages of differentially driven phase modulators having 2×2 multimode interference coupler between the stages. A transfer matrix approach is used to model the operation of the architecture. The predictions of the model are validated by simulations performed using an industry standard software tool. The intrinsic conversion efficiency of the proposed design is improved by 6 dB over the alternative functionally equivalent circuit based on dual parallel Mach-Zehnder modulators known in the prior art. A two-tone analysis is presented to study the linearity of the proposed circuit, and a comparison is provided over the alternative. The proposed circuit is suitable for integration in any platform that offers linear electro-optic phase modulation such as LiNbO(3), silicon, III-V, or hybrid technology. PMID:26512513
ERIC Educational Resources Information Center
Roberts, James S.; Donoghue, John R.; Laughlin, James E.
The generalized graded unfolding model (J. Roberts, J. Donoghue, and J. Laughlin, 1998, 1999) is an item response theory model designed to unfold polytomous responses. The model is based on a proximity relation that postulates higher levels of expected agreement with a given statement to the extent that a respondent is located close to the…
NASA Astrophysics Data System (ADS)
Kienreich, I. W.; Muhr, N.; Veronig, A. M.; Berghmans, D.; De Groof, A.; Temmer, M.; Vršnak, B.; Seaton, D. B.
2013-08-01
We investigate the interaction of three consecutive large-scale coronal waves with a polar coronal hole, simultaneously observed on-disk by the Solar TErrestrial Relations Observatory (STEREO)-A spacecraft and on the limb by the PRoject for On-Board Autonomy 2 (PROBA2) spacecraft on 27 January 2011. All three extreme ultraviolet (EUV) waves originate from the same active region, NOAA 11149, positioned at N30E15 in the STEREO-A field of view and on the limb in PROBA2. For the three primary EUV waves, we derive starting velocities in the range of ≈ 310 km s-1 for the weakest up to ≈ 500 km s-1 for the strongest event. Each large-scale wave is reflected at the border of the extended coronal hole at the southern polar region. The average velocities of the reflected waves are found to be smaller than the mean velocities of their associated direct waves. However, the kinematical study also reveals that in each case the ending velocity of the primary wave matches the initial velocity of the reflected wave. In all three events, the primary and reflected waves obey the Huygens-Fresnel principle, as the incident angle with ≈ 10° to the normal is of the same magnitude as the angle of reflection. The correlation between the speed and the strength of the primary EUV waves, the homologous appearance of both the primary and the reflected waves, and in particular the EUV wave reflections themselves suggest that the observed EUV transients are indeed nonlinear large-amplitude MHD waves.
Characterizing curves satisfying the Gauss-Christoffel theorem
NASA Astrophysics Data System (ADS)
Berriochoa, E.; Cachafeiro, A.
2009-12-01
In this paper we obtain the reciprocal of the classical Gauss theorem for quadrature formulas. Indeed we characterize the support of the measures having quadrature formulas with the exactness given in the Gauss theorem.
Compensation of front-end IQ-mismatch in coherent optical receiver
NASA Astrophysics Data System (ADS)
Chang, Sun Hyok; Chung, Hwan Seok; Kim, Kwangjoon
2011-03-01
Impacts of in-phase/quadrature-mismatch (IQ-mismatch) in polarization division multiplexed-16 level quadrature amplitude modulation (PDM-16QAM) coherent optical receiver are investigated and the IQ-mismatch compensation by digital signal processing is examined. All the results are compared with those of PDM-quadrature phase shift keying (QPSK) receiver.
Two-mode optical tomograms: a possible experimental check of the Robertson uncertainty relations
NASA Astrophysics Data System (ADS)
Man'ko, V. I.; Marmo, G.; Simoni, A.; Ventriglia, F.
2012-02-01
An experimental check of the two-mode Robertson uncertainty relations and inequalities for the highest quadrature moments using homodyne photon detection is suggested. The relation between optical tomograms and symplectic tomograms is used to connect the tomographic dispersion matrix and the quadrature components dispersion matrix of the two-mode field states.
A note on generalized averaged Gaussian formulas
NASA Astrophysics Data System (ADS)
Spalevic, Miodrag
2007-11-01
We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss?Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss?Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.
NASA Technical Reports Server (NTRS)
Canright, R. B., Jr.; Semler, T. T.
1972-01-01
Several approximations to the Doppler broadening functions psi(x, theta) and chi(x, theta) are compared with respect to accuracy and speed of evaluation. A technique, due to A. M. Turning (1943), is shown to be at least as accurate as direct numerical quadrature and somewhat faster than Gaussian quadrature. FORTRAN 4 listings are included.
Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object
NASA Astrophysics Data System (ADS)
Lecocq, F.; Clark, J. B.; Simmonds, R. W.; Aumentado, J.; Teufel, J. D.
2015-10-01
By coupling a macroscopic mechanical oscillator to two microwave cavities, we simultaneously prepare and monitor a nonclassical steady state of mechanical motion. In each cavity, correlated radiation pressure forces induced by two coherent drives engineer the coupling between the quadratures of light and motion. We, first, demonstrate the ability to perform a continuous quantum nondemolition measurement of a single mechanical quadrature at a rate that exceeds the mechanical decoherence rate, while avoiding measurement backaction by more than 13 dB. Second, we apply this measurement technique to independently verify the preparation of a squeezed state in the mechanical oscillator, resolving quadrature fluctuations 20% below the quantum noise.
On generalized averaged Gaussian formulas
NASA Astrophysics Data System (ADS)
Spalevic, Miodrag M.
2007-09-01
We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x)equiv w^{(alpha,beta)}(x)D(1-x)^alpha(1+x)^beta ( alpha,beta>-1 ) we give a necessary and sufficient condition on the parameters alpha and beta such that the optimal averaged Gaussian quadrature formulas are internal.
Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object
Lecocq, F.; Clark, J. B.; Simmonds, R.W.; Aumentado, J.; Teufel, J. D.
2016-01-01
By coupling a macroscopic mechanical oscillator to two microwave cavities, we simultaneously prepare and monitor a nonclassical steady state of mechanical motion. In each cavity, correlated radiation pressure forces induced by two coherent drives engineer the coupling between the quadratures of light and motion. We, first, demonstrate the ability to perform a continuous quantum nondemolition measurement of a single mechanical quadrature at a rate that exceeds the mechanical decoherence rate, while avoiding measurement backaction by more than 13 dB. Second, we apply this measurement technique to independently verify the preparation of a squeezed state in the mechanical oscillator, resolving quadrature fluctuations 20% below the quantum noise. PMID:27057422
Harmonic demodulation of nonstationary shot noise.
Gray, M B; Stevenson, A J; Bachor, H A; McClelland, D E
1993-05-15
We report on experimental demodulation of nonstationary shot noise, which is associated with strongly modulated light. For sinusoidal modulation and demodulation, measurements confirm theoretical predictions of 1.8-dB excess noise in the modulation quadrature and 3-dB noise reduction in the opposite quadrature, relative to the standard quantum limit. Demodulation with a third harmonic produces noise correlated with that which is due to the fundamental. Reducing excess noise by 0.8 dB in the modulation quadrature, by combining the fundamental and third harmonics in a 2:1 ratio, is shown to be feasible. PMID:19802263
NASA Technical Reports Server (NTRS)
Hickey, Michael Philip
1988-01-01
A proposed replacement scheme for the integration of the barometric and diffusion equations in the NASA Marshall Engineering Thermosphere (MET) model is presented. This proposed integration scheme is based on Gaussian Quadrature. Extensive numerical testing reveals it to be faster, more accurate and more reliable than the present integration scheme (a modified form of Simpson's Rule) used in the MET model. Numerous graphical examples are provided, along with a listing of a modified form of the MET model in which subroutine INTEGRATE (using Simpson's Rule) is replaced by subroutine GAUSS (which uses Gaussian Quadrature). It is recommended that the Gaussian Quadrature integration scheme, as used here, be used in the MET model.
Quantum frequency up-conversion of continuous variable entangled states
Liu, Wenyuan; Wang, Ning; Li, Zongyang; Li, Yongmin
2015-12-07
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 pump field, making it a practical building block for quantum information processing and communication networks.
Asronomical refraction: Computational methods for all zenith angles
NASA Technical Reports Server (NTRS)
Auer, L. H.; Standish, E. M.
2000-01-01
It is shown that the problem of computing astronomical refraction for any value of the zenith angle may be reduced to a simple, nonsingular, numerical quadrature when the proper choice is made for the independent variable of integration.
Discrete elements method of neutral particle transport
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method.
A Tandem Coupler for Terahertz Integrated Circuits
NASA Technical Reports Server (NTRS)
Reck, Theodore J.; Deal, William; Chattopadhyay, Goutam
2013-01-01
A coplanar waveguide 3 dB quadrature coupler operating from 500 to 700 GHz is designed, fabricated and measured. On-wafer measurements demonstrate an amplitude balance of +/-2 dB and phase balance of +/-20 deg.
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.
2006-06-01
From an experimental-mathematical perspective we analyze"Ising-class" integrals. Our experimental results involvedextreme-precision, multidimensional quadrature on intricate integrands;thus, highly parallel computation was required.
HYBRID FAST HANKEL TRANSFORM ALGORITHM FOR ELECTROMAGNETIC MODELING
A hybrid fast Hankel transform algorithm has been developed that uses several complementary features of two existing algorithms: Anderson's digital filtering or fast Hankel transform (FHT) algorithm and Chave's quadrature and continued fraction algorithm. A hybrid FHT subprogram ...
Quantum frequency up-conversion of continuous variable entangled states
NASA Astrophysics Data System (ADS)
Liu, Wenyuan; Wang, Ning; Li, Zongyang; Li, Yongmin
2015-12-01
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 pump field, making it a practical building block for quantum information processing and communication networks.
Free space optical communications for ultra high-capacity PON system
NASA Astrophysics Data System (ADS)
Shahpari, Ali; Sousa, Artur N.; Ferreira, Ricardo; Lima, Mário; Teixeira, António
2014-08-01
We experimentally demonstrate a set of ultra-high capacity free space passive optical networks (PONs) using quadrature phase shift keying (QPSK), 16-quadrature amplitude modulation (16-QAM) Nyquist pulse shaped and orthogonal frequency-division multiplexing (OFDM) modulations. Moreover, these technologies support up to 10 Gb/s services per user and allow a smooth and full integration between fiber and optical wireless access networks.
Coherent communication with continuous quantum variables
Wilde, Mark M.; Krovi, Hari; Brun, Todd A.
2007-06-15
The coherent bit (cobit) channel is a resource intermediate between classical and quantum communication. It produces coherent versions of teleportation and superdense coding. We extend the cobit channel to continuous variables by providing a definition of the coherent nat (conat) channel. We construct several coherent protocols that use both a position-quadrature and a momentum-quadrature conat channel with finite squeezing. Finally, we show that the quality of squeezing diminishes through successive compositions of coherent teleportation and superdense coding.
Discrete ordinates methods in xy geometry with spatially varying angular discretization
Bal, G.; Warin, X.
1997-10-01
The efficiency of a new quadrature rule adapted to the numerical resolution of a neutron transport problem in xy geometry is presented based on the use of the discrete ordinates method for the angular variable. The purpose of introducing this quadrature rule is to couple two different angular discretizations used on two nonoverlapping subdomains, which is useful for performing local refinement. This coupling and some numerical results of source problems are presented.
On the discrete-ordinates method via Case`s solution
Ganguly, K.; Allen, E.J.; Coskun, E.; Nielsen, S.
1993-07-01
In this paper, we have used Case`s analysis of the neutron transport equation to obtain a new set of quadrature coefficients for the discrete-ordinates method. We perform the transport calculations by this set of quadratures, dependent on the medium. We also use the orthogonality relations in the discrete case to derive the full-range formulation of the half-range problem. This solution can, be profitably used in the new discrete-ordinates method.
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.
Updated version of the DOT 4 one- and two-dimensional neutron/photon transport code
Rhoades, W.A.; Childs, R.L.
1982-07-01
DOT 4 is designed to allow very large transport problems to be solved on a wide range of computers and memory arrangements. Unusual flexibilty in both space-mesh and directional-quadrature specification is allowed. For example, the radial mesh in an R-Z problem can vary with axial position. The directional quadrature can vary with both space and energy group. Several features improve performance on both deep penetration and criticality problems. The program has been checked and used extensively.
On Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae
NASA Astrophysics Data System (ADS)
Joulak, Hédi; Beckermann, Bernhard
2009-12-01
Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the present note we show the positivity of the corresponding weights; this positivity has been conjectured already by Gautschi. As a consequence, we establish several convergence theorems for these quadrature formulae.
Some remarks on the numerical computation of integrals on an unbounded interval
NASA Astrophysics Data System (ADS)
Capobianco, M.; Criscuolo, G.
2007-08-01
An account of the error and the convergence theory is given for Gauss?Laguerre and Gauss?Radau?Laguerre quadrature formulae. We develop also truncated models of the original Gauss rules to compute integrals extended over the positive real axis. Numerical examples confirming the theoretical results are given comparing these rules among themselves and with different quadrature formulae proposed by other authors (Evans, Int. J. Comput. Math. 82:721?730, 2005; Gautschi, BIT 31:438?446, 1991).
NASA Astrophysics Data System (ADS)
Gautschi, Walter
2009-06-01
The generation of generalized Gauss-Radau and Gauss-Lobatto quadrature formulae by methods developed by us earlier breaks down in the case of Jacobi and Laguerre measures when the order of the quadrature rules becomes very large. The reason for this is underflow resp. overflow of the respective monic orthogonal polynomials. By rescaling of the polynomials, and other corrective measures, the problem can be circumvented, and formulae can be generated of orders as high as 1,000.
Comparisons of Remote And In-situ CME Features
NASA Astrophysics Data System (ADS)
Reinard, Alysha; Mulligan, T.; Lynch, B.
2011-05-01
We present a comparison of remote and in-situ CME ejecta using data from the Ulysses and SOHO missions. Quadrature occurs when two spacecraft form a 90 degree angle with the Sun. Quadrature studies allow the comparison of visible features of limb CMEs and and in-situ ICME properties. We investigate several events, including so-called "cannibal" CMEs, and compare the relationship between CME morphology and in-situ structures such as magnetic field, composition, and plasma properties.
Research on numerical algorithms for large space structures
NASA Technical Reports Server (NTRS)
Denman, E. D.
1981-01-01
Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.
Graphical rule of transforming continuous-variable graph states by local homodyne detection
Zhang Jing
2010-09-15
Graphical rule, describing that any single-mode homodyne detection turns a given continuous-variable (CV) graph state into a new one, is presented. Employing two simple graphical rules--local complement operation and vertex deletion (single quadrature-amplitude x measurement)--the graphical rule for any single-mode quadrature component measurement can be obtained. The shape of CV weighted graph state may be designed and constructed easily from a given larger graph state by applying this graphical rule.
The multiparty coherent channel and its implementation with linear optics.
He, Guangqiang; Liu, Taizhi; Tao, Xin
2013-08-26
The continuous-variable coherent (conat) channel is a useful resource for coherent communication, supporting coherent teleportation and coherent superdense coding. We extend the conat channel to multiparty conditions by proposing definitions on multiparty position-quadrature and momentum-quadrature conat channel. We additionally provide two methods to implement this channel using linear optics. One method is the multiparty version of coherent communication assisted by entanglement and classical communication (CCAECC). The other is multiparty coherent superdense coding. PMID:24105527
Development of the Adaptive Collision Source (ACS) method for discrete ordinates
Walters, W.; Haghighat, A.
2013-07-01
We have developed a new collision source method to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This allows for an optimal use of processing power, by using a high order quadrature for the first few iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and we call it the adaptive collision source method (ACS). The ACS methodology has been implemented in the TITAN discrete ordinates code, and has shown a relative speedup of 1.5-2.5 on a test problem, for the same desired level of accuracy. (authors)
Yang, Bo; Wang, Xingjun; Deng, Yunpeng; Hu, Di
2016-01-01
This paper presents technology for the suppression of the mechanical coupling errors for an improved decoupled dual-mass micro-gyroscope (DDMG). The improved micro-gyroscope structure decreases the moment arm of the drive decoupled torque, which benefits the suppression of the non-ideal decoupled error. Quadrature correction electrodes are added to eliminate the residual quadrature error. The structure principle and the quadrature error suppression means of the DDMG are described in detail. ANSYS software is used to simulate the micro-gyroscope structure to verify the mechanical coupling error suppression effect. Compared with the former structure, simulation results demonstrate that the rotational displacements of the sense frame in the improved structure are substantially suppressed in the drive mode. The improved DDMG structure chip is fabricated by the deep dry silicon on glass (DDSOG) process. The feedback control circuits with quadrature control loops are designed to suppress the residual mechanical coupling error. Finally, the system performance of the DDMG prototype is tested. Compared with the former DDMG, the quadrature error in the improved dual-mass micro-gyroscope is decreased 9.66-fold, and the offset error is decreased 6.36-fold. Compared with the open loop sense, the feedback control circuits with quadrature control loop decrease the bias drift by 20.59-fold and the scale factor non-linearity by 2.81-fold in the ±400°/s range. PMID:27070616
Mechanical Coupling Error Suppression Technology for an Improved Decoupled Dual-Mass Micro-Gyroscope
Yang, Bo; Wang, Xingjun; Deng, Yunpeng; Hu, Di
2016-01-01
This paper presents technology for the suppression of the mechanical coupling errors for an improved decoupled dual-mass micro-gyroscope (DDMG). The improved micro-gyroscope structure decreases the moment arm of the drive decoupled torque, which benefits the suppression of the non-ideal decoupled error. Quadrature correction electrodes are added to eliminate the residual quadrature error. The structure principle and the quadrature error suppression means of the DDMG are described in detail. ANSYS software is used to simulate the micro-gyroscope structure to verify the mechanical coupling error suppression effect. Compared with the former structure, simulation results demonstrate that the rotational displacements of the sense frame in the improved structure are substantially suppressed in the drive mode. The improved DDMG structure chip is fabricated by the deep dry silicon on glass (DDSOG) process. The feedback control circuits with quadrature control loops are designed to suppress the residual mechanical coupling error. Finally, the system performance of the DDMG prototype is tested. Compared with the former DDMG, the quadrature error in the improved dual-mass micro-gyroscope is decreased 9.66-fold, and the offset error is decreased 6.36-fold. Compared with the open loop sense, the feedback control circuits with quadrature control loop decrease the bias drift by 20.59-fold and the scale factor non-linearity by 2.81-fold in the ±400°/s range. PMID:27070616
Generating and verifying entangled-itinerant microwave fields
NASA Astrophysics Data System (ADS)
Ku, H. S.
This thesis presents the experimental achievements of (1) generating entangled-microwave fields propagating on two physically separate transmission lines and (2) verifying the entangled states with efficient measurements. Shared entanglement between two parties is an essential resource for quantum information processing and quantum communication protocols. Experimentally, entangled pairs of electromagnetic fields can be realized by distributing a squeezed vacuum over two separated modes. As a result, entanglement is revealed by the strong cross-correlations between specific quadratures of the two modes. Although it is possible to verify the presence of entanglement with low-efficiency quadrature measurements, higher detection efficiencies are desired for performing protocols that exploit entanglement with high fidelity. In the microwave regime, Josephson parametric amplifiers (JPAs) fulfill the two major tasks mentioned above: JPAs prepare the required squeezed states to generate entanglement and enable us to perform efficient quadrature measurements. Therefore, for the purposes of entanglement generation and verification, ultralow-noise--frequency-tunable JPAs have been developed. Additionally, to increase the efficiency of entanglement generation, we integrate JPAs with two on-chip microwave passive components, a directional coupler and a quadrature hybrid, to form an entangler circuit. The two-mode entangled states are created at the two output modes of the entangler and are measured with a two-channel measurement apparatus where each of the two channels incorporates a JPA as a single-quadrature preamplifier. By employing this measurement scheme, the two measured quadratures of the two output modes can be chosen independently of each other, enabling a full characterization of the two-mode state. To definitively demonstrate the two-mode entanglement, I prove that the measured quadrature variances satisfy the inseparability criterion.
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 restricted 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)
Discrete elements method of neutral particle transport. Doctoral thesis
Mathews, K.A.
1983-10-01
A new 'discrete elements' (LN) transport method is derived and compared to the discrete ordinates SN method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, LN is more consistently convergent toward a Monte Carlo benchmark solution than SN, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the LN method. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The zeroth and first angular moments of the directional flux, over each element, are estimated by numerical quadrature and yield a flux-weighted average streaming direction for the element. (Data for this estimation are fluxes in fixed directions calculated as in SN.)
Enhancing the ADMX-HF Search Rate via Quantum Squeezing
NASA Astrophysics Data System (ADS)
Palken, Daniel; Malnou, Maxime; Lehnert, Konrad
2016-03-01
ADMX-HF seeks to detect dark matter axions in the 4-12 GHz band by reading out the state of a microwave cavity. Utilizing a quantum-limited, phase-insensitive amplifier such as a Josephson Parametric Amplifier (JPA) to read out both quadratures of the putative axion signal adds a full quantum of noise atop that signal. The two halves of that quantum are attributed to the noncommutation of the quadrature operators with the cavity Hamiltonian and with one another. We propose a method whereby both halves of this quantum may be circumvented. A JPA is used to create a squeezed microwave state and inject it into the axion cavity, whereupon an axion field, if present, displaces the squeezed state in phase space. The squeezed state then decays out of the cavity, and a second JPA is used for a phase-sensitive readout of only the squeezed quadrature of the field. A single quadrature measurement need not add noise, and, because the cavity field will be prepared in an approximate eigenstate of one quadrature operator, and not of its Hamiltonian, that half-quantum is averted as well. The limiting factor in this protocol will be the efficient transport of the squeezed microwave state between the JPAs and the axion cavity. We estimate that with currently achievable efficiency, we can increase the axion search rate by a factor of four.
Real-time implementation of square 16-QAM transmission system
NASA Astrophysics Data System (ADS)
Al-Bermani, Ali; Wördehoff, Christian; Hoffmann, Sebastian; Puntsri, Kidsanapong; Rückert, Ulrich; Noé, Reinhold
2011-05-01
Combination of quadrature amplitude modulation with coherent detection is attractive for optical transmission systems, since it permits an increase of data rate without increasing the symbol rate or the required bandwidth. 16-point Quadrature Amplitude Modulation (16-QAM) is most interesting in this context. In-phase (I) and quadrature (Q) signals transmit 2 bit each. Together with polarization division multiplex this amounts to 8 bit/symbol. 2.5 Gbit/s synchronous coherent 16-QAM data is transmitted and received in a realtime intradyne setup with BER below FEC (7% overhead) threshold. A phase noise tolerant feedforward carrier recovery concept with hardware-efficient implementation was tested. Transmission was error-free in a back-to-back electrical test for various PRBS lengths. The carrier recovery does not contain any feedback loop and is therefore highly tolerant against laser phase noise.
Optimal Signal Filtration in Optical Sensors with Natural Squeezing of Vacuum Noises
NASA Technical Reports Server (NTRS)
Gusev, A. V.; Kulagin, V. V.
1996-01-01
The structure of optimal receiver is discussed for optical sensor measuring a small displacement of probe mass. Due to nonlinear interaction of the field and the mirror, a reflected wave is in squeezed state (natural squeezing), two quadratures of which are correlated and therefore one can increase signal-to-noise ratio and overcome the SQL. A measurement procedure realizing such correlation processing of two quadratures is clarified. The required combination of quadratures can be produced via mixing of pump field reflected from the mirror with local oscillator phase modulated field in duel-detector homodyne scheme. Such measurement procedure could be useful not only for resonant bar gravitational detector but for laser longbase interferometric detectors as well.
NASA Astrophysics Data System (ADS)
Milburn, T. J.; Kim, M. S.; Vanner, M. R.
2016-05-01
Nonclassical-state generation is an important component throughout experimental quantum science for quantum information applications and probing the fundamentals of physics. Here, we investigate permutations of quantum nondemolition quadrature measurements and single quanta addition or subtraction to prepare quantum superposition states in bosonic systems. The performance of each permutation is quantified and compared using several different nonclassicality criteria including Wigner negativity, nonclassical depth, and optimal fidelity with a coherent-state superposition. We also compare the performance of our protocol using squeezing instead of a quadrature measurement and find that the purification provided by the quadrature measurement can significantly increase the nonclassicality generated. Our approach is ideally suited for implementation in light-matter systems such as quantum optomechanics and atomic spin ensembles, and offers considerable robustness to initial thermal occupation.
Critical fluctuations in an optical parametric oscillator: when light behaves like magnetism
NASA Astrophysics Data System (ADS)
Dechoum, Kaled; Rosales-Zárate, Laura; Drummond, Peter D.
2016-05-01
We study the nondegenerate optical parametric oscillator in a planar interferometer near threshold, where critical phenomena are expected. These phenomena are associated with nonequilibrium quantum dynamics that are known to lead to quadrature entanglement and squeezing in the oscillator field modes. We obtain a universal form for the equation describing this system, which allows a comparison with other phase transitions. We find that the unsqueezed quadratures of this system correspond to a two-dimensional XY-type model with a tricritical Lifshitz point. This leaves open the possibility of a controlled experimental investigation into this unusual class of statistical models. We evaluate the correlations of the unsqueezed quadrature using both an exact numerical simulation and a Gaussian approximation, and obtain an accurate numerical calculation of the non-Gaussian correlations.
Waveform Synthesizer For Imaging And Ranging Applications
DUDLEY, PETER A.; [et al
2004-11-30
Frequency dependent corrections are provided for quadrature imbalance. An operational procedure filters imbalance effects without prior calibration or equalization. Waveform generation can be adjusted/corrected in a synthetic aperture radar system (SAR), where a rolling phase shift is applied to the SAR's QDWS signal where it is demodulated in a receiver; unwanted energies, such as imbalance energy, are separated from a desired signal in Doppler; the separated energy is filtered from the receiver leaving the desired signal; and the separated energy in the receiver is measured to determine the degree of imbalance that is represented by it. Calibration methods can also be implemented into synthesis. The degree of quadrature imbalance can be used to determine calibration values that can then be provided as compensation for frequency dependent errors in components, such as the QDWS and SSB mixer, affecting quadrature signal quality.
Flexible digital modulation and coding synthesis for satellite communications
NASA Technical Reports Server (NTRS)
Vanderaar, Mark; Budinger, James; Hoerig, Craig; Tague, John
1991-01-01
An architecture and a hardware prototype of a flexible trellis modem/codec (FTMC) transmitter are presented. The theory of operation is built upon a pragmatic approach to trellis-coded modulation that emphasizes power and spectral efficiency. The system incorporates programmable modulation formats, variations of trellis-coding, digital baseband pulse-shaping, and digital channel precompensation. The modulation formats examined include (uncoded and coded) binary phase shift keying (BPSK), quatenary phase shift keying (QPSK), octal phase shift keying (8PSK), 16-ary quadrature amplitude modulation (16-QAM), and quadrature quadrature phase shift keying (Q squared PSK) at programmable rates up to 20 megabits per second (Mbps). The FTMC is part of the developing test bed to quantify modulation and coding concepts.
Bimodal score distributions and the Myers-Briggs Type Indicator: fact or artifact?
Bess, Tammy L; Harvey, Robert J
2002-02-01
We examined Myers-Briggs Type Indicator (MBTI) score distributions computed using item response theory (IRT) to assess the generalizability of earlier bimodality reports that have been cited in support of the "type" versus "trait" view of personality. Using the BILOG IRT program to score a sample of approximately 12,000 individuals who participated in leadership development programs, theta score distributions for the 4 dimensions of the MBTI computed using 10 (the BILOG default) versus 50 quadrature points were compared. Results indicated that past reports of bimodality were artifacts caused by BILOG's default use of a small number of quadrature points; when larger numbers of points were used, score distributions became strongly center-weighted. Although our findings are not supportive of the "type"-based hypothesis, the extremely high correlations between theta scores (rs > .996) suggest that no practical differences would be expected as a function of the number-of-quadrature-points decision. PMID:11936208
Entanglement formulation in the framework of electrically pumped laser cavity
NASA Astrophysics Data System (ADS)
Getahun, Solomon
2016-02-01
We analyze electrically pumped atomic cavity coupled to a two-mode vacuum reservoirs via a single-port mirror whose open cavity contains N nondegenerate three-level cascade atoms. We carry out our analysis by putting the noise operators associated with a vacuum reservoir in normal order. It is found that unlike the mean photon number, the quadrature squeezing and the degree of entanglement do not depend on the number of atoms. This implies that the quadrature squeezing and the degree of entanglement of the cavity light do not depend on the number of photons. We have also shown that the light generated by the three-level laser is in a squeezed and entangled state, with maximum quadrature squeezing and degree of entanglement being 50%. Moreover, the mean photon number of the system in which the laser operating at threshold and above threshold does not depend on the spontaneous decay constant.
Ka-Band SiGe Receiver Front-End MMIC for Transponder Applications
NASA Technical Reports Server (NTRS)
Venkatesan, Jaikrishna; Mysoor, Narayan R.; Hashemi, Hassein; Aflatouni, Firooz
2010-01-01
A fully integrated, front-end Ka-band monolithic microwave integrated circuit (MMIC) was developed that houses an LNA (low noise amplifier) stage, a down-conversion stage, and output buffer amplifiers. The MMIC design employs a two-step quadrature down-conversion architecture, illustrated in the figure, which results in improved quality of the down-converted IF quadrature signals. This is due to the improved sensitivity of this architecture to amplitude and phase mismatches in the quadrature down-conversion process. Current sharing results in reduced power consumption, while 3D-coupled inductors reduce the chip area. Improved noise figure is expected over previous SiGe-based, frontend designs
NASA Astrophysics Data System (ADS)
Mao, Xuefeng; Zhou, Xinlei; Yu, Qingxu
2016-02-01
We describe a stabilizing operation point technique based on the tunable Distributed Feedback (DFB) laser for quadrature demodulation of interferometric sensors. By introducing automatic lock quadrature point and wavelength periodically tuning compensation into an interferometric system, the operation point of interferometric system is stabilized when the system suffers various environmental perturbations. To demonstrate the feasibility of this stabilizing operation point technique, experiments have been performed using a tunable-DFB-laser as light source to interrogate an extrinsic Fabry-Perot interferometric vibration sensor and a diaphragm-based acoustic sensor. Experimental results show that good tracing of Q-point was effectively realized.
On the collocation methods for singular integral equations with Hilbert kernel
NASA Astrophysics Data System (ADS)
Du, Jinyuan
2009-06-01
In the present paper, we introduce some singular integral operators, singular quadrature operators and discretization matrices of singular integral equations with Hilbert kernel. These results both improve the classical theory of singular integral equations and develop the theory of singular quadrature with Hilbert kernel. Then by using them a unified framework for various collocation methods of numerical solutions of singular integral equations with Hilbert kernel is given. Under the framework, it is very simple and obvious to obtain the coincidence theorem of collocation methods, then the existence and convergence for constructing approximate solutions are also given based on the coincidence theorem.
New Multithreaded Hybrid CPU/GPU Approach to Hartree-Fock.
Asadchev, Andrey; Gordon, Mark S
2012-11-13
In this article, a new multithreaded Hartree-Fock CPU/GPU method is presented which utilizes automatically generated code and modern C++ techniques to achieve a significant improvement in memory usage and computer time. In particular, the newly implemented Rys Quadrature and Fock Matrix algorithms, implemented as a stand-alone C++ library, with C and Fortran bindings, provides up to 40% improvement over the traditional Fortran Rys Quadrature. The C++ GPU HF code provides approximately a factor of 17.5 improvement over the corresponding C++ CPU code. PMID:26605582
Einstein-Podolsky-Rosen Correlations via Dissociation of a Molecular Bose-Einstein Condensate
Kheruntsyan, K.V.; Drummond, P.D.; Olsen, M.K.
2005-10-07
Recent experimental measurements of atomic intensity correlations through atom shot noise suggest that atomic quadrature phase correlations may soon be measured with a similar precision. We propose a test of local realism with mesoscopic numbers of massive particles based on such measurements. Using dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic atoms, we demonstrate that strongly entangled atomic beams may be produced which possess Einstein-Podolsky-Rosen (EPR) correlations in field quadratures in direct analogy to the position and momentum correlations originally considered by EPR.
Nguyen, Thach G; Shoeiby, Mehrdad; Chu, Sai T; Little, Brent E; Morandotti, Roberto; Mitchell, Arnan; Moss, David J
2015-08-24
We demonstrate a photonic RF Hilbert transformer for broadband microwave in-phase and quadrature-phase generation based on an integrated frequency optical comb, generated using a nonlinear microring resonator based on a CMOS compatible, high-index contrast, doped-silica glass platform. The high quality and large frequency spacing of the comb enables filters with up to 20 taps, allowing us to demonstrate a quadrature filter with more than a 5-octave (3 dB) bandwidth and an almost uniform phase response. PMID:26368182
Dupree, S. A.
1980-06-01
The use of adjoint techniques to determine the interaction of externally incident collimated beams of particles with cylindrical targets is a convenient means of examining a class of problems important in radiation transport studies. The theory relevant to such applications is derived, and a simple example involving a fissioning target is discussed. Results from both discrete ordinates and Monte Carlo transport-code calculations are presented, and comparisons are made with results obtained from forward calculations. The accuracy of the discrete ordinates adjoint results depends on the order of angular quadrature used in the calculation. Reasonable accuracy by using EQN quadratures can be expected from order S/sub 16/ or higher.
Standard errors for EM estimates in generalized linear models with random effects.
Friedl, H; Kauermann, G
2000-09-01
A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulas are used to approximate the integrals in the EM algorithm, where two different approaches are pursued, i.e., Gauss-Hermite quadrature in the case of Gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations. PMID:10985213
A Heterogeneous Medium Analytical Benchmark
Ganapol, B.D.
1999-09-27
A benchmark, called benchmark BLUE, has been developed for one-group neutral particle (neutron or photon) transport in a one-dimensional sub-critical heterogeneous plane parallel medium with surface illumination. General anisotropic scattering is accommodated through the Green's Function Method (GFM). Numerical Fourier transform inversion is used to generate the required Green's functions which are kernels to coupled integral equations that give the exiting angular fluxes. The interior scalar flux is then obtained through quadrature. A compound iterative procedure for quadrature order and slab surface source convergence provides highly accurate benchmark qualities (4- to 5- places of accuracy) results.
Noncommutative q -photon-added coherent states
NASA Astrophysics Data System (ADS)
Dey, Sanjib; Hussin, Véronique
2016-05-01
We construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a q -deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher-order quadrature squeezing, namely, the Hillery type and the Hong-Mandel type, and second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. Also, we compare the behavior of different types of quadrature and photon number squeezing of our system with those of the ordinary harmonic oscillator by considering the same set of parameters.
Squeezing of Quantum Noise of Motion in a Micromechanical Resonator.
Pirkkalainen, J-M; Damskägg, E; Brandt, M; Massel, F; Sillanpää, M A
2015-12-11
A pair of conjugate observables, such as the quadrature amplitudes of harmonic motion, have fundamental fluctuations that are bound by the Heisenberg uncertainty relation. However, in a squeezed quantum state, fluctuations of a quantity can be reduced below the standard quantum limit, at the cost of increased fluctuations of the conjugate variable. Here we prepare a nearly macroscopic moving body, realized as a micromechanical resonator, in a squeezed quantum state. We obtain squeezing of one quadrature amplitude 1.1±0.4 dB below the standard quantum limit, thus achieving a long-standing goal of obtaining motional squeezing in a macroscopic object. PMID:26705631
NASA Technical Reports Server (NTRS)
Yuen, H. P.; Shapiro, J. H.
1980-01-01
Homodyne detection is shown to achieve the same signal-to-noise ratio as the quantum field quadrature measurement, thus providing a receiver which realizes linear modulation TCS performance gain. The full equivalence of homodyne detection and single-quadrature field measurement is established. A heterodyne configuration which uses a TCS image-band oscillator in addition to the usual coherent state local oscillator is studied. Results are obtained by means of a representation theorem which shows that photoemissive detection realizes the photon flux density measurement.
Improvements to the kernel function method of steady, subsonic lifting surface theory
NASA Technical Reports Server (NTRS)
Medan, R. T.
1974-01-01
The application of a kernel function lifting surface method to three dimensional, thin wing theory is discussed. A technique for determining the influence functions is presented. The technique is shown to require fewer quadrature points, while still calculating the influence functions accurately enough to guarantee convergence with an increasing number of spanwise quadrature points. The method also treats control points on the wing leading and trailing edges. The report introduces and employs an aspect of the kernel function method which apparently has never been used before and which significantly enhances the efficiency of the kernel function approach.
A radial basis function Galerkin method for inhomogeneous nonlocal diffusion
Lehoucq, Richard B.; Rowe, Stephen T.
2016-02-01
We introduce a discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. The stiffness matrix entries are assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. As a result, we explore approximating the solution to anisotropic differential equations by solving anisotropic nonlocal integral equations using the radial basis function method.
The second Hamiltonian structure for a special case of the Lotka-Volterra equations
NASA Astrophysics Data System (ADS)
Bibik, Yu. V.
2007-08-01
A special case of the Lotka-Volterra equations is considered for which it is possible to find the second Hamiltonian structure that is complementary to the known one. The form of the new Hamiltonian makes it possible to solve the equations by quadratures, which is the main feature of the case under examination. As a consequence, the period can also be represented by quadratures. In terms of the new variables, the equations of motion admit a mechanical analogy with the oscillations of a mass on a nonlinear spring.
NASA Technical Reports Server (NTRS)
Kot, R. A.; Oliver, J. D.; Wilson, S. G.
1984-01-01
A monolithic, GaAs, dual mode, quadrature amplitude shift keying and quadrature phase shift keying transceiver with one and two billion bits per second data rate is being considered to achieve a low power, small and ultra high speed communication system for satellite as well as terrestrial purposes. Recent GaAs integrated circuit achievements are surveyed and their constituent device types are evaluated. Design considerations, on an elemental level, of the entire modem are further included for monolithic realization with practical fabrication techniques. Numerous device types, with practical monolithic compatability, are used in the design of functional blocks with sufficient performances for realization of the transceiver.
Operator Factorization and the Solution of Second-Order Linear Ordinary Differential Equations
ERIC Educational Resources Information Center
Robin, W.
2007-01-01
The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…
Generalized elastica on 2-dimensional de Sitter space S12
NASA Astrophysics Data System (ADS)
Huang, Rongpei; Yu, Junyan
2016-02-01
In this paper, the extremals of curvature energy actions on non-null regular curves in 2-dimensional de Sitter space are studied. We completely solve the Euler-Lagrange equation by quadratures. By using the Killing field, we construct three special coordinate systems and express the generalized elastica in 2-dimensional de Sitter space S12 by integral explicitly.
Toward a Reduced-Wire Readout System for Ultrasound Imaging
Lim, Jaemyung; Arkan, Evren F.; Degertekin, F. Levent; Ghovanloo, Maysam
2015-01-01
We present a system-on-a-chip (SoC) for use in high-frequency capacitive micromachined ultrasonic transducer (CMUT) imaging systems. This SoC consists of trans-impedance amplifiers (TIA), delay locked loop (DLL) based clock multiplier, quadrature sampler, and pulse width modulator (PWM). The SoC down converts RF echo signal to baseband by quadrature sampling which facilitates modulation. To send data through a 1.6 m wire in the catheter which has limited bandwidth and is vulnerable to noise, the SoC creates a pseudo-digital PWM signal which can be used for back telemetry or wireless readout of the RF data. In this implementation, using a 0.35-μm std. CMOS process, the TIA and single-to-differential (STD) converter had 45 MHz bandwidth, the quadrature sampler had 10.1 dB conversion gain, and the PWM had 5-bit ENoB. Preliminary results verified front-end functionality, and the power consumption of a TIA, STD, quadrature sampler, PWM, and clock multiplier was 26 mW from a 3 V supply. PMID:25571135
Circumstances for Pluto-Charon mutual events in 1989
NASA Technical Reports Server (NTRS)
Tholen, David J.; Buie, Marc W.
1988-01-01
Circumstances for 90 Pluto-Charon mutual events occurring during the 1989 opposition are presented. It is found that the deepest and longest events will occur near postopposition quadrature in early August. Two new stars are selected as comparison stars for events occurring before opposition in 1989, and it is noted that the 1988 comparison stars should be used for events occurring after opposition.
Toward a reduced-wire readout system for ultrasound imaging.
Lim, Jaemyung; Arkan, Evren F; Degertekin, F Levent; Ghovanloo, Maysam
2014-01-01
We present a system-on-a-chip (SoC) for use in high-frequency capacitive micromachined ultrasonic transducer (CMUT) imaging systems. This SoC consists of trans-impedance amplifiers (TIA), delay locked loop (DLL) based clock multiplier, quadrature sampler, and pulse width modulator (PWM). The SoC down converts RF echo signal to baseband by quadrature sampling which facilitates modulation. To send data through a 1.6 m wire in the catheter which has limited bandwidth and is vulnerable to noise, the SoC creates a pseudo-digital PWM signal which can be used for back telemetry or wireless readout of the RF data. In this implementation, using a 0.35-μm std. CMOS process, the TIA and single-to-differential (STD) converter had 45 MHz bandwidth, the quadrature sampler had 10.1 dB conversion gain, and the PWM had 5-bit ENoB. Preliminary results verified front-end functionality, and the power consumption of a TIA, STD, quadrature sampler, PWM, and clock multiplier was 26 mW from a 3 V supply. PMID:25571135
Performance Analysis of Different Modulation Formats in Optical Communication
NASA Astrophysics Data System (ADS)
Singh, Kulwinder; Singh, Maninder; Bhatia, Kamaljit Singh; Ryait, Hardeep Singh
2016-06-01
In this paper, we demonstrated the variation of different parameters with quadrature amplitude modulation (QAM) and differential phase shift key (DPSK) sequence generator, which generates modulated signals, in data transmission for communication and analysed that how the difference of these sequence generators effect its resonant frequency (RF) value, eye diagram and electrical constellation representation of the system.
NASA Astrophysics Data System (ADS)
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2015-03-01
We revisit Ozawa's uncertainty principle (OUP) in the framework of noncommutative (NC) quantum mechanics. We derive a matrix version of OUP accommodating any NC structure in the phase space, and compute NC corrections to lowest order for two measurement interactions, namely the backaction evading quadrature amplifier and noiseless quadrature transducers. These NC corrections alter the nature of the measurement interaction, as a noiseless interaction may acquire noise, and an interaction of independent intervention may become dependent on the object system. However the most striking result is that noncommutativity may lead to a violation of the OUP itself. The NC corrections for the backaction evading quadrature amplifier reveal a new term which may potentially be amplified in such a way that the violation of the OUP becomes experimentally testable. On the other hand, the NC corrections to the noiseless quadrature transducer shows an incompatibility of this model with NC quantum mechanics. We discuss the implications of this incompatibility for NC quantum mechanics and for Ozawa's uncertainty principle.
A Lagrange-type projector on the real line
NASA Astrophysics Data System (ADS)
Mastroianni, G.; Notarangelo, I.
2010-01-01
We introduce an interpolation process based on some of the zeros of the m th generalized Freud polynomial. Convergence results and error estimates are given. In particular we show that, in some important function spaces, the interpolating polynomial behaves like the best approximation. Moreover the stability and the convergence of some quadrature rules are proved.
30 years of squeezed light generation
NASA Astrophysics Data System (ADS)
Andersen, Ulrik L.; Gehring, Tobias; Marquardt, Christoph; Leuchs, Gerd
2016-05-01
Squeezed light generation has come of age. Significant advances on squeezed light generation have been made over the last 30 years—from the initial, conceptual experiment in 1985 till today’s top-tuned, application-oriented setups. Here we review the main experimental platforms for generating quadrature squeezed light that have been investigated in the last 30 years.
Real-time measurements of a 40 Gb/s coherent system.
Sun, Han; Wu, Kuang-Tsan; Roberts, Kim
2008-01-21
Continuous real-time measurements are shown from a coherent 40 Gb/s transmission system that uses Dual-Polarization Quadrature Phase Shift Keying (DP-QPSK) modulation. Digital compensation is used for dispersion and polarization effects, with little performance degradation created by 150 ps of rapidly varying 1st-order PMD. PMID:18542161
Shaping Transmitted Pulses To Provide Synchronizing Signals
NASA Technical Reports Server (NTRS)
Satorius, Edgar H.; Mulligan, James J.
1994-01-01
Report presents theoretical analysis of relationships among: shapes and bandwidths of data pulses in pulse-amplitude modulation (PAM) and quadrature amplitude modulation (QAM); pulse-repetition rates (baud rates); and presence or absence of sinusoidal baud-frequency components in envelopes (magnitudes) of overall received signals.
Temprana, E; Myslivets, E; Liu, L; Ataie, V; Wiberg, A; Kuo, B P P; Alic, N; Radic, S
2015-08-10
We demonstrate a two-fold reach extension of 16 GBaud 16-Quadrature Amplitude Modulation (QAM) wavelength division multiplexed (WDM) system based on erbium doped fiber amplifier (EDFA)-only amplified standard and single mode fiber -based link. The result is enabled by transmitter-side digital backpropagation and frequency referenced carriers drawn from a parametric comb. PMID:26367930
Almaiman, Ahmed; Chitgarha, Mohammad Reza; Daab, Wajih; Ziyadi, Morteza; Mohajerin-Ariaei, Amirhossein; Khaleghi, Salman; Willner, Moshe; Vusirikala, Vijay; Zhao, Xiaoxue; Kilper, Dan; Paraschis, Loukas; Ahsan, Atiyah; Wang, Michael; Bergman, Keren; Tur, Moshe; Touch, Joseph D; Willner, Alan E
2015-05-01
We experimentally studied the performance of a delay-line interferometer-based optical signal-to-noise ratio (OSNR) monitor that is pre-calibrated in optimal conditions for 25-Gbaud pol-muxed quadrature-amplitude-modulation (QAM) signals, when unpredicted changes outside the monitor occurred either in the transmitter or the link. PMID:25927771
Nonclassicality in phase-number uncertainty relations
Matia-Hernando, Paloma; Luis, Alfredo
2011-12-15
We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.
DelGrande, J. Mark; Mathews, Kirk A.
2001-09-15
Conventional discrete ordinates transport calculations often produce negative fluxes due to unphysical negative scattering cross sections and/or as artifacts of spatial differencing schemes such as diamond difference. Inherently nonnegative spatial methods, such as the nonlinear, exponential characteristic spatial quadrature, eliminate negative fluxes while providing excellent accuracy, presuming the group-to-group, ordinate-to-ordinate cross sections are all nonnegative. A hybrid approach is introduced in which the flow from spatial cell to spatial cell uses discrete ordinates spatial quadratures, while anisotropic scattering of flux from one energy-angle bin (energy group and discrete element of solid angle) to another such bin is modeled using a Monte Carlo simulation to evaluate the bin-to-bin cross sections. The directional elements tile the sphere of directions; the ordinates for the spatial quadrature are at the centroids of the elements. The method is developed and contrasted with previous schemes for positive cross sections. An algorithm for evaluating the Monte Carlo (MC)-discrete elements (MC-DE) cross sections is described, and some test cases are presented. Transport calculations using MC-DE cross sections are compared with calculations using conventional cross sections and with MCNP calculations. In this testing, the new method is about as accurate as the conventional approach, and often is more accurate. The exponential characteristic spatial quadrature, using the MC-DE cross sections, is shown to provide useful results where linear characteristic and spherical harmonics provide negative scalar fluxes in every cell in a region.
PENTRAN Modeling for Design and Optimization of the Spherical-Shell Transmission Experiments
Kucukboyaci, Vefa; Haghighat, Alireza; Adams, James M.; Carlson, Allan D.; Grimes, Steven M.; Massey, Thomas N.
2001-06-17
The development of PENTRAN models and new methodologies for accurate and efficient simulations for the design and analysis of time-of-flight (TOF) experiments is discussed. The experimental setup measures the transmission of accelerator-generated neutrons (E > 1 MeV) through spherical iron shells using the TOF spectroscopy. The TOF facility includes a collimator, a thick wall with a hole, a TOF tunnel, and a detector placed {approx}620 cm from the neutron source. The goal of the experiment is to correlate the measured spectrum to different types of interactions, such as the total nonelastic-scattering cross section and its various components. The development of several 3-D PENTRAN models and the effectiveness of new quadrature sets are discussed. Initial calculations by means of the developed 3-D discrete ordinates model of the TOF experimental setup using the PENTRAN code with the S{sub 20} level-symmetric quadrature resulted in inaccurate solutions due to ray effects. To overcome this difficulty, new quadrature sets with local refinement capability were used. These new quadrature sets allowed more accurate, yet efficient, calculations. This study indicated that for the TOF model the P{sub n}-T{sub n} (Chebyshev) set with ordinate-splitting yields accurate results in a relatively short time.
L/sub 2/-error estimates for the discrete ordinates method for three-dimensional neutron transport
Asadzadeh, M.
1988-02-01
We prove L/sub 2/-error estimates for the discrete ordinates method for the angular discretization of the three-dimensional neutron transport equation. The analysis is for monoenergetic three-dimensional transport of neutrons in a homogeneous uniform media and isotropic scattering is assumed. A special quadrature rule with relatively uniformly distributed discrete directions is considered.
Modification of the Varian XL-100 NMR spectrometer for submilligram natural abundance C-13 analyses
NASA Technical Reports Server (NTRS)
Wilson, D. M.; Olsen, R. W.; Burlingame, A. L.
1974-01-01
Quadrature detection modifications and a microcell arrangement are described for the Varian XL-100 NMR spectrometer which routinely improve sensitivity in C-13 Fourier transform sample-limited studies by a factor of 4 to 5. The power requirement of the RF pulse amplifier is relaxed by a factor of 4. Previously attainable resolution is not affected.
Modulation for terrestrial broadcasting of digital HDTV
NASA Technical Reports Server (NTRS)
Kohn, Elliott S.
1991-01-01
The digital modulation methods used by the DigiCipher, DSC-HDTV, ADTV, and ATVA-P digital high-definition television (HDTV) systems are discussed. Three of the systems use a quadrature amplitude modulation method, and the fourth uses a vestigial sideband modulation method. The channel equalization and spectrum sharing of the digital HDTV systems is discussed.
Quantization noise in adaptive weighting networks
NASA Astrophysics Data System (ADS)
Davis, R. M.; Sher, P. J.-S.
1984-09-01
Adaptive weighting networks can be implemented using in-phase and quadrature, phase-phase, or phase-amplitude modulators. The statistical properties of the quantization error are derived for each modulator and the quantization noise power produced by the modulators are compared at the output of an adaptive antenna. Other relevant characteristics of the three types of modulators are also discussed.
Eigenchannel decomposition for continuous-variable quantum key distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, L.; Imre, S.
2015-03-01
We develop a singular layer transmission model for continuous-variable quantum key distribution (CVQKD). In CVQKD, the transmit information is carried by continuous-variable (CV) quantum states, particularly by Gaussian random distributed position and momentum quadratures. The reliable transmission of the quadrature components over a noisy link is a cornerstone of CVQKD protocols. The proposed singular layer uses the singular value decomposition of the Gaussian quantum channel, which yields an additional degree of freedom for the phase space transmission. This additional degree of freedom can further be exploited in a multiple-access scenario. The singular layer defines the eigenchannels of the Gaussian physical link, which can be used for the simultaneous reliable transmission of multiple user data streams. We demonstrate the results through the adaptive multicarrier quadrature division-multiuser quadrature allocation (AMQD-MQA) CVQKD multiple-access scheme. We define the singular model of AMQD-MQA and characterize the properties of the eigenchannel interference. The singular layer transmission provides improved simultaneous transmission rates for the users with unconditional security in a multiple-access scenario, particularly in crucial low signal-to-noise ratio regimes.
Asif, Rameez; Lin, Chien-Yu; Holtmannspoetter, Michael; Schmauss, Bernhard
2013-01-14
We numerically report on the complexity reduction of digital backward propagation (DBP) by utilizing correlative encoded transmission (dual-polarization quadrature duobinary) at a bit-rate of 112Gbit/s over 1640km fiber link. The single channel (N=1) and multi-channel (N=10) transmission performances are compared in this paper. In case of multi-channel system, 10 transmitters are multiplexed with 25GHz channel spacing. The fiber link consists of Large A(eff) Pure-Silica core fiber with 20 spans of 82km each. No in-line optical dispersion compensator is employed in the link. The system performances are evaluated by monitoring the bit-error-ratio and the forward error correction limit corresponds to bit-error-ratio of 3.8×10(-3). The DBP algorithm is implemented after the coherent detection and is based on the logarithmic step-size based split-step Fourier method. The results depict that dual-polarization quadrature duobinary can be used to transmit 112Gbit/s signals with an spectral efficiency of 4-b/s/Hz, but at the same time has a higher tolerance to nonlinear transmission impairments. By utilizing dual-polarization quadrature duobinary modulation, comparative system performance with respect to dual-polarization 16-quadrature amplitude modulation transmission can be achieved with 60% less computations and with a step-size of 205km. PMID:23388970
Directional dual-tree complex wavelet packet transform.
Serbes, Gorkem; Aydin, Nizamettin; Gulcur, Halil Ozcan
2013-01-01
Doppler ultrasound systems, which are widely used in cardiovascular disorders detection, have quadrature format outputs. Various types of algorithms were described in literature to process quadrature Doppler signals (QDS), such as phasing filter technique (PFT), fast Fourier transform method, frequency domain Hilbert transform method and complex continuous wavelet transform. However for the discrete wavelet transform (DWT) case, which becomes a common method for processing QDSs, there was not a direct method to recover flow direction from quadrature signals. Traditionally, to process QDSs with DWT, firstly directional signals have to be extracted and later two DWTs must be applied. Although there exists a complex DWT algorithm called dual tree complex discrete wavelet transform (DTCWT), it does not provide directional signal decoding during analysis because of the unwanted energy leaks into its negative frequency bands. Modified DTCWT, which is a combination of PFT and DTCWT, has the capability of extracting directional information while decomposing QDSs into different frequency bands, but it uses an additional Hilbert transform filter and it increases the computational complexity of whole transform. Discrete wavelet packet transform (DWPT), which is a generalization of the ordinary DWT allowing subband analysis without the constraint of dyadic decomposition, can perform an adaptive decomposition of the frequency axis. In this study, a novel complex DWPT, which maps directional information while processing QDSs, is proposed. The success of proposed method will be measured by using simulated quadrature signals. PMID:24110370
Optical Field-Strength Polarization of Two-Mode Single-Photon States
ERIC Educational Resources Information Center
Linares, J.; Nistal, M. C.; Barral, D.; Moreno, V.
2010-01-01
We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of…
Linearity optimization in a class of analog phase modulators
NASA Technical Reports Server (NTRS)
Hearn, C. P.
1985-01-01
This paper examines the ultimate modulating linearity attainable with a phase modulation technique based on the linear addition of quadrature phase carrier signals which have been multiplied by precisely defined nonlinear transformations of the modulating signal. Optimum gain coefficients are derived and plotted to permit implementation of analog phase modulators capable of exceptionally good linearity of phase deviations as large as 5 radians.
An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems
NASA Technical Reports Server (NTRS)
Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.
1974-01-01
The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.
Optimal cloning for finite distributions of coherent states
Cochrane, P.T.; Ralph, T.C.; Dolinska, A.
2004-04-01
We derive optimal cloning limits for finite Gaussian distributions of coherent states and describe techniques for achieving them. We discuss the relation of these limits to state estimation and the no-cloning limit in teleportation. A qualitatively different cloning limit is derived for a single-quadrature Gaussian quantum cloner.
Voltage-controlled attenuator with low phase shift
NASA Technical Reports Server (NTRS)
Lutes, G. F., Jr.
1980-01-01
Five megahertz RF (radiofrequency) signal attenuator utilizing RF quadrature hybrid, and optically viable-resistance load controlled by lamp circuit exhibits little phase shift. Circuit is designed to help distribute standard RF signal of controlled amplitude, and phase throughout complex of facilities could be useful in application to precision test equipment and communication electronics.
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). A…
Magnetoelectric resonance engine
Moscrip, W.M.
1992-09-15
This patent describes a magnetoelectric resonance thermal machine. It comprises a reciprocating, multiple-piston, Alpha-type Stirling-cycle mechanical assembly; an electronic quadrature phase-lock circuit; an ancillary external energy and mass transfer subsystem; and a master microcomputer control system.
On the effects of phase jitter on QPSK lock detection
NASA Technical Reports Server (NTRS)
Mileant, A.; Hinedi, S.
1993-01-01
The performance of a QPSK (quadrature phase-shift keying) lock detector is described, taking into account the degradation due to carrier phase jitter. Such an analysis is necessary for accurate performance prediction purposes in scenarios where both the loop SNR is low and the estimation period is short. The derived formulas are applicable to several QPSK loops and are verified using computer simulations.
To the theory of volterra integral equations of the first kind with discontinuous kernels
NASA Astrophysics Data System (ADS)
Apartsin, A. S.
2016-05-01
A nonclassical Volterra linear integral equation of the first kind describing the dynamics of an developing system with allowance for its age structure is considered. The connection of this equation with the classical Volterra linear integral equation of the first kind with a piecewise-smooth kernel is studied. For solving such equations, the quadrature method is applied.
Nonlinear fiber gyroscope for quantum metrology
NASA Astrophysics Data System (ADS)
Luis, Alfredo; Morales, Irene; Rivas, Ángel
2016-07-01
We examine the performance of a nonlinear fiber gyroscope for improved signal detection beating the quantum limits of its linear counterparts. The performance is examined when the nonlinear gyroscope is illuminated by practical field states, such as coherent and quadrature squeezed states. This is compared with the case of more ideal probes such as photon-number states.
Interferometer for the measurement of plasma density
Jacobson, Abram R.
1980-01-01
An interferometer which combines the advantages of a coupled cavity interferometer requiring alignment of only one light beam, and a quadrature interferometer which has the ability to track multi-fringe phase excursions unambiguously. The device utilizes a Bragg cell for generating a signal which is electronically analyzed to unambiguously determine phase modulation which is proportional to the path integral of the plasma density.
Separation of variables for some systems with a fourth-order integral of motion
NASA Astrophysics Data System (ADS)
Grigoryev, Yu. A.; Khudobakhshov, V. A.; Tsiganov, A. V.
2013-12-01
We construct separation variables for Yehia's integrable deformations of the Kovalevskaya top and the Chaplygin system on a sphere. In the general case, the corresponding quadratures are given by the Abel-Jacobi map on a two-dimensional submanifold of the Jacobian of a genus-three algebraic curve, which is not hyperelliptic.
Nonclassical states of the second optical harmonic in the presence of self-action
NASA Technical Reports Server (NTRS)
Chirkin, A. S.; Korolkova, N. V.
1993-01-01
The quantum theory of coherent radiation frequency doubling in crystals with quadratic and cubic optical nonlinearities is developed. The possibility of producing the quadrature-squeezed state of the second harmonic (SH) field is shown. The nonclassical SH states arise due to self-action effect.
Collocation and Galerkin Time-Stepping Methods
NASA Technical Reports Server (NTRS)
Huynh, H. T.
2011-01-01
We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.
Analysis of synchronous digital-modulation schemes for satellite communication
NASA Technical Reports Server (NTRS)
Takhar, G. S.; Gupta, S. C.
1975-01-01
The multipath communication channel for space communications is modeled as a multiplicative channel. This paper discusses the effects of multiplicative channel processes on the symbol error rate for quadrature modulation (QM) digital modulation schemes. An expression for the upper bound on the probability of error is derived and numerically evaluated. The results are compared with those obtained for additive channels.
Carrier recovery techniques on satellite mobile channels
NASA Technical Reports Server (NTRS)
Vucetic, B.; Du, J.
1990-01-01
An analytical method and a stored channel model were used to evaluate error performance of uncoded quadrature phase shift keying (QPSK) and M-ary phase shift keying (MPSK) trellis coded modulation (TCM) over shadowed satellite mobile channels in the presence of phase jitter for various carrier recovery techniques.
Translation and integration of numerical atomic orbitals in linear molecules.
Heinäsmäki, Sami
2014-02-14
We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively. PMID:24527905
Translation and integration of numerical atomic orbitals in linear molecules
NASA Astrophysics Data System (ADS)
Heinäsmäki, Sami
2014-02-01
We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.
Atomic homodyne detection of continuous-variable entangled twin-atom states.
Gross, C; Strobel, H; Nicklas, E; Zibold, T; Bar-Gill, N; Kurizki, G; Oberthaler, M K
2011-12-01
Historically, the completeness of quantum theory has been questioned using the concept of bipartite continuous-variable entanglement. The non-classical correlations (entanglement) between the two subsystems imply that the observables of one subsystem are determined by the measurement choice on the other, regardless of the distance between the subsystems. Nowadays, continuous-variable entanglement is regarded as an essential resource, allowing for quantum enhanced measurement resolution, the realization of quantum teleportation and quantum memories, or the demonstration of the Einstein-Podolsky-Rosen paradox. These applications rely on techniques to manipulate and detect coherences of quantum fields, the quadratures. Whereas in optics coherent homodyne detection of quadratures is a standard technique, for massive particles a corresponding method was missing. Here we report the realization of an atomic analogue to homodyne detection for the measurement of matter-wave quadratures. The application of this technique to a quantum state produced by spin-changing collisions in a Bose-Einstein condensate reveals continuous-variable entanglement, as well as the twin-atom character of the state. Our results provide a rare example of continuous-variable entanglement of massive particles. The direct detection of atomic quadratures has applications not only in experimental quantum atom optics, but also for the measurement of fields in many-body systems of massive particles. PMID:22139418
Full complex spectrum simultaneous obtaining SD-OCT
NASA Astrophysics Data System (ADS)
Gelikonov, Grigory V.; Gelikonov, Valentin M.; Shilyagin, Pavel A.
2011-03-01
An efficient technique of simultaneous obtaining of quadrature spectral components of interference signal in spectrometer-based OCT is proposed. The components are obtained in air-spaced non-polarization interferometer by partition of reference beam onto two parts and using an achromatic phase shifter. Several setups of phase sifter are described and compared.
ERIC Educational Resources Information Center
Cai, Li
2013-01-01
Lord and Wingersky's (1984) recursive algorithm for creating summed score based likelihoods and posteriors has a proven track record in unidimensional item response theory (IRT) applications. Extending the recursive algorithm to handle multidimensionality is relatively simple, especially with fixed quadrature because the recursions can be defined…
NASA Astrophysics Data System (ADS)
Revil, A.; Binley, A.; Mejus, L.; Kessouri, P.
2015-08-01
Low-frequency quadrature conductivity spectra of siliclastic materials exhibit typically a characteristic relaxation time, which either corresponds to the peak frequency of the phase or the quadrature conductivity or a typical corner frequency, at which the quadrature conductivity starts to decrease rapidly toward lower frequencies. This characteristic relaxation time can be combined with the (intrinsic) formation factor and a diffusion coefficient to predict the permeability to flow of porous materials at saturation. The intrinsic formation factor can either be determined at several salinities using an electrical conductivity model or at a single salinity using a relationship between the surface and quadrature conductivities. The diffusion coefficient entering into the relationship between the permeability, the characteristic relaxation time, and the formation factor takes only two distinct values for isothermal conditions. For pure silica, the diffusion coefficient of cations, like sodium or potassium, in the Stern layer is equal to the diffusion coefficient of these ions in the bulk pore water, indicating weak sorption of these couterions. For clayey materials and clean sands and sandstones whose surface have been exposed to alumina (possibly iron), the diffusion coefficient of the cations in the Stern layer appears to be 350 times smaller than the diffusion coefficient of the same cations in the pore water. These values are consistent with the values of the ionic mobilities used to determine the amplitude of the low and high-frequency quadrature conductivities and surface conductivity. The database used to test the model comprises a total of 202 samples. Our analysis reveals that permeability prediction with the proposed model is usually within an order of magnitude from the measured value above 0.1 mD. We also discuss the relationship between the different time constants that have been considered in previous works as characteristic relaxation time, including
Cross-Spectra Over the Sea from Observations and Mesoscale Modelling
NASA Astrophysics Data System (ADS)
Vincent, C. L.; Larsén, X. G.; Larsen, S. E.; Sørensen, P.
2013-02-01
Cospectra and quadrature spectra are calculated for six pairs of tall offshore measurement masts near the Horns Rev I wind farm in the Danish North Sea and the Nysted wind farm in the Baltic sea. The mast-pairs are separated from one another by horizontal distances of 2.13-12.4 km. Cospectra and quadrature spectra for the two sites are classified in terms of the angle between the mean wind direction and the line connecting each pair of masts. The frequency axes of the spectra are normalized to remove the effect of mean wind speed and separation distance. Results indicate a larger contribution to the quadrature spectrum for flow from the sea than for flow from the land, and the patterns in the spectra are clearer and better defined for Horns Rev I (which has a long uninterrupted sea-fetch from the west) than for Nysted (which is surrounded by a more complicated coastline). The analysis is replicated based on 3-month simulations using the weather research and forecasting (WRF) numerical model with a horizontal grid spacing of 2 km. For the sea-fetch directions, good agreement in spectral properties between the model and observations is found. Analytical expressions based on the properties of the cross-correlation function and an exponentially decaying coherence function are fitted to the normalized cospectra and quadrature spectra. The expressions are shown to be a good fit to the spectra calculated from the WRF simulations and to the observed spectra for directions with a long sea-fetch, which suggests that to a good approximation, the average cospectra and quadrature spectra over the sea can be written as functions of frequency, mean wind speed, separation distance and the angle between the wind direction and the orientation of the masts.
NASA Astrophysics Data System (ADS)
Abdel Aal, Gamal Z.; Atekwana, Estella A.; Revil, A.
2014-09-01
Previous studies have linked biogeophysical signatures to the presence of iron minerals resulting from distinct biophysicochemical processes. Utilizing geophysical methods as a proxy of such biophysicochemical processes requires an understanding of the geophysical signature of the different iron minerals. Laboratory experiments were conducted to investigate the complex conductivity and magnetic susceptibility signatures of five iron minerals disseminated in saturated porous media under variable iron mineral content and grain size. Both pyrite and magnetite show high quadrature and inphase conductivities compared to hematite, goethite, and siderite, whereas magnetite was the highly magnetic mineral dominating the magnetic susceptibility measurements. The quadrature conductivity spectra of both pyrite and magnetite exhibit a well-defined characteristic relaxation peak below 10 kHz, not observed with the other iron minerals. The quadrature conductivity and magnetic susceptibility of individual and a mixture of iron minerals are dominated and linearly proportional to the mass fraction of the highly conductive (pyrite and magnetite) and magnetic (magnetite) iron minerals, respectively. The quadrature conductivity magnitude increased with decreasing grain size diameter of magnetite and pyrite with a progressive shift of the characteristic relaxation peak toward higher frequencies. The quadrature conductivity response of a mixture of different grain sizes of iron minerals is shown to be additive, whereas magnetic susceptibility measurements were insensitive to the variation in grain size diameters (1-0.075 mm). The integration of complex conductivity and magnetic susceptibility measurements can therefore provide a complimentary tool for the successful investigation of in situ biophysicochemical processes resulting in biotransformation or secondary iron mineral precipitation.
Quantum Squeezing of Motion in a Mechanical Resonator
NASA Astrophysics Data System (ADS)
Wollman, Emma E.
Quantum mechanics places limits on the minimum energy of a harmonic oscillator via the ever-present "zero-point" fluctuations of the quantum ground state. Through squeezing, however, it is possible to decrease the noise of a single motional quadrature below the zero-point level as long as noise is added to the orthogonal quadrature. While squeezing below the quantum noise level was achieved decades ago with light, quantum squeezing of the motion of a mechanical resonator is a more difficult prospect due to the large thermal occupations of megahertz-frequency mechanical devices even at typical dilution refrigerator temperatures of ~ 10 mK. Kronwald, Marquardt, and Clerk (2013) propose a method of squeezing a single quadrature of mechanical motion below the level of its zero-point fluctuations, even when the mechanics starts out with a large thermal occupation. The scheme operates under the framework of cavity optomechanics, where an optical or microwave cavity is coupled to the mechanics in order to control and read out the mechanical state. In the proposal, two pump tones are applied to the cavity, each detuned from the cavity resonance by the mechanical frequency. The pump tones establish and couple the mechanics to a squeezed reservoir, producing arbitrarily-large, steady-state squeezing of the mechanical motion. In this dissertation, I describe two experiments related to the implementation of this proposal in an electromechanical system. I also expand on the theory presented in Kronwald et. al. to include the effects of squeezing in the presence of classical microwave noise, and without assumptions of perfect alignment of the pump frequencies. In the first experiment, we produce a squeezed thermal state using the method of Kronwald et. al. We perform back-action evading measurements of the mechanical squeezed state in order to probe the noise in both quadratures of the mechanics. Using this method, we detect single-quadrature fluctuations at the level of 1
NASA Astrophysics Data System (ADS)
Meng, Fanwei; Liu, Chengying; Li, Zhijun; Wang, Liping
2013-01-01
Due to low damping ratio, flat permanent magnet linear synchronous motor's vibration is difficult to be damped and the accuracy is limited. The vibration suppressing results are not good enough in the existing research because only the longitudinal direction vibration is considered while the normal direction vibration is neglected. The parameters of the direct-axis current controller are set to be the same as those of the quadrature-axis current controller commonly. This causes contradiction between signal noise and response. To suppress the vibration, the electromagnetic force model of the flat permanent magnet synchronous linear motor is formulated first. Through the analysis of the effect that direct-axis current noise and quadrature-axis current noise have on both direction vibration, it can be declared that the conclusion that longitudinal direction vibration is only related to the quadrature-axis current noise while the normal direction vibration is related to both the quadrature-axis current noise and direct-axis current noise. Then, the simulation test on current loop with a low-pass filter is conducted and the results show that the low-pass filter can not suppress the vibration but makes the vibration more severe. So a vibration suppressing strategy that the proportional gain of direct-axis current controller adapted according to quadrature-axis reference current is proposed. This control strategy can suppress motor vibration by suppressing direct-axis current noise. The experiments results about the effect of K p and T i on normal direction vibration, longitudinal vibration and the position step response show that this strategy suppresses vibration effectively while the motor's motion performance is not affected. The maximum reduction of vibration can be up to 40%. In addition, current test under rated load condition is also conducted and the results show that the control strategy can avoid the conflict between the direct-axis current and the quadrature
Symbol rate identification for auxiliary amplitude modulation optical signal
NASA Astrophysics Data System (ADS)
Wei, Junyu; Dong, Zhi; Huang, Zhiping; Zhang, Yimeng
2016-09-01
In this paper, we creatively propose and demonstrate a method for symbol rate identification (SRI) of auxiliary amplitude modulation (AAM) optical signal based on asynchronous delay-tap sampling (ADTS) and average magnitude difference function (AMDF). The method can accurately estimate symbol rate and has large transmission impairments tolerance. Furthermore, it can be realized in the digital signal processor (DSP) with low logical resources because of multiplication-free. In order to improve the accuracy of SRI, the peak to valley ratio (PTVR) of AMDF is introduced into our method for blind chromatic dispersion (CD) compensation. The results of the numerical simulations show that the overall maximum SRI error is smaller 0.079% for return-to-zero (RZ) on-off keying (OOK), RZ differential phase-shift keying (DPSK), RZ differential quadrature phase-shift keying (DQPSK) and RZ 16-ary quadrature amplitude modulation (QAM) with 50% duty cycles.
Accurate solution of the Dirac equation on Lagrange meshes.
Baye, Daniel; Filippin, Livio; Godefroid, Michel
2014-04-01
The Lagrange-mesh method is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. With a basis of Lagrange functions involving associated Laguerre polynomials related to the Gauss quadrature, the method is applied to the Dirac equation. The potential may possess a 1/r singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers n+1 of mesh points, where n is the principal quantum number. Numerically exact mean values of powers -2 to 3 of the radial coordinate r can also be obtained with n+2 mesh points. For the Yukawa potential, a 15-digit agreement with benchmark energies of the literature is obtained with 50 or fewer mesh points. PMID:24827362
Cryptographie quantique à variables continues
NASA Astrophysics Data System (ADS)
Bencheikh, K.; Jankovic, A.; Symul, T.; Levenson, J. A.
2002-06-01
Nous avons élaboré un protocole de cryptographie quantique qui permet de générer et de distribuer une clé secrète aléatoire. Le protocole repose sur l'utilisation de paires de champs électromagnétiques dont les quadratures présentent des corrélations quantiques de type Einstein-Podolsky-Rosen. Les fluctuations quantiques instantanése constituent les bits aléatoires de la clé secrète, et la dégradation irréversible des corrélations quantiques des quadratures causée par une tierce personne permet de la détecter et de garantir la sécurité d'échange.
Power optimized OSSB modulation to support multi-band OFDM services along hybrid long-reach WDM-PONs
NASA Astrophysics Data System (ADS)
Almeida, Paulo; Silva, Henrique
2015-06-01
In this paper, optical single sideband (OSSB) transmission of multi-services based on orthogonal frequency division multiplexing (OFDM) with different signal constellations is investigated through numerical simulation, when the modulation efficiency obtained with a dual-electrode Mach-Zehnder modulator (DE-MZM) is optimized by biasing it below its quadrature point. Furthermore, in order to overcome the intermodulation distortion resulting from modulation efficiency optimization, it is demonstrated that driving each electrical signal with a different electrical power is an effective solution for the signals considered. As result of the optimization, successful delivery after 130 km of a hybrid OSSB signal composed by a custom 16-quadrature amplitude modulation (QAM) OFDM gigabit Ethernet (GbE) signal, a 20 MHz 64-QAM LTE signal and three independent OFDM-UWB channels of the first group of ECMA-386 is demonstrated, with negligible power penalty.
Photon number squeezed states in semiconductor lasers
NASA Technical Reports Server (NTRS)
Yamamoto, Yoshihisa; Machida, Susumu; Richardson, Wayne H.
1992-01-01
Electromagnetic fields, with the noise on one quadrature component reduced to below the quantum mechanical zero-point fluctuation level and the noise on the other quadrature component enhanced to above it, are currently of great interest in quantum optics because of their potential applications to various precision measurements. Such squeezed states of light are usually produced by imposing nonlinear unitary evolution on coherent (or vacuum) states. On the other hand, squeezed states with reduced photon number noise and enhanced phase noise are generated directly by a constant current-driven semiconductor laser. This is the simplest scheme for the generation of nonclassical light, and so far it has yielded the largest quantum noise reduction. The mutual coupling between a lasing junction and an external electrical circuit provides opportunities for exploring the macroscopic and microscopic quantum effects in open systems.
Double reference pulsed phase locked loop
NASA Technical Reports Server (NTRS)
Heyman, J. S. (Inventor)
1986-01-01
A double reference pulse phase locked loop is described which measures the phase shift between tone burst signals initially derived from the same periodic signal source (voltage controlled oscillator) and delayed by different amounts because of two different paths. A first path is from the transducer to the surface of a sample and back. A second path is from the transducer to the opposite surface and back. A first pulse phase locked loop including a phase detector and a phase shifter forces the tone burst signal delayed by the second path in phase quadrature with the periodic signal source. A second pulse phase locked loop including a second phase detector forces the tone burst signals delayed by the first path into phase quadrature with the phase shifted periodic signal source.
Advances in Optical Fiber-Based Faraday Rotation Diagnostics
White, A D; McHale, G B; Goerz, D A
2009-07-27
In the past two years, we have used optical fiber-based Faraday Rotation Diagnostics (FRDs) to measure pulsed currents on several dozen capacitively driven and explosively driven pulsed power experiments. We have made simplifications to the necessary hardware for quadrature-encoded polarization analysis, including development of an all-fiber analysis scheme. We have developed a numerical model that is useful for predicting and quantifying deviations from the ideal diagnostic response. We have developed a method of analyzing quadrature-encoded FRD data that is simple to perform and offers numerous advantages over several existing methods. When comparison has been possible, we have seen good agreement with our FRDs and other current sensors.
A Multi-axis Control Board Implemented via an FPGA
NASA Astrophysics Data System (ADS)
Longo, Domenico; Muscato, Giovanni
Most of robotic applications rely on the use of DC motors with quadrature encoder feedback. Typical applications are legged robots or articulated chassis multi-wheeled robots. In these applications system designer must implement multi-axis control systems able to handle an high number of quadrature encoder signals and to generate the same number of PWM signals. Moreover the adopted CPU must be able to execute the same number of control loop algorithms in a time slot of about ten milliseconds. Very few commercial SoC (System on Chip) can handle up to six channels. In this work the implementation of a SoC on FPGA able to handle up to 20 channels within a time slot of 20 ms and up to 100 channels within a time slot of 100 ms is described. In order to demonstrate the effectiveness of the design, the board was used to control a small six wheels outdoor robot.
NASA Astrophysics Data System (ADS)
Chen, Duan; Cai, Wei; Zinser, Brian; Cho, Min Hyung
2016-09-01
In this paper, we develop an accurate and efficient Nyström volume integral equation (VIE) method for the Maxwell equations for a large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for cubes, spheres and cylinders, that are frequently encountered in the design of meta-materials. The resulting Nyström VIE method is shown to have high accuracy with a small number of collocation points and demonstrates p-convergence for computing the electromagnetic scattering of these objects. Numerical calculations of multiple scatterers of cubic, spherical, and cylindrical shapes validate the efficiency and accuracy of the proposed method.
Shen, G X; Wu, J F; Boada, F E; Thulborn, K R
1999-02-01
A new theoretical method is presented for designing frequency responses of double-tuned, low-pass birdcage coils. This method is based on Kirchhoff's equations through a nonsymmetric matrix algorithm and extended through a modification of the corresponding eigenvalue system from a single-tuned mode. Designs from this method are verified for sodium/proton, dual-tuned, double-quadrature, low-pass birdcage coils at 1.5 Tesla and 3.0 Tesla and then are used to design dual-tuned, double-quadrature, lithium/proton and phosphorus/proton birdcage coils for 3.0 Tesla. All frequencies show experimental deviations of less than 3% from theory under unloaded conditions. The frequency shifts caused by loading and radiofrequency shielding are less than 1 MHz and can be compensated readily by adjustment of variable capacitors. Applications to human neuroimaging and spectroscopy are demonstrated. PMID:10080273
ACS Algorithm in Discrete Ordinates for Pressure Vessel Dosimetry
NASA Astrophysics Data System (ADS)
Walters, William; Haghighat, Alireza
2016-02-01
The Adaptive Collision Source (ACS) method can solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. This is similar to, and essentially an extension of, the first collision source method. Previously, the ACS methodology has been implemented into the TITAN discrete ordinates code, and has shown speedups of 2-4 on a simple test problem, with very little loss of accuracy (within a provided adaptive tolerance). This work examines the use of the ACS method for a more realistic problem: pressure vessel dosimetry with the VENUS-2 MOX-fuelled reactor dosimetry benchmark. The ACS method proved to be able to obtain accurate results while being approximately twice as efficient as using a constant quadrature in a standard source iteration scheme.
A fast high-order method to calculate wakefields in an electron beam
NASA Astrophysics Data System (ADS)
Qiang, Ji; Mitchell, Chad; Ryne, Robert D.
2012-08-01
In this paper, we report on a high-order fast method to numerically calculate wakefields in an electron beam given a wake function model. This method is based on a Newton-Cotes quadrature rule for integral approximation and an FFT method for discrete summation that results in an O(N log(N)) computational cost, where N is the number of grid points. Using the Simpson quadrature rule with an accuracy of O(h4), where h is the grid size, we present numerical calculation of the wakefields from a resonator wake function model and from a one-dimensional coherent synchrotron radiation (CSR) wake model. Besides the fast speed and high numerical accuracy, the calculation using the direct line density instead of the first derivative of the line density avoids numerical filtering of the electron density function for computing the CSR wakefield.
Zhang, Junwen; Yu, Jianjun; Chi, Nan; Chien, Hung-Chang
2014-08-25
We theoretically and experimentally investigate a time-domain digital pre-equalization (DPEQ) scheme for bandwidth-limited optical coherent communication systems, which is based on feedback of channel characteristics from the receiver-side blind and adaptive equalizers, such as least-mean-squares (LMS) algorithm and constant or multi- modulus algorithms (CMA, MMA). Based on the proposed DPEQ scheme, we theoretically and experimentally study its performance in terms of various channel conditions as well as resolutions for channel estimation, such as filtering bandwidth, taps length, and OSNR. Using a high speed 64-GSa/s DAC in cooperation with the proposed DPEQ technique, we successfully synthesized band-limited 40-Gbaud signals in modulation formats of polarization-diversion multiplexed (PDM) quadrature phase shift keying (QPSK), 8-quadrature amplitude modulation (QAM) and 16-QAM, and significant improvement in both back-to-back and transmission BER performances are also demonstrated. PMID:25321257
Pilot-symbols-aided cycle slip mitigation for DP-16QAM optical communication systems.
Cheng, Haiquan; Li, Yan; Zhang, Fangzheng; Wu, Jian; Lu, Jianxin; Zhang, Guoyi; Xu, Jian; Lin, Jintong
2013-09-23
A pilot-symbols-aided phase unwrapping (PAPU), which utilizes the time-division multiplexed pilot symbols that are transmitted with data, is proposed to do cycle slip detection and correction with the carrier phase estimation (CPE). Numerical simulations for 10 Gbaud dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) systems show that the block averaging quadrature phase-shift keying (QPSK) partitioning with PAPU greatly eliminates the performance degradation caused by cycle slips, maintains a low CS probability with less influence of filter length, and achieves a bit-error-rate (BER) performance below soft-decision forward error correction (FEC) limit 2 × 10⁻² at 15 dB optical signal-to-noise ratio with only 1.56% overhead and 6 MHz combined laser linewidth. PMID:24104108
Zhang, Fan; Yang, Chuanchuan; Fang, Xi; Zhang, Tingting; Chen, Zhangyuan
2013-03-11
Orthogonal transmission with frequency division multiplexing technique is investigated for next generation optical communication systems. Coherent optical orthogonal frequency division multiplexing (OFDM) and single-carrier frequency division multiplexing (SCFDM) schemes are compared in combination with polarization-division multiplexing quadrature phase shift keying (QPSK) or 16-QAM (quadrature amplitude modulation) formats. Multi-granularity transmission with flexible bandwidth can be realized through ultra-dense wavelength division multiplexing (UDWDM) based on the orthogonal technique. The system performance is numerically studied with special emphasis on transmission degradations due to fiber Kerr nonlinearity. The maximum reach and fiber capacity for different spectral efficiencies are investigated for systems with nonlinear propagation over uncompensated standard single-mode fiber (SSMF) links with lumped amplification. PMID:23482180
Transmission and reception of PDM dual-subcarrier coherent 16QAM-OFDM signals
NASA Astrophysics Data System (ADS)
Li, Fan; Zhang, Junwen; Yu, Jianjun; Li, Xinying
2015-12-01
In this paper, 16-Gbaud polarization-division-multiplexed (PDM) dual-subcarrier coherent optical orthogonal frequency division multiplexing (CO-OFDM) transmission and reception are successfully demonstrated without overhead. The in-phase and quadrature (I/Q) components of dual-subcarrier 16-ary quadrature amplitude modulation (QAM) OFDM signal are both seven-level signals in time domain, and thus can be equalized like a 49 QAM signal in time domain with cascaded multi-modulus algorithm (CMMA) equalization method. The experimental results show that there is no power penalty observed between optical back to back (OBTB) and after 80-km single-mode fiber-28 (SMF-28) with time domain CMMA equalization method. A 0.4 dB optical signal to noise ratio (OSNR) penalty in OBTB is observed when the bandwidth of channel is set at 26 GHz at the BER of 2.0 × 10-2.
Optical performance monitoring technique using software-based synchronous amplitude histograms.
Choi, H G; Chang, J H; Kim, Hoon; Chung, Y C
2014-10-01
We propose and demonstrate a simple technique to monitor both the optical signal-to-noise ratio (OSNR) and chromatic dispersion (CD) by using the software-based synchronous amplitude histogram (SAH) analysis. We exploit the software-based synchronization technique to construct SAHs from the asynchronously sampled intensities of the signal. The use of SAHs facilitates the accurate extraction of the monitoring parameters at the center of the symbol. Thus, unlike in the case of using the technique based on the asynchronous amplitude histogram (AAH), this technique is not affected by the transient characteristics of the modulated signals. The performance of the proposed monitoring technique is evaluated experimentally by using 10-Gbaud quadrature phase-shift keying (QPSK) and quadrature amplitude modulation (QAM) signals over wide ranges of OSNR and CD. We also evaluate the robustness of the proposed technique to the signal's transient characteristics. PMID:25321978
High spectral density transmission emulation using amplified spontaneous emission noise.
Elson, Daniel J; Galdino, Lidia; Maher, Robert; Killey, Robert I; Thomsen, Benn C; Bayvel, Polina
2016-01-01
We demonstrate the use of spectrally shaped amplified spontaneous emission (SS-ASE) noise for wideband channel loading in the investigation of nonlinear transmission limits in wavelength-division multiplexing transmission experiments using Nyquist-spaced channels. The validity of this approach is explored through statistical analysis and experimental transmission of Nyquist-spaced 10 GBaud polarization-division multiplexing (PDM) quadrature phase-shift keying and PDM-16-ary quadrature amplitude modulation (QAM) channels, co-propagated with SS-ASE over single mode fiber. It is shown that this technique, which is simpler to implement than a fully modulated comb of channels, is valid for distances exceeding 240 km for PDM-16QAM with dispersion of 16 ps/nm/km, yields a good agreement with theory, and provides a conservative measure of system performance. PMID:26696160
NASA Astrophysics Data System (ADS)
Cao, Zhang; Song, Wei; Peng, Zhicong; Xu, Lijun
2014-11-01
There exist a number of algorithms to map the phase to amplitude in direct digital synthesis (DDS). For DDS with more than 14 output bits, the Coordinate Rotation Digital Computer (CORDIC) algorithm is well known for its high precision. Also, it is effective in solutions where there is the need of in-phase and quadrature components simultaneously because the algorithm calculates both. In this paper, a Taylor expansion based method was proposed to calculate both in-phase and quadrature at the same time. Numerical simulations for different data format, e.g., double and finite bits, were carried out in Matlab and Quartus, which were followed by the hardware implementation in Field Programmable Gate Array. The results demonstrated that the proposed method possessed higher precision and exhausted less logic elements than the CORDIC algorithm.
Garcia, R.D.M.; Ono, S.
1999-09-01
An improved implementation of the discrete ordinates method for computing neutral particle transport in ducts is presented. The considered one-dimensional model makes use of two basic functions to represent the transverse and azimuthal dependencies of the particle angular flux in the duct. It is shown that if the problem is decomposed into uncollided and collided problems prior to using the discrete ordinates approximation, the number of ordinates necessary to achieve a desired degree of accuracy in the solution can be greatly reduced, especially for long ducts with significant wall absorption. Further savings in computer time can be attained by employing a composite quadrature based on a (nonstandard) half-range quadrature that can be generated in an effective and efficient way with one of the classical methods in the constructive theory of orthogonal polynomials.
Barichello, L.B.; Siewert, C.E.
1998-09-01
In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given.
Boltzmann-Fokker-Planck calculations using standard discrete-ordinates codes
Morel, J.E.
1987-01-01
The Boltzmann-Fokker-Planck (BFP) equation can be used to describe both neutral and charged-particle transport. Over the past several years, the author and several collaborators have developed methods for representing Fokker-Planck operators with standard multigroup-Legendre cross-section data. When these data are input to a standard S/sub n/ code such as ONETRAN, the code actually solves the Boltzmann-Fokker-Planck equation rather than the Boltzmann equation. This is achieved wihout any modification to the S/sub n/ codes. Because BFP calculations can be more demanding from a numerical viewpoint than standard neutronics calculations, we have found it useful to implement new quadrature methods ad convergence acceleration methods in the standard discrete-ordinates code, ONETRAN. We discuss our BFP cross-section representation techniques, our improved quadrature and acceleration techniques, and present results from BFP coupled electron-photon transport calculations performed with ONETRAN. 19 refs., 7 figs.
Miller, R.L.
1998-11-01
A numerically stable, accurate, and robust form of the exponential characteristic (EC) method, used to solve the time-independent linearized Boltzmann Transport Equation, is derived using direct affine coordinate transformations on unstructured meshes of tetrahedra. This quadrature, as well as the linear characteristic (LC) spatial quadrature, is implemented in the transport code, called TETRAN. This code solves multi-group neutral particle transport problems with anisotropic scattering and was parallelized using High Performance Fortran and angular domain decomposition. A new, parallel algorithm for updating the scattering source is introduced. The EC source and inflow flux coefficients are efficiently evaluated using Broyden`s rootsolver, started with special approximations developed here. TETRAN showed robustness, stability and accuracy on a variety of challenging test problems. Parallel speed-up was observed as the number of processors was increased using an IBM SP computer system.
Moment-Preserving SN Discretizations for the One-Dimensional Fokker-Planck Equation
Warsa, James S.; Prinja, Anil K.
2012-06-14
The Fokker-Planck equation: (1) Describes the transport and interactions of charged particles, (2) Many small-angle scattering collisions, (3) Asymptotic limit of the Boltzmann equation (Pomraning, 1992), and (4) The Boltzmann collision operator becomes the angular Laplacian. SN angular discretization: (1) Angular flux is collocated at the SN quadrature points, (2) The second-order derivatives in the Laplacian term must be discretized, and (3) Weighted finite-difference method preserves zeroth and first moments (Morel, 1985). Moment-preserving methods: (1) Collocate the Fokker-Planck operator at the SN quadrature points, (2) Develop several related and/or equivalent methods, and (3) Motivated by discretizations for the angular derivative appearing in the transport equation in one-dimensional spherical coordinates.
Balanced Waveguide HEB Mixer for APEX 1.3 THz receiver
NASA Astrophysics Data System (ADS)
Meledin, Denis; Pantaleev, Miroslav; Pavolotsky, Alexey; Risacher, Christophe; Perez Robles, Victor A.; Belitsky, Victor; Drakinskiy, Vladimir; Cherednichenko, Sergey
2005-05-01
We present results on the design and construction of a waveguide balanced Hot Electron Bolometer (HEB) Terahertz mixer for Atacama Pathfinder EXperiment (APEX), band T2 covering 1250-1390 GHz frequency range. In the proposed design, a waveguide balanced mixer is realized using a quadrature scheme. The two identical HEB elements are integrated with RF choke filters, DC-bias, IF circuitry, and fabricated from 4 nm thick NbN film deposited on a crystalline quartz substrate with dimensions of 1100 μm×70 μm × 17 μm. We have designed and fabricated an input 3 dB quadrature waveguide hybrid. For its fabrication, we use micromachining approach to achieve low insertion loss and symmetrical division of the RF and local oscillator (LO) power within the band of interest. We plan to use two HEB mixer configurations with different probe impedance values of 55, 70 Ohm within 1250-1390 GHz frequency range.
Demonstration of optical multicasting using Kerr frequency comb lines.
Bao, Changjing; Liao, Peicheng; Kordts, Arne; Karpov, Maxim; Pfeiffer, Martin H P; Zhang, Lin; Yan, Yan; Xie, Guodong; Cao, Yinwen; Almaiman, Ahmed; Ziyadi, Morteza; Li, Long; Zhao, Zhe; Mohajerin-Ariaei, Amirhossein; Wilkinson, Steven R; Tur, Moshe; Fejer, Martin M; Kippenberg, Tobias J; Willner, Alan E
2016-08-15
We experimentally demonstrate optical multicasting using Kerr frequency combs generated from a Si_{3}N_{4} microresonator. We obtain Kerr combs in two states with different noise properties by varying the pump wavelength in the resonator and investigate the effect of Kerr combs on multicasting. Seven-fold multicasting of 20 Gbaud quadrature phase-shift-keyed signals and four-fold multicasting of 16-quadrature amplitude modulation signals have been achieved when low-phase-noise combs are input into a periodically poled lithium niobate waveguide. In addition, we find that the wavelength conversion efficiency in the PPLN waveguide for chaotic combs with high noise is similar to that for low-noise combs, while the signal quality of the multicast copy is significantly degraded. PMID:27519112
NASA Astrophysics Data System (ADS)
Petrov, A. G.
2011-07-01
A numerical method for computing the potential flow past a lattice of airfoils is described. The problem is reduced to a linear integrodifferential equation on the lattice contour, which is then approximated by a linear system of equations with the help of specially derived quadrature formulas. The quadrature formulas exhibit exponential convergence in the number of points on an airfoil and have a simple analytical form. Due to its fast convergence and high accuracy, the method can be used to directly optimize the airfoils as based on any given integral characteristics. The shear stress distribution and the separation points are determined from the velocity distribution at the airfoil boundary calculated by solving the boundary layer equations. The method proposed is free of laborious grid generation procedures and does not involve difficulties associated with numerical viscosity at high Reynolds numbers.
Analytical results on channel capacity in uncompensated optical links with coherent detection.
Bosco, G; Poggiolini, P; Carena, A; Curri, V; Forghieri, F
2011-12-12
Based on a recently introduced model of non-linear propagation, we propose analytical formulas for the capacity limit of polarization-multiplexed ultra-dense WDM uncompensated coherent optical systems at the Nyquist limit, assuming both lumped and ideally distributed amplification. According to these formulas, capacity fundamentally depends on the transmitted power spectral density and on the total optical WDM bandwidth, whereas it does not depend on symbol-rate. Also, capacity approximately decreases by 2 [bit/s/Hz] for every doubling of link length. We show examples of capacity calculations for specific ultra-long-haul links with different polarization-multiplexed (PM) constellations, i.e. ideal PM-Gaussian, PM-QPSK (quadrature-phase shift keying) and PM-QAM (quadrature amplitude modulation). We show that the launch power maximizing capacity is independent of link length and modulation format. We also discuss the usable range of PM-QAM systems and validate analysis with simulations. PMID:22274054
NASA Technical Reports Server (NTRS)
Simon, M. K.; Huth, G. K.; Polydoros, A.
1982-01-01
Bandwidth-conserving modulation techniques, which trade average power for bandwidth in a favorable exchange, have recently found widespread application in digital radio and satellite communication systems. Quadrature amplitude-shift-keying (QASK) is a particular type of the considered techniques. QASK makes use of multilevel signals to amplitude modulate the in-phase and quadrature components of a carrier. Frequency hopping (FH) is used to protect a conventional communication system from radio frequency interference (RFI) or jamming. Differentially coherent detection provides a possible solution to the effect of phase discontinuities introduced by FH. The application of such a detection technique to QASK signals is discussed. A receiver structure is proposed and its symbol error probability performance for an additive white Gaussian noise (AWGN) background is investigated.
Accurate solution of the Dirac equation on Lagrange meshes
NASA Astrophysics Data System (ADS)
Baye, Daniel; Filippin, Livio; Godefroid, Michel
2014-04-01
The Lagrange-mesh method is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. With a basis of Lagrange functions involving associated Laguerre polynomials related to the Gauss quadrature, the method is applied to the Dirac equation. The potential may possess a 1/r singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers n +1 of mesh points, where n is the principal quantum number. Numerically exact mean values of powers -2 to 3 of the radial coordinate r can also be obtained with n +2 mesh points. For the Yukawa potential, a 15-digit agreement with benchmark energies of the literature is obtained with 50 or fewer mesh points.
Cao, Zhang; Song, Wei; Peng, Zhicong; Xu, Lijun
2014-11-01
There exist a number of algorithms to map the phase to amplitude in direct digital synthesis (DDS). For DDS with more than 14 output bits, the Coordinate Rotation Digital Computer (CORDIC) algorithm is well known for its high precision. Also, it is effective in solutions where there is the need of in-phase and quadrature components simultaneously because the algorithm calculates both. In this paper, a Taylor expansion based method was proposed to calculate both in-phase and quadrature at the same time. Numerical simulations for different data format, e.g., double and finite bits, were carried out in Matlab and Quartus, which were followed by the hardware implementation in Field Programmable Gate Array. The results demonstrated that the proposed method possessed higher precision and exhausted less logic elements than the CORDIC algorithm. PMID:25430130
Design of Pound-Drever-Hall laser frequency stabilization system without phase shifter
NASA Astrophysics Data System (ADS)
Su, Juan; Jiao, Mingxing; Xing, Junhong; Li, Zhe
2015-02-01
The Pound-Drever-Hall (PDH) laser frequency stabilization is a wide spread adopted technique for narrow linewidth and ultra-stable lasers, and a phase shifter is an important part in a traditional PDH frequency stabilization system. A PDH laser frequency stabilization system without phase shifter was proposed, in which quadrature coherent detection method was used to extract the frequency drifts. Orthogonal reference signals are generated using direct digital frequency synthesizer (DDS) and mixed with the output of a photo-detector. Over-sampling technique and cumulative average algorithm were used to improve the detection resolution and SNR, orthogonal phase sensitive detection algorithm was adopted to obtain the frequency drifts. Both the quadrature demodulation system structure and the signal processing methods were adopted, the systematic detection error is reduced, the anti-noise performance is raised and long term frequency stability is improved with the PDH laser frequency stabilization system without phase shifter.
Unidimensional continuous-variable quantum key distribution
NASA Astrophysics Data System (ADS)
Usenko, Vladyslav C.; Grosshans, Frédéric
2015-12-01
We propose the continuous-variable quantum key distribution protocol based on the Gaussian modulation of a single quadrature of the coherent states of light, which is aimed to provide simplified implementation compared to the symmetrically modulated Gaussian coherent-state protocols. The protocol waives the necessity in one of the quadrature modulations and the corresponding channel transmittance estimation. The security of the protocol against collective attacks in a generally phase-sensitive Gaussian channel is analyzed and is shown achievable upon certain conditions. Robustness of the protocol to channel imperfections is compared to that of the symmetrical coherent-state protocol. The simplified unidimensional protocol is shown possible at a reasonable quantitative cost in terms of key rate and of tolerable channel excess noise.
Millimeter wave I-Q standoff biosensor
NASA Astrophysics Data System (ADS)
Liao, Shaolin; Bakhtiari, Sasan; Elmer, Thomas; Raptis, Apostolos C.; Mikhelson, Ilya V.; Sahakian, Alan V.
2012-06-01
A continuous wave (CW) 94-GHz millimeter wave (mmW) standoff biosensor has been developed for remote biometric sensing applications. The sensor measures the demodulated in-phase (I) and quadrature-phase (Q) components of the received reflected mmW signal from a subject. Both amplitude and phase of the reflected signal are obtained from downconverted I and Q channels from the quadrature mixer. The mmW sensor can faithfully monitor human vital signs (heartbeat and respiration) at relatively long standoff distances. Principle Component Analysis (PCA) is used to extract the heartbeat, the respiration and the body motion signals. The approach allows one to deduce information about amplitude and beat-to-beat rate of the respiration and the heartbeat. Experimental results collected from a subject were analyzed and compared to the signal obtained with a three-electrode ECG monitoring instrument.
New canonic lossy inductor using a single CDBA and its application
NASA Astrophysics Data System (ADS)
Pathak, J. K.; Singh, A. K.; Senani, R.
2016-01-01
A new lossy inductor (parallel R-L type) using single current differencing buffered amplifier (CDBA) is presented, which employs only two resistors and a grounded capacitor. The proposed lossy inductor is shown to be useful in realizing an oscillator circuit, which provides quadrature voltage outputs using only two CDBAs, three resistors and two grounded capacitors and offers independent control on condition of oscillation and frequency of oscillation up to a frequency of 61 MHz. Detailed non-ideal analysis including single-pole model for voltage and current gain has also been carried out. SPICE simulation results and experimental results based upon the CDBA constructed from commercially available IC AD844 have been included which confirm the practical workability of the proposed lossy inductor and quadrature oscillator circuit.
Performance Analysis for LTE Wireless Communication
NASA Astrophysics Data System (ADS)
Tholhath, S.; Tiong, T. C.
2015-04-01
Long Term Evolution (LTE) is the new upgrade path for carrier with both GSM/UMTS networks and CDMA2000 networks. The LTE is targeting to become the first global mobile phone standard regardless of the different LTE frequencies and bands use in other countries barrier. Adaptive Modulation and Coding (AMC) is used to increase the network capacity or downlink data rates. Various modulation types are discussed such as Quadrature Phase Shift Keying (QPSK) and Quadrature Amplitude Modulation (QAM). Spatial multiplexing techniques for 4×4 MIMO antenna configurations are considered. This paper has outlined various estimation techniques to increase the throughput of the LTE network by simulating the estimation techniques with various parameters in the LTE downlink mode 4 (spatial multiplexing). Three techniques i.e. channel estimation technique, estimation of channel models and MIMO receiver algorithm are simulated to provide the ideal LTE wireless communication system.
Adaptive Modulation and Coding for LTE Wireless Communication
NASA Astrophysics Data System (ADS)
Hadi, S. S.; Tiong, T. C.
2015-04-01
Long Term Evolution (LTE) is the new upgrade path for carrier with both GSM/UMTS networks and CDMA2000 networks. The LTE is targeting to become the first global mobile phone standard regardless of the different LTE frequencies and bands use in other countries barrier. Adaptive Modulation and Coding (AMC) is used to increase the network capacity or downlink data rates. Various modulation types are discussed such as Quadrature Phase Shift Keying (QPSK), Quadrature Amplitude Modulation (QAM). Spatial multiplexing techniques for 4×4 MIMO antenna configuration is studied. With channel station information feedback from the mobile receiver to the base station transmitter, adaptive modulation and coding can be applied to adapt to the mobile wireless channels condition to increase spectral efficiencies without increasing bit error rate in noisy channels. In High-Speed Downlink Packet Access (HSDPA) in Universal Mobile Telecommunications System (UMTS), AMC can be used to choose modulation types and forward error correction (FEC) coding rate.
NASA Technical Reports Server (NTRS)
Fromme, J.; Golberg, M.
1978-01-01
The numerical calculation of unsteady two dimensional airloads which act upon thin airfoils in subsonic ventilated wind tunnels was studied. Neglecting certain quadrature errors, Bland's collocation method is rigorously proved to converge to the mathematically exact solution of Bland's integral equation, and a three way equivalence was established between collocation, Galerkin's method and least squares whenever the collocation points are chosen to be the nodes of the quadrature rule used for Galerkin's method. A computer program displayed convergence with respect to the number of pressure basis functions employed, and agreement with known special cases was demonstrated. Results are obtained for the combined effects of wind tunnel wall ventilation and wind tunnel depth to airfoil chord ratio, and for acoustic resonance between the airfoil and wind tunnel walls. A boundary condition is proposed for permeable walls through which mass flow rate is proportional to pressure jump.
Third and fourth virial coefficients for hard disks in narrow channels.
Mon, K K
2014-06-28
The third (B3) and fourth (B4) virial coefficients of hard disks in narrow channels have been evaluated accurately by Gaussian quadrature for a range of channel widths (2Rp), Rp < (√3 + 2)/4 = 0.9930... (in units of the hard disk diameter). These widths correspond to the important regime of fluids in single file formations with only nearest-neighbor interactions. Accurate results are obtained by using N-point Gaussian quadrature and extrapolating to the infinite N limits. Since not much is known about these B3 and B4, our new results should provide guidance for exact calculations of the virial coefficients and benchmarks for other numerical methods. PMID:24985651
Feedback-Enhanced Parametric Squeezing of Mechanical Motion
NASA Astrophysics Data System (ADS)
Vinante, A.; Falferi, P.
2013-11-01
We present a single-quadrature feedback scheme able to overcome the conventional 3 dB limit on parametric squeezing. The method is experimentally demonstrated in a micromechanical system based on a cantilever with a magnetic tip. The cantilever is detected at low temperature by a SQUID susceptometer, while parametric pumping is obtained by modulating the magnetic field gradient at twice the cantilever frequency. A maximum squeezing of 11.5 dB and 11.3 dB is observed, respectively, in the response to a sinusoidal test signal and in the thermomechanical noise. So far, the maximum squeezing factor is limited only by the maximum achievable parametric modulation. The proposed technique might be used to squeeze one quadrature of a mechanical resonator below the quantum noise level, even without the need for a quantum limited detector.
Phase-space noncommutative formulation of Ozawa's uncertainty principle
NASA Astrophysics Data System (ADS)
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Costa Dias, Nuno; Prata, João Nuno
2014-08-01
Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature amplifiers and for noiseless quadrature transducers. Several distinctive features appear as a consequence of the noncommutative extension: measurement interactions which are noiseless, and observables which are undisturbed by a measurement, or of independent intervention in ordinary quantum mechanics, may acquire noise, become disturbed by the measurement, or no longer be an independent intervention in noncommutative quantum mechanics. It is also found that there can be states which violate Ozawa's universal noise-disturbance trade-off relation, but verify its noncommutative deformation.
H-beta photometry of V1010 Ophiuchi
NASA Technical Reports Server (NTRS)
Corcoran, M. F.; Siah, M. J.; Guinan, E. F.
1991-01-01
An analysis is presented of previously unpublished intermediate and narrow band H-beta light curves of the short period eclipsing binary V1010 Oph. The temperature of the primary is determined directly by comparing the UV continuum with Kurucz model atmospheres and solve the broadband lightcurve using the Wilson-Devinney program. The present solution has the primary filling its Roche lobe while the secondary is detached from its lobe. An asymmetry in the light curve in which first quadrature (0.25 P) is brighter than the second quadrature (0.75 P) may be the result of local heating of the inner surface of the secondary by mass transfer from the primary. The present semidetached solution indicates that the system is probably evolved.
Application of TITAN for Simulation of Particle Streaming in a Duct
NASA Astrophysics Data System (ADS)
Royston, Katherine; Haghighat, Alireza; Yi, Ce
2016-02-01
The TITAN hybrid deterministic transport code is applied to the simulation of particle streaming in a nuclear power plant duct. A simple model is used consisting of a concrete duct emerging from the pressure vessel with an isotropic surface source with a U-235 fission spectrum located at the pressure vessel end. Multiple methods of simulating the duct using the TITAN code are considered to demonstrate the flexibility of the code and the advantages of TITAN's algorithms. These methods include a discrete ordinates (SN) calculation, a characteristics method calculation, and the use of a fictitious quadrature set with simplified ray-tracing. The TITAN code's results are compared with MCNP5 solutions. While all TITAN solutions are obtained in a shorter computation time than the MCNP5 solution, the TITAN solution with the fictitious quadrature set shows the largest speedup.
A fast conservative spectral solver for the nonlinear Boltzmann collision operator
Gamba, Irene M.; Haack, Jeffrey R.; Hu, Jingwei
2014-12-09
We present a conservative spectral method for the fully nonlinear Boltzmann collision operator based on the weighted convolution structure in Fourier space developed by Gamba and Tharkabhushnanam. This method can simulate a broad class of collisions, including both elastic and inelastic collisions as well as angularly dependent cross sections in which grazing collisions play a major role. The extension presented in this paper consists of factorizing the convolution weight on quadrature points by exploiting the symmetric nature of the particle interaction law, which reduces the computational cost and memory requirements of the method to O(M{sup 2}N{sup 4}logN) from the O(N{sup 6}) complexity of the original spectral method, where N is the number of velocity grid points in each velocity dimension and M is the number of quadrature points in the factorization, which can be taken to be much smaller than N. We present preliminary numerical results.
Quantum squeezing of a mechanical resonator
NASA Astrophysics Data System (ADS)
Lei, Chan U.; Weinstein, Aaron; Suh, Junho; Wollman, Emma; Schwab, Keith
Generating nonclassical states of a macroscopic object has been a subject of considerable interest. It offers a route toward fundamental test of quantum mechanics in an unexplored regime. However, a macroscopic quantum state is very susceptible to decoherence due to the environment. One way to generate robust quantum states is quantum reservoir engineering. In this work, we utilize the reservoir engineering scheme developed by Kronwald et al. to generate a steady quantum squeezed state of a micron-scale mechanical oscillator in an electromechanical system. Together with the backaction evading measurement technique, we demonstrate a quantum nondemolition measurement of the mechanical quadratures to characterize the quantum squeezed state. By measuring the quadrature variances of the mechanical motion, more than 3dB squeezing below the zero-point level has been achieved.
Jin, Z.; Stamnes, K.; Zak, B.D.
1995-04-01
This article describes a comprehensive radiative transfer model pertinent to the atmosphere-sea ice-ocean system. The main features of the model include: The atmosphere, sea ice, and ocean each represented by a sufficient number of layers to resolve the change in the optical properties of each stratum; An appropriate quadrature structure to take into account the total reflection at the air-ice or air-water interface, as well as to solve the radiative transfer equation in the coupled system consistently; Provision for a different number of streams (quadrature points) in the atmosphere, ice, and ocean, chosen based on the optical properties in each stratum and the computational accuracy method.
NASA Astrophysics Data System (ADS)
Coral, W.; Rossi, C.; Curet, O. M.
2015-12-01
This paper presents a Differential Quadrature Element Method for free transverse vibration of a robotic fish based on a continuous and non-uniform flexible backbone with distributed masses (fish ribs). The proposed method is based on the theory of a Timoshenko cantilever beam. The effects of the masses (number, magnitude and position) on the value of natural frequencies are investigated. Governing equations, compatibility and boundary conditions are formulated according to the Differential Quadrature rules. The convergence, efficiency and accuracy are compared to other analytical solution proposed in the literature. Moreover, the proposed method has been validate against the physical prototype of a flexible fish backbone. The main advantages of this method, compared to the exact solutions available in the literature are twofold: first, smaller computational cost and second, it allows analysing the free vibration in beams whose section is an arbitrary function, which is normally difficult or even impossible with other analytical methods.
Speeding up DFT: A faster method for integrating band energy in SCF cycles
NASA Astrophysics Data System (ADS)
Burbidge, Matthew M.; Jorgensen, Jeremy J.; Rosenbrock, Conrad W.; Thomas, Derek C.; Hess, Bret C.; Forcade, Rodney W.; Curtarolo, Stefano; Hart, Gus L. W.
2015-03-01
Typically in SCF cycles, a ``rectangle rule'' is used on uniformly spaced points (Monk Pack meshes)1 to integrate the band energy. The use of rectangles is motivated by their fast convergence when used on the fully occupied bands of semiconductors. Unfortunately integration with rectangles is extremely inefficient for metals. This motivates the use of gauss quadrature (or other higher order methods) for integrating the band energy. As we show, however, even in the case of semiconductors where the rectangle convergence is extremely efficient, higher order methods are still more efficient. The savings in semiconductors alone are sufficient to motivate the implementation of a higher order method in current DFT codes. Even though higher order quadrature methods were discussed immediately following the original Monkhorst and Pack1 paper, we revisit the issue in light of modern DFT calculations. MMB acknowledges support by NSF (DMR-0908753). JJJ, CWR, DCT, RWF, SC, GLWH was supported by ONR (MURI N00014-13-1-0635).
Application of efficient algorithm for solving six-dimensional molecular Ornstein-Zernike equation.
Ishizuka, R; Yoshida, N
2012-03-21
In this article, we propose an efficient algorithm for solving six-dimensional molecular Ornstein-Zernike (MOZ) equation. In this algorithm, the modified direct inversion in iterative subspace, which is known as the fast convergent method for solving the integral equation theory of liquids, is adopted. This method is found to be effective for the convergence of the MOZ equation with a simple initial guess. For the accurate averaging of the correlation functions over the molecular orientations, we use the Lebedev-Laikov quadrature. The appropriate number of grid points for the quadrature is decided by the analysis of the dielectric constant. We also analyze the excess chemical potential of aqueous ions and compare the results of the MOZ with those of the reference interaction site model. PMID:22443748
Application of efficient algorithm for solving six-dimensional molecular Ornstein-Zernike equation
NASA Astrophysics Data System (ADS)
Ishizuka, R.; Yoshida, N.
2012-03-01
In this article, we propose an efficient algorithm for solving six-dimensional molecular Ornstein-Zernike (MOZ) equation. In this algorithm, the modified direct inversion in iterative subspace, which is known as the fast convergent method for solving the integral equation theory of liquids, is adopted. This method is found to be effective for the convergence of the MOZ equation with a simple initial guess. For the accurate averaging of the correlation functions over the molecular orientations, we use the Lebedev-Laikov quadrature. The appropriate number of grid points for the quadrature is decided by the analysis of the dielectric constant. We also analyze the excess chemical potential of aqueous ions and compare the results of the MOZ with those of the reference interaction site model.
Numerical calculation of mean intensity and radiative flux in plane-parallel stellar atmospheres
NASA Astrophysics Data System (ADS)
Nariai, K.; Yoshioka, K.
The four-point Gaussian-quadrature formulas of Kegel (1962) for the evaluation of the intensity and flux (F) integrals is improved by using Bessel's interpolation technique and by subdividing the integral range. Steps in the analysis include the calculation of the Gaussian points of division and weightings for the interval (y, z), for a small (y, z), and for (O, z); determination of the precision of n-point formulas in calculating intensity and F; and the derivation of a four-point version of the two-point quadrature method of Cayrel (1960) and Norton (Mihalas, 1967). The numerical results are presented and compared with those of other models. The gray-model delta-F/F ratio calculated by this method is found to be less than 0.01 percent.
50 Gbit/s real-time test environment for integrated photonic DQPSK receivers
NASA Astrophysics Data System (ADS)
Föhn, T.; Fischer, C.; Berroth, M.
2014-11-01
In this paper an FPGA-based test system for high-speed transmission experiments with integrated photonic receivers is presented. Pseudorandom binary sequences are generated inside the FPGA and encoded as either differential quadrature phase shift keying (DQPSK) or quadrature phase shift keying (QPSK) signals. The DQPSK encoder uses a 64-fold parallel-prefix-layers architecture for real-time operation which allows for a maximum internal encoder data rate of 64 Gbit/s. Two-fold parallel data streams of I and Q signals suitable for driving an optical IQ-modulator can be transmitted and received by four 12.5 Gbit/s transceivers. Integrated bit error testers are used to determine bit error rates in real-time.
NASA Astrophysics Data System (ADS)
Le Duff, Alain; Plantier, Guy; Valière, Jean C.; Gazengel, Bruno
2016-03-01
A signal processing technique, based on the use of an Extended Kalman Filter, has been developed to measure sound fields by means of Laser Doppler Velocimetry in weak flow. This method allows for the parametric estimation of both the acoustic particle and flow velocity for a forced sine-wave excitation where the acoustic frequency is known. The measurements are performed from the in-phase and the quadrature components of the Doppler downshifted signal thanks to an analog quadrature demodulation technique. Then, the estimated performance is illustrated by means of Monte-Carlo simulations obtained from synthesized signals and compared with asymptotic and analytical forms for the Cramer-Rao Bounds. Results allow the validity domain of the method to be defined and show the availability for free-field measurements in a large range. Finally, an application based on real data obtained in free field is presented.
NASA Technical Reports Server (NTRS)
Gevargiz, J. M.; Holmes, J. K.
1991-01-01
The next generation of digital receivers for NASA's Deep Space Network is composed of in-phase and quadrature-phase channels. The authors have modeled and simulated a quadrature-phase baseband channel that includes a low-pass filter and a digital matched filter. The simulation is used to study the performance of the three schemes of digital matched filtering that use digital weighted integrate-and-dump filters. Using three methods for calculating the near-optimum matched filter weight coefficients, the simulation results are analyzed for the NRZ and Manchester data formats. The performances of the digital matched filters are studied in the presence of a timing error between the demodulated symbols and the integrate-and-dump filters.
Communication: An efficient algorithm for evaluating the Breit and spin-spin coupling integrals
NASA Astrophysics Data System (ADS)
Shiozaki, Toru
2013-03-01
We present an efficient algorithm for evaluating a class of two-electron integrals of the form {r}_{12}⊗ {r}_{12}/r_{12}^n over one-electron Gaussian basis functions. The full Breit interaction in four-component relativistic theories beyond the Gaunt term is such an operator with n = 3. Another example is the direct spin-spin coupling term in the quasi-relativistic Breit-Pauli Hamiltonian (n = 5). These integrals have been conventionally evaluated by expensive derivative techniques. Our algorithm is based on tailored Gaussian quadrature, similar to the Rys quadrature for electron repulsion integrals (ERIs), and can utilize the so-called horizontal recurrence relation to reduce the computational cost. The CPU time for computing all six Cartesian components of the Breit or spin-spin coupling integrals is found to be only 3 to 4 times that of the ERI evaluation.
Communication: An efficient algorithm for evaluating the Breit and spin-spin coupling integrals.
Shiozaki, Toru
2013-03-21
We present an efficient algorithm for evaluating a class of two-electron integrals of the form r12⊗r12/r12(n) over one-electron Gaussian basis functions. The full Breit interaction in four-component relativistic theories beyond the Gaunt term is such an operator with n = 3. Another example is the direct spin-spin coupling term in the quasi-relativistic Breit-Pauli Hamiltonian (n = 5). These integrals have been conventionally evaluated by expensive derivative techniques. Our algorithm is based on tailored Gaussian quadrature, similar to the Rys quadrature for electron repulsion integrals (ERIs), and can utilize the so-called horizontal recurrence relation to reduce the computational cost. The CPU time for computing all six Cartesian components of the Breit or spin-spin coupling integrals is found to be only 3 to 4 times that of the ERI evaluation. PMID:23534619
State-constrained booster trajectory solutions via finite elements and shooting
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.; Seywald, Hans
1993-01-01
This paper presents an extension of a FEM formulation based on variational principles. A general formulation for handling internal boundary conditions and discontinuities in the state equations is presented, and the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions which only touch the state constraint and solutions which have a boundary arc of finite length are considered. Suitable shape and test functions are chosen for a FEM discretization. All element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form. The final form of the algebraic equations is then derived. A simple state-constrained problem is solved. Then, for a practical application of the use of the FEM formulation, a launch vehicle subject to a dynamic pressure constraint (a first-order state inequality constraint) is solved. The results presented for the launch-vehicle trajectory have some interesting features, including a touch-point solution.
NASA Astrophysics Data System (ADS)
Won, Yong-Yuk; Seo, Dong-Sun; Yoon, Sang Min
2016-04-01
We propose a technique that improves the channel capacity of an optical wireless orthogonal frequency division multiplexing (OFDM) transmission, which employs a visible light-emitting diode. An OFDM waveform encoded by quadrature phase shift keying (QPSK) or 16-quadrature amplitude modulation is compressed and then transformed into a sparse waveform using a proposed advanced systematic sampling. At the optical wireless receiver, the original waveform is recovered by L1-minimization based on a Bayesian compressive sensing. Our experimental results show the significant increase in the channel capacity from 31.12 to 51.87 Mbit/s at forward error correction limit (i.e., error vector magnitude of 32%) in case of QPSK symbols.
A fast high-order method to calculate wakefield forces in an electron beam
Qiang, Ji; Mitchell, Chad; Ryne, Robert D.
2012-03-22
In this paper we report on a high-order fast method to numerically calculate wakefield forces in an electron beam given a wake function model. This method is based on a Newton-Cotes quadrature rule for integral approximation and an FFT method for discrete summation that results in an O(Nlog(N)) computational cost, where N is the number of grid points. Using the Simpson quadrature rule with an accuracy of O(h4), where h is the grid size, we present numerical calculation of the wakefields from a resonator wake function model and from a one-dimensional coherent synchrotron radiation (CSR) wake model. Besides the fast speed and high numerical accuracy, the calculation using the direct line density instead of the first derivative of the line density avoids numerical filtering of the electron density function for computing the CSR wakefield force. I. INTRODUCTION
Unruh, W.P.
1987-03-23
Method and apparatus are provided for deriving positive and negative Doppler spectrum to enable analysis of objects in motion, and particularly, objects having rotary motion. First and second returned radar signals are mixed with internal signals to obtain an in-phase process signal and a quadrature process signal. A broad-band phase shifter shifts the quadrature signal through 90/degree/ relative to the in-phase signal over a predetermined frequency range. A pair of signals is output from the broad-band phase shifter which are then combined to provide a first side band signal which is functionally related to a negative Doppler shift spectrum. The distinct positive and negative Doppler spectra may then be analyzed for the motion characteristics of the object being examined.
Non-contact displacement estimation using Doppler radar.
Gao, Xiaomeng; Singh, Aditya; Yavari, Ehsan; Lubecke, Victor; Boric-Lubecke, Olga
2012-01-01
Non-contact Doppler radar has been used extensively for detection of physiological motion. Most of the results published to date have been focused on estimation of the physiological rates, such as respiratory rate and heart rate, with CW and modulated waveforms in various settings. Accurate assessment of chest displacement may take this type of monitoring to the new level, by enabling the estimation of associated cardiopulmonary volumes, and possibly pulse pressure. To obtain absolute chest displacement with highest precision, full nonlinear phase demodulation of the quadrature radar outputs must be performed. The accuracy of this type of demodulation is limited by the drifting received RF power, varying dc offset, and channel quadrature imbalance. In this paper we demonstrate that if relatively large motion is used to calibrate the system, smaller motion displacement may be acquired with the accuracy on the order of 30 µm. PMID:23366212
NASA Astrophysics Data System (ADS)
Yamamoto, Shu; Tomishige, Kazuhiro; Ara, Takahiro
The direct and quadrature axes inductances of flux barrier type Synchronous Reluctance Motors (SynRM) change depending on the magnitude of both direct and quadrature axes currents under the influence of the cross-magnetic saturation. This paper presents a maximum efficiency operation method of SynRMs with cross-magnetic saturation. An improved approximate equation that accurately expresses the inductance variation caused by cross-magnetic saturation is utilized for calculating the Maximum Efficiency Operation Current (MEOC, i.e., the d-axis current at maximum efficiency) at each load point. A vector control system in which the steady-state driving efficiency is maximized by selecting a d-axis current command from the obtained MEOC is shown. By considering cross-magnetic saturation the proposed method not only maximizes the efficiency but also improves the torque control accuracy. The validity of this method is demonstrated with calculated and measured results of on-load characteristics.
NASA Astrophysics Data System (ADS)
Rao, Wei
2011-10-01
The constant modulus algorithm (CMA) for blind equalization requires a separate carrier-recovery system for phase recovery. A modified CMA, called the multimodulus algorithm (MMA), which may perform joint blind equalization and carrier recovery without the need for a separate carrier-recovery system for quadrature amplitude modulation (QAM) signal constellations. This letter mathematically analyzes the steady-state mean square error (MSE) of MMA. Analysis results indicate that MMA produces 50% fewer steady-state MSE than CMA.
False lock performance in polarity-type Costas receivers in the presence of periodic data patterns
NASA Technical Reports Server (NTRS)
Wang, James June-Ming; Lai, Dennis Teng-Tsun; Heng, Veronica Siang-Gek; Godfrey, Robert D.
1987-01-01
The authors address the false-lock performance of receivers which use polarity-type Costas loops for the carrier recovery of unbalanced quadrature phase-shift keyed (QPSK), asynchronous QPSK or binary PSK (BPSK) signals in the presence of periodic data patterns. The potential false-lock frequencies are first identified. Expressions for both true-lock and false-lock components are also derived, thereby allowing numerical evaluation of various key parameters for cases of practical interest.
Multiple-Trellis-Coded Modulation
NASA Technical Reports Server (NTRS)
Divsalar, D.; Simon, M. K.
1990-01-01
Theoretical gain over simple multiple-phase-shift keying at least 2 to 3 decibels. Multiple-trellis-coded modulation scheme combined with M-ary modulation shows theoretically to yield asymptotic gains in performance over uncoded multiple-phase-shift keying, while employing symmetric multiple-phase-shift signal constellations and avoiding code catastrophe. Suitable for satellite and terrestrial-mobile/satellite communications or other communications requiring burst-error correction. Extended to such higher dimensional modulations as quadrature amplitude modulation.
Detecting Eve in communication with continuous-variable Einstein-Podolsky-Rosen correlations
Messikh, A.
2007-03-15
We study the validity of the entanglement parameter introduced in a recent publication by Guangqiang et al. [Phys. Rev. A 73, 012314 (2006)] for detecting Eve, the eavesdropper. We have found that Eve can be detected using this parameter only if Alice establishes a quantum correlation between the Einstein-Podolsky-Rosen (EPR) pair. This quantum correlation is related to the possibility of an apparent violation of the Heisenberg inequality for the quadrature components of the EPR pair.
High resolution heterodyne interferometer based on time-to-digital converter.
Wang, Fei; Long, Zhangcai; Zhang, Bin; Zhao, Meirong
2012-04-01
A new heterodyne interferometer is presented, which adopts time-to-digital converter (TDC) measuring the time intervals of zero crossings of heterodyne signal for phase demodulation. Thanks to the 0.1 ns time resolution of TDC and linear phase demodulation, it can achieve high resolution and avoids nonlinear measuring distortion in other indirect high precise phase demodulation methods, such as pulse width modulation (PWM) and in-phase∕quadrature (I∕Q) method. PMID:22559581
Bandwidth efficient coherent lidar based on phase-diversity detection.
Liao, Tongqing; Hameed, Mahmood; Hui, Rongqing
2015-04-10
Bandwidth efficient coherent lidar based on phase-diversity detection is reported for the first time, to the best of our knowledge, which allows the doubling of bandwidth efficiency through the simultaneous utilization of the in-phase (I) and quadrature (Q) components. By maintaining RF phase continuity between linearly frequency-chirped I and Q components through digital signal processing, the range resolution of the lidar system can be improved. PMID:25967299
A mathematical model for the doubly-fed wound rotor generator, part 2
NASA Technical Reports Server (NTRS)
Brady, F. J.
1984-01-01
A mathematical analysis of a doubly-fed wound rotor generator is presented. The constraints of constant stator voltage and frequency to the circuit equations were applied and expressions for the currents and voltages in the machine obtained. The derived variables are redefined as direct and quadrature components. In addition, the apparent (complex) power for both the rotor and the stator are derived in terms of these redefined components.
A mathematical model for the doubly-fed wound rotor generator. II
NASA Technical Reports Server (NTRS)
Brady, F. J.
1986-01-01
A mathematical analysis of a doubly-fed wound rotor generator is presented. The constraints of constant stator voltage and frequency to the circuit equations were applied and expressions for the currents and voltages in the machine obtained. The derived variables are redefined as direct and quadrature components. In addition, the apparent (complex) power for both the rotor and the stator are derived in terms of these redefined components.
Determination of linear displacement by envelope detection with maximum likelihood estimation
Lang, Kuo-Chen; Teng, Hui-Kang
2010-09-20
We demonstrate in this report an envelope detection technique with maximum likelihood estimation in a least square sense for determining displacement. This technique is achieved by sampling the amplitudes of quadrature signals resulted from a heterodyne interferometer so that the resolution of displacement measurement of the order of {lambda}/10{sup 4} is experimentally verified. A phase unwrapping procedure is also described and experimentally demonstrated and indicates that the unambiguity range of displacement can be measured beyond a single wavelength.
Electronic systems for transverse coupled-bunch feedback in the Advanced Light Source (ALS)
Barry, W.; Lambertson, G.R.; Lo, C.C.
1993-10-01
In order to effectively control a large number of transverse coupled-bunch modes in the LBL Advanced Light Source (ALS) storage ring, a broad-band, bunch-by-bunch feedback system has been designed, and is beginning to undergo testing and commissioning. This paper addresses, in some detail, the major electronic components of the feedback system. In particular, the components described include: broad-band microwave position detection receivers, closed orbit offset signal rejection circuitry, and baseband quadrature processing circuitry.
High resolution heterodyne interferometer based on time-to-digital converter
NASA Astrophysics Data System (ADS)
Wang, Fei; Long, Zhangcai; Zhang, Bin; Zhao, Meirong
2012-04-01
A new heterodyne interferometer is presented, which adopts time-to-digital converter (TDC) measuring the time intervals of zero crossings of heterodyne signal for phase demodulation. Thanks to the 0.1 ns time resolution of TDC and linear phase demodulation, it can achieve high resolution and avoids nonlinear measuring distortion in other indirect high precise phase demodulation methods, such as pulse width modulation (PWM) and in-phase/quadrature (I/Q) method.
Szidarovszky, Tamás; Császár, Attila G; Czakó, Gábor
2010-08-01
Several techniques of varying efficiency are investigated, which treat all singularities present in the triatomic vibrational kinetic energy operator given in orthogonal internal coordinates of the two distances-one angle type. The strategies are based on the use of a direct-product basis built from one-dimensional discrete variable representation (DVR) bases corresponding to the two distances and orthogonal Legendre polynomials, or the corresponding Legendre-DVR basis, corresponding to the angle. The use of Legendre functions ensures the efficient treatment of the angular singularity. Matrix elements of the singular radial operators are calculated employing DVRs using the quadrature approximation as well as special DVRs satisfying the boundary conditions and thus allowing for the use of exact DVR expressions. Potential optimized (PO) radial DVRs, based on one-dimensional Hamiltonians with potentials obtained by fixing or relaxing the two non-active coordinates, are also studied. The numerical calculations employed Hermite-DVR, spherical-oscillator-DVR, and Bessel-DVR bases as the primitive radial functions. A new analytical formula is given for the determination of the matrix elements of the singular radial operator using the Bessel-DVR basis. The usually claimed failure of the quadrature approximation in certain singular integrals is revisited in one and three dimensions. It is shown that as long as no potential optimization is carried out the quadrature approximation works almost as well as the exact DVR expressions. If wave functions with finite amplitude at the boundary are to be computed, the basis sets need to meet the required boundary conditions. The present numerical results also confirm that PO-DVRs should be constructed employing relaxed potentials and PO-DVRs can be useful for optimizing quadrature points for calculations applying large coordinate intervals and describing large-amplitude motions. The utility and efficiency of the different algorithms
Relativistic Three-Nucleon Calculations within the Bethe-Salpeter Approach
NASA Astrophysics Data System (ADS)
Bondarenko, S. G.; Burov, V. V.; Yurev, S. A.
2016-02-01
The relativistic properties of the three-nucleon system are investigated using the Faddeev equations within the Bethe-Salpeter approach. The nucleon-nucleon interaction is chosen in a separable form. The Gauss quadrature method is used to calculate the integrals. The system of the integral equations is solved by an iterative method. The binding energy and the partial-wave amplitudes (1S0 and 3S1) of the triton are found.
Amplitude and phase modulation of radiation in a travelling-wave amplifier based on a laser diode
Bogatov, A P; D'yachkov, N V; Drakin, A E; Gushchik, T I
2013-08-31
An analytical solution (in quadratures) to the problem of propagation of quasi-monochromatic optical signal in a semiconductor amplifier under harmonic modulation of its pump current is obtained for the first time. It is shown that the modulation of the output radiation has amplitude and phase features. The relation is found between the coefficients of the amplitude and phase modulation with the effect of gain saturation taken into account. Adequacy of the results obtained is confirmed experimentally. (control of laser radiation parameters)
Programmable rate modem utilizing digital signal processing techniques
NASA Technical Reports Server (NTRS)
Naveh, Arad
1992-01-01
The need for a Programmable Rate Digital Satellite Modem capable of supporting both burst and continuous transmission modes with either Binary Phase Shift Keying (BPSK) or Quadrature Phase Shift Keying (QPSK) modulation is discussed. The preferred implementation technique is an all digital one which utilizes as much digital signal processing (DSP) as possible. The design trade-offs in each portion of the modulator and demodulator subsystem are outlined.
Crowther, Michael J; Andersson, Therese M-L; Lambert, Paul C; Abrams, Keith R; Humphreys, Keith
2016-03-30
A now common goal in medical research is to investigate the inter-relationships between a repeatedly measured biomarker, measured with error, and the time to an event of interest. This form of question can be tackled with a joint longitudinal-survival model, with the most common approach combining a longitudinal mixed effects model with a proportional hazards survival model, where the models are linked through shared random effects. In this article, we look at incorporating delayed entry (left truncation), which has received relatively little attention. The extension to delayed entry requires a second set of numerical integration, beyond that required in a standard joint model. We therefore implement two sets of fully adaptive Gauss-Hermite quadrature with nested Gauss-Kronrod quadrature (to allow time-dependent association structures), conducted simultaneously, to evaluate the likelihood. We evaluate fully adaptive quadrature compared with previously proposed non-adaptive quadrature through a simulation study, showing substantial improvements, both in terms of minimising bias and reducing computation time. We further investigate, through simulation, the consequences of misspecifying the longitudinal trajectory and its impact on estimates of association. Our scenarios showed the current value association structure to be very robust, compared with the rate of change that we found to be highly sensitive showing that assuming a simpler trend when the truth is more complex can lead to substantial bias. With emphasis on flexible parametric approaches, we generalise previous models by proposing the use of polynomials or splines to capture the longitudinal trend and restricted cubic splines to model the baseline log hazard function. The methods are illustrated on a dataset of breast cancer patients, modelling mammographic density jointly with survival, where we show how to incorporate density measurements prior to the at-risk period, to make use of all the available
Sampling Downconverter For Radio-Frequency Signals
NASA Technical Reports Server (NTRS)
Thomas, J. B.; Rayhrer, B.; Young, L. E.
1990-01-01
Phase and delay errors reduced greatly. Proposed GaAs integrated-circuit for receiver of radio signals at gigahertz frequencies samples incoming signal in phase and in quadrature, digitizes it, and down-converts it to baseband in single step. Incorporates both digital and analog components in design offering improved stability, versatility, and sampling bandwidth. Eliminates need for several components found in conventional analog designs, including mixers, postmixer filters, and 90 degree phase shifter.
The origin of non-classical effects in a one-dimensional superposition of coherent states
NASA Technical Reports Server (NTRS)
Buzek, V.; Knight, P. L.; Barranco, A. Vidiella
1992-01-01
We investigate the nature of the quantum fluctuations in a light field created by the superposition of coherent fields. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the 1-D superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states.
NASA Astrophysics Data System (ADS)
Kerimov, M. K.; Selimkhanov, E. V.
2016-05-01
The work is devoted to exact estimates of the convergence rate of Fourier series in the trigonometric system in the space of square summable 2π-periodic functions with the Euclidean norm on certain classes of functions characterized by the generalized modulus of continuity. Some N-widths of these classes are calculated, and the residual term of one quadrature formula over equally spaced nodes for a definite integral connected with the issues under consideration is found.
Equivalent Circuit Modeling of Hysteresis Motors
Nitao, J J; Scharlemann, E T; Kirkendall, B A
2009-08-31
We performed a literature review and found that many equivalent circuit models of hysteresis motors in use today are incorrect. The model by Miyairi and Kataoka (1965) is the correct one. We extended the model by transforming it to quadrature coordinates, amenable to circuit or digital simulation. 'Hunting' is an oscillatory phenomenon often observed in hysteresis motors. While several works have attempted to model the phenomenon with some partial success, we present a new complete model that predicts hunting from first principles.
NASA Technical Reports Server (NTRS)
Schwenke, David W.; Mladenovic, Mirjana; Zhao, Meishan; Truhlar, Donald G.; Sun, Yan
1988-01-01
The computational steps in calculating quantum mechanical reactive scattering amplitudes by the L2 generalized Newton variational principle are discussed with emphasis on computational strategies and recent improvements that make the calculations more efficient. Special emphasis is placed on quadrature techniques, storage management strategies, use of symmetry, and boundary conditions. It is concluded that an efficient implementation of these procedures provides a powerful algorithm for the accurate solution of the Schroedinger equation for rearrangements.
Hesketh, Graham D; Petropoulos, Periklis
2016-09-01
Using analytic and numerical modelling of fibre transmission systems that employ optical phase conjugation (OPC), we show inter-channel cross-phase modulation depends on the integrated square error between nonlinear profiles before and after OPC and that arranging amplifiers and tuning power levels is crucial to minimizing noise. We derive modulation transparent formulas for phase noise and optimal power settings. Examples are shown for 16 and 64 quadrature amplitude modulation. PMID:27607633