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Description: An equilibrium theory of the length of intense electron bunches circulating in a storage ring is presented. The consequence of electrical interaction with various resonant structures is expressed in terms of quadratures over the impedance of the structures, and impedance functions for a variety of elements are evaluated. It is shown that elements having resonances at high frequency can, above transition, cause bunches to increase in length with increasing current. The parametric dependence of the bunch lengthening is found to be in good agreement with observations, and numerical estimates, which are in substantial agreement with experiment, are presented.
Date: August 7, 1970
Creator: Pellegrini, C. & Sessler, A.M.
Partner: UNT Libraries Government Documents Department

Fourth-Order Method for Numerical Integration of Age- and Size-Structured Population Models

Description: In many applications of age- and size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth-order method based on composite Newton-Cotes quadratures for a size-structured population model.
Date: January 8, 2008
Creator: Iannelli, M; Kostova, T & Milner, F A
Partner: UNT Libraries Government Documents Department

The Analysis of Thin Wires Using Higher-Order Elements and Basis Functions

Description: Thin wire analysis was applied to curved wire segments in [1], but a special procedure was needed to evaluate the self and near-self terms. The procedure involved associating the singular behavior with a straight segment tangent to the curved source segment, permitting use of algorithms for straight wires. Recently, a procedure that avoids the singularity extraction for straight wires was presented in [2-4]. In this paper, the approach in [4] is applied to curved (or higher-order) wires using a procedure similar to that used in [1] for singularity extraction. Here, the straight tangent segment is used to determine the quadrature rules to be used on the curved segment. The result is a formulation that allows for a general mixture of higher-order basis functions [5] and higher-order wire segments.
Date: January 23, 2006
Creator: Champagne, N. J.; Wilton, D. R. & Rockway, J. W.
Partner: UNT Libraries Government Documents Department

Spatially-discretized high-temperature approximations and theirO(N) implementation on a grid

Description: We consider the problem of performing imaginary-time propagation of wavefunctions on a grid. We demonstrate that spatially-continuous high-temperature approximations can be discretized in such a way that their convergence order is preserved. Requirements of minimal computational work and reutilization of data then uniquely determine the optimal grid, quadrature technique, and propagation method. It is shown that the optimal propagation technique is O(N) with respect to the grid size. The grid technique is utilized to compare the Monte Carlo efficiency of the Trotter-Suzuki approximation against a recently introduced fourth-order high-temperature approximation, while circumventing the issue of statistical noise, which usually prevents such comparisons from being carried out. We document the appearance of a systematic bias in the Monte Carlo estimators that involve temperature differentiation of the density matrix, bias that is due to the dependence of the eigenvalues on the inverse temperature. This bias is negotiated more successfully by the short-time approximations having higher convergence order, leading to non-trivial computational savings.
Date: October 1, 2006
Creator: Predescu, Cristian
Partner: UNT Libraries Government Documents Department

Wave-Based Inversion & Imaging for the Optical Quadrature Microscope

Description: 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.
Date: October 27, 2005
Creator: Lehman, S K
Partner: UNT Libraries Government Documents Department


Description: We added data transmission to the through-the-earth communications system using quadrature synchronous detection. The results are adequate for computer-to-computer communication as well as for sensor data transmission. We added a feature to the in-mine communications system that allows a person to call an individual, rather than broadcasting, by dialing an identification number before speaking.
Date: January 1, 2003
Creator: Meiksin, Zvi H.
Partner: UNT Libraries Government Documents Department

A sampling-based Bayesian model for gas saturation estimationusing seismic AVA and marine CSEM data

Description: We develop a sampling-based Bayesian model to jointly invertseismic amplitude versus angles (AVA) and marine controlled-sourceelectromagnetic (CSEM) data for layered reservoir models. The porosityand fluid saturation in each layer of the reservoir, the seismic P- andS-wave velocity and density in the layers below and above the reservoir,and the electrical conductivity of the overburden are considered asrandom variables. Pre-stack seismic AVA data in a selected time windowand real and quadrature components of the recorded electrical field areconsidered as data. We use Markov chain Monte Carlo (MCMC) samplingmethods to obtain a large number of samples from the joint posteriordistribution function. Using those samples, we obtain not only estimatesof each unknown variable, but also its uncertainty information. Thedeveloped method is applied to both synthetic and field data to explorethe combined use of seismic AVA and EM data for gas saturationestimation. Results show that the developed method is effective for jointinversion, and the incorporation of CSEM data reduces uncertainty influid saturation estimation, when compared to results from inversion ofAVA data only.
Date: April 4, 2006
Creator: Chen, Jinsong; Hoversten, Michael; Vasco, Don; Rubin, Yoram & Hou,Zhangshuan
Partner: UNT Libraries Government Documents Department

Box Integrals

Description: By a "box integral" we mean here an expectation $\langle|\vec r - \vec q|^s \rangle$ where $\vec r$runs over the unit $n$-cube,with $\vec q$ and $s$ fixed, explicitly:\begin eqnarray*&&\int_01 \cdots \int_01 \left((r_1 - q_1)2 + \dots+(r_n-q_n)2\right)^ s/2 \ dr_1 \cdots dr_n.\end eqnarray* The study ofbox integrals leads one naturally into several disparate fields ofanalysis. While previous studies have focused upon symbolic evaluationand asymptotic analysis of special cases (notably $s = 1$), we workherein more generally--in interdisciplinary fashion--developing resultssuch as: (1) analytic continuation (in complex $s$), (2) relevantcombinatorial identities, (3) rapidly converging series, (4) statisticalinferences, (5) connections to mathematical physics, and (6)extreme-precision quadrature techniques appropriate for these integrals.These intuitions and results open up avenues of experimental mathematics,with a view to new conjectures and theorems on integrals of thistype.
Date: June 1, 2006
Creator: Bailey, David H.; Borwein, Jonathan M. & Crandall, Richard E.
Partner: UNT Libraries Government Documents Department

Nonlinear integrable ion traps

Description: Quadrupole ion traps can be transformed into nonlinear traps with integrable motion by adding special electrostatic potentials. This can be done with both stationary potentials (electrostatic plus a uniform magnetic field) and with time-dependent electric potentials. These potentials are chosen such that the single particle Hamilton-Jacobi equations of motion are separable in some coordinate systems. The electrostatic potentials have several free adjustable parameters allowing for a quadrupole trap to be transformed into, for example, a double-well or a toroidal-well system. The particle motion remains regular, non-chaotic, integrable in quadratures, and stable for a wide range of parameters. We present two examples of how to realize such a system in case of a time-independent (the Penning trap) as well as a time-dependent (the Paul trap) configuration.
Date: October 1, 2011
Creator: Nagaitsev, S.; /Fermilab; Danilov, V. & /SNS Project, Oak Ridge
Partner: UNT Libraries Government Documents Department


Description: During the past ten years, the means of ventilating single-family residences has received considerable attention. In many areas, the use of natural ventilation for infiltration has either come under close scrutiny, or has already been supplanted by mechanical ventilation systems. To evaluate the energy efficiency and ventilation effectiveness of both mechanical and natural ventilation strategies, both complex and simplified infiltration models are used. This paper examines the inaccuracies associated with using simplified models to compare ventilation strategies. Two simplified techniques for combining mechanical ventilation flows to the flows caused by wind and stack effects are examined. The simplified combination techniques are compared with the results obtained with an iterative flow-balance simulation. The flow-balance simulation determines the ventilation by balancing the incoming and outgoing flows under the pressure conditions resulting from the combination of wind effect, stack effect and mechanical ventilation. These comparisons result in three major conclusions: (1) the commonly used flow superposition technique (flow combination in quadrature) provides better estimates of the total flow than does a technique that takes into account measured flow exponents, (2) although flow combination in quadrature overpredicts ventilation when combining wind-induced and stack-induced flows, this is not the case when mechanical ventilation is added to the picture, and (3) a simple correction for the errors caused by the simplified flow superposition technique is not easy to achieve due to the large variations in error that occur with changes in wind direction and individual flow ratios.
Date: January 1, 1985
Creator: Modera, M. & Peterson, F.
Partner: UNT Libraries Government Documents Department

A hybrid FEM-BEM unified boundary condition with sub-cycling for electromagnetic radiation

Description: Hybrid solutions to time-domain electromagnetic problems offer many advantages when solving open-region scattering or radiation problems. Hybrid formulations use a finite-element or finite-difference discretization for the features of interest, then bound this region with a layer of planar boundary elements. The use of volume discretization allows for intricate features and many changes in material within the structure, while the boundary-elements provide a highly accurate radiating boundary condition. This concept has been implemented previously, using the boundary elements to set the E-field, H-field, or both for an FDTD grid, for example in [1][2][3], or as a mixed boundary condition for the second order wave equation solved by finite elements [4]. Further study has focused on using fast methods, such as the Plane Wave Time Domain method [3][4] to accelerate the BEM calculations. This paper details a hybrid solver using the coupled first-order equations for the E and H fields in the finite-element region. This formulation is explicit, with a restriction on the time step for stability. When this time step is used in conjunction with the boundary elements forming either a inhomogeneous Dirichlet or Neuman boundary condition on the finite-element mesh, late time instabilities occur. To combat this, a Unified Boundary Condition (UBC), similar to the one in [4] for the second-order wave equation, is used. Even when this UBC is used, the late time instabilities are merely delayed if standard testing in time is used. However, the late time instabilities can be removed by replacing centroid based time interpolation with quadrature point based time interpolation for the boundary elements, or by sub-cycling the boundary element portion of the formulation. This sub-cycling, used in [3] for FDTD to reduce complexity, is shown here to improve stability and overall accuracy of the technique.
Date: January 12, 2006
Creator: Fasenfest, B; White, D; Stowell, M; Rieben, R; Sharpe, R; Madsen, N et al.
Partner: UNT Libraries Government Documents Department

Angular quadratures for improved transport computations

Description: This paper introduces new octant-range, composite-type Gauss and mid-point rule angular quadrature formulas for neutron and photon transport computations. A generalization to octant-range quadratures is also introduced in order to allow for discontinuities at material interfaces for two- and three-dimensional transport problems which can be modeled with 60-degree triangular or hexagonal mesh subdivisions in the x-y plane.
Date: July 22, 1999
Creator: Abu-Shumays, I.K.
Partner: UNT Libraries Government Documents Department

Exponential Monte Carlo Convergence on a Homogeneous Right Parallelepiped Using the Reduced Source Method with Legendre Expansion

Description: In previous work, exponential convergence of Monte Carlo solutions using the reduced source method with Legendre expansion has been achieved only in one-dimensional rod and slab geometries. In this paper, the method is applied to three-dimensional (right parallelepiped) problems, with resulting evidence suggesting success. As implemented in this paper, the method approximates an angular integral of the flux with a discrete-ordinates numerical quadrature. It is possible that this approximation introduces an inconsistency that must be addressed.
Date: September 1, 1999
Creator: Favorite, J.A.
Partner: UNT Libraries Government Documents Department

Quadrature Mixer LO Leakage Suppression Through Quadrature DC Bias

Description: 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.
Date: May 1, 2002
Partner: UNT Libraries Government Documents Department

Sets of Fourier coefficients using numerical quadrature

Description: One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r) = {line_integral}{sub 0}{sup 1} f(x)e{sup -2{pi}irx}dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x) = h{sub p-1}(x) + g{sub p}(x), where h{sub -1}(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g{sub p}(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h{sub p-1}(x) and numerical quadrature to approximately those of g{sub p}(x).
Date: October 10, 2001
Creator: Lyness, J. N.
Partner: UNT Libraries Government Documents Department

RF System Modeling for the CEBAF Energy Upgrade

Description: An RF system model, based on MATLAB/SIMULINK, has been developed for analyzing the basic characteristics of the low level RF (LLRF) control system being designed for the CEBAF 12 GeV Energy Upgrade. In our model, a typical passband cavity representation is simplified to in-phase and quadrature (I&Q) components. Lorentz Force and microphonic detuning are incorporated as a new quadrature carrier frequency (frequency modulation). Beam is also represented as in-phase and quadrature components and superpositioned with the cavity field vector. Signals pass through two low pass filters, where the cutoff frequency is equal to half of the cavity bandwidth, then they are demodulated using the same detuning frequency. Because only baseband I&Q signals are calculated, the simulation process is very fast when compared to other controller-cavity models. During the design process we successfully analyzed gain requirements vs. field stability for different superconducting cavity microphonic backgrounds and Lorentz Force coefficients. Moreover, we were able to evaluate different types of a LLRF system’s control algorithm: GDR (Generator Driven Resonator) and SEL (Self Excited Loop) [1] as well as klystron power requirements for different cavities and beam loads.
Date: May 1, 2009
Creator: Tomasz Plawski, J. Hovater
Partner: UNT Libraries Government Documents Department

Meshless Solution of the Vlasov Equation Using a Low Discrepancy Sequence

Description: A good method for solving the nonlinear Vlasov equation is the semi-Lagrangian algorithm, in which the phase space density is represented by its values on a fixed Cartesian grid with interpolation to off-grid points. At each time step, orbits are followed backward from grid points. Since this method is expensive with phase space dimension D > 2, we seek a more efficient discretization of the density. Taking a cue from the theory of numerical quadrature in high dimensions, we explore the idea of replacing the grid by scattered data sites from a low-discrepancy (quasirandom) sequence. We hope to see a reduction in the required number of sites, especially for D > 2. In our first implementation we follow forward orbits rather than backward, and work only with D = 2. We are able to reduce the number of sites by a factor of 8, at least for a limited time of integration. A much bigger reduction is expected in higher dimensions.
Date: January 28, 2009
Creator: Warnock, R.L.; /SLAC; Ellison, J.A.; Heinemann, K.; Zhang, G.Q. & U., /New Mexico
Partner: UNT Libraries Government Documents Department

Stochastic methods for uncertainty quantification in radiation transport

Description: The use of generalized polynomial chaos (gPC) expansions is investigated for uncertainty quantification in radiation transport. The gPC represents second-order random processes in terms of an expansion of orthogonal polynomials of random variables and is used to represent the uncertain input(s) and unknown(s). We assume a single uncertain input-the total macroscopic cross section-although this does not represent a limitation of the approaches considered here. Two solution methods are examined: The Stochastic Finite Element Method (SFEM) and the Stochastic Collocation Method (SCM). The SFEM entails taking Galerkin projections onto the orthogonal basis, which, for fixed source problems, yields a linear system of fully -coupled equations for the PC coefficients of the unknown. For k-eigenvalue calculations, the SFEM system is non-linear and a Newton-Krylov method is employed to solve it. The SCM utilizes a suitable quadrature rule to compute the moments or PC coefficients of the unknown(s), thus the SCM solution involves a series of independent deterministic transport solutions. The accuracy and efficiency of the two methods are compared and contrasted. The PC coefficients are used to compute the moments and probability density functions of the unknown(s), which are shown to be accurate by comparing with Monte Carlo results. Our work demonstrates that stochastic spectral expansions are a viable alternative to sampling-based uncertainty quantification techniques since both provide a complete characterization of the distribution of the flux and the k-eigenvalue. Furthermore, it is demonstrated that, unlike perturbation methods, SFEM and SCM can handle large parameter uncertainty.
Date: January 1, 2009
Creator: Fichtl, Erin D; Prinja, Anil K & Warsa, James S
Partner: UNT Libraries Government Documents Department

The First Estimate of BR(\bar B to X_s\gamma) at O(\alpha_s^2)

Description: Combining our results for various {Omicron}({alpha}{sub s}{sup 2}) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find {Beta}({bar B} {yields} X{sub s}{gamma}) = (3.15 {+-} 0.23) x 10{sup -4} for E{sub {gamma}} > 1.6 GeV in the {bar B}-meson rest frame. The four types of uncertainties: non-perturbative (5%), parametric (3%), higher-order (3%) and m{sub c}-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.
Date: October 24, 2006
Creator: Misiak, M.; Asatrian, H. M.; Bieri, K.; Czakon, M.; Czarnecki, A.; Ewerth, T. et al.
Partner: UNT Libraries Government Documents Department

Review of The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing

Description: In the January 2002 edition of SIAM News, Nick Trefethen announced the '$100, 100-Digit Challenge'. In this note he presented ten easy-to-state but hard-to-solve problems of numerical analysis, and challenged readers to find each answer to ten-digit accuracy. Trefethen closed with the enticing comment: 'Hint: They're hard! If anyone gets 50 digits in total, I will be impressed.' This challenge obviously struck a chord in hundreds of numerical mathematicians worldwide, as 94 teams from 25 nations later submitted entries. Many of these submissions exceeded the target of 50 correct digits; in fact, 20 teams achieved a perfect score of 100 correct digits. Trefethen had offered $100 for the best submission. Given the overwhelming response, a generous donor (William Browning, founder of Applied Mathematics, Inc.) provided additional funds to provide a $100 award to each of the 20 winning teams. Soon after the results were out, four participants, each from a winning team, got together and agreed to write a book about the problems and their solutions. The team is truly international: Bornemann is from Germany, Laurie is from South Africa, Wagon is from the USA, and Waldvogel is from Switzerland. This book provides some mathematical background for each problem, and then shows in detail how each of them can be solved. In fact, multiple solution techniques are mentioned in each case. The book describes how to extend these solutions to much larger problems and much higher numeric precision (hundreds or thousands of digit accuracy). The authors also show how to compute error bounds for the results, so that one can say with confidence that one's results are accurate to the level stated. Numerous numerical software tools are demonstrated in the process, including the commercial products Mathematica, Maple and Matlab. Computer programs that perform many of the algorithms mentioned in the ...
Date: January 25, 2005
Creator: Bailey, David
Partner: UNT Libraries Government Documents Department

Coarse-mesh rebalance methods compatible with the spherical harmonic fictitious source in neutron transport calculations

Description: The coarse-mesh rebalance method, based on neutron conservation, is used in discrete ordinates neutron transport codes to accelerate convergence of the within-group scattering source. Though very powerful for this application, the method is ineffective in accelerating the iteration on the discrete-ordinates-to- spherical-harmonics fictitious sources used for ray-effect elimination. This is largely because this source makes a minimum contribution to the neutron balance equation. The traditional rebalance approach is derived in a variational framework and compared with new rebalance approaches tailored to be compatible with the fictitious source. The new approaches are compared numerically to determine their relative advantages. It is concluded that there is little incentive to use the new methods. (3 tables, 5 figures) (auth)
Date: October 1, 1975
Creator: Miller, W.F. Jr.
Partner: UNT Libraries Government Documents Department

On the implementation of a modified Sag-Szekeres quadrature method

Description: The authors describe a modified Sag-Szekeres multidimensional quadrature algorithm and discuss its implementation as a general-purpose library procedure on serial and parallel architectures. Examples illustrate its effectiveness for both smooth and singular integrands. The procedure has been implemented as a parallel library routine, running on transputer-based systems, as part of Esprit project P2528: Supernode II; (see Plowman (1992)). This routine is scheduled to appear in the quadrature section of the Liverpool-NAG Transputer Software Library. The authors give here some results obtained using this routine, to demonstrate the rapid convergence obtained with both smooth and singular integrands, and to demonstrate the routine`s effectiveness on a parallel NIMD architecture.
Date: July 1997
Creator: Lyness, J. N. & Delves, L. M.
Partner: UNT Libraries Government Documents Department