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Lg excitation, attenuation, and source spectral scaling in central and eastern North America

Description: Seismic moments and corner frequencies were obtained for many earthquakes in the central and eastern United States, and for a few events in the western United States, using the Lg phase and a recently developed inversion algorithm. Additionally, Q values for the Lg phase along paths to individual stations were obtained simultaneously with the source parameters. Both corner frequencies and magnitudes were found to vary systematically with moment. For moments between 0.15 and 400 x 10{sup 15} N-m corner frequencies vary between about 4 and 0.2 Hz while body-wave magnitude varies between about 3.5 and 5.8. A map of Lg Q values displays a systematic decrease from east and west. Maximum and minimum values are 989 and 160, respectively. Lg coda Q values were obtained for the entire United States with excellent coverage in the eastern and western portions of the country and somewhat poorer coverage in the central portion. Lg coda Q is highest (700-750) in a region of the northeastern United States that includes portions of New York and Pennsylvania and lowest (>200) in California. Lg coda Q is lower (250-450) everywhere west of Rocky Mountains than in the rest of the country (450-750). Q determinations for both the direct Lg phase and Lg coda indicate that, for an earthquake of a given magnitude, Lg and its coda will propagate much more efficiently, and cause damage over a wider area, in the eastern and central United States than it will in the United States.
Date: October 1, 1997
Creator: Mitchell, B.J.; Xie, J. & Baqer, S.
Partner: UNT Libraries Government Documents Department

Moment-Based Probability Modeling and Extreme Response Estimation, The FITS Routine Version 1.2

Description: This report documents the use of the FITS routine, which provides automated fits of various analytical, commonly used probability models from input data. It is intended to complement the previously distributed FITTING routine documented in RMS Report 14 (Winterstein et al., 1994), which implements relatively complex four-moment distribution models whose parameters are fit with numerical optimization routines. Although these four-moment fits can be quite useful and faithful to the observed data, their complexity can make them difficult to automate within standard fitting algorithms. In contrast, FITS provides more robust (lower moment) fits of simpler, more conventional distribution forms. For each database of interest, the routine estimates the distribution of annual maximum response based on the data values and the duration, T, over which they were recorded. To focus on the upper tails of interest, the user can also supply an arbitrary lower-bound threshold, {chi}{sub low}, above which a shifted distribution model--exponential or Weibull--is fit.
Date: November 1, 1999
Partner: UNT Libraries Government Documents Department

Moment approach to high-order accelerator beam optics

Description: High-current beams must be matched to high order to minimize emittance growth and particle losses. For matching problems, the moment approach, in which the author describes the particle beam by the moments of its distributions, is particularly valuable. A variety of analytical results are available for linear motion. The moment approach is also the basis of the 3-D space-charge simulation code BEDLAM, in which the dynamical variables are the moments. Moment simulation codes are particularly useful for computing beams matched to nonlinear systems. This paper outlines what is known about the moment approach, describes work in progress on new space-charge models, and describes further potential applications of and improvements to moment-method simulations.
Date: October 1, 1994
Creator: Lysenko, W. P.
Partner: UNT Libraries Government Documents Department

Evaluation of the discrete complex-image method for a NEC-like moment-method solution

Description: The discrete image approximation for the field of a half-space is tested in the NEC antenna modeling program as an alternative to the interpolation method presently used. The accuracy and speed of the discrete image approximation are examined for varying number of images and approximation contour, and the solution for current is obtained on a horizontal wire approaching the interface.
Date: January 5, 1996
Creator: Burke, G.J.
Partner: UNT Libraries Government Documents Department

Ionization cooling and muon dynamics

Description: Muon colliders potential to provide a probe for fundamental particle physics is very interesting. To obtain the needed collider luminosity, the phase space volume must be greatly reduced within the muon life time. The Ionization cooling is the preferred method used to compress the phase space and reduce the emittance to obtain high luminosity muon beams. The authors note that, the ionization losses results not only in damping, but also heating. They discuss methods used including moments methods, Focker Plank Equation, and Multi Particle Codes. In addition they show how a simple analysis permits us to estimate the most part of the optimal system parameters, such as optimal damping rates, length of the system and energy.
Date: January 1, 1998
Creator: Parsa, Z.
Partner: UNT Libraries Government Documents Department

Energy dependent bias in plutonium verification measurements using thermal neutron multiplicity counters

Description: Multiplicity analysis algorithms are extended to include the effect of ({alpha}, n) neutron energies on the detector efficiencies, induced fission probabilities, and induced fission factorial moments. The analysis is restricted to plutonium oxide. Bias is calculated as a function of ({alpha}, n) neutron energy for six thermal neutron coincidence counters: HLNC, AWCC, 3RMC, PSMC, PYRO, and 5RMC. Ring ratio data for the 3RMC are used to reduce energy dependent bias in the verification of impure plutonium oxide. The utility of the AWCC as a multiplicity counter is considered.
Date: October 1, 1997
Creator: Krick, M.S.; Langner, D.G. & Stewart, J.E.
Partner: UNT Libraries Government Documents Department

Flux limiting nature`s own way -- A new method for numerical solution of the transport equation

Description: The transport equation may be solved by expanding it in spherical harmonics, Y{sub lm}, and truncating the resultant infinite set of equations at some finite order L. This procedure leaves the (L + 1)th order moments which appear in the Lth order equation undetermined, and the standard procedure for obtaining a closed set of equations has been to set all the (L + 1)th order moments to zero. It has been shown here that this procedure actually violates the apriori knowledge that one is solving for the moments of a probability measure on the unit sphere. Using the theory of moments of a probability measure on the unit sphere. Using the theory of moments as discussed above, the (L + 1)th order moments can be chosen in accordance with apriori knowledge. The resultant truncated set of equations has properties much truer to the original transport equation than the usual set obtained by setting the (L + 1)th order moments to zero. In particular the truncated set of equations gets the solution of the transport equation exactly right in both the diffusion limit and the free streaming limit. Furthermore, this has been achieved by merely truncating the set of equations properly and not by any ad hoc changes in the basic equations as is the case in the approaches that use flux limiters.
Date: July 29, 1976
Creator: Kershaw, D.S.
Partner: UNT Libraries Government Documents Department

Nuclear Level Densities for Modeling Nuclear Reactions: An Efficient Approach Using Statistical Spectroscopy

Description: The general goal of the project is to develop and implement computer codes and input files to compute nuclear densities of state. Such densities are important input into calculations of statistical neutron capture, and are difficult to access experimentally. In particular, we will focus on calculating densities for nuclides in the mass range A {approx} 50-100. We use statistical spectroscopy, a moments method based upon a microscopic framework, the interacting shell model. Second year goals and milestones: Develop two or three competing interactions (based upon surface-delta, Gogny, and NN-scattering) suitable for application to nuclei up to A = 100. Begin calculations for nuclides with A = 50-70.
Date: August 10, 2005
Creator: Johnson, Calvin W.
Partner: UNT Libraries Government Documents Department

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

Description: The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.
Date: June 1, 2002
Partner: UNT Libraries Government Documents Department

Fitting: Subroutine to fit four-moment probability distributions to data

Description: FITTING is a Fortran subroutine that constructs a smooth, generalized four-parameter probability distribution model. It is fit to the first four statistical moments of the random variable X (i.e., average values of X, X{sup 2}, X{sup 3}, and X{sup 4}) which can be calculated from data using the associated subroutine CALMOM. The generalized model is produced from a cubic distortion of the parent model, calibrated to match the first four moments of the data. This four-moment matching is intended to provide models that are more faithful to the data in the upper tail of the distribution. Examples are shown for two specific cases.
Date: January 1, 1995
Creator: Winterstein, S. R.; Lange, C. H. & Kumar, S.
Partner: UNT Libraries Government Documents Department

Inverse scattering code

Description: A methodology for the evaluation of complex electromagnetics problems is presented. The methodology reduces the computational requirements for the analysis of large scale computational electromagnetics problems by hybridizing the method of moments and physical optics techniques. The target model is based on triangular facets and the incident field source by its system response function. Data which can be obtained from the analysis are radar cross section, power spectral density, and range profiles.
Date: September 1, 1997
Creator: Hale, A. & King, A.
Partner: UNT Libraries Government Documents Department

Moment series for moment estimators of the parameters of a Weibull density

Description: Taylor series for the first four moments of the coefficients of variation in sampling from a 2-parameter Weibull density are given: they are taken as far as the coefficient of n/sup -24/. From these a four moment approximating distribution is set up using summatory techniques on the series. The shape parameter is treated in a similar way, but here the moment equations are no longer explicit estimators, and terms only as far as those in n/sup -12/ are given. The validity of assessed moments and percentiles of the approximating distributions is studied. Consideration is also given to properties of the moment estimator for 1/c.
Date: January 1, 1982
Creator: Bowman, K.O. & Shenton, L.R.
Partner: UNT Libraries Government Documents Department

Moments in particle-in-cell simulations

Description: The moment equations that form the basis of the BEDLAM simulation code can also be used as a check on Particle-In-Cell (PIC) simulations. Moments can be computed as sums over the macroparticles used in the PIC simulations. These moments should satisfy the moment equations if the simulation is valid. A check has been done to sixth order for two cases: the RFQRZP code, which simulated a radio-frequency quadrupole (RFQ) linac, and the BEAMTRACE code, which simulated the final focusing system in a heavy ion fusion facility. Because our modified PIC codes were able to compute moments that satisfied the correct moment equations, we were able to use our modified version of RFQRZP, which we called RFQMOM, to work on another problem. Every moment simulation code has to include some truncation approximation. The error of this approximation can be determined by RFQMOM before actually writing the moment code. As an example, we investigated the accuracy of the truncation approximation that is used in the BEDLAM code. 6 refs., 4 figs.
Date: January 1, 1985
Creator: Berz, M.M. & Lysenko, W.P.
Partner: UNT Libraries Government Documents Department

Multiple time-scale methods in particle simulations of plasmas

Description: This paper surveys recent advances in the application of multiple time-scale methods to particle simulation of collective phenomena in plasmas. These methods dramatically improve the efficiency of simulating low-frequency kinetic behavior by allowing the use of a large timestep, while retaining accuracy. The numerical schemes surveyed provide selective damping of unwanted high-frequency waves and preserve numerical stability in a variety of physics models: electrostatic, magneto-inductive, Darwin and fully electromagnetic. The paper reviews hybrid simulation models, the implicitmoment-equation method, the direct implicit method, orbit averaging, and subcycling.
Date: February 14, 1985
Creator: Cohen, B.I.
Partner: UNT Libraries Government Documents Department

Moment series for the coefficient of variation in Weibull sampling

Description: For the 2-parameter Weibull distribution function F(t) = 1 - exp(-t/b)/sup c/, t > 0, with c and b positive, a moment estimator c* for c is the solution of the equationGAMMA(1 + 2/c*)/GAMMA/sup 2/ (1 + 1/c*) = 1 + v*/sup 2/ where v* is the coefficient of variation in the form ..sqrt..m/sub 2//m/sub 1/', m/sub 1/' being the sample mean, m/sub 2/ the sample second central moment (it is trivial in the present context to replace m/sub 2/ by the variance). One approach to the moments of c* (Bowman and Shenton, 1981) is to set-up moment series for the scale-free v*. The series are apparently divergent and summation algorithms are essential; we consider methods due to Levin (1973) and one, introduced ourselves (Bowman and Shenton, 1976).
Date: January 1, 1981
Creator: Bowman, K.O. & Shenton, L.R.
Partner: UNT Libraries Government Documents Department

Moment approach to charged particle beam dynamics

Description: We have derived the hierarchy of moment equations that describes the dynamics of charged-particle beams in linear accelerators and can truncate the hierarchy at any level either by discarding higher moments or by a cumulant expansion discarding only correlation functions. We have developed a procedure for relating the density expansion linearly to the moments to any order. The relation of space-charge fields to the density has been derived; and an accurate, systematic, and computationally convenient expansion of the resultant integrals has been developed.
Date: January 1, 1983
Creator: Channell, P.J.
Partner: UNT Libraries Government Documents Department

RCS and antenna modeling with MOM using hybrid meshes

Description: In this presentation, the authors will investigate the use of hybrid meshes for modeling RCS and antenna problems in three dimensions. They will consider two classes of hybrid basis functions. These include combinations of quadrilateral and triangular meshes for arbitrary 3D geometries, and combinations of axisymmetric body-of-revolution (BOR) basis functions and triangular facets. In particular, they will focus on the problem of enforcing current continuity between two surfaces which are represented by different types of surface discretizations and unknown basis function representations. They will illustrate the use of an operator-based code architecture for the implementation of these formulations, and how it facilitates the incorporation of the various types of boundary conditions in the code. Both serial and parallel code implementation issues for the formulations will be discussed. Results will be presented for both scattering and antenna problems. The emphasis will be on accuracy, and robustness of the techniques. Comparisons of accuracy between triangular meshed and quadrilateral meshed geometries will be shown. The use of hybrid meshes for modeling BORs with attached appendages will also be presented.
Date: February 1, 1997
Creator: Putnam, J.M. & Kotulski, J.D.
Partner: UNT Libraries Government Documents Department

Nuclear Level Densities for Modeling Nuclear Reactions: An Efficient Approach Using Statistical Spectroscopy: Annual Report 2003-2004

Description: The general goal of the project is to develop and implement computer codes and input files to compute nuclear densities of state. Such densities are important input into calculations of statistical neutron capture, and are difficult to access experimentally. In particular, we will focus on calculating densities for nuclides in the mass range A ?????? 50 - 100. We use statistical spectroscopy, a moments method based upon a microscopic framework, the interacting shell model. In this report we present our progress for the past year.
Date: July 30, 2004
Creator: Johnson, Calvin W.
Partner: UNT Libraries Government Documents Department

Digital simulation and modeling of nonlinear stochastic systems

Description: Digitally generated solutions of nonlinear stochastic systems are not unique, but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system, but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions resulting from different integration algorithms and comparing the moments to those arising from various stochastic integral definitions. Monte Carlo simulations and statistical tests are applied to illustrate the determining role that computational procedures play in generating solutions. This algorithm dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases, in which unique solutions are determined by any convergent numerical algorithm. Consequences of this relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. 2 figures.
Date: January 1, 1980
Creator: Richardson, J. M. & Rowland, J. R.
Partner: UNT Libraries Government Documents Department

Finite order polynomial moment solutions of the homogeneous Grad-Shafranov equation

Description: A method for generating the finite positive order polynomial moment solutions of the homogeneous Grad-Shafranov equation to arbitrary order and the explicit form of the first few moments are given. A criticism of the method is discussed, and several practical examples are given.
Date: February 1, 1984
Creator: Reusch, M.F. & Neilson, G.H.
Partner: UNT Libraries Government Documents Department

Modeling pollutant dispersion over irregular terrain with second moments and cubic splines

Description: Under ideal conditions, dispersion can be reasonably predicted with analytical methods, such as Gaussian puff/plume theory. However, analytical methods are typically inflexible under variable wind conditions, particularly in cases where dispersion occurs over irregular surfaces. A specific need exists for more detailed study into the effect of surface irregularities on dispersion. The requirement is to establish an accurate and efficient numerical solution algorithm for three-dimensional mesoscale atmospheric transport and diffusion over irregular terrain. Herein, a three-dimensional method-of-moments technique is employed to calculate pollutant advection. The method is based on the calculation of moment distributions of a concentration within a cell (volume). By summing moments over the solution domain, and using a Lagrangian advection scheme, concentration can be transported without generation of numerical dispersion error. Because the method maintains subgrid scale resolution, problems involving steep gradients can be calculated without significant computational damping. Three-dimensional diffusion is solved by the method of cubic splines. The cubic spline method is based on continuous-curvature cubic spline relations used as interpolation functions for first and second derivative terms. After solution of the diffusion terms, the first and second moments are recalculated to ensure continuity with the advection terms. To reduce computer programming complexity, the procedure of fractional steps is used to calculate the three-dimensional solutions. A coordinate transformation is employed to transform the terrain-lid variability into regular intervals in the computational domain. Simple tests are conducted to determine the accuracy of the numerical methods. The effect of topography on a continuous emission is examined under ideal conditions and the results compared with values obtained from an analytical Gaussian plume relation.
Date: January 1, 1978
Creator: Pepper, D.W. & Baker, A.J.
Partner: UNT Libraries Government Documents Department