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Assessing non-uniqueness: An algebraic approach

Description: Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.
Date: September 16, 2002
Creator: Vasco, Don W.
Partner: UNT Libraries Government Documents Department

Linear Gain for the Microbunching Instability in an RF Compressor

Description: Velocity (or rf) compression has been suggested as a technique for bunch compression complementary to the more established technique involving magnetic chicanes and represents an important research item being investigated at the SPARC test facility. One of the aspects of this technique still not sufficiently understood is its possible impact on the microbunching instability. The purpose of this report is to present the analytical framework for investigating this instability in rf compressors. We use methods similar to those successfully applied to magnetic compressors and derive some integral equations yielding the gain for the instability in linear approximation. The focus here is on the derivation of the relevant equations. Although examples of solutions to these equations are provided we defer a more comprehensive discussion of their implication to a future report. The present study is part of a larger effort for a more comprehensive investigation that eventually will include macroparticle simulations and experiments.
Date: May 1, 2009
Creator: Venturini, M.; Migliorati, M.; Ronsivalle, C. & Vaccarezza, C.
Partner: UNT Libraries Government Documents Department

An Existence Theorem for an Integral Equation

Description: The principal theorem of this thesis is a theorem by Peano on the existence of a solution to a certain integral equation. The two primary notions underlying this theorem are uniform convergence and equi-continuity. Theorems related to these two topics are proved in Chapter II. In Chapter III we state and prove a classical existence and uniqueness theorem for an integral equation. In Chapter IV we consider the approximation on certain functions by means of elementary expressions involving "bent line" functions. The last chapter, Chapter V, is the proof of the theorem by Peano mentioned above. Also included in this chapter is an example in which the integral equation has more than one solution. The first chapter sets forth basic definitions and theorems with which the reader should be acquainted.
Date: May 1985
Creator: Hunt, Cynthia Young
Partner: UNT Libraries

Turbulent Boundary Layer on a Yawed Cone in a Supersonic Stream

Description: "The momentum integral equations are derived for the boundary layer on an arbitrary curved surface, using a streamline coordinate system. Computations of the turbulent boundary layer on a slightly yawed cone are made for a Prandtl number 0.70, wall to free-stream temperature ratios of 1/2, 1, and 2, and Mach numbers from 1 to 4. Deflection of the fluid in the boundary layer from outer stream direction, local friction coefficient, displacement surface, lift coefficient, and pitching-moment coefficient are presented" (p. 1).
Date: January 1958
Creator: Braun, Willis H.
Partner: UNT Libraries Government Documents Department

Final Report for Time Domain Boundary Element and Hybrid Finite Element Simulation for Maxwell's Equations

Description: This report summarizes the work performed for Lawrence Livermore National Laboratory (LLNL) at the University of Washington between September 2004 and May 2006. This project studied fast solvers and stability for time domain integral equations (TDIE), especially as applied to radiating boundary for a massively parallel FEM solver.
Date: March 1, 2007
Creator: Pingenot, J & Jandhyala, V
Partner: UNT Libraries Government Documents Department

Efficient imaging of single-hole electromagnetic data

Description: The extended Born, or localized nonlinear (LN) approximation, of integral equation (IE) solution has been applied to inverting single-hole electromagnetic (EM) data using a cylindrically symmetric model. The extended Born approximation is less accurate than a full solution but much superior to the simple Born approximation. When applied to the cylindrically symmetric model with a vertical magnetic dipole source, however, the accuracy of the extended Born approximation is shown to be greatly improved because the electric field is scalar and continuous everywhere. One of the most important steps in the inversion is the selection of a proper regularization parameter for stability. The extended Born solution provides an efficient means for selecting an optimum regularization parameter, because the Green's functions, the most time consuming part in IE methods, are repeatedly re-usable at each iteration. In addition, the IE formulation readily contains a sensitivity matrix, which can be revised at each iteration at little expense. In this paper we show inversion results using synthetic and field data. The result from field data is compared with that of a 3-D inversion scheme.
Date: April 1, 2002
Creator: Lee, Ki Ha; Kim, Hee Joon & Wilt, Mike
Partner: UNT Libraries Government Documents Department

Efficient computation of periodic and nonperiodic Green`s functions in layered media using the MPIE

Description: The mixed potential integral equation (MPIE) formulation is convenient for problems involving layered media because potential quantities involve low order singularities, in comparison to field quantities. For nonperiodic problems, the associated Green`s potentials involve spectral integrals of the Sommerfeld type, in the periodic case, discrete sums over sampled values of the same spectra are required. When source and observation points are in the same or in adjacent layers, the convergence of both representations is enhanced by isolating the direct and quasi-static image contributions associated with the nearby layers. In the periodic case, the convergence of direct and image contributions may be rapidly accelerated by means of the Ewadd method.
Date: March 27, 1998
Creator: Wilton, D.R.; Jackson, D.R. & Champagne, N.J.
Partner: UNT Libraries Government Documents Department

Variational correction to the FERMI beam solution

Description: We consider the time-independent, monoenergetic searchlight problem for a purely scattering, homogeneous slab with a pencil beam of nuclear particles impinging upon one surface. The scattering process is assumed sufficiently peaked in the forward direction so that the Fokker-Planck differential scattering operator can be used. Further, the slab is assumed sufficiently thin so that backscattering is negligibly small. Generally, this problem is approximated by the classic Fermi solution. A number of modifications of Fermi theory, aiming at improved accuracy, have been proposed. Here, we show that the classic Fermi solution (or any approximate solution) can I be improved via a variational formalism.
Date: October 1, 1996
Creator: Su, Bingjing & Pomraning, G.C.
Partner: UNT Libraries Government Documents Department

NLO conformal symmetry in the Regge limit of QCD

Description: The authors show that a scale invariant approximation to the next-to-leading order BFKL kernel, constructed via transverse momentum diagrams, has a simple conformally invariant representation in impact parameter space. That a conformally invariant representation exists is shown first by relating the kernel directly to Feynman diagrams contributing to two photon diffractive dissociation.
Date: September 18, 1996
Creator: Coriano, C.; White, A. R. & Wuesthoff, M.
Partner: UNT Libraries Government Documents Department

Thermodynamic and structural properties of strongly coupled plasma mixtures from the perturbative HNC-equation

Description: Recently, we developed the perturbative hypernetted-chain (PHNC) integral equation which can predict reliable thermodynamic and structural data for a system of particles interacting with either short range or long range (Coulomb) potential. The present work extends this earlier work to mixtures. This is done by employing a reference potential which is designed to satisfy a thermodynamic consistency on the isothermal compressibility as described in the next section. We test the present theory in Sec. III by applying it to plasma mixtures interacing with either an unscreened or a screened Coulomb potential. We made comparisons of results from the present theory with those from the best available theory, i.e., Rosenfeld`s density functional theory (DFT). The DFT was shown to give internal energy with three to five fignre accuracy compared to a wide range of Monte Carlo data. Meanwhile, small deviations of excess internal energy from the so-called ``liner mixing rule`` (LMR) are better predicted by a less sophiscated theory like the hypernetted- chain (HNC) equation. This rule relates thermodynamics of an unscreened mixture to those for individual components in a strongly coupled regime where the potential energy of a constituent particle is much larger than its kinetic energy. We also apply the present theory to a H{sub 2} + H mixture interacting with Morse potentials. For this sytem, comparison of thermodynamic properties and radial distribution functions from the present theory will be made with those from another successful theory of dense fluid, i.e., the HMSA equation of Zerah and Hansen.
Date: December 1, 1997
Creator: Kang, H.S. & Ree, F.H.
Partner: UNT Libraries Government Documents Department

Integrated Quantum/Classical Modeling of Hydrogenic Materials

Description: Path integral Monte Carlo simulations and calculations were performed on molecular hydrogen liquids. The equation-of-state, internal energies, and vapor liquid phase diagrams from simulation were found to be in quantitative agreement with experiments. Analytical calculations were performed on,H2 liquids using integral equation methods to study the degree of localization of the hydrogen molecules. Very little self-trapping or localization was found as a function of temperature and density. Good qualitative agreement was found between the integral equation calculations and the quantum Monte Carlo simulations for the radius of gyration of the hydrogen molecules. Path integral simulations were also performed on molecular hydrogen on graphite surfaces, slit pores, and in carbon nanotubes. Significant quantum effects on the adsorption of hydrogen were observed.
Date: November 1, 1999
Partner: UNT Libraries Government Documents Department

Efficient second order remapping on arbitrary two dimensional meshes

Description: The authors have developed an efficient method of remapping physical variables from one unstructured grid composed of arbitrary polygons to another, based on the work of Ramshaw and Dukowicz. Eulerian cycles are used to convert the mesh into a single chain of connected edge,s which eliminates grid searching. The error is second order in the zone size. The algorithm handles degenerate meshes well. Computational effort to perform a remap scales linearly with the number of zones in the two grids, which is an improvement over typical N log N methods.
Date: March 18, 1996
Creator: Miller, D.S.; Burton, D.E. & Oliviera, J.S.
Partner: UNT Libraries Government Documents Department

An Extension of the Krieger-Li-Iafrate Approximation to the Optimized-Effective-Potential Method

Description: The Krieger-Li-Iafrate approximation can be expressed as the zeroth order result of an unstable iterative method for solving the integral equation form of the optimized-effective-potential method. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. A comparison of calculated total energies are given with Krieger-Li-Iafrate, Local Density Functional, and Hyper-Hartree-Fock results for non-relativistic atoms and ions.
Date: November 11, 1999
Creator: Wilson, B.G.
Partner: UNT Libraries Government Documents Department

Solutions of the Reactor Kinetics Equations for Time-Dependent Reactivities

Description: Abstract: The reactor kinetics equations are combined into a single integral equation whose kernel describes the time-dependent characteristics of the reactor including six delayed groups of neutrons. Numerical solutions of the integral equation are given for constant, linear, and ∫sin²kx dx reactivities. An approximate solution of the integral equation is obtained which provides a basis for the formulation and solution of the reactor system control problem using the methods of servomechanisms theory. The reactor frequency response function, a product of the approximate solution, is calculated and plot given.
Date: December 14, 1955
Creator: Ash, Milton S.
Partner: UNT Libraries Government Documents Department