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Pole-factorization theorem in quantum electrodynamics

Description: In quantum electrodynamics a classical part of the S-matrix is normally factored out in order to obtain a quantum remainder that can be treated perturbatively without the occurrence of infrared divergences. However, this separation, as usually performed, introduces spurious large-distance effects that produce an apparent breakdown of the important correspondence between stable particles and poles of the S-matrix, and, consequently, lead to apparent violations of the correspondence principle and to incorrect results for computations in the mesoscopic domain lying between the atomic and classical regimes. An improved computational technique is described that allows valid results to be obtained in this domain, and that leads, for the quantum remainder, in the cases studied, to a physical-region singularity structure that, as regards the most singular parts, is the same as the normal physical-region analytic structure in theories in which all particles have non-zero mass. The key innovations here are to define the classical part in coordinate space, rather than in momentum space, and to define there a separation of the photon-electron coupling into its classical and quantum parts that has the following properties: (1) The contributions from the terms containing only classical couplings can be summed to all orders to give a unitary operator that generates the coherent state that corresponds to the appropriate classical process, and (2) The quantum remainder can be rigorously shown to exhibit, as regards its most singular parts, the normal analytic structure. 22 refs.
Date: January 1, 1996
Creator: Stapp, H.P.
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

Supergravity Analysis of Hybrid Inflation Model from D3--D7 System

Description: The slow-roll inflation is a beautiful paradigm, yet the inflaton potential can hardly be sufficiently flat when unknown gravitational effects are taken into account. However, the hybrid inflation models constructed in D = 4 N = 1 supergravity can be consistent with N = 2 supersymmetry, and can be naturally embedded into string theory. This article discusses the gravitational effects carefully in the string model, using D = 4 supergravity description. We adopt the D3--D7 system of Type IIB string theory compactified on K3 x T^2/Z_2 orientifold for definiteness. It turns out that the slow-roll parameter can be sufficiently small despite the non-minimal Kahler potential of the model. The conditions for this to happen are clarified in terms of string vacua. We also find that the geometry obtained by blowing up singularity, which is necessary for the positive vacuum energy, is stabilized by introducing certain 3-form fluxes.
Date: November 20, 2003
Creator: Koyama, Fumikazu; Tachikawa, Yuji & Watari, Taizan
Partner: UNT Libraries Government Documents Department

Singularity detection for structural health monitoring using holder exponents.

Description: The majority of structural health monitoring studies reported in the technical literature focus on identifying damage sensitive features that can be extracted from dynamic response data . However, many of these studies assume the structure can be modeled as a linear system before and after damage and use parameters of these models as the damage sensitive features. The study summarized in this paper proposes a damage sensitive feature that takes advantage of the nonlinearities associated with discontinuities introduced into the dynamic response data as a result of certain types of damage. Specifically, the Holder exponent, a measure of the degree to which a signal is differentiable, is the feature that is used to detect the presence of damage and when that damage occurred . A procedure for capturing the time varying nature of the Holder exponent based on wavelet transforms is demonstrated through applications to non-stationary random signals with underlying discontinuities and then to a harmonically excited mechanical system that contains a loose part . Also, a classification procedure is developed to quantify when changes in the Holder exponent are significant . The results presented herein show the Holder exponent to be an effective feature for identifying damage that introduces discontinuities into the measured dynamic response data .
Date: January 1, 2003
Creator: Robertson, A. N. (Amy N.); Farrar, C. R. (Charles R.) & Sohn, H. (Hoon)
Partner: UNT Libraries Government Documents Department

Tensor methods for large, sparse unconstrained optimization

Description: Tensor methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate size problems. This paper extends these methods to large, sparse unconstrained optimization problems. This requires an entirely new way of solving the tensor model that makes the methods suitable for solving large, sparse optimization problems efficiently. We present test results for sets of problems where the Hessian at the minimizer is nonsingular and where it is singular. These results show that tensor methods are significantly more efficient and more reliable than standard methods based on Newton`s method.
Date: November 1996
Creator: Bouaricha, A.
Partner: UNT Libraries Government Documents Department

Fast 3-D seismic modeling and prestack depth migration using generalized screen methods. Final report for period January 1, 1998 - December 31, 2000

Description: Completed a theoretical analysis of phase screen propagators to answer several critical questions: the existence of a singularity in the Green's function for the case of a zero vertical wavenumber, the stability and accuracy of such propagators, and the effects of backscattering for large contrast heterogeneous media. The theory is based on separating the wavefield into forescattering and backscattering parts. The approach is robust and appropriate for earth structures with high velocity contrast. This theory also resolves the apparent singularity problem that has persisted in generalized screen propagator formulations. With this formulation we studied the effects of the commonly used approximations as a function of the degree of velocity contrast in the media.
Date: March 31, 2001
Creator: Toksoz, M. Nafi
Partner: UNT Libraries Government Documents Department

Confinement through a relativistic generalization of the linear interaction

Description: Generalizing a covariant framework previously developed, it is shown that confinement insures that meson {r_arrow} q + {anti q} decay amplitudes vanish when both quarks are on-shell. Regularization of singularities in a covariant linear potential associated with nonzero energy transfers (i.e. q{sup 2}=0, q{sup {mu}} {ne} 0) is improved.
Date: June 1, 1998
Creator: Savkli, Cetin & Gross, Franz
Partner: UNT Libraries Government Documents Department

Orbit Correction Methods - Basic Formulation, Current Applications at Jefferson Lab, and Future Possibilities

Description: A. Orbit Correction System Optimization: Recipes for optimizing an orbit correction system configuration at the design level are presented. Linear algebraic tools are applied to various flavors of response matrices to uniformly control unobservability, uncorrectability, and response matrix singularity. Application at Jefferson Lab is discussed. B. Orbit Correction at Jefferson Lab: Unique challenges posed by orbit correction, as well as algorithms and tools developed at the CEBAF accelerator at Jefferson Lab are discussed. C. Orbit Interpretation and Virtual Monitors: A new approach to developing an orbit correction package with software structural, algorithmic and operational advantages is introduced. It consists of an orbit interpretation module, a virtual monitor module, and a generic steering engine. Mathematical formulation, algorithms prototyped and tested on simulated and real data, and future possibilities are discussed.
Date: December 1, 1999
Creator: Chao, Y.C.
Partner: UNT Libraries Government Documents Department

String solitons and singularities of K{sub 3}

Description: T-duality in string theory is discussed in this paper. Two issues are emphasized: (1) How the type IIA string on {bold R}{sup 6} x K{sup 3} behaves near the orbifold singularity where the 2-cycle degenerates. (2) How the enhancement of gauge symmetry occurs non-perturbatively along the line of Storminger`s proposal. Since the details have been presented elsewhere, here I only describe the main details of these discussions.
Date: December 1, 1995
Creator: Ooguri, H.
Partner: UNT Libraries Government Documents Department

On the strong coupling dynamics of heterotic string theory onC3/Z3

Description: The authors study the strong coupling dynamics of the heterotic E{sub 8} x E{sub 8} string theory on the orbifolds T{sup 6}/Z{sub 3} and C{sup 3}/Z{sub 3} using the duality with the Horava-Witten M-theory picture. This leads us to a conjecture about the low energy description of the five dimensional E{sub 0}-theory (the CFT that describes the singularity region of M-theory on C{sup 3}/Z{sub 3}) compactified on S{sup 1}/Z{sub 2}.
Date: February 28, 2002
Creator: Ganor, O.J. & Sonnenschein, J.
Partner: UNT Libraries Government Documents Department

Cartesian Methods for the Shallow Water Equations on a Sphere

Description: The shallow water equations in a spherical geometry are solved using a 3-dimensional Cartesian method. Spatial discretization of the 2-dimensional, horizontal differential operators is based on the Cartesian form of the spherical harmonics and an icosahedral (spherical) grid. Computational velocities are expressed in Cartesian coordinates so that a problem with a singularity at the pole is avoided. Solution of auxiliary elliptic equations is also not necessary. A comparison is made between the standard form of the Cartesian equations and a rotational form using a standard set of test problems. Error measures and conservation properties of the method are reported for the test problems.
Date: February 14, 2000
Creator: Drake, J.B.
Partner: UNT Libraries Government Documents Department

Interfacial electronic charge transfer and density of states in short period Cu/Cr multilayers

Description: Nanometer period metallic multilayers are ideal structures to investigate electronic phenomena at interfaces between metal films since interfacial atoms comprise a large atomic fraction of the samples. The Cu/Cr binary pair is especially suited to study the interfaces in metals since these elements are mutually insoluble, thus eliminating mixing effects and compound formation and the lattice mismatch is very small. This allows the fabrication of high structural quality Cu/Cr multilayers that have a structure which can be approximated in calculations based on idealized atomic arrangements. The electronic structure of the Cu and the Cr layers in several samples of thin Cu/Cr multilayers were studied using x-ray absorption spectroscopy (XAS). Total electron yield was measured and used to study the white lines at the Cu L{sub 2} and L{sub 3} absorption edges. The white lines at the Cu absorption edges are strongly related to the unoccupied d-orbitals and are used to calculate the amount of charge transfer between the Cr and Cu atoms in interfaces. Analysis of the Cu white lines show a charge transfer of 0.026 electrons/interfacial Cu atom to the interfacial Cr atoms. In the Cu XAS spectra we also observe a van Hove singularity between the L{sub 2} and L{sub 3} absorption edges as expected from the structural analysis. The absorption spectra are compared to partial density of states obtained from a full-potential linear muffin-tin orbital calculation. The calculations support the presence of charge transfer and indicate that it is localized to the first two interfacial layers in both Cu and Cr.
Date: July 1999
Creator: Barbee, T. W.; Bello, A. F.; Klepeis, J. E. & Van Buuren, T.
Partner: UNT Libraries Government Documents Department

Singularity fitting in hydrodynamical calculations II

Description: This is the second report in a series on the development of techniques for the proper handling of singularities in fluid-dynamical calculations; the first was called Progress Report on the Shock-Fitting Project. This report contains six main results: derivation of a free-surface condition, which relates the acceleration of the surface with the gradient of the square of the sound speed just behind it; an accurate method for the early and middle stages of the development of a rarefaction wave, two orders of magnitude more accurate than a simple direct method used for comparison; the similarity theory of the collapsing free surface, where it is shown that there is a two-parameter family of self- similar solutions for $gamma$ = 3.9; the similarity theory for the outgoing shock, which takes into account the entropy increase; a ''zooming'' method for the study of the asymptotic behavior of solutions of the full initial boundary- value problem; comparison of two methods for determining the similarity parameter delta by zooming, which shows that the second method is preferred. Future reports in the series will contain discussions of the self-similar solutions for this problem, and for that of the collapsing shock, in more detail and for the full range (1, infinity) of $gamma$; the values of certain integrals related to neutronic and thermonuclear rates near collapse; and methods for fitting shocks, contact discontinuities, interfaces, and free surfaces in two-dimensional flows. (auth)
Date: September 1, 1975
Creator: Richtmyer, R.D. & Lazarus, R.B.
Partner: UNT Libraries Government Documents Department

A Scalable Implementation of a Finite-Volume Dynamical Core in the Community Atmosphere Model

Description: A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the Community Atmosphere Model is presented. Due to the data dependencies resulting from the polar singularity of the latitude-longitude coordinate system, it is necessary to employ two separate domain decompositions within the dynamical core. Data must be periodically redistributed between these two decompositions. In addition, the domains contain halo regions that cover the nearest neighbor data dependencies. A combination of several techniques, such as one-sided communication and multithreading, are presented to optimize data movements. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.
Date: June 25, 2004
Creator: Sawyer, W & Mirin, A
Partner: UNT Libraries Government Documents Department

Catastrophe theory. Part I. Mathematical aspects

Description: This reasonably self-contained report on Catastrophe Theory begins with the mathematical history of Catastrophe Theory and discusses the relation between Catastrophe Theory and the ''Catastrophe Theorem'' presented in the report. Catastrophe Theory consists of a ''local'' classification theorem for unfoldings of germ singularities, which satisfy certain conditions. The ''classification'' is a list of seven (nonsimilar) irreducible unfoldings (and their respective germs), such that the given unfolding must be reduced with index zero to exactly one of these (or to the ''constant'' unfolding of the same unfolding dimension). The Catastrophe Theorem is stated (together with background definitions and commentary) and a summary of the proof of this theorem is given. 6 tables. (RWR)
Date: October 8, 1976
Creator: Zaslawsky, E. G.
Partner: UNT Libraries Government Documents Department

Betatron-Function Measurement in Lattices with 90-Degrees Sections

Description: Lattice functions derived from betatron phase-advance measurements have been used successfully at many e{sup +}-e{sup -} facilities in the world, including at the PEP-II High Energy Ring. For the Low energy Ring of PEP-II, however, extraction of meaningful beta functions is hampered by the 90{sup o} phase advance/cell in the arcs, which causes a singularity in the expressions for beta. An algorithm has been developed calculating beta functions based on {beta} and {alpha} at the beginning of an arc and tracking the Twiss parameters through the arc while matching the observed phase advance/cell. Stability of the algorithm is improved by doing the same calculation 'backward' as well as forward and averaging the result. The algorithm allows estimating beta functions at bad BPMs in many cases. The paper presents the algorithm used as well as examples of use in PEP.
Date: April 24, 2012
Creator: Wienands, U.; /SLAC; Biagini, M.E. & /Frascati
Partner: UNT Libraries Government Documents Department

Anomalous Fermi-Surface Dependent Pairing in a Self-Doped High-Tc Superconductor

Description: We report the discovery of a self-doped multi-layer high T{sub c} superconductor Ba{sub 2}Ca{sub 3}Cu{sub 4}O{sub 8}F{sub 2} (F0234) which contains distinctly different superconducting gap magnitudes along its two Fermi surface(FS) sheets. While formal valence counting would imply this material to be an undoped insulator, it is a self-doped superconductor with a T{sub c} of 60K, possessing simultaneously both electron- and hole-doped FS sheets. Intriguingly, the FS sheet characterized by the much larger gap is the electron-doped one, which has a shape disfavoring two electronic features considered to be important for the pairing mechanism: the van Hove singularity and the antiferromagnetic ({pi}/a, {pi}/a) scattering.
Date: May 3, 2010
Creator: Chen, Y.
Partner: UNT Libraries Government Documents Department

The Implementation of the Finite-Volume Dynamical Core in the Community Atmosphere Model

Description: A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the Community Atmosphere Model 3.0 is presented. These three-dimensional equations can be decoupled into a set of two-dimensional equations by the introduction of a floating vertical coordinate, resulting in considerable potential parallelism. Subsequent analysis of the data dependencies --in particular those arising from the polar singularity of the latitude-longitude coordinate system--suggests that two separate domain decompositions should be employed, each tailored for a different part of the model. The implementation requires that data be periodically redistributed between these two decompositions. Furthermore, data from nearest neighbors are kept in halo regions, which are updated between iterations. These data movements are optimized through one-sided communication primitives and multithreading. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.
Date: July 26, 2005
Creator: Sawyer, W B & Mirin, A A
Partner: UNT Libraries Government Documents Department

A scalable implementation of a finite-volume dynamical core in the Community Atmosphere Model

Description: A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the Community Atmosphere Model is presented. Due to the data dependencies resulting from the polar singularity of the latitude-longitude coordinate system, we employ two separate domain decompositions within the dynamical core--one in latitude/level space, and the other in longitude/latitude space. This requires that the data be periodically redistributed between these two decompositions. In addition, the domains contain halo regions that cover the nearest neighbor data dependencies. A combination of several techniques, such as one-sided communication and multithreading, are presented to optimize data movements. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.
Date: September 24, 2004
Creator: Mirin, A. A. & Sawyer, W. B.
Partner: UNT Libraries Government Documents Department

Simple Stringy Dynamical SUSY Breaking

Description: We present simple string models which dynamically break supersymmetry without non-Abelian gauge dynamics. The Fayet model, the Polonyi model, and the O'Raifeartaigh model each arise from D-branes at a specific type of singularity. D-brane instanton effects generate the requisite exponentially small scale of supersymmetry breaking.
Date: August 8, 2007
Creator: Aharony, Ofer; /Weizmann Inst. /Stanford U., Phys. Dept. /SLAC; Kachru, Shamit; Silverstein, Eva & /Stanford U., Phys. Dept. /SLAC
Partner: UNT Libraries Government Documents Department

Singularity detection using holder exponent.

Description: A signal processing technique called Holder exponent is presented to detect the presence of a discontinuity and when the discontinuity occurs in a dynamic signal. Wavelet transforms are incorporated with the Holder exponent to capture the time varying nature of discontinuities, and a classification procedure is developed to quantify when changes in the Holder exponent are significant, The proposed Holder exponent analysis is applied to acceleration response of a mechanical system with a rattling internal part. The experimental results demonstrate the effectiveness of the Holder exponent for identifying certain types of events that introduce discontinuities into the measured dynamic response data.
Date: January 1, 2002
Creator: Sohn, H. (Hoon); Robertson, A. N. (Amy N.) & Farrar, C. R. (Charles R.)
Partner: UNT Libraries Government Documents Department

Robust incremental condition estimation

Description: This paper presents an improved version of incremental condition estimation, a technique for tracking the extremal singular values of a triangular matrix as it is being constructed one column at a time. We present a new motivation for this estimation technique using orthogonal projections. The paper focuses on an implementation of this estimation scheme in an accurate and consistent fashion. In particular, we address the subtle numerical issues arising in the computation of the eigensystem of a symmetric rank-one perturbed diagonal 2 {times} 2 matrix. Experimental results show that the resulting scheme does a good job in estimating the extremal singular values of triangular matrices, independent of matrix size and matrix condition number, and that it performs qualitatively in the same fashion as some of the commonly used nonincremental condition estimation schemes.
Date: March 29, 1991
Creator: Bischof, C. H. & Tang, P. T. P.
Partner: UNT Libraries Government Documents Department