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Some remarks on antenna response in a reverberation chamber

Description: The simple formula, {l_angle}P{sub r}{r_angle}=(E{sub o}{sup 2}/{eta})({lambda}{sup 2}/8{pi}), for the received power of an antenna with a matched load in an over-moded cavity actually holds for an antenna of any shape and size. This can be seen from the close connection between the correlation tensor of the cavity field at two different points and the imaginary part of the free-space dyadic Green's function.
Date: March 15, 2000
Creator: WARNE,LARRY K. & LEE,K.S.H.
Partner: UNT Libraries Government Documents Department

ON OPERATOR SOLUTIONS OF BOUNDARY-VALUE PROBLEMS

Description: A discussion of properties of operator solutions, of relations between operator solutions, and of the class of all operator solutions is given. Solutions of inhomogeneous boundary-value problems by Green operators are discussed. The connections between operator solutions of scalar and vector problems are studied. (C.J.G.)
Date: December 1, 1959
Creator: Wyler, O.
Partner: UNT Libraries Government Documents Department

Of FFT-based convolutions and correlations, with application to solving Poisson's equation in an open rectangular pipe

Description: A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs)to perform mixed convolutions and correlations of the charge density with the Green function. Descriptions are provided for algorithms based on theordinary Green function and for an integrated Green function (IGF). Due to its similarity to the widely used Hockney algorithm for solving Poisson'sequation in free space, this capability can be easily implemented in many existing particle-in-cell beam dynamics codes.
Date: November 7, 2011
Creator: Ryne, Robert D.
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

Two-particle picture and electronic structure calculations

Description: We derive exact formal expressions for the self-energy, (capital Sigma <sup>(<i>n</i>)</sup>, describing the in- teraction of <i>n</i> particles with one another and with the rest of the particles in an interacting quantum N-particle system In contrast to traditional treatments, in which the single-particle self-energy is built out of interactions of a particle with the rest of the system, here a general n-particle quantity, (capital sigma)<sup>(<i>n</i>)</sup>, is obtained in a straight- forward fashion by integrating the exact <i>N</i>-particle Green function, <i>G</i><sup>(N)</sup>, over the coordinates of N <sup>_</sup> <i>n</i> particles and inverting An alternative expression, based on the canonical many-body equation of motion for the Green function is also discussed and compared with that derived through the integration process. The methodology is developed with respect to two-particle states, with the two-particle Green function being the central quantity from which the single-particle self-energy and Green function are derived It is suggested that the two-particle Green function be calculated directly in six-dimensional space in a two-particle generalization of density functional theory and the corresponding local density approximation. Methods for the calculation of the single-particle, <i>n</i> = 1, self-energy and effective single-particle t-matrix are discussed, and the methodology is illustrated by means of calculations on a model system.
Date: June 24, 1998
Creator: Gonis, A; Schulthess, T C & Turchi, P E A
Partner: UNT Libraries Government Documents Department

The planar Green`s function in an infinite multiplying medium

Description: Throughout the history of neutron transport theory, the study of simplified problems that have analytical or semi-analytical solutions has been a foundation for more complicated analyses. Analytical transport results are often used as benchmarks or in pedagogical settings. Benchmark problems in infinite homogeneous media have been studied continually, beginning with the monograph by Case, DeHoffmann, and Placzek. A fundamental problem considered in this work is the Green`s function in an infinite medium. The Green`s function problem considers an infinite planar source emitting neutral particles in the single directions`. Recently, this Green`s function has been used to obtain solutions for finite media. These solutions, which hinge on accurate and fast evaluation of the infinite medium Green`s function, use Fourier and Laplace transform inversion techniques for the evaluation. Until now, only absorbing media have been considered, and applications were therefore limited to non-multiplying media. In an effort to relax this limitation, the infinite medium Green`s function is numerically evaluated for an infinite multiplying medium using the double-sided Laplace transform inversion. Of course, no steady-state mathematical solution exists for an infinite multiplying medium with a source present; however, the non-physical solution in an infinite medium can be used in finite media problems where the solution is physically realizable.
Date: October 1, 1996
Creator: Kornreich, D.E. & Ganapol, B.D.
Partner: UNT Libraries Government Documents Department

Strong ground motion synthesis along the Sanyi-Tungshih-Puli seismic zone using empirical Green`s functions

Description: We synthesize strong ground motion from a M=7.25 earthquake along the NW-trending Sanyi-Tungshih-Puli seismic zone. This trend extends from Houlong to Taichung and forms a nearly continuous 78 km long seismic zone identified by the occurrence of M<5 events. It extends from a shallow depth all the way down to about 40 km. The entire length of the fault, if activated at one time, can lead to an event comparable to that the 1995 Kobe earthquake. With the improved digital CWBSN data now provided routinely by CWBSN, it becomes possible to use these data as empirical Green`s functions to synthesize potential ground motion for future large earthquakes. We developed a suite of 100 rupture scenarios for the earthquake and computed the commensurate strong ground motion time histories. We synthesized strong ground motion with physics-based solutions of earthquake rupture and applied physical bounds on rupture parameters. the synthesized ground motions obtained for a fixed magnitude and identifying the hazard to a site from the statistical distribution of engineering parameters, we have introduced a probabilistic component to the deterministic hazard calculation, The time histories suggested for engineering design are the ones that most closely match either the average or one standard deviation absolute acceleration response values.
Date: January 1, 1997
Creator: Hutchings, L.; Foxall, W.; Kasameyer, P.; Wu, F.T.; Rau, R.-J. & Jarpe, S.
Partner: UNT Libraries Government Documents Department

The Green`s function method for critical heterogeneous slabs

Description: Recently, the Green`s Function Method (GFM) has been employed to obtain benchmark-quality results for nuclear engineering and radiative transfer calculations. This was possible because of fast and accurate calculations of the Green`s function and the associated Fourier and Laplace transform inversions. Calculations have been provided in one-dimensional slab geometries for both homogeneous and heterogeneous media. A heterogeneous medium is analyzed as a series of homogeneous slabs, and Placzek`s lemma is used to extend each slab to infinity. This allows use of the infinite medium Green`s function (the anisotropic plane source in an infinite homogeneous medium) in the solution. To this point, a drawback of the GFM has been the limitation to media with c < 1, where c is the number of secondary particles produced in a collision. Clearly, no physical steady-state solution exists for an infinite medium that contains an infinite source and is described by c >1; however, mathematical solutions exist which result in oscillating Green`s functions. Such calculations are briefly discussing. The limitation to media with c < 1 has been relaxed so that the Green`s function may also be calculated for media with c {ge} 1. Thus, materials that contain fissionable isotopes may be modeled.
Date: October 1, 1996
Creator: Kornreich, D.E.
Partner: UNT Libraries Government Documents Department

Depth of burial experiments at Balapan

Description: We report of a series of experiments designed to discriminate underground explosion sources at various depths by means of their seismic signatures at regional distances. This series was a joint effort of the US Department of Energy (DOE), the US Defense Special Weapons Agency (DSWA), and the National Nuclear Center of the Republic of Kazakhstan (NNC). The series consisted of three 25-ton explosions, at depths of 55 m, 300 m, and 50 m. In addition, a 5-ton checkout explosion was fired at a depth of 630 m, and small-scale explosions at each site were carried out so that the empirical Green`s functions could be derived. Broadband and short-period seismic data were recorded at an eight-station network within Kazakhstan, at nominal ranges varying from 100-1500 km, and with good azimuthal coverage for regional phases. In addition, seismic measurements were made at former NRDC sites (BAY and KKL), infrasound recordings were made at the cross array at Kurchatov, and close-in seismic measurements were also made at ranges from ground zero to 20 km. Although the main objective of this series was to study depth-of- burial (DOB) effects on the excitation of regional phases such as LG and RG, and to determine whether peaks in the coda spectral shape correlate well with DOB, a secondary objective was to help calibrate the site of the Kazakhstan seismic network, especially the primary IMS station at MAKanchi, and the auxiliary IMS stations at KURchatov and AKTyubinsk.
Date: November 1, 1997
Creator: Glenn, L.A. & Myers, S.C.
Partner: UNT Libraries Government Documents Department

Strong ground motion synthesis for a M=7.2 earthquake in the Gulf of Corinth, Greece using Empirical Green`s functions

Description: We synthesize strong ground motion at three sites from a M=7.2 earthquake along the MW-trending Gulf of Cornith seismic zone. We model rupture along an 80 segment of the zone. The entire length of the fault, if activated at one time, can lead to an event comparable to that of the 1995 Kobe earthquake. With the improved digital data now routinely available, it becomes possible to use recordings of small earthquakes as empirical Green`s functions to synthesize potential ground motion for future large earthquakes. We developed a suite of 100 rupture scenarios for the earthquake and computed the commensurate strong ground motion time histories. We synthesized strong ground motion with physics-based solutions of earthquake rupture and applied physical bounds on rupture parameters. The synthesized ground motions obtained are source and site specific. By having a suite of rupture scenarios of hazardous earthquakes for a fixed magnitude and identifying the hazard to a site from the statistical distribution of engineering parameters, we have introduced a probabilistic component to the deterministic hazard calculation. The time histories suggested for engineering design are the ones that most closely match either the average or one standard deviation absolute accelerations response values.
Date: January 1, 1998
Creator: Hutchings, L.; Stavrakakis, G.N.; Ioannidou, E.; Wu, F.T.; Jarpe, S. & Kasameyer, P.
Partner: UNT Libraries Government Documents Department

Predictability of Minimum Noise in Electron Transport Through a Disordered Semiconductor

Description: The authors present an inverse method for electron transport which allows one to minimize the value of shot noise for a given value of the conductance by optimizing the spatial structure of a disordered semiconductor region. The method is based on the Green's function approach which is usually applied to the direct transport problem. A specific experimentally realizable example of a two-dimensional disordered semiconductor is presented which demonstrates the method of minimization of shot noise for insulator, metallic, and transitional conductance regions.
Date: May 11, 1998
Creator: Berman, G.P.; Doolen, G.D.; Nagaev, K.E. & Rehacek, J.
Partner: UNT Libraries Government Documents Department

Independent seismic evaluation of the 24-580-980 south connector ramps

Description: The interchange for highways 24, 580, and 980 (the Stack) in Oakland, California, lies 4.3 km from the surface expression of the Hayward fault and 26 km from the San Andreas fault. The purpose of this project is to compute realistic, linear, strong ground motion (rock outcrop motion) likely to affect this interchange during a hazardous earth-quake on the Hayward fault. With the exception of very long period ( >20 sec) motion, the Hayward fault will be the controlling deterministic ground motion hazard to this structure. We identified a magnitude M = 7.25 earthquake that ruptures 82 km of the Hayward fault as the principal hazard to the Stack; it has a moment of 8.5 x 10{sup 26} dyne-cm. Moment magnitudes (Hanks and Kanamori, 1979) are used in this report. Our goal is to produce realistic synthesized ground motion for three components and the full wavetrain and for frequencies from 0.05 to 33.0 Hz.
Date: May 1, 1997
Creator: Hutchings, L.J.; Kasameyer, P.W.; Jarpe, S.P. & Foxall, W.
Partner: UNT Libraries Government Documents Department

The screening of the lamb shift in heavy helium-like ions. Final technical report

Description: The project was undertaken in collaboration with Dr. Neal Snyderman of Lawrence Livermore National Laboratory (LLNL) through a project under the directorship of Dr. Kennedy Reed of LLNL. It is a collaboration of the work started at LLNL during the summers of 1994 and 1995, and continued at Spelman College. Spelman students Adrienne Stiff and Joy Harris were supported under this project. The main question under investigation was whether a Sturmian representation of the electron Green function is suitable for numerical calculations of QED effects in high-Z helium-like atoms. The frequency-independent part of the two-photon exchange graphs was calculated with this representation and compared with the results of other recent calculations. Only the Coulomb part of these graphs were calculated under this project.
Date: November 1, 1997
Creator: Hylton, D.J.
Partner: UNT Libraries Government Documents Department

Four-button BPM coefficients in cylindrical and elliptic beam chambers.

Description: Beam position monitor (BPM) coefficients are calculated from induced charges on four-button BPMs in circular and elliptic beam chambers for {gamma} &gt;&gt;1. Since the beam chamber cross-section for the APS storage ring is different from an exact elliptic geometry, numerical values of the BPM coefficients and their inversions are computed from two-dimensional electrostatic field distributions inside an exact geometry of the beam chamber. Utilizing Green's reciprocation theorem, a potential value is applied to the buttons rather than changing the beam position, and potential distributions corresponding to the beam positions are then computed.
Date: April 8, 1999
Creator: Kim, S. H.
Partner: UNT Libraries Government Documents Department

Decay rates of spherical and deformed proton emitters

Description: Using Green's function techniques, the authors derive expressions for the width of a proton decaying state in spherical and deformed nuclei. The authors show that the proton decay widths calculated by the exact expressions of Maglione et al. are equivalent to the distorted wave expressions of Bugrov et al., and that of {angstrom} berg et al. in the spherical case.
Date: November 23, 1999
Creator: Davids, C. N. & Esbensen, H.
Partner: UNT Libraries Government Documents Department

The linear algebraic method for electron-molecule collisions

Description: In order to find numerical solutions to many problems in physics, chemistry and engineering it is necessary to place the equations of motion (classical or quantal) of the variables of dynamical interest on a discrete mesh. The formulation of scattering theory in quantum mechanics is no exception and leads to partial differential or integral equations which may only be solved on digital computers. Typical approaches introduce a numerical grid or basis set expansion of the scattering wavefunction in order to reduce `the problem to the solution of a set of algebraic equations. Often it is more convenient to deal with the scattering matrix or phase amplitude rather than the wavefunction but the essential features of the numerics are unchanged. In this section we will formulate the Linear Algebraic Method (LAM) for electron-atom/molecule scattering for a simple, one-dimensional radial potential. This will illustrate the basic approach and enable the uninitiated reader to follow the subsequent discussion of the general, multi-channel, electron-molecule formulation without undue difficulty. We begin by writing the Schroedinger equation for the s-wave scattering of a structureless particle by a short-range, local potential.
Date: September 1995
Creator: Collins, L. A. & Schneider, B. I.
Partner: UNT Libraries Government Documents Department

Verification of multiplicative renormalization of a model with spontaneously broken symmetry

Description: The multiplicative renormalization program, performed in an Abelian gauge model with spontaneously broken symmetry, is verified explicitly at the one loop level. By utilizing the two parameter gauge freedom which was introduced in a previous note, the off-, as well as on-, mass-shell Green's functions can be made finite after renormalization. (auth)
Date: January 1, 1972
Creator: Yao, Y.P.
Partner: UNT Libraries Government Documents Department

IMPACT-T User Document Version 1.6

Description: IMPACT-T is a fully three-dimensional program to track relativistic particles taking into account space charge forces and short-range longitudinal and transverse wakenelds. IMPACT-T is one of the few codes used in the photoinjector community that has a parallel implementation, making it very useful for high statistics simulations of beam halos and beam diagnostics. It has a comprehensive set of beamline elements, and furthermore allows arbitrary overlap of their fields, which gives the IMPACT-T a capability to model both the standing wave structure and traveling wave structure. It is also unique in its use of space-charge solvers based on an integrated Green function to efficiently and accurately treat beams with large aspect ratio, and a shifted Green function to efficiently treat image charge effects of a cathode. It is also unique in its inclusion of energy binning in the space-charge calculation to model beams with large energy spread. IMPACT-T has a flexible data structure that allows particles to be stored in containers with common characteristics; for photoinjector simulations the containers represent multiple slices, but in other applications they could correspond, e.g., to particles of different species. Together, all these features make IMPACT-T a powerful and versatile tool for modeling beams in photoinjectors and other systems.
Date: May 17, 2010
Creator: Qiang, Ji
Partner: UNT Libraries Government Documents Department

GENERALIZED FUNCTIONS OF GREEN FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Description: The adjoint operator of a matrix operator and adjoint boundary conditions for adjoint matrix operators are defined. It is shown that a matrix operator can be associated in various ways with a scalar differential operator and if two adjoint matrix operators are associated with scalar differential operators then the scalar operators are adjoint. Generalized Green's functions are obtained and their use for solving boundary-value problems is discussed. Properties which characterize a generalized function of Green are obtained and it is shown that the generalized functions of Green of adjoint boundary-value problems are adjoint kernel matrices. Generalized Green's functions for scalar boundaryvalue problems are discussed and special cases taken up. (C.J.G.)
Date: July 1, 1959
Creator: Wyler, O.
Partner: UNT Libraries Government Documents Department

PERTURBATION-THEORY RULES FOR COMPUTING THE SELF-ENERGY OPERATOR IN QUANTUM STATISTICAL MECHANICS

Description: Highly convenient rules are given for the general term in the time- independent perturbation-theory expansion for the self-energy operator of quantum statistical mechanics. The rules are derived by starting from the usual formalism involving time-independent Green&#x27;s functions. The well-known formulas for thermodynamic quantities in terms of the self-energy operator are included for completeness. (auth)
Date: December 17, 1962
Creator: Baym, G. & Sessler, A.M.
Partner: UNT Libraries Government Documents Department

Rigorous fluid model for 3D analysis of the diocotron instability

Description: A refinement to the theory published by Finn et al. is presented here. Compression effects are taken into account by a rigorous definition of the plasma length and by modifying the expression of the velocity field. The perturbation of the plasma length is calculated exactly by a suitable Green function. Growth rates and real frequencies of the unstable m{sub {theta}} = 1 mode are compared with the experimental values, showing a good agreement when compression effects are strong (i.e., for short traps).
Date: January 1, 2001
Creator: Coppa, G. M. (Gianni M.); Angola, A. D. (Antonio D.); Delzanno, G. L. (Gian L.) & Lapenta, G. M. (Giovanni M.)
Partner: UNT Libraries Government Documents Department