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Elastic wave scattering methods: assessments and suggestions

Description: The author was asked by the meeting organizers to review and assess the developments over the past ten or so years in elastic wave scattering methods and to suggest areas of future research opportunities. He highlights the developments, focusing on what he feels were distinct steps forward in our theoretical understanding of how elastic waves interact with flaws. For references and illustrative figures, he decided to use as his principal source the proceedings of the various annual Reviews of Progress in Quantitative Nondestructive Evaluation (NDE). These meetings have been the main forum not only for presenting results of theoretical research but also for demonstrating the relevance of the theoretical research for the design and interpretation of experiment. In his opinion a quantitative NDE is possible only if this relevance exists, and his major objective is to discuss and illustrate the degree to which relevance has developed.
Date: January 1, 1985
Creator: Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

Application of Pade approximants to elastic wave scattering. [Spherical void differential cross sections]

Description: Several Pade methods were used to try to accelerate the convergence of partial wave sums for scattering amplitudes. A specific test problem of longitudinal-to-longitudinal scattering from a spherical void was studied in detail. Results for this test case and the behavior of partial wave amplitudes for general cases are presented and discussed. 16 references.
Date: January 1, 1979
Creator: Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

Monte Carlo simulations of fermion systems: the determinant method

Description: Described are the details for performing Monte Carlo simulations on systems of fermions at finite temperatures by use of a technique called the Determinant Method. This method is based on a functional integral formulation of the fermion problem (Blankenbecler et al., Phys. Rev D 24, 2278 (1981)) in which the quartic fermion-fermion interactions that exist for certain models are transformed into bilinear ones by the introduction (J. Hirsch, Phys. Rev. B 28, 4059 (1983)) of Ising-like variables and an additional finite dimension. It is on the transformed problem the Monte Carlo simulations are performed. A brief summary of research on two such model problems, the spinless fermion lattice gas and the Anderson impurity problem, is also given.
Date: January 1, 1985
Creator: Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

The spatial dependence of spin and charge correlations in a one-dimensional, single impurity, Anderson model

Description: Summarized are the results of a series of quantum Monte Carlo calculations of the spatial dependence of spin and charge correlations in a one-dimensional, single impurity, symmetric Anderson model. We corroborated several features of the model of Gubernatis, Hirsch, and Scalapino, and because we achieved lower temperatures, we were able to identify several additional unusual features in the behavior of the correlations as functions of U and ..beta... We also showed the existence of a charge compensation sum role and found a power law decay of the correlations at low temperatures.
Date: January 1, 1986
Creator: Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

Crack identification and characterization in long wavelength elastic wave scattering

Description: We discuss apparent characteristic features of Rayleigh scattering of elastic waves from cracks. Interpreting these features, a procedure is suggested that in some experimental situations may be useful to distinguish generally-shaped cracks from volume defects and to determine from elliptically-shaped cracks the orientation, shape and size.
Date: January 1, 1978
Creator: Gubernatis, J.E. & Domany, E.
Partner: UNT Libraries Government Documents Department

Residual-stress characterization by use of elastic-wave-scattering measurements

Description: The presence of a state of residual stress in a material can impair its structural quality by adversely affecting its elastic limit, yield point, etc. In this paper we derive the appropriate equations for the use of elastic waves to probe an inhomogeneous state of residual stress. As in other treatments of ultrasonic residual stress measurement, we start with nonlinear effects and require knowledge of third order elastic constants. Unlike other treatments, which relate these nonlinear effects to small relative changes in propagation speed of an incident wave, we identify these effects as a source of scattering of the incident wave. Like other treatments, one difficulty with ultrasonic residual stress measurements is separating small residual stress effects from other effects. However, we will give an example of at least one class of problems where this separation appears possible using our approach. It is demonstrated that elastic wave propagation in the presence of non-uniform residual stress can be viewed as a scattering problem. One should note that in various limits, such as that of short wavelength, this scattering problem (as well as any other) can be treated by optical methods (ray bendings, diffraction, etc.). The special features of a scattering situation are expected to be important for smaller wavelengths, and therefore their experimental observability is questionable, and can be resolved only by careful and thorough measurements.
Date: January 1, 1982
Creator: Domany, E. & Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

Effects of microstructure on the speed and attenuation of elastic waves

Description: A unified theory pertaining to the sensitivity of the propagation of an elastic wave to changes in the microstructural details of a material is discussed. In contrast to nearly all previous treatments a first principles approach, using developments from other multiple scattering problems and adapting them to the elastic wave case, is followed. We then present several simple, standard approximations. In the process the validity of the commonly made assumption that ..cap alpha.. = n anti sigma is clarified, and the effective speed, illustrating its complementary character to the attenuation, is computed. The principal objective is to present the formal analysis necessary to treat systematically the dependency of the wave propagation on microstructural statistics.
Date: January 1, 1982
Creator: Gubernatis, J.E. & Domany, E.
Partner: UNT Libraries Government Documents Department

Spin--wave spectrum of an amorphous ferromagnet

Description: The spin-wave spectruin of an amorphous Heisenberg ferromagnet is calculated by a diagrammatic expansion making use of a transformation due to Taylor and Wu Phys. Rev., B2: 1752 (1970). The upper limit of the spectrum is found to occur at frequencies below that of the corresponding crystalline system, while the low-frequency part of the spectrum is enhanced. Internal van Hove singularities are absent in the spin-wave spectrum of the amorphous ferromagnet. (auth)
Date: January 1, 1973
Creator: Gubernatis, J.E. & Taylor, P.L.
Partner: UNT Libraries Government Documents Department

Elastic wave scattering calculations, the Born series, and the matrix-variational Pade approximant method

Description: The matrix variational Pade approximant and its generalization to elastic wave scattering are discussed. Predictions of the method for the scattering of a longitudinal plane wave are compared with the exact scattering from spherical voids and inclusions. Its predictions are also compared to those of the first four partial sums of the Born Series for the scattered amplitude. Generally, the fourth partial sum and the variational results compare poorly with the exact results for ka less than or equal to 2 if the scatterer is strong, but compare well for ka less than or equal to 10 if the scatterer strength is at best modest. The breakdown of the favorable comparison is traced to the divergence of the Born Series for strong scatterers. It is also demonstrated that by use of the N-point Pade approximant a good comparison with exact results can be obtained for all scatterer strengths.
Date: January 1, 1981
Creator: Gubernatis, J.E. & Baker, G.A. Jr.
Partner: UNT Libraries Government Documents Department

Elastic wave propagation through polycrystals

Description: Propagating elastic waves are commonly used to characterize nondestructively polycrystalline microstructure. To develop a fully quantitative characterization procedure, one needs a better understanding of what microstructural features most strongly influence the propagation and how these features appear in the measured, frequency dependent wave speed and attenuation. We report on our progress in a first principle investigation of these questions. We started with the equations of motion for elastic wave propagation and systematically developed a new approximation that is both well characterized and a potential improvement upon existing approximations. One of our objectives is studying the sensitivity of this approximation to changes in microstructural parameterization.
Date: January 1, 1984
Creator: Gubernatis, J.E. & Maradudin, A.A.
Partner: UNT Libraries Government Documents Department

Brillouin-zone integration schemes: an efficiency study for the phonon frequency moments of the harmonic, solid, one-component plasma

Description: The efficiency of four different Brillouin-zone integration schemes including the uniform mesh, special point method, special directions method, and Holas method are compared for calculating moments of the harmonic phonon frequencies of the solid one-component plasma. Very accurate values for the moments are also presented. The Holas method for which weights and integration points can easily be generated has roughly the same efficiency as the special directions method, which is much superior to the uniform mesh and special point methods for this problem.
Date: January 1, 1981
Creator: Albers, R.C. & Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

A bivariate multicanonical Monte Carlo of the 3D {+-}J spin glass

Description: A bivariate multicanonical Monte Carlo simulation of the three-dimensional {+-}J Ising spin glass is described. The autocorrelation time is approximately proportional to the system size, which is a great improvement over previous spin-glass simulations. The Binder plot indicates the critical temperature T{sub c}{approximately}1.3. The order parameter distribution function P(q) exhibits a feature of the droplet picture of the low-temperature phase.
Date: March 1, 1999
Creator: Hatano, N. & Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

Cluster algorithms with empahsis on quantum spin systems

Description: The purpose of this lecture is to discuss in detail the generalized approach of Kawashima and Gubernatis for the construction of cluster algorithms. We first present a brief refresher on the Monte Carlo method, describe the Swendsen-Wang algorithm, show how this algorithm follows from the Fortuin-Kastelyn transformation, and re=interpret this transformation in a form which is the basis of the generalized approach. We then derive the essential equations of the generalized approach. This derivation is remarkably simple if done from the viewpoint of probability theory, and the essential assumptions will be clearly stated. These assumptions are implicit in all useful cluster algorithms of which we are aware. They lead to a quite different perspective on cluster algorithms than found in the seminal works and in Ising model applications. Next, we illustrate how the generalized approach leads to a cluster algorithm for world-line quantum Monte Carlo simulations of Heisenberg models with S = 1/2. More succinctly, we also discuss the generalization of the Fortuin- Kasetelyn transformation to higher spin models and illustrate the essential steps for a S = 1 Heisenberg model. Finally, we summarize how to go beyond S = 1 to a general spin, XYZ model.
Date: October 6, 1995
Creator: Gubernatis, J.E. & Kawashima, Naoki
Partner: UNT Libraries Government Documents Department

Fundamental theory of elastic wave scattering by defects in elastic materials: integral equation methods for application to ultrasonic flaw detection

Description: The use of ultrasonic methods in nondestructive testing depends on the interpretation of the scattering of sound waves by flaws. The theory of elastic waves and their scattering in non-uniform media is developed in detail from first principles, and in generality. Both integral equation and differential methods are discussed, with emphasis on the former. General methods for defining scattering cross sections are presented, and conservation theorems are noted. The Born Approximation to the integral equation is presented, and computed results for several experimental situations are discussed. Several corrections to papers in the literature are made, and in particular the exact scattering of a transverse wave by a spherical flaw is compared with the Rayleigh (long wave) limit.
Date: May 1, 1976
Creator: Gubernatis, J.E.; Domany, E.; Krumhansl, J.A. & Huberman, M.
Partner: UNT Libraries Government Documents Department

Quantum Monte Carlo simulations of the one-dimensional extended Hubbard model

Description: We report preliminary results of an investigation of the thermodynamic properties of the extended Hubbard model in one- dimension, calculated with the world-line Monte Carlo method described by Hirsch et al. With strictly continuous world-lines, we are able to measure the expectation of operators that conserve fermion number locally, such as the energy and (spatial) occupation number. By permitting the world-lines to be broken'' stochastically, we may also measure the expectation of operators that conserve fermion number only globally, such as the single-particle Green's function. For a 32 site lattice we present preliminary calculations of the average electron occupancy as a function of wavenumber when U = 4, V = 0 and {beta} = 16. For a half-filled band we find no indications of a Fermi surface. Slightly away from half-filling, we find Fermi-surface-like behavior similar to that found in other numerical investigations. 8 refs., 3 figs.
Date: January 1, 1989
Creator: Somsky, W.R. & Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

Quantum Monte Carlo by message passing

Description: We summarize results of quantum Monte Carlo simulations of the degenerate single-impurity Anderson model using the impurity algorithm of Hirsch and Fye. Using methods of Bayesian statistical inference, coupled with the principle of maximum entropy, we extracted the single-particle spectral density from the imaginary-time Green's function. The variations of resulting spectral densities with model parameters agree qualitatively with the spectral densities predicted by NCA calculations. All the simulations were performed on a cluster of 16 IBM R6000/560 workstations under the control of the message-passing software PVM. We described the trivial parallelization of our quantum Monte Carlo code both for the cluster and the CM-5 computer. Other issues for effective parallelization of the impurity algorithm are also discussed.
Date: January 1, 1993
Creator: Bonca, J. & Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

Quantum Monte Carlo by message passing

Description: We summarize results of quantum Monte Carlo simulations of the degenerate single-impurity Anderson model using the impurity algorithm of Hirsch and Fye. Using methods of Bayesian statistical inference, coupled with the principle of maximum entropy, we extracted the single-particle spectral density from the imaginary-time Green`s function. The variations of resulting spectral densities with model parameters agree qualitatively with the spectral densities predicted by NCA calculations. All the simulations were performed on a cluster of 16 IBM R6000/560 workstations under the control of the message-passing software PVM. We described the trivial parallelization of our quantum Monte Carlo code both for the cluster and the CM-5 computer. Other issues for effective parallelization of the impurity algorithm are also discussed.
Date: May 1, 1993
Creator: Bonca, J. & Gubernatis, J. E.
Partner: UNT Libraries Government Documents Department

Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data

Description: We present brief description of how methods of Bayesian inference are used to obtain real frequency information by the analytic continuation of imaginary-time quantum Monte Carlo data. We present the procedure we used, which is due to R. K. Bryan, and summarize several bottleneck issues.
Date: December 31, 1995
Creator: Gubernatis, J.E.; Bonca, J. & Jarrell, M.
Partner: UNT Libraries Government Documents Department

Symmetry breaking in a quantum double-well chain

Description: We present numerical evidence that quantum fluctuations can produce a symmetric ground-state in the double-well chain, restoring the symmetry that is broken classically. In particular, we present the phase diagram for this model that shows the symmetry restoration occurs more easily than predicted by a perturbation theory calculation of the continuum limit of the model. 13 refs., 1 fig.
Date: January 1, 1991
Creator: Gubernatis, J.E.; Campbell, D.K. & Wang, Xidi.
Partner: UNT Libraries Government Documents Department

Quantum Monte Carlo study of symmetry breaking in a double-well chain

Description: We report the results of a quantum Monte Carlo simulation of a double-well chain. This chain is a system of particles that move on a lattice of symmetric, double-well potentials which are coupled harmonically to one another. The physical properties of this system are invariant, like those of the Ising model, under the symmetry operations of the Z{sub 2} group. In this case, changing the sign of the displacement variables leaves the energy unchanged and leads to a doubly-degenerate ground-state. Classically, this symmetry is always broken, and the particles all sit in the left- or the right-hand side of their wells. Quantum mechanically, however, we find that below a critical value of the double-well coupling constant the symmetry is restored by quantum fluctuations. Our interest in this model was motivated by a series of quantum Monte Carlo simulations we are performing on one-dimensional models of conducting polymers and synthetic metals. The properties of these materials are described by a system of interacting electrons coupled to a system of phonons. Several years ago, for similar models, Fradkin and Hirsch investigated how the electron motion can generate an effective double-well potential for the phonons and thereby cause the lattice to dimerize. They also argued, based on continuum renormalization group considerations and quantum Monte Carlo simulations, that for certain models quantum fluctuations at low temperatures restore symmetry (i.e., destroy the dimerization). We were attracted to the quantum double-well chain because it is a simpler problem than the electron-phonon models on which to test new numerical methods and to study similar issues.
Date: January 1, 1991
Creator: Gubernatis, J.E.; Campbell, D.K. & Wang, Xidi.
Partner: UNT Libraries Government Documents Department

Dynamical properties from quantum Monte Carlo by the Maximum Entropy Method

Description: An outstanding problem in the simulation of condensed matter phenomena is how to obtain dynamical information. We consider the numerical analytic continuation of imaginary time Quantum Monte Carlo data to obtain real frequency spectral functions. We suggest an image reconstruction approach which has been widely applied to data analysis in experimental research, the Maximum Entropy Method (MaxEnt). We report encouraging preliminary results for the Fano-Anderson model of an impurity state in a continuum. The incorporation of additional prior information, such as sum rules and asymptotic behavior, can be expected to significantly improve results. We also compare MaxEnt to alternative methods. 17 refs., 4 figs.
Date: January 1, 1989
Creator: Silver, R.N.; Sivia, D.S. & Gubernatis, J.E.
Partner: UNT Libraries Government Documents Department

Stable matrix-multiplication algorithms for low-temperature numerical simulations of fermions

Description: In this note, we discuss the use of matrix factorizations to stabilize the numerical matrix multiplications and inversions needed to simulate systems of interacting fermions at low temperatures. While the essence of a stable numerical algorithm is presented, we mainly emphasize the concepts of stabilization. 10 refs.
Date: January 1, 1988
Creator: Loh, E.Y. Jr.; Gubernatis, J.E.; Scalettar, R.T.; Sugar, R.L. & White, S.R.
Partner: UNT Libraries Government Documents Department