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Use of the Lorentz-operator in relativistic quantum mechanics to guarentee a single-energy root

Description: The Lorentz-operator form of relativistic quantum mechanics, with relativistic wave equation i{h_bar}{partial_derivative}{psi}/{partial_derivative}t=(mc{sup 2}{gamma}+e{Phi}){psi}, is implemented to guarantee a single-energy root. The Lorentz factor as modified by Pauli's ansatz is given by {gamma}={radical}1+[{rvec {sigma}}{center_dot}(i{h_bar}{rvec {del}}+(e/c){rvec A})]{sup 2}/m{sup 2}c{sup 2}, such that the theory is appropriate for electrons. Magnetic fine structure in the Lorentz relativistic wave equation emerges on the use of an appropriate operator form of the Lienard-Wiechert four- potential ({Phi},{rvec A}) from electromagnetic theory. Although computationally more intensive the advantage of the theory is the elimination of the negative-root of the energy and an interpretation of the wave function based on a one-particle, positive definite probability density like that of nonrelativistic quantum mechanics.
Date: August 1, 1998
Creator: Ritchie, A B
Partner: UNT Libraries Government Documents Department

Chirp Z-transform spectral zoom optimization with MATLAB.

Description: The MATLAB language has become a standard for rapid prototyping throughout all disciplines of engineering because the environment is easy to understand and use. Many of the basic functions included in MATLAB are those operations that are necessary to carry out larger algorithms such as the chirp z-transform spectral zoom. These functions include, but are not limited to mathematical operators, logical operators, array indexing, and the Fast Fourier Transform (FFT). However, despite its ease of use, MATLAB's technical computing language is interpreted and thus is not always capable of the memory management and performance of a compiled language. There are however, several optimizations that can be made within the chirp z-transform spectral zoom algorithm itself, and also to the MATLAB implementation in order to take full advantage of the computing environment and lower processing time and improve memory usage. To that end, this document's purpose is two-fold. The first demonstrates how to perform a chirp z-transform spectral zoom as well as an optimization within the algorithm that improves performance and memory usage. The second demonstrates a minor MATLAB language usage technique that can reduce overhead memory costs and improve performance.
Date: November 1, 2005
Creator: Martin, Grant D.
Partner: UNT Libraries Government Documents Department

Conventions for quantum pseudocode

Description: A few conventions for thinking about and writing quantum pseudocode are proposed. The conventions can be used for presenting any quantum algorithm down to the lowest level and are consistent with a quantum random access machine (QRAM) model for quantum computing. In principle a formal version of quantum pseudocode could be used in a future extension of a conventional language.
Date: June 1, 1996
Creator: Knill, E.
Partner: UNT Libraries Government Documents Department

Second Order Perturbations of Monte Carlo Criticality Calculations

Description: Perturbation techniques are powerful tools for determining the effects of small changes, or perturbations, to a problem. Perturbations have long been problematic in Monte Carlo calculations because the effects of small changes to the problem are usually masked by the inherent statistical uncertainties. The recently released MCNP4B Monte Carlo computer code uses the differential operator technique, to calculate changes in tallies caused by perturbations in density and composition over given energy ranges and reaction types. This technique will allow for precise calculation of the changes in tallies even if the standard deviation of the unperturbed tally is larger than the change. The differential operator is approximated by a second order Taylor series. The implementation of the Taylor series expansion assumes that the coefficients are independent of any perturbed cross-sections. However, if the tally is multiplied by cross-section data this assumption is invalid and incorrect results will be generated. Of significant interest is the use of perturbations in criticality calculations. Although the criticality source feature for MCNP cannot directly calculate perturbed eigenvalues, a track-length estimate for Keff can be tallied and the perturbation feature can be applied to this tally. However, since the tally multiplies the flux by the macroscopic fission cross-section, this tally is dependent on perturbed cross-section data and incorrect results will be calculated by the perturbation feature. In order to compute the correct tally, a correction term is needed that will account for the dependence of the Taylor series coefficients on the perturbed cross-section data.
Date: July 1, 1997
Creator: Densmore, J.D.; Hendricks, J.S. & McKinney, G.W.
Partner: UNT Libraries Government Documents Department

Effects of operator splitting in computing curved shocks

Description: Dimensionally split numerical methods have been in common use in computational physics for many years. This is due to the need for speed, the formal convergence of Strang splittings, and the accessibility of shock capturing techniques in one dimension. However, the lack of genuinely unsplit multidimensional shock capturing methods has made it difficult to access just how large the errors are in a dimensionally split approach. This applies in spite of splitting corrections that have been used to obtain formally "unsplit" methods. A new class of methods that are genuinely unsplit have recently been developed. These are the so-called "Conservation Element and Solution Element" (CE/SE) methods. Using these high accuracy methods, we show that converging flows and the subsequent expanding flows are accurately captured by CE/SE methods. Contrariwise, it will be shown that dimensionally-split Godunov and unsplit wave propagation methods distort the flow for the same cases, sometimes seriously.
Date: October 1, 1998
Creator: Cook, G O & Rathkopf, J
Partner: UNT Libraries Government Documents Department

Dynamic Restarting Schemes for Eigenvalue Problems

Description: In studies of restarted Davidson method, a dynamic thick-restart scheme was found to be excellent in improving the overall effectiveness of the eigen value method. This paper extends the study of the dynamic thick-restart scheme to the Lanczos method for symmetric eigen value problems and systematically explore a range of heuristics and strategies. We conduct a series of numerical tests to determine their relative strength and weakness on a class of electronic structure calculation problems.
Date: March 10, 1999
Creator: Wu, Kesheng & Simon, Horst D.
Partner: UNT Libraries Government Documents Department


Description: The overlap operator provides an elegant definition for the winding number of lattice gauge field configurations. Only for a set of configurations of measure zero is this procedure undefined. Without restrictions on the lattice fields, however, the space of gauge fields is simply connected. I present a simple low dimensional illustration of how the eigenvalues of a truncated overlap operator flow as one travels between different topological sectors.
Date: June 29, 2002
Creator: CREUTZ,M.
Partner: UNT Libraries Government Documents Department

Measurement accuracy, bit-strings, Manthey`s quaternions, and RRQM

Description: The author continues the discussion started last year. By now three potentially divergent research programs have surfaced in ANPA: (1) the Bastin-Kilmister understanding of the combinatorial hierarchy (Clive`s {open_quotes}Menshevik{close_quotes} position); (2) the author`s bit-string {open_quotes}Theory of Everything{close_quotes} (which Clive has dubbed {open_quotes}Bolshevik{close_quotes}); (3) Manthey`s cycle hierarchy based on co-occurrence and mutual exclusion that Clive helped him map onto quaternions (as an yet unnamed heresy?). Unless a common objective can be found, these three points of view will continue to diverge. The authors suggests the reconstruction of relativistic quantum mechanism (RRQM) as a reasonable, and attainable, goal that might aid convergence rather than divergence.
Date: February 1, 1995
Creator: Noyes, H. P.
Partner: UNT Libraries Government Documents Department

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

Description: This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.
Date: October 1, 2007
Creator: Wagner, Gregory John (Sandia National Laboratories, Livermore, CA); Collis, Samuel Scott; Templeton, Jeremy Alan (Sandia National Laboratories, Livermore, CA); Lehoucq, Richard B.; Parks, Michael L.; Jones, Reese E. (Sandia National Laboratories, Livermore, CA) et al.
Partner: UNT Libraries Government Documents Department

Multilinear operators for higher-order decompositions.

Description: We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties of the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.
Date: April 1, 2006
Creator: Kolda, Tamara Gibson
Partner: UNT Libraries Government Documents Department

Standing wave solutions to the inhomogeneous equation for identical particle scattering

Description: The standing wave solution to the inhomogeneous equation describing identical particle scattering is re-examined. Although the form of that solution is correct, its content is shown to be incorrect. A paradigm for constructing the correct solution, based on unitarity, is discussed, and the proper solution is then obtained. A comparison of different standing wave solutions with differing K operators is given. The results are shown to be an extension to the multi-channel case of those derived previously for the potential well case. (auth)
Date: January 1, 1973
Creator: Kouri, D.J. & Levin, F.S.
Partner: UNT Libraries Government Documents Department

Non-binary unitary error bases and quantum codes

Description: Error operator bases for systems of any dimension are defined and natural generalizations of the bit-flip/ sign-change error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of Abelian groups. As a consequence, quantum codes can be constructed form linear codes over {ital Z}{sub {ital n}} for any {ital n}. The generalization of the punctured code construction leads to many codes which permit transversal (i.e. fault tolerant) implementations of certain operations compatible with the error basis.
Date: June 1, 1996
Creator: Knill, E.
Partner: UNT Libraries Government Documents Department

Multidimensional electron-photon transport with standard discrete ordinates codes

Description: A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electronphoton transport problems.
Date: December 31, 1995
Creator: Drumm, C.R.
Partner: UNT Libraries Government Documents Department

A generalized stationary point convergence theory for evolutionary algorithms

Description: This paper presents a convergence theory for evolutionary pattern search algorithms (EPSAs). EPSAs are self-adapting evolutionary algorithms that modify the step size of the mutation operator in response to the success of previous optimization steps. Previously, the authors have proven a stationary point convergence theory for EPSAs for which the step size is not allowed to increase. The present analysis generalizes this analysis to prove a convergence theory for EPSAs that are allowed to both increase and decrease the step size. This convergence theory is based on an extension of the convergence theory for generalized pattern search methods.
Date: February 1, 1997
Creator: Hart, W.E.
Partner: UNT Libraries Government Documents Department

Mimetic difference approximations of partial differential equations

Description: Goal was to construct local high-order difference approximations of differential operators on nonuniform grids that mimic the symmetry properties of the continuum differential operators. Partial differential equations solved with these mimetic difference approximations automatically satisfy discrete versions of conservation laws and analogies to Stoke`s theorem that are true in the continuum and therefore more likely to produce physically faithful results. These symmetries are easily preserved by local discrete high-order approximations on uniform grids, but are difficult to retain in high-order approximations on nonuniform grids. We also desire local approximations and use only function values at nearby points in the computational grid; these methods are especially efficient on computers with distributed memory. We have derived new mimetic fourth-order local finite-difference discretizations of the divergence, gradient, and Laplacian on nonuniform grids. The discrete divergence is the negative of the adjoint of the discrete gradient, and, consequently, the Laplacian is a symmetric negative operator. The new methods derived are local, accurate, reliable, and efficient difference methods that mimic symmetry, conservation, stability, the duality relations and the identities between the gradient, curl, and divergence operators on nonuniform grids. These methods are especially powerful on coarse nonuniform grids and in calculations where the mesh moves to track interfaces or shocks.
Date: August 1, 1997
Creator: Hyman, J.M.; Shashkov, M.; Staley, M.; Kerr, S.; Steinberg, S. & Castillo, J.
Partner: UNT Libraries Government Documents Department

The geometry of SU(3)

Description: The group SU(3) is parameterized in terms of generalized {open_quotes}Euler angles{close_quotes}. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.
Date: October 1, 1997
Creator: Byrd, M.
Partner: UNT Libraries Government Documents Department

Phase Reconstruction from FROG Using Genetic Algorithms[Frequency-Resolved Optical Gating]

Description: The authors describe a new technique for obtaining the phase and electric field from FROG measurements using genetic algorithms. Frequency-Resolved Optical Gating (FROG) has gained prominence as a technique for characterizing ultrashort pulses. FROG consists of a spectrally resolved autocorrelation of the pulse to be measured. Typically a combination of iterative algorithms is used, applying constraints from experimental data, and alternating between the time and frequency domain, in order to retrieve an optical pulse. The authors have developed a new approach to retrieving the intensity and phase from FROG data using a genetic algorithm (GA). A GA is a general parallel search technique that operates on a population of potential solutions simultaneously. Operators in a genetic algorithm, such as crossover, selection, and mutation are based on ideas taken from evolution.
Date: April 12, 1999
Creator: Omenetto, F.G.; Nicholson, J.W.; Funk, D.J. & Taylor, A.J.
Partner: UNT Libraries Government Documents Department

Bounds for approximation in total variation distance by quantum circuits

Description: It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and,functions are exponentially hard to approximate. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD). TVD is the most relevant metric for the performance of a quantum circuit. In this paper we obtain asymptotically tight bounds for TVD. We show that in a natural sense, almost all states are hard to approximate to within a TVD of 2/e -- {epsilon} even for exponentially small {epsilon}. The quantity 2/e -- {epsilon} is asymptotically the average distance to the uniform distribution. Almost all states with probability amplitudes concentrated in a small fraction of the space are hard to approximate to within a TVD of 2 -- {epsilon}. These results imply that non-uniform quantum circuit complexity is non-trivial in any reasonable model. They also reinforce the notion that the relative information distance between states (which is based on the difficulty of transforming one state to another) fully reflects the dimensionality of the space of qubits, not the number of qubits.
Date: September 1, 1995
Creator: Knill, E.
Partner: UNT Libraries Government Documents Department

Smoothing of mixed complementarity problems

Description: The authors introduce a smoothing approach to the mixed complementarity problem, and study the limiting behavior of a path defined by approximate minimizers of a nonlinear least squares problem. The main result guarantees that, under a mild regularity condition, limit points of the iterates are solutions to the mixed complementarity problem. The analysis is applicable to a wide variety of algorithms suitable for large-scale mixed complementarity problems.
Date: September 1, 1995
Creator: Gabriel, S.A. & More, J.J.
Partner: UNT Libraries Government Documents Department

OBV methods. [For solving linear systems Ax = b]

Description: The properties of OB relaxation of Varga iterative methods are investigated, with particular emphasis on diagonal relaxation. Generalizations of the results of Beauwens and Quenon (SIAM J. Numer. Anal., 13, 615-643 (1976)) are presented, and their relations with the works of Axelsson and Gustafsson are indicated. Finally, the combination of this formalism with the Axelsson-Gustafsson analysis to enlarge the scope of the latter is illustrated.
Date: August 1, 1979
Creator: Beauwens, R.
Partner: UNT Libraries Government Documents Department

An angular weighting approach for calculating gradients and divergences

Description: There are several desirable properties for a free Lagrange algorithm: a Lagrangian nature, reciprocity, minimization of numerical noise, numerical efficiency, and the ability to extend the algorithms to 3-D. In addition, some integral hydro formulations allow the mass points to drift among the other points because the divergences and gradients do not depend explicitly on the position of a mass point between two other mass points. Therefore, another desirable property is a restoring force that keeps the mesh regular. An algorithm based on the angles subtended by the Voronoi polygon sides satisfies all the above criteria, except the fourth; this is because of the necessity of using trigonometric functions. Nevertheless, this loss of efficiency may be compensated by the avoidance of reconnection noise. 3 refs., 3 figs.
Date: January 1, 1990
Creator: Kirkpatrick, R. C.
Partner: UNT Libraries Government Documents Department