Showing papers by "Sandia National Laboratories published in 1987"

Influence of Geologic Discontinuities on Hydraulic Fracture Propagation (includes associated papers 17011 and 17074 )

Abstract: Geologic discontinuities, such as joints, faults, and bedding planes, can significantly affect the overall geometry of hydraulic fractures. This can occur by arresting the growth of the fracture, increasing fluid leakoff, hindering proppant transport, and enhancing the creation of multiple fractures. Results from mineback experiments and laboratory tests and analyses of these data are integrated to describe this complex fracture behavior.

Synthesis of digital holograms by direct binary search

Abstract: A new approach to the design of computer-generated holograms makes optimal use of the available device resolution. An iterative search algorithm minimizes an error criterion by directly manipulating the binary hologram and observing the effect on the desired reconstruction. Several measures of error and efficiency useful in assessing the optimality of digital holograms are defined. Methods for designing digital holograms that are based on projections and error diffusion are presented as established techniques for comparison to direct binary search.

Application of the embedded-atom method to covalent materials: A semiempirical potential for silicon.

Abstract: The embedded-atom method, a semiempirical theory of metal bonding, is investigated as a method to calculate the bonding in a covalent material. A simple first-neighbor embedded-atom method model is sufficient to explain the geometry and structure of many metastable phases of silicon, but not its shear behavior. To obtain realistic shear behavior of silicon, an angle-dependent electron density is included to model the effects of bond bending. This model uses only the experimental bulk properties of silicon. Calculated properties of metastable phases and point defects are presented.

Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms

Abstract: There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix. Separate routines are also provided for dense and sparse Jacobian matrices. A high-level driver is included for the special case of polynomial systems.

Cellular automata method for phase unwrapping

Abstract: Research into two-dimensional phase unwrapping has uncovered interesting and troublesome inconsistencies that cause path-dependent results. Cellular automata, which are simple, discrete mathematical systems, offered promise of computation in a nondirectional, parallel manner. A cellular automaton was discovered that can unwrap consistent phase data in n dimensions in a path-independent manner and can automatically accommodate noise-induced (pointlike) inconsistencies and arbitrary boundary conditions (region partitioning). For data with regional (nonpointlike) inconsistencies, no phase-unwrapping algorithm will converge, including the cellular-automata approach. However, the automata method permits more simple visualization of the regional inconsistencies. Examples of its behavior on one- and two-dimensional data are presented.

Application of the embedded atom method to Ni 3 Al

Abstract: The embedded atom method [M. S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984) used to calculate phase stability, lattice vibrational frequencies, point defect properties, antiphase boundary energies, and surface energies and relaxations for Ni3Al. The empirical embedding functions and core-core repulsions used by this method are obtained. The equilibrium phases for the Ni-rich half of the composition range of Ni–Al are determined for 1000 K and compared with experiment. The elastic constants and vibrational modes of Ni3Al are calculated and the elastic constants are compared with experiment. The formation energy, formation volume, and migration energies of vacancies are computed, and it is found that the formation energy of vacancies on the Ni sublattice is less than that on the Al sublattice. The (100) antiphase boundary is shown to be significantly lower in energy than the (111) antiphase boundary. The surface energies and atomic relaxations of the low index faces are computed, and it is shown that for the (100) and (110) faces that the preferred surface geometry corresponds to the bulk lattice with the mixed composition plane exposed.

Integral-equation theory of the structure of polymer melts.

Abstract: A general, analytically tractable, nonperturbative theory of the equilibrium structure of dense polymer melts is proposed on the basis of modern integral-equation theories of molecular liquids Calculations are presented for polymer rings obeying Gaussian statistics and interacting via hard-core repulsions The correlation hole, compressibility, and static structure factor are found to be sensitive functions of liquid density and degree of polymerization

A note on the description of surface roughness using fractal dimension

Abstract: Self-affine fractals are useful models of the surfaces of rock fractures. The scaling properties of these surfaces are described by two parameters, the fractal dimension and the crossover length. Two methods for estimating the fractal dimension of a profile of a rough surface are compared, the divider method and the spectral method. It is shown that the two methods yield the same results, if the horizontal resolution at which the profile is measured is smaller than the crossover length. However, for resolutions greater than the crossover length, the divider method always gives a fractal dimension close to 1. To guide future work, the crossover length is estimated for typical joint surfaces and for the San Andreas fault. Additionally, a simple method is proposed to obtain the correct fractal dimension without prior knowledge of the crossover length. copyright American Geophysical Union 1987

Fourier Synthesis of Ocean Scenes

Abstract: Considerable interest in scene synthesis has focused on fractal techniques such as 1/f noise filtering. However, these techniques produce poor synthetic ocean scenes. A superior technique is presented here that used an empirical sea spectrum model to represent a fully developed sea in nautre. A computer program has been written whereby a user supplies a wind velocity, and a two-dimensional Fourier-domain filter is created whose shape is decribed by the modified Pierson-Moskowitz spectrum. A white-noise image can then be filtered and rendered with a ray-tracing algorithm to produce a realistic ocean scene. Wave motion may be invoked by manipulating teh phase of the Fourier-transormed white-noise image. Several phase-manipulating techniques have been implemented.

Equilibrium theory of polymer liquids: Linear chains

Abstract: An equilibrium theory of polymer melts, developed previously by us for polymer rings, is generalized to include linear polymer chains. This theory is based on the reference interaction site model (RISM) integral equation approach developed by Chandler and co‐workers for molecular liquids. We are able to construct a tractable formalism for the high polymer problem by employing the fact that a polymer molecule in a melt is ideal. This leads to a set of coupled, nonlinear integral equations for the intermolecular radial distribution functions. A simple optimized perturbative scheme is developed for long linear chains based on the relative unimportance of end effects. To lowest order, the theory reduces to a single nonlinear integral equation. Chain end corrections to the site‐averaged intermolecular correlation functions vanish according to N−2, where N is the degree of polymerization. Numerical techniques were used to compute the radial distribution function and structure factor for hard core linear Gaussia...

The growth of unstable thermoplastic shear with application to steady-wave shock compression in solids*

Abstract: T he catastrophic growth of unstable thermoplastic shear following the transition from homogeneous deformation to heterogeneous localized deformation through distributed shear banding is studied through approximate analytic and computational methods. The calculations provide expressions for shear band widths, spacing, catastrophic growth times and the rate of stress communication between shear bands. The optimum shear band width and spacing are found to be consistent with a minimum work principle. The model predicts that the product of the energy dissipated and the localization time in the shear localization process is invariant with respect to changes in the driving strain rate. Such behavior has been noted in the steady-wave shock compression of a number of solids. The calculations are applied to heterogeneous shear localization observed in the shock compression of aluminum.

Autocatalytic cure kinetics from DSC measurements: Zero initial cure rate

Abstract: A new, simplified technique for obtaining the kinetic parameters of an autocatalyzed cure reaction from isothermal DSC measurements is presented. The method is appropriate to reactions that have a zero initial rate and relies solely upon characteristics of the exotherm peak with no assumptions being made about the overall reaction order. This technique is illustrated by obtaining the phenomenological cure kinetics of a commercial epoxy film adhesive. The derived kinetic model reproduces the measured isotherms in their entirety. In addition, the predictive capability of the model is demonstrated by comparison with an independent measurement of the adhesive's low temperature curing behavior. Glass transition temperature measurements are also made on partially cured samples and a good correlation with the degree of cure is found.

A measure of top-down correlation

Abstract: Many situations exist in which n objects are ranked by two or more independent sources, where interest centers primarily on agreement in the top rankings and disagreements on items at the bottom of the rankings are of little or no importance. A problem with Spearman's rho or Kendall's coefftcient of concordance in this setting is that they are equally influenced by disagreement on the assignment of rankings at all levels. In this article, a concordance measure is provided that is more sensitive to agreement on the top rankings. The statistics used in this setting are functions of the ordinary correlation coeRicient computed on Savage (1956) scores. The asymptotic distributions of these statistics are presented, and a summary of the quantiles of the exact distribution for the two sample case are provided for n = 3(1)14. The statistic for the two-sample case is shown to provide a locally most powerful rank test for a model given by Hajek and Sidak (1967).

Three-laser coherent anti-Stokes Raman scattering measurements of two species.

Abstract: A three-laser, coherent anti-Stokes Raman scattering (CARS) technique for the simultaneous acquisition of spectra from two species has been developed. A narrow-band, tunable dye-laser beam is used as one of the CARS pump beams. The frequency spacing between the spectra of the two species can be adjusted by changing the frequency of the dye-laser pump beam, enabling the spectra to be displayed at high resolution (0.5 cm(-1)) on the same intensified diode array detector.

Theory of Polymer Melts: An Integral Equation Approach'

Abstract: A general theory is developed for the equilibrium structure of dense polymer melts. This theory is based on an integral equation approach developed by Chandler and co-workers for molecular liquids. We are able to construct a tractable formalism for the polymer problem by employing the fact that a polymer molecule in a melt is ideal. This leads to a set of integral equations for the intermolecular radial distribution functions. In the case of a polymer ring, this set reduces to a single integral equation, which we have solved numerically for the case of Gaussian intramolecular statistics with repeat units interacting via hard-core repulsions. From this solution we obtained the radial distribution function, structure factor, and compressibility as functions of liquid de,nsity and degree of polymerization. Unlike the random phase approximation (RPA) approach of de Gennes, the present theory allows for density fluctuations. These density fluctuations, which decay on a length scale comparable to a few monomer units, are crucial for the calculation of the structure factor and thermodynamic properties such as the equation of state of the polymer fluid. Generalizations of the present theory to include linear chains, chain stiffness effects, and attractive interactions are possible.

Numerical evaluation of path-integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients

Abstract: A path-integral solution to truly nonlinear Fokker-Planck equations is derived. Such equations exhibit in the drift and diffusion coefficients a functional dependence on the distribution function. This type of implicit time dependence is shown to introduce terms into the propagator function of the exact same order in the time step tau, as does an explicit time dependence if the functional dependence is sufficiently smooth. A standard discrete lattice formulation of the path integral is then used to reproduce the appropriate, truly nonlinear Fokker-Planck equation. This discrete formulation provides a basis for an efficient numerical algorithm and is applied with excellent results to several example problems where exact solutions can be calculated.

An accurate numerical algorithm for stress integration with finite rotations

Abstract: An accurate numerical algorithm for the integration of constitutive equations under both large deformations and/or large rotations is presented. The algorithm is based on the choice of the unrotated configuration as the frame of reference for all constitutive equations. The algorithm does not entail excessive computational time or memory expense. The accuracy of the method is demonstrated by several numerical examples.

Development of a many-body Tersoff-type potential for silicon.

Abstract: An empirical potential for silicon recently introduced by Tersoff has been found to be unusable for global structural calculations since the bcc structure has lower energy than the diamond structure, by roughly 1 eV/atom, with this potential Simulated annealing optimization studies of the fitting parameters to the quantum-mechanical data base for silicon reveal that serious structural pathologies (relative to the behavior of silicon) cannot be avoided We introduce a modification of the Tersoff potential which retains the accurate treatment of surface and defect properties exhibited by that potential but which yields a reasonable fit to the bulk and high-density structural properties of silicon The resulting potential can be used for global structural calculations

An Evaluation of Low-Energy X-Ray and Cobalt-60 Irradiations of MOS Transistors

Abstract: An evaluation of methodologies for irradiating MOS transistors with low-energy x-ray and Co-60 sources has been performed. We find that comparisons of voltage shifts produced by bulk trapped charge and interface states in MOS transistors irradiated using two different low energy x-ray sources (an ARACOR 10 keV W source and an 8 keV Cu source) agree to within better than 30 percent. This quality of agreement is similar in magnitude to that between MOS devices irradiated by different Co-60 sources. In contrast, the measurements indicate that interlaboratory comparisons of ratios of shifts produced by x-ray and Co-60 sources can lead to differences in ratios as large as a factor of ~1.7. Improved electron-hole recombination data for oxides is presented. This recombination correction, in conjunction with a correction for interface dose enhancement, is used to predict the ratios of shifts produced by x-ray and Co-60 sources. However, the results show that corrections for electron-hole recombination and interface dose enhancement do not, by themselves, adequately predict the field dependent behavior of these transistors.

Numerical study of vortex reconnection.

Abstract: With a Biot-Savart model of vortex filaments to provide initial conditions, a finite difference scheme for the incompressible Navier-Stokes equation is used in the region of closest approach of two vortex rings. In the Navier-Stokes solution, we see that the low pressure which develops between the interacting vorticity regions causes the distortion of the initially circular vortex cross section and forces the rearrangement of vorticity on a convective time scale which is much faster than that estimated from viscous transport.

The Craft of Scientific Writing

Abstract: 1. Introduction: Deciding Where to Begin. 2. Structure: Organizing your Documents. 3. Structure: Depth, Transition, and Emphasis. 4. Language: Being Precise. 5. Language: Being Clear. 6. Language: Being Forthright. 7. Language: Being Familiar. 8. Language: Being Concise 9. Language: Being Fluid. 10. Illustation: Making the Right Choices. 11. Illustration: Creating the Best Designs. 12. Handling Special Stituations. 13. Actually Sitting Down to Write.