We investigate the rate of convergence of stochastic basis elements to the solution of a stochastic operator equation. As in deterministic finite elements, the solution may be approximately represented as the linear combination of basis elements. In the stochastic case, however, the solution belongs to a Hilbert space of functions defined on a cross product domain endowed with the product of a deterministic and probabilistic measure. We show that if the dimension of the stochastic space is n, and the desired accuracy is of order {var_epsilon}, the number of stochastic elements required to achieve this level of precision, in the Galerkin method, is on the order of | ln {var_epsilon} |{sup n}.
The GEO-SEQ Project is investigating methods for geological sequestration of CO{sub 2}. This project, which is directed by LBNL and includes a number of other industrial, university, and national laboratory partners, is evaluating computer simulation methods including TOUGH2 for this problem. The TOUGH2 code, which is a widely used code for flow and transport in porous and fractured media, includes simplified methods for gas diffusion based on a direct application of Fick's law. As shown by Webb (1998) and others, the Dusty Gas Model (DGM) is better than Fick's Law for modeling gas-phase diffusion in porous media. In order to improve gas-phase diffusion modeling for the GEO-SEQ Project, the EOS7R module in the TOUGH2 code has been modified to include the Dusty Gas Model as documented in this report. In addition, the liquid diffusion model has been changed from a mass-based formulation to a mole-based model. Modifications for separate and coupled diffusion in the gas and liquid phases have also been completed. The results from the DGM are compared to the Fick's law behavior for TCE and PCE diffusion across a capillary fringe. The differences are small due to the relatively high permeability (k = 10{sup -11} m{sup 2}) of the problem and the small mole fraction of the gases. Additional comparisons for lower permeabilities and higher mole fractions may be useful.
Measurement and signal intelligence demands has created new requirements for information management and interoperability as they affect surveillance and situational awareness. Integration of on-board autonomous learning and adaptive control structures within a remote sensing platform architecture would substantially improve the utility of intelligence collection by facilitating real-time optimization of measurement parameters for variable field conditions. A problem faced by conventional digital implementations of intelligent systems is the conflict between a distributed parallel structure on a sequential serial interface functionally degrading bandwidth and response time. In contrast, optically designed networks exhibit the massive parallelism and interconnect density needed to perform complex cognitive functions within a dynamic asynchronous environment. Recently, all-optical self-organizing neural networks exhibiting emergent collective behavior which mimic perception, recognition, association, and contemplative learning have been realized using photorefractive holography in combination with sensory systems for feature maps, threshold decomposition, image enhancement, and nonlinear matched filters. Such hybrid information processors depart from the classical computational paradigm based on analytic rules-based algorithms and instead utilize unsupervised generalization and perceptron-like exploratory or improvisational behaviors to evolve toward optimized solutions. These systems are robust to instrumental systematics or corrupting noise and can enrich knowledge structures by allowing competition between multiple hypotheses. This property enables them to rapidly adapt or self-compensate for dynamic or imprecise conditions which would be unstable using conventional linear control models. By incorporating an intelligent optical neuroprocessor in the back plane of an imaging sensor, a broad class of high-level cognitive image analysis problems including geometric change detection, pattern recognition, and correlated feature extraction can be realized in an inherently parallel fashion without information bottlenecking or external supervision, Using this approach, we believe that autonomous control systems embodied with basic adaptive decision-theoretic capabilities can be developed for imaging and surveillance sensors to improve discrimination in stressing operational environments.
Conventional systems surety analysis is basically restricted to measurable or physical-model-derived data. However, most analyses, including high-consequence system surety analysis, must also utilize subjective information. In order to address this need, there has been considerable effort on analytically incorporating engineering judgment. For example, Dempster-Shafer theory establishes a framework in which frequentist probability and Bayesian incorporation of new data are subsets. Although Bayesian and Dempster-Shafer methodology both allow judgment, neither derives results that can indicate the relative amounts of subjective judgment and measurable data in the results. The methodology described in this report addresses these problems through a hybrid-mathematics-based process that allows tracking of the degree of subjective information in the output, thereby providing more informative (as well as more appropriate) results. In addition, most high consequence systems offer difficult-to-analyze situations. For example, in the Sandia National Laboratories nuclear weapons program, the probability that a weapon responds safely when exposed to an abnormal environment (e.g., lightning, crush, metal-melting temperatures) must be assured to meet a specific requirement. There are also non-probabilistic DOE and DoD requirements (e.g., for determining the adequacy of positive measures). The type of processing required for these and similar situations transcends conventional probabilistic and human factors methodology. The results described herein address these situations by efficiently utilizing subjective and objective information in a hybrid mathematical structure in order to directly apply to the surety assessment of high consequence systems. The results can also improve the quality of the information currently provided to decision-makers. To this end, objective inputs are processed in a conventional manner; while subjective inputs are derived from the combined engineering judgment of experts in the appropriate disciplines. In addition to providing output constituents (including portrayal of uncertainty) corresponding to combination of these input types, their individual contributions to the resultant uncertainty are determined and provided as part of the output information. Finally, the safety assessment is complemented by a latent effects analysis, facilitated by soft-aggregation accumulation of observed operational constituents.
An effort is underway at Sandia National Laboratories to develop a library of algorithms to search for potential interactions between surfaces represented by analytic and discretized topological entities. This effort is also developing algorithms to determine forces due to these interactions for transient dynamics applications. This document describes the Application Programming Interface (API) for the ACME (Algorithms for Contact in a Multiphysics Environment) library.
A self-consistent set of thermochemical data for 55 molecules in the Al-H-C-O-F-Cl system are obtained from ab initio quantum-chemistry calculations using the BAC-G2 method. Calculations were performed for both stable and radical species. Good agreement is found between the calculations and experimental heats of formation in most cases where data are available for comparison. Electronic energies, molecular geometries, moments of inertia, and vibrational frequencies are provided in the Supporting Information, as are polynomial fits of the thermodynamic data (heat of formation, entropy, and heat capacity) over the 300--3000 K temperature range.
We study the ballistic and diffusive magnetoquantum transport using a typical quantum point contact geometry for single and tunnel-coupled double wires that are wide (less than or similar to1 mum) in one perpendicular direction with densely populated sublevels and extremely confined in the other perpendicular (i.e., growth) direction. A general analytic solution to the Boltzmann equation is presented for multisublevel elastic scattering at low temperatures. The solution is employed to study interesting magnetic-field dependent behavior of the conductance such as a large enhancement and quantum oscillations of the conductance for various structures and field orientations. These phenomena originate from the following field-induced properties: magnetic confinement, displacement of the initial- and final-state wave functions for scattering, variation of the Fermi velocities, mass enhancement, depopulation of the sublevels and anticrossing (in double quantum wires). The magnetoconductance is strikingly different in long diffusive (or rough. dirty) wires from the quantized conductance in short ballistic (or clean) wires. Numerical results obtained for the rectangular confinement potentials in the growth direction are satisfactorily interpreted in terms of the analytic solutions based on harmonic confinement potentials. Some of the predicted features of the field-dependent diffusive and quantized conductances are consistent with recent data from GaAs/AlxGa1-xAs double quantum wires.
Reduced prestressing and degradation of prestressing tendons in concrete containment vessels were investigated using finite element analysis of a typical prestressed containment vessel. The containment was analyzed during a loss of coolant accident (LOCA) with varying levels of prestress loss and with reduced tendon area. It was found that when selected hoop prestressing tendons were completely removed (as if broken) or when the area of selected hoop tendons was reduced, there was a significant impact on the ultimate capacity of the containment vessel. However, when selected hoop prestressing tendons remained, but with complete loss of prestressing, the predicted ultimate capacity was not significantly affected for this specific loss of coolant accident. Concrete cracking occurred at much lower levels for all cases. For cases where selected vertical tendons were analyzed with reduced prestressing or degradation of the tendons, there also was not a significant impact on the ultimate load carrying capacity for the specific accident analyzed. For other loading scenarios (such as seismic loading) the loss of hoop prestressing with the tendons remaining could be more significant on the ultimate capacity of the containment vessel than found for the accident analyzed. A combination of loss of prestressing and degradation of the vertical tendons could also be more critical during other loading scenarios.
The Sandia coilgun [1,2,3,4,5] is an inductive electromagnetic launcher. It consists of a sequence of powered, multi-turn coils surrounding a flyway of circular cross-section through which a conducting armature passes. When the armature is properly positioned with respect to a coil, a charged capacitor is switched into the coil circuit. The rising coil currents induce a current in the armature, producing a repulsive accelerating force. The basic numerical tool for modeling the coilgun is the SLINGSHOT code, an expanded, user-friendly successor to WARP-10 [6]. SLINGSHOT computes the currents in the coils and armature, finds the forces produced by those currents, and moves the armature through the array of coils. In this approach, the cylindrically symmetric coils and armature are subdivided into concentric hoops with rectangular cross-section, in each of which the current is assumed to be uniform. The ensemble of hoops are treated as coupled circuits. The specific heats and resistivities of the hoops are found as functions of temperature and used to determine the resistive heating. The code calculates the resistances and inductances for all hoops, and the mutual inductances for all hoop pairs. Using these, it computes the hoop currents from their circuit equations, finds the forces from the products of these currents and the mutual inductance gradient, and moves the armature. Treating the problem as a set of coupled circuits is a fast and accurate approach compared to solving the field equations. Its use, however, is restricted to problems in which the symmetry dictates the current paths. This paper is divided into three parts. The first presents a demonstration of the code. The second describes the input and output. The third part describes the physical models and numerical methods used in the code. It is assumed that the reader is familiar with coilguns.
The methodology in this report addresses the safety effects of organizational and operational factors that can be measured through ''inspection.'' The investigation grew out of a preponderance of evidence that the safety ''culture'' (attitude of employees and management toward safety) was frequently one of the major root causes behind accidents or safety-relevant failures. The approach is called ''Markov latent effects'' analysis. Since safety also depends on a multitude of factors that are best measured through well known risk analysis methods (e.g., fault trees, event trees, FMECA, physical response modeling, etc.), the Markov latent effects approach supplements conventional safety assessment and decision analysis methods. A top-down mathematical approach is developed for decomposing systems, for determining the most appropriate items to be measured, and for expressing the measurements as imprecise subjective metrics through possibilistic or fuzzy numbers. A mathematical model is developed that facilitates combining (aggregating) inputs into overall metrics and decision aids, also portraying the inherent uncertainty. A major goal of the modeling is to help convey the top-down system perspective. Metrics are weighted according to significance of the attribute with respect to subsystems and are aggregated nonlinearly. Since the accumulating effect responds less and less to additional contribution, it is termed ''soft'' mathematical aggregation, which is analogous to how humans frequently make decisions. Dependence among the contributing factors is accounted for by incorporating subjective metrics on commonality and by reducing the overall contribution of these combinations to the overall aggregation. Decisions derived from the results are facilitated in several ways. First, information is provided on input ''Importance'' and ''Sensitivity'' (both Primary and Secondary) in order to know where to place emphasis on investigation of root causes and in considering new controls that may be necessary. Second, trends in inputs and outputs are tracked in order to obtain significant information, including cyclic information, for the decision process. Third, Early Alerts are provided in order to facilitate pre-emptive action. Fourth, the outputs are compared to soft thresholds provided by sigmoid functions. The methodology has been implemented in a software tool.
The unique properties of carbon have made it both a fascinating and an important subject of experimental and theoretical studies for many years [1]-[4]. The contrast between its best-known elemental forms, graphite and diamond, is particularly striking. Graphite is black, has a rather low density and high compressibility (close to that of magnesium), and is greasy enough to be useful as a lubricant and in pencil leads. Diamond is brilliantly translucent, 60% more dense than graphite, less compressible than either tungsten or corundum, and its hardness makes it useful for polishing and cutting. This variability in properties, as well as that observed among the many classes of carbon compounds, arises because of profound differences in electronic structure of the carbon bonds [5]. A number of other solid forms of carbon are known. Pyrolytic graphite [6] is a polycrystalline material in which the individual crystallites have a structure quite similar to that of natural graphite. Fullerite (solid C 60), discovered only ten years ago [7], consists of giant molecules in which the atoms are arranged into pentagons and hexagons on the surface of a spherical cage. Amorphous carbon [8][9], including carbon black and ordinary soot, is a disordered form of graphite in which the hexagonally bonded layers are randomly oriented. Glassy carbons [9][10], on the other hand, have more random structures. Many other structures have been discussed [1][9].
This report describes least squares solution methods and linearized estimates of solution errors caused by data errors. These methods are applied to event locating systems which use time-of-arrival (TOA) data. Analyses are presented for algorithms that use the TOA data in a ''direct'' manner and for algorithms utilizing Time-of-arrival Squared (TSQ) methods. Location and error estimation results were applied to a ''typical'' satellite TOA detecting system. Using Monte Carlo methods, it was found that the linearized location error estimates were valid for random data errors with relatively large variances and relatively poor event/sensor geometries. In addition to least squares methods, which use an L{sub 2} norm, methods were described for L{sub 1} and L{sub {infinity}} norms. In general, these latter norms offered little improvement over least squares methods. Reduction of the location error variances can be effected by using information in addition to the TOA data themselves by adding judiciously chosen ''conditioning'' equation(s) to the least squares system. However, the added information can adversely affect the mean errors. Also, conditioned systems may offer location solutions where nonconditioned scenarios may not be solvable. Solution methods and linearized error estimates are given for ''conditioned'' systems. It was found that for significant data errors, the linearized estimates were also close to the Monte Carlo results.
Aluminum oxide (ALOX) filled epoxy is the dielectric encapsulant in shock driven high-voltage power supplies. ALOX encapsulants display a high dielectric strength under purely electrical stress, but minimal information is available on the combined effects of high voltage and mechanical shock. We report breakdown results from applying electrical stress in the form of a unipolar high-voltage pulse of the order of 10-{micro}s duration, and our findings may establish a basis for understanding the results from proposed combined-stress experiments. A test specimen geometry giving approximately uniform fields is used to compare three ALOX encapsulant formulations, which include the new-baseline 459 epoxy resin encapsulant and a variant in which the Alcoa T-64 alumina filler is replaced with Sumitomo AA-10 alumina. None of these encapsulants show a sensitivity to ionizing radiation. We also report results from specimens with sharp-edged electrodes that cause strong, localized field enhancement as might be present near electrically-discharged mechanical fractures in an encapsulant. Under these conditions the 459-epoxy ALOX encapsulant displays approximately 40% lower dielectric strength than the older Z-cured Epon 828 formulation. An investigation of several processing variables did not reveal an explanation for this reduced performance. The 459-epoxy encapsulant appears to suffer electrical breakdown if the peak field anywhere reaches a critical level. The stress-strain characteristics of Z-cured ALOX encapsulant are measured under high triaxial pressure and we find that this stress causes permanent deformation and a network of microscopic fractures. Recommendations are made for future experimental work.
Hafnium diboride-silicon carbide (HS) and zirconium diboride-silicon carbide (ZS) composites are potential materials for high temperature, thermal shock applications such as for components on re-entry vehicles. In order to establish material constants necessary for evaluation of in situ fracture, bars fractured in four-point flexure were examined using fractographic principles. The fracture toughness was determined from measurements of the critical crack sizes and the strength values and the crack branching constants were established to use in forensic fractography for future in-flight tests. The fracture toughnesses range from about 13 MPam{sup 1/2} at room temperature to about 6 MPam{sup 1/2} at 1400 C for ZrB{sub 2}-Sic composites and from about 13 MPam{sup 1/2} at room temperature to about 4 MPam{sup 1/2} at 1400 C for HfB{sub 2}-SiC composites. Thus, the toughnesses of either the HS or ZS composites have the potential for use in thermal shock applications. Processing and manufacturing defects limited the strength of the test bars. However, examination of the microstructure on the fracture surfaces shows that the processing of these composites can be improved. There is potential for high toughness composites with high strength to be used in thermal shock conditions if the processing and handling are controlled.