The FETI algorithms are numerically scalable iterative domain decomposition methods. These methods are well documented for solving equations arising from the Finite Element discretization of second or fourth order elasticity problems. The one level FETI method equipped with the Dirichlet preconditioned was shown to be numerically scalable for second order elasticity problems while the two level FETI method was designed to be numerically scalable for fourth order elasticity problems. The second level coarse grid is an enriched version of the original one level FETI method with coarse grid. The coarse problem is enriched by enforcing transverse displacements to be continuous at the corner points. This coarse problem grows linearly with the number of subdomains. Current implementations use a direct solution method to solve this coarse problem. However, the current implementation gives rise to a full matrix system. This full matrix can lead to increased storage requirements especially if working within a distributed memory environment. Also, the factorization and subsequent forward/backward substitutions of the second level coarse problem becomes the dominant factor in solving the global problem as the number of subdomains becomes large (N{sub s} > 1,000). The authors introduce an alternative formulation of the two level coarse problem that leads to a sparse system better suited for a direct method. Then they show extensions to the alternate formulation that allow optional admissible constraints to be added to improve convergence. Lastly, they report on the numerical performance, parallel efficiency, memory requirements, and overall CPU time as compared to the classical two level FETI on some large scale fourth order elasticity problems.
A mechanical isolator has been developed for a piezoresistive accelerometer. The purpose of the isolator is to mitigate high frequency shocks before they reach the accelerometer because the high frequency shocks may cause the accelerometer to resonate. Since the accelerometer is undamped, it often breaks when it resonates. The mechanical isolator was developed in response to impact test requirements for a variety of structures at Sandia National Laboratories (SNL). An Extended Technical Assistance Program (ETAP) with the accelerometer manufacturer has resulted in a commercial mechanically isolated accelerometer that is available to the general public, the ENDEVCO 7270AM6*, for three shock acceleration ranges of 6,000 g, 20,000 g, and 60,000 g. The in-axis response shown in this report has acceptable frequency domain performance from DC to 10 kHz and 10(XO)over a temperature range of {minus}65 F to +185 F. Comparisons with other isolated accelerometers show that the ENDEVCO 7270AM6 has ten times the bandwidth of any other commercial isolator. ENDEVCO 7270AM6 cross-axis response is shown in this report.
The main objective of this project was to develop reliable, low-cost techniques for joining silicon nitride (Si{sub 3}N{sub 4}) to itself and to metals. For Si{sub 3}N{sub 4} to be widely used in advanced turbomachinery applications, joining techniques must be developed that are reliable, cost-effective, and manufacturable. This project addressed those needs by developing and testing two Si{sub 3}N{sub 4} joining systems; oxynitride glass joining materials and high temperature braze alloys. Extensive measurements were also made of the mechanical properties and oxidation resistance of the braze materials. Finite element models were used to predict the magnitudes and positions of the stresses in the ceramic regions of ceramic-to-metal joints sleeve and butt joints, similar to the geometries used for stator assemblies.
Preliminary shielding calculations were performed for a prototype National Spent Nuclear Fuel Program (NSNFP) transport cask. This analysis is intended for use in the selection of cask shield material type and preliminary estimate of shielding thickness. The radiation source term was modeled as cobalt-60 with radiation exposure strength of 100,000 R/hr. Cobalt-60 was chosen as a surrogate source because it simultaneous emits two high-energy gammas, 1.17 MeV and 1.33 MeV. This gamma spectrum is considered to be large enough that it will upper bound the spectra of all the various spent nuclear fuels types currently expected to be shipped within the prototype cask. Point-kernel shielding calculations were performed for a wide range of shielding thickness of lead and depleted uranium material. The computational results were compared to three shielding limits: 200 mrem/hr dose rate limit at the cask surface, 50 mR/hr exposure rate limit at one meter from the cask surface, and 10 mrem/hr limit dose rate at two meters from the cask surface. The results obtained in this study indicated that a shielding thickness of 13 cm is required for depleted uranium and 21 cm for lead in order to satisfy all three shielding requirements without taking credit for stainless steel liners. The system analysis also indicated that required shielding thicknesses are strongly dependent upon the gamma energy spectrum from the radiation source term. This later finding means that shielding material thickness, and hence cask weight, can be significantly reduced if the radiation source term can be shown to have a softer, lower energy, gamma energy spectrum than that due to cobalt-60.
The effects of chemical aging on the behavior of carbon black filled rubber were investigated by two types of tests, aging under no strain and aging under a constant strain. A slight modification of the damage-based theory of Segalman, used previously on unaged samples, was found to be consistent with the experimental data.
The U. S. Department of Energy Strategic Petroleum Reserve currently has approximately 500 million barrels of crude oil stored in 62 caverns solution-mined in salt domes along the Gulf Coast of Louisiana and Texas. One of the challenges of operating these caverns is ensuring that none of the fluids in the caverns are leaking into the environment. The current approach is to test the mechanical integrity of all the wells entering each cavern approximately once every five years. An alternative approach to detecting cavern leaks is to monitor the cavern pressure, since leaking fluid would act to reduce cavern pressure. Leak detection by pressure monitoring is complicated by other factors that influence cavern pressure, the most important of which are thermal expansion and contraction of the fluids in the cavern as they come into thermal equilibrium with the host salt, and cavern volume reduction due to salt creep. Cavern pressure is also influenced by cavern enlargement resulting from salt dissolution following introduction of raw water or unsaturated brine into the cavern. However, this effect only lasts for a month or two following a fluid injection. In order to implement a cavern pressure monitoring program, a software program called CaveMan has been developed. It includes thermal, creep and salt dissolution models and is able to predict the cavern pressurization rate based on the operational history of the cavern. Many of the numerous thermal and mechanical parameters in the model have been optimized to produce the best match between the historical data and the model predictions. Future measurements of cavern pressure are compared to the model predictions, and significant differences in cavern pressure set program flags that notify cavern operators of a potential problem. Measured cavern pressures that are significantly less than those predicted by the model may indicate the existence of a leak.
The spatial and temporal origin of a seismic energy source are estimated with a first grid search technique. This approach has greater likelihood of finding the global rninirnum of the arrival time misiit function compared with conventional linearized iterative methods. Assumption of a homogeneous and isotropic seismic velocity model allows for extremely rapid computation of predicted arrival times, but probably limits application of the method to certain geologic environments and/or recording geometries. Contour plots of the arrival time misfit function in the vicinity of the global minimum are extremely useful for (i) quantizing the uncertainty of an estimated hypocenter solution and (ii) analyzing the resolving power of a given recording configuration. In particular, simultaneous inversion of both P-wave and S-wave arrival times appears to yield a superior solution in the sense of being more precisely localized in space and time. Future research with this algorithm may involve (i) investigating the utility of nonuniform residual weighting schemes, (ii) incorporating linear and/or layered velocity models into the calculation of predicted arrival times, and (iii) applying it toward rational design of microseismic monitoring networks.
We present mathematical proofs for two useful properties of the clusters generated by the visual empirical region of influence (VERI) shape. The first proof shows that, for any d-dimensional vector set with more than one distinct vector, that there exists a bounded spherical volume about each vector v which contains all of the vectors that can VERI cluster with v, and that the radius of this d-dimensional volume scales linearly with the nearest neighbor distance to v. We then prove, using only each vector's nearest neighbor as an inhibitor, that there is a single upper bound on the number of VERI clusterings for each vector in any d-dimensional vector set, provided that there are no duplicate vectors. These proofs guarantee significant improvement in VERI algorithm runtimes over the brute force O(N{sup 3}) implementation required for general d-dimensional region of influence implementations and indicate a method for improving approximate O(NlogN) VERI implementations. We also present a related region of influence shape called the VERI bow tie that has been recently used in certain swam intelligence algorithms. We prove that the VERI bow tie produces connected graphs for arbitrary d-dimensional data sets (if the bow tie boundary line is not included in the region of influence). We then prove that the VERI bow tie also produces a bounded number of clusterings for each vector in any d-dimensional vector set, provided that there are no duplicate vectors (and the bow tie boundary line is included in the region of influence).
Multivariate calibration techniques have been used in a wide variety of spectroscopic situations. In many of these situations, spectral variation can be partitioned into separate classes. For example, suppose that multiple spectra are obtained from each of a number of different objects wherein the level of the analyze of interest varies within each object over time. In such situations, the total spectral variation observed across all measurements has two distinct general sources of variation: intraobject and interobject. One might want to develop a global multivariate calibration model that predicts the analyze of interest accurately both within and across objects, including new objects not involved in developing the calibration model. However, this goal might be hard to realize if the interobject spectral variation is complex and difficult to model. If the intraobject spectral variation is consistent across objects, an effective alternative approach might be to develop a generic intraobject model that can be adapted to each object separately. This paper contains recommendations for experimental protocols and data analysis in such situations. The approach is illustrated with an example involving the noninvasive measurement of glucose using near-infrared reflectance spectroscopy. Extensions to calibration maintenance and calibration transfer are discussed.
Careful characterization of laser beams used in materials processing such as welding and drilling is necessary to obtain robust, reproducible processes and products. Recently, equipment and techniques have become available which make it possible to rapidly and conveniently characterize the size, shape, mode structure, beam quality (Mz), and intensity of a laser beam (incident power/unit area) as a function of distance along the beam path. This facilitates obtaining a desired focused spot size and also locating its position. However, for a given position along the beam axis, these devices typically measure where the beam intensity level has been reduced to I/ez of maximum intensity at that position to determine the beam size. While giving an intuitive indication of the beam shape since the maximum intensity of the beam varies greatly, the contour so determined is not an iso-contour of any parameter related to the beam intensity or power. In this work we shall discuss an alternative beam shape formulation where the same measured information is plotted as contour intervals of intensity.
The authors study multi-photon-assisted transmission of electrons through single-step, single-barrier and double-barrier potential-energy structures as a function of the photon energy and the temperature. Sharp resonances in the spectra of the tunneling current through double-barrier structures are relevant to infra-red detectors.
The diffusion, uptake, and release of H in p-type GaN are modeled employing state energies from density-function theory and compared with measurements of deuterium uptake and release using nuclear-reaction analysis. Good semiquantitative agreement is found when account is taken of a surface permeation barrier.