We present an error estimation method for immersed interface solutions of elliptic boundary value problems. As opposed to an asymptotic rate that indicates how the errors in the numerical method converge to zero, we seek a posteriori estimates of the errors, and their spatial distribution, for a given solution. Our estimate is based upon the classical idea of defect corrections, which requires the application of a higher-order discretization operator to a solution achieved with a lower-order discretization. Our model problem will be an elliptic boundary value problem in which the coefficients are discontinuous across an internal boundary.
The algebraic multigrid approach known as smoothed aggregation is very efficient at solving systems that arise from elasticity problems. In order to construct an efficient algebraic multilevel method, a multigrid solver should be provided with a small set of vectors that represent the error components that are difficult to resolve. It is well-known that for linear elasticity problems, these components correspond to the the so-called rigid body modes (RBMs). The present document summarizes some new development within the Albany code base that has enabled the application of algebraic multigrid preconditioners from the ML package of Trilinos to mechanics problems implemented within Albany via a new function that calculates the RBMs using information about the problem's underlying mesh. The performance of these preconditioners is evaluated on four problems: a 3D static elasticity problem, a 3D non-linear elasticity problem, a 3D thermo-elasticity problem, and a 3D thermo-poro-plasticity problem. The tests reveal the superiority of the ML preconditioners over ILU preconditioners from the Trilinos Ifpack package for mechanics problems in Albany.
Two separate processes to produce either ethanol or a fatty acid ethyl ester (FAEE) - identical to oil-derived biodiesel - via the fermentation of sugars obtained from lignocellulosic materials were analyzed in terms of economic and environmental metrics. Simplified process models were introduced and employed to estimate fuel production, net energy consumption, minimum fuel selling price, and water consumption for both processes. Monte Carlo analyses were carried out to identify the parameters governing process performance, and an analysis of the impact of potential improvements to the FAEE process was performed. The results of the analyses, capturing both the current state of technology development as well as paths to improve the performance of the FAEE process relative to that for producing ethanol, are presented. This is an abstract of a paper presented at the 2012 AIChE Spring National Meeting and 8th Global Congress on Process Safety (Houston, TX 4/1-5/2012).
The construction of high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for π/2 and π pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from π/2 and π pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.
This white paper makes a case for Sandia National Laboratories investments in complex adaptive systems science and technology (S&T) -- investments that could enable higher-value-added and more-robustly-engineered solutions to challenges of importance to Sandia's national security mission and to the nation. Complex adaptive systems are ubiquitous in Sandia's national security mission areas. We often ignore the adaptive complexity of these systems by narrowing our 'aperture of concern' to systems or subsystems with a limited range of function exposed to a limited range of environments over limited periods of time. But by widening our aperture of concern we could increase our impact considerably. To do so, the science and technology of complex adaptive systems must mature considerably. Despite an explosion of interest outside of Sandia, however, that science and technology is still in its youth. What has been missing is contact with real (rather than model) systems and real domain-area detail. With its center-of-gravity as an engineering laboratory, Sandia's has made considerable progress applying existing science and technology to real complex adaptive systems. It has focused much less, however, on advancing the science and technology itself. But its close contact with real systems and real domain-area detail represents a powerful strength with which to help complex adaptive systems science and technology mature. Sandia is thus both a prime beneficiary of, as well as potentially a prime contributor to, complex adaptive systems science and technology. Building a productive program in complex adaptive systems science and technology at Sandia will not be trivial, but a credible path can be envisioned: in the short run, continue to apply existing science and technology to real domain-area complex adaptive systems; in the medium run, jump-start the creation of new science and technology capability through Sandia's Laboratory Directed Research and Development program; and in the long run, inculcate an awareness at the Department of Energy of the importance of supporting complex adaptive systems science through its Office of Science.
The purpose of this report is to provide a background to Synthetic Aperture Radar (SAR) image formation using the Polar Format (PFA) processing algorithm. This is meant to be an aid to those tasked to implement real-time image formation using the Polar Format processing algorithm.
This 'campus executive' project sought to advance solar thermochemical technology for producing the chemical fuels. The project advanced the common interest of Sandia National Laboratories and the University of Arizona in creating a sustainable and viable alternative to fossil fuels. The focus of this effort was in developing new methods for creating unique monolithic composite structures and characterizing their performance in thermochemical production of hydrogen from water. The development and processing of the materials was undertaken in the Materials Science and Engineering Department at the University of Arizona; Sandia National Laboratories performed the thermochemical characterization. Ferrite/yttria-stabilized zirconia composite monoliths were fabricated and shown to have exceptionally high utilization of the ferrite for splitting CO{sub 2} to obtain CO (a process analogous to splitting H{sub 2}O to obtain H{sub 2}).
This report estimates inductively-coupled energy to a low-impedance load in a loop-to-loop arrangement. Both analytical models and full-wave numerical simulations are used and the resulting fields, coupled powers and energies are compared. The energies are simply estimated from the coupled powers through approximations to the energy theorem. The transmitter loop is taken to be either a circular geometry or a rectangular-loop (stripline-type) geometry that was used in an experimental setup. Simple magnetic field models are constructed and used to estimate the mutual inductance to the receiving loop, which is taken to be circular with one or several turns. Circuit elements are estimated and used to determine the coupled current and power (an equivalent antenna picture is also given). These results are compared to an electromagnetic simulation of the transmitter geometry. Simple approximate relations are also given to estimate coupled energy from the power. The effect of additional loads in the form of attached leads, forming transmission lines, are considered. The results are summarized in a set of susceptibility-type curves. Finally, we also consider drives to the cables themselves and the resulting common-to-differential mode currents in the load.
Field-structured chemiresistors (FSCRs) are polymer based sensors that exhibit a resistance change when exposed to an analyte of interest. The amount of resistance change depends on the polymer-analyte affinity. The affinity can be manipulated by modifying the polymer within the FSCRs. In this paper, we investigate the ability of chemically modified FSCRs to sense hydrogen peroxide vapor. Five chemical species were chosen based on their hydrophobicity or reactivity with hydrogen peroxide. Of the five investigated, FSCRs modified with allyl methyl sulfide exhibited a significant response to hydrogen peroxide vapor. Additionally, these same FSCRs were evaluated against a common interferrant in hydrogen peroxide detection, water vapor. For the conditions investigated, the FSCRs modified with allyl methyl sulfide were able to successfully distinguish between water vapor and hydrogen peroxide vapor. A portion of the results presented here will be submitted to the Sensors and Actuators journal.